DUCTOR ad ASTRONOMIAM & GEOGRAPHIAM. vel usus GLOBI, Celestis quam Terrestris. In Libris sex, viz.

  • Astron. & Geogr. Rudimē.
  • Astrō. & Geogr. Problē.
  • Nautica. Problē.
  • Astrologica. Problē.
  • Gnomonica. Problē.
  • Sphaeric. Triang. Problē.

Per Josephum Moxon.

LONDINI, Sumptibus Josephi Moxon.

A TUTOR to ASTRONOMIE and GEOGRAPHIE: Or an Easie and speedy way to know the Use of both the GLOBES, Coelestial and Terrestrial. In six BOOKS.

  • The First teaching the Rudiments of Astronomy and Geography.
  • The 2. Shewing by the Globes the solution of Astronomical & Geographical Probl.
  • The 3. Shewing by the Globes the solution of Problemes in Navigation.
  • The 4. Shewing by the Globes the solution of Astrological Problemes.
  • The 5. Shewing by the Globes the solution of Gnomonical Problemes.
  • The 6. Of Spherical Triangles.

More fully and amply then hath ever been set forth ei­ther by Gemma Frisius, Metius, Hues, Wright, Blaew, or any others that have taught the Use of the Globes: And that so plainly and methodically that the meanest Capacity may at first reading apprehend it; and with a little Practise grow expert in these Divine Sciences.

By Joseph Moxon.

Whereunto is added the Antient Poetical Stories of the Stars: shewing Reasons why the several shapes and forms are pi­ctured on the Coelestial Globe. Collected from Dr Hood. As also a Discourse of the Antiquity, Progress and Augmenta­tion of Astnonomie.

Psal. 111. 2.

The Works of the Lord are great: sought out of them that have pleasure therein.

Job. 26. 13.

By his Spirit he hath garnished the Heavens: His hand hath framed the crooked Serpent.

LONDON, Printed by Joseph Moxon: and fold at his Shop on Corn-hill, at the signe of Atlas. 1659.

A Catalogue of Books and Instruments, Made and sold by Joseph Moxon, at his shop on Corn-hil, at the Signe of Atlas.

GLobes of all sizes; Coelestial and Terrestrial.

Sphears, according to the

  • Ptolemean
  • Tychonean
  • Copernican

Systeme

The Catholick Planisphere, call'd Blagrave's Mathematical Jewel; made very exactly on Past-boards; about 17. inches Di­ameter. And a Book of the Use of it newly set forth by I. Pal­mer M. A.

The Spiral Line.

Gunters Quadrant and Nocturnal; Printed and pasted, &c. Stirrups Universal Quadrat. Printed and Pasted, &c,

Sea-Plats, Printed on Paper, or Parchment, and Pasted on Boards.

Wrights Corrections of Errors, in the Art of Navigation. The third Edition, with Additions.

Vignola, or the Compleat Architect, useful for all Carpenters, Masons, Painters, Carvers, or any Gentlemen or others that de­light in rare Building.

A new Invention to raise Water higher then the Spring. With certain Engines to produce either Motion or Sound by the Wa­ter: very useful, profitable and delightful for such as are addict­ed to rare curiosities: by Isaac de Caus.

A Help to Calculation By J. Newton.

A Mathematical Manuel, shewing the use of Napiers bones, by J. Dansie.

A Tutor to Astrology, with an Ephemeris for the Year 1659. intended to be Annually continued, by W. E.

Also all manner of Mathematical Books, or Instruments, and Maps whatsoever, are sold by the foresaid Joseph Moxon.

To the Reader.

Courteous Reader,

IFormerly Printed a Book of the Use of the Globes, Intituled A Tutor to Astronomy and Geography: The Book was Com­posed by William Blaew, but the Title was mine own; and therefore I hope I may be the bolder to use it when and where I list. The sale of that Impressi­on had almost perswaded me to have Printed it again: But when I considered it wanted many necessary Problemes, both in Astro­nomy, Navigation. Astrology, Dyalling, and the whole Doctrine of Triangles by the Globe; And also that the Examples through­out that Book were made for the Citty of Amsterdam; which by the general sale of the Book I found rendred it less acceptable then it would have been if they had been made for London; And when I considered that to add so many Problemes, and alter all the Examples would both Metamorphose that Book, and be as Laborious a work to me as if I should write a new one; Then I re­solved to take this Task upon me; which at length with Gods Assistance I have finished; And now expose it to thy acceptance.

The Globes is the first Studie a Learner ought to undertake: for without a competent knowledge therein he will never be able to understand any Author either in Astronomy, Astrology, Navi­gation, or Trigonometry: Therefore my aim hath been to make the Use of then very plain and easie to the meanest Capacities: In prosecution of which Designe, I doubt the Learneder sort may be apt to Censure me guilty of Prolixity, if not Tautology: Because the Precepts being plain, they may account some of the Examples Useless. But I desire them to consider that I write not to expert Practitioners, but to Learners; to whom Examples may prove more Instructive then Precepts. Besides, I hope to encourage those by an ample liberal plainness to fall in love with these Studies, that formerly have been disheartned by the Crabbed brevity of those Authors that have (in Characters as it were) rather writ Notes for their own Memories, then sufficient Documents for their Read­ers Instructions.

[Page] The Globes for which this Book is written are the Globes I set forth about four years ago: which as I told you in my Epistle to the Reader of Blaew's Book differs somewhat from other Globes, and that both the Coelestial and the Terrestrial; mine being the latest done of any, and to the accomplishing of which, I have not only had the help of all or most of the best of other Globes, Maps, Plats; and Sea-drafts, of New Discoveries that were then ex­tant, for the Terrestrial Globe, but also the Advice and directi­ons of divers learned and able Mathematicians both in England and Holland for Tables and Calculations both of Lines and Stars for the Coelestial: upon which Globe I have placed every Star that was observed by Tycho Brahe one degree of Longitude far­ther in the Ecliptick then they are on any other Globes: So that whereas on other Globes the places of the Stars were correspond­ent with their places in Heaven 58. Years ago, when Tycho ob­served them, and therefore according to his Rule want about 47. minutes of their true places in Heaven at this Time: I have set every Star one degree farther in the Ecliptick, and Rectified them on the Globe according to the true place they will have in Heaven in the Year 1671.

On the Terrestrial Globe I have inserted all the New Disco­veries that have been made, either by our own or Forraigne Navigators, and that both in the East, West, North, and South, parts of the Earth. In the East Indies we have by these later Times many spacious Places discovered, many Ilands inserted, and generally the whole Draft of the Country rectified and amen­ded, even to the Coast of China, Japan, Giloli, &c. In the South Sea between the East and West Indies are scattered many Ilands, which for the uncertain knowledge former Times had of them are either wholely left out of other Globes, or else laid down so erroneously that little of credit can be attributed unto them: California is found to be an Iland, though formerly supposed to be part of the main Continent, whose North West shoar was imagined to thrust it self forth close to the Coasts of Cathaio, and so make the supposed Straits of Anian. The Western Shoars of the West Indies are more accurately discribed then formerly, as you may see if you compare my Terrestrial Globe with the Journals of the latest Navigators: And if you compare them with other Globes you will find 5, 6, yea 7, degrees difference in Longitude, in most Places of these Coasts. Magellanica which heretofore was thought [Page] to be part of the South Continent called Terra Incognita is now al­so found to be an Iland. All that Track of Land called Terra In­cognita I have purposely omitted, because as yet we have no cer­tainty whether it be Sea or Land, unless it be of some parts lately found out by the Dutch; who having a convenient Port at Bantam in Java, have from thence sent forth Ships Southwards, where they have found several very large Countries; one whereof they have called Hollandia Nova, another Zelandia Nova, another Anthoni van Diemans Land; and divers others; some whereof lies near our Antipodes; as you may see by my Terrestrial Globe. Again, Far to the Northwards there are some New Discoveries, even within 6. degrees of the Pole: The Drafts to the North Eastwards I have laid down even as they were discribed by the Searchers of these Parts, for a Passage into the East Indies. And also the Discoveries of Baffin, Capt. James, and Capt. Fox, (our own Country men that attempted the finding a passage that way into the South Sea.

I also told you what difference there is in several Authors a­bout placing their first Meridian, which is the beginning of Lon­gitude; that Ptolomy placed it at the Fortunate Ilands, which Mr Hues pag. 4. chap 1. in his Treatise of Globes proves to be the Ilands of Cabo Verde, and not those now called the Canary Ilands; because in his Time they were the furthest Places of the Discovered World towards the Setting of the Sun: Others placed it at Pico in Teneriffa; Others at Corvus and Flora; because under that Meridian the Compass had no Variation, but did then duely respect the North and South; Others for the same Reason began their Longitude at St Michaels; and others between the Ilands of Flores and Fayal: And the Spaniards of late by reason of their great Negotiation in the West Indies, have begun their Longitude at Toledo there, and contrary to all others account it Westwards.

Therefore I seeing such diversity among all Nations, and as yet a Uniformity at home, chose with our own Country men to place my First Meridian at the Ile Gratiosa, one of the Iles of the Azores.

By the different placing of this first Meridian it comes to pass that the Longitude of places are diversly set down in different Tables: For those Globes or Maps that have their first Meridi­an placed to the Eastwards of Gratiosa have all places counted Eastward between the first Mertdian and the Meridian of Gra­tiosa [Page] in fewer degrees of Longitude: And those Globes and Maps that have their first Meridian placed to the Westwards, have all Places counted Eastwards from the Meridian of Gratiosa and their first Meridian in a greater number of degrees of Longitude, and that according as the Arch of Difference is.

I have annexed a smal Collection out of Dr Hood, which de­clares the Re son why such strange Figures and Forms are pictu­red on the Caelestial Globe: and withall the Poetical Stories of e­every Constellation.

I also thought good to add at the latter end of this Book a smal Treatise, intituled The Antiquity, Progress, and Augmentation of Astronomy. I may without Partiallity give it the Encomium of a Pithy, Pleasant, and Methodical peece: It was written by a Learned Author; and is worthy the Perusal of all Ingenuous Lovers of these Studies.

Joseph Moxon.

Encomiastic Achrosticon Authoris.

ITs now since Atlas raign'd thousands of Years,
OF whom 'tis Fabl'd, Heavens hee did Uphold,
SO Ancient Authors write: But it appeares
EXcell he others did, for we are told
PRoject he did the Sphear: and for his Skil
HE had therein, his Fame will Flourish still.
MUst we not also Praise in this our Age
OUr Authors skill, and Pains, who doth ingage
X Thousand Thanks, not for this Book alone
OF his, But for the Globes he makes there's none
NOw extant made so perfect: This is known
The Contents of the First Book.
  • [Page] Chap. 1. WHat a Globe is. fol. 4
    • 2. Of the two Poles. 4
    • 3. Of the Axis. 4
    • 4. Of the Brazen Meridian. 4
    • 5. Of the Horizon. 5
    • 6. Of the Quadrant of Altitude. 6
    • 7. Of the Hour-Circle, and its Index. 6
    • 8. Of the Nautical Compass, or Box and Needle. 7
    • 9. Of the Semi-Circle of Position. 7
  • Chap. 2. Of the Circles Lines, &c. described upon the superficies of the Globe; beginning with the Terrestrial Globe; and 7
    • 1. Of the Equator. 7
    • 2. Of the Meridians. 8
    • 3. Of the Parallels. 8
    • 4. Of the Ecliptique, Tropicks, and Polar Circles. 8
    • 5. Of the Rhumbs. 9
    • 6. Of the Lands, Seas, Ilands, &c. Discribed upon the Terrestrial Globe, 9
    • 7. Longitude. 10
    • 8. Latitude. 11
  • Chap. 3. Of the Celestial Globe, or the Eighth Sphear, represented by the Celestial Globe: its motion, and of the Circles, Lines, Ima­ges, Stars, &c. described thereon. 11
    • 1. Of the eight Sphear. 11
    • 2. Of the Motion of the eighth Sphear. 12
    • 3. Of the Equinoctial. 13
    • 4. Of the Ecliptick. 15
    • 5. Of the Poles of the Ecliptick. 15
    • 6. Of the Axis of the Ecliptick. 16
    • 7. Of the Colures, and Cardinal Points. 16
    • [Page] 8. Of the Tropick. fol. 16
    • 9. Of the Circles Arctick and Antarctick. 17
    • 10. Of the Images called Constellations, drawn upon the Celestial Globe. 17
    • 11. Of the number of the Stars. 19
    • 12. Of the Scituation of the Stars. 20
    • 13. Of the Magnitudes of the Stars. 20
    • The proportion of the Diameters of the fixed Stars; Compared with the Diameter of the Earth. 21
    • The proportions of the fixed Stars Compared with the Globe of the Earth, 22
    • 14. Of the Nature of the Stars. 23
    • 15. Of Via Lactea, or the Milky way. 23
The Contents Of the Second Book.
  • Prob. 1. SOme Advertisements in Choosing and Using the Globes. 35
  • To find the Longitude and Latitude of Places, on the Terrestrial Globe. fol. 37
  • Prob. 2. The Longitude and Latitude being known, to Rectifie the Globe fit for use. 38
  • Prob. 3. To find the Place of the Sun in the Ecliptick, the day of the Moneth being first known. 39
  • Prob. 4. To find the Day of the Moneth, the Place of the Sun being gi­ven. 40
  • Prob. 5. The Place of the Sun given, to find its Declination. 40
  • Prob. 6. The Place of the Sun given, to find us Meridian Altitude. 41
  • Prob. 7. The Suns Place given, to find the Hour of Sun Rising, and the length of the Night and Day. 42
  • Prob. 8. To find the Hour of Sun Set. 42
  • Prob. 9. To find how long it is Twilight in the Morning and Evening. 43
  • Prob. 10. The Suns Place given, to find its Amplitude; And also to know upon what point of the Compass it Riseth. 44
  • Prob. 11, The Hour of the Day given to find the Height of the Sun. 45
  • Prob. 12. The Altitude of the Sun, and Day of the Moneth given, to find [Page] the Hour of the Day. fol. 46
  • Prob. 13. How to know whether it be Before or After Noon. 47
  • How to take Altitudes by the Quadrant, Astrolabe, and Cross-staff. 47
  • To take Altitudes by the Astrolabe. 50
  • To take Altitudes by the Cross-staff. 51
  • Prob. 14. To observe with the Globe the Altitude of the Sun. 52
  • Prob. 15. To find the Elevation of the Pole [...] by the Meridian Altitude of the Sun, and Day of the Moneth given. 53
  • Prob. 16. To take the Altitude of any Star above the Horizon; by the Globe. 54
  • Prob. 17. By the Meridian Altitude of any Star given, to find the Height of the Pole. 54
  • Prob. 18. Another way to find the Height of the Pole by the Globe; if the Place of the Sun be given: and also to find the Hour of the Day, and Azimuth, and Almicanter of the Sun, 56
  • Prob. 19. To observe by the Globe the Distance of two Stars. 57
  • Prob. 20. How you may learn to give a guess at the number of degrees that any two Stars are distant from one another; or the number of degrees of Altitude the Sun or any Star is Elevated above the Horizon: only by looking up to Heaven, without any In­strument. 58
  • Prob. 21. The Day of the Moneth, and Altitude of any Star given, to find the Hour of the Night, 59
  • Prob. 22. The Place of the Sun, and Hour of the Day given, to find its Azimuth in any Latitude assigned. 60
  • Prob. 23. The Place of the Sun, and Hour of the Day given, to find the Almicantar of the Sun. 61
  • Prob. 24. The Place of the Sun given, to find what Hour it comes to the East, or West, and what Almicantar it then shall have. 61
  • Prob. 25. To know at any time what a clock it is in any other Part of the Earth. 62
  • Prob. 26. To find the Right Ascension of the Sun, or Stars. 63
  • Prob. 27. To find the Declination of the Sun, or Stars. 64
  • A Table of the Right Ascensions and Declinations of 100. Select fixed Stars; Calculated by Tycho Brahe, for the Years 1600, and 1670. As also their Difference of Right Ascensions and Declinations, in 70. Years. 65
  • Prob. 28. The Place of the Sun or any Star given, to find the Right Des­cension, and the Oblique Ascension, and the Oblque Descen­sion. [Page] fol. 71
  • Prob. 29. Any Place on the Terrestrial Globe being given, to find its Anti­podes. 72
  • Prob. 30. To find the Perecij of any given Place, by the Terrestrial Globe. 73
  • Prob. 31. To find the Antecij of any given Place, upon the Terrestrial Globe. 73
  • Prob. 32. To find the Longitude and Latitude of the Stars, by the Coelesti­al Globe. 73
  • Prob. 33. To find the Distance between any two Places on the Terrestri­al Globe. 74
  • Prob. 34. To find by the Terrestrial Globe upon what point of the Compass any [...] Places are scituate one from another. 75
  • Prob. 35. To find by the Coelestial Globe the Cosmical Rising and Setting of the Stars. 76
  • Prob. 36. To find by the Coelestial Globe the Acronical Rising and Setting of the Stars. 77
  • Prob. 37. To find by the Coelestial Globe the Heliacal Rising, and Setting of the Stars. 78
  • Prob. 38. To find the Diurnal and Nocturnal Arch of the Sun, or Stars, in any given Latitude. 79
  • Prob. 39. To find the Azimuth and Almicantar of any Star. 81
  • Prob. 40. To find the Hour of the Night, by observing two known Stars in one Azimuth, or Almicantar. 81
  • Prob. 41. The Hour given that any Star in Heaven comes to the Meridi­an, to know thereby the Place of the Sun, and by consequence the Day of the Moneth, though it were lost. 82
  • Prob. 42. The Day of the Moneth given, to find in the Circle of Letters on the Plain of the Horizon, the Day of the Week. 83
  • Prob. 43. The Azimuth of any Star given, to find its Hour in any given Latitude. 84
  • Prob. 44. How you may learn to know all the Stars in Heaven, by the Coelestial Globe. 84
  • Prob. 45. How to hang the Terrestrial Globe in such a position that by the Suns shining upon it you may with great delight at once behold the demonstration of many Principles in Astronomy, and Geo­graphy. 89
  • Prob. 46. To know by the Terrestrial Globe in the Zenith of what Place of the Earth the S [...] is. 91
  • Prob. 47. To find in what different Places of the Earth the Sun hath the [Page] same Altitude, at the same time. 92
  • Prob. 48. To find the length of the Longest and shortest Artificial Day or Night. 95
  • Prob. 49. To find how much the Pole is Raised, or Depressed, where the longest Day is an Hour longer or shorter then it is in your Ha­bitation. 96
  • Prob. 50. The Suns Place given, to find what alteration of Declination he must have to make the Day an Hour longer, or shorter: And in what number of Daies it will be. 97
  • Prob. 51. Of the difference of Civil and Natural Daies, commonly called the Equation of Civil Daies. And how it may be found by the Globe. 99
  • Prob. 52. How to find the Hour of the Night, when the Moon shines on a Sun Dyal, by help of the Globe. 101
  • Prob. 53. To find the Dominical Letter, the Prime, Epact, Easter Day, and the rest of the Moveable Feasts, for ever. 102
  • Prob. 54. The Age of the Moon given, to find her place in the Ecliptick according to her mean motion. 104
  • Prob. 55. Having the Longitude and Latitude, or Right Ascension and Declination of any Planet, or Comet, to place it on the Globe, to correspond with its place in Heaven. 105
The Contents Of the Third Book.
  • Prob. 1. THe Suns Amplitude and difference of Ascension given, to find the Height of the Pole, and Declination of the Sun. 108
  • Prob. 2. The Suns Declination and Amplitude given, to find the Poles E­levation. 108
  • Prob. 3. The Suns Declination and Hour at East given, to find the Heigth of the Pole. 109
  • Prob. 4. The Declination of the Sun and his Altitude at East given, to find the Heigth of the Pole. 110
  • Prob. 5. By the Suns Declination and Azimuth at 6, of the Clock given, to find the Heigth of the Pole, and Almicantar at 6. 11 [...]
  • [Page] Prob. 6. By the Hour of the Night and a known Star Observed Rising or Setting, to find the Heigth of the Pole. fol. 112
  • Prob. 7. Two Places given in the same Latitude, to find the Difference of Longitude. 112
  • Prob. 8. Two Places given in the same Longitude, to find the difference of Latitude. 113
  • Prob. 9. Course and Distance between two Places given, to find their dif­ference in Longitude and Latitude. 113
  • Prob. 10. To find how many Miles are contained in a Degree of any Pa­rallel. 114
  • Prob. 11. The Rhumb you have sailed upon, and the Latitudes you departed from, and are arived to, given, to find the Difference of Lon­gitude, and the number of Leagues you have Sailed. 114
  • Prob. 12. The Longitudes and Latitudes of two Places given, to find Course, and Great Circle distance between them. 116
  • Prob. 13. The Latitude you departed from, and the Latitude you are arri­ved to, and the number of Lagues you have sailed given, to find the Rhumb you have sailed on, and difference of Longitude. 116
  • Prob. 14. To find by the Globe the Variation of the Needle; commonly call­ed the Variation of the Compass. 117
  • Prob. 15. To keep a Journal by the Globe. 118
  • Prob. 16. To Steer in the Night by the Stars. 119
  • Prob. 17. How to platt on the Globe a New Land, never before Disco­vered. 119
  • Prob. 18. Seeing two known points or Capes of Land, as you sail along, how to know the distance of your Ship from them. 120
  • Prob. 19. Of Tides, and how by help of the Globe you may in general judge of them. 121
The Contents Of the Fourth Book.
  • Prob 1. To Erect a Figure of the 12 Houses of Heaven. 123
  • Prob. 2. [...]o Erect a Figure of Heaven according to Campanus. 128
  • Prob. 3. To find the length of a Planetary Hour. 129
  • Prob. 4. The length of a Planetary Hour known; to find what Planet [Page] Reigneth any given Hour of the Day, or Night. fol. 131
  • Prob. 5. To find Part of Fortune by the Globe. 132
  • Prob. 6. To find in what Circle of Position any Star, or any degree of the Ecliptick is. 133
  • Prob. 7. To find the Right Ascensions, the Oblique Ascensions, and the Declinations of the Planets. 133
  • Prob. 8. How to Direct a Figure, by the Globe. 134
  • Prob. 9. Of Revolutions: and how they are found by the Globe. 135
  • Prob. 10. How a Figure of Heaven may be erected by the Revolution thus found. 135
The Contents Of the Fifth Book.
  • Prob. 1. HOw by one position of the Globe to find the distance of the Hour lines on all manner of Planes. fol. 143
  • Prob. 2. To make an Equinoctial Dyal. 147
  • Prob. 3. To make an Horizontal Dyal. 149
  • Prob. 4. To make an Erect Direct South Dyal. 153
  • Prob. 5. To make an Erect Direct North Dyal. 156
  • Prob. 6. To make an Erect Direct East Dyal. 156
  • Prob. 7. To make an Erect Direct West Dyal. 159
  • Prob. 8. To make a Polar Dyal. 159
  • Prob. 9. To make Erect South Dyals, Declining Eastwards, or West­wards. 160
  • Prob. 10. To make a North Erect Dyal declining Eastwards or West­wards. 163
  • Prob. 11. To make Direct Reelining or Inclining Dyals. 164
  • Prob. 12. To make Declining Reclining, or Declining Inclining Dyals. 164
  • Prob. 13. To make a Dyal upon a Declining Inclining Plane. 168
  • Prob. 14. To find in what Place of the Earth any manner of Plane that in your Habitation is not Horizontal, shall be Horizontal. 171
  • Prob. 15. To make a Dyal on the [...]e [...]ling of a Room, where the Direct Beams of the Sun never come. 175
  • Prob. 16. To make a Dyal upon a solid Ball or Globe, that shall shew the Hour of the Day without a Gnomon. 178
  • Prob. 17. To make a Dyal upon a Glass Globe, whose Axis shall cast a sha­dow upon the Hour of the Day. 180
The Contents Of the Sixth Book.
  • [Page]Of the Parts and Kindes of Spherical Triangles. fol. 183
  • Prob. 1. The Legs of a Right Angled Spherical Triangle given; to find the Hypothenusa, and the two other Angles. 184
  • Prob. 2. A Leg and the Hypothenusa given, to find the Rest. 187
  • Prob. 3. The Hypothenusa and an Angle given, to find the Rest. 187
  • Prob. 4. A Leg and Angle adjoyning given, to find the Rest. 188
  • Prob. 5. A Leg and the Angle opposite given, to find the Rest. 188
  • Prob. 6. The Angle given, to find the Sides. 189
  • Prob. 7. Oblique Triangles. The three Sides given, to find the Angles. 190
  • Prob. 8. Two Sides and the Angle contained between them given, to find the Rest. 193
  • Prob. 9. Two Sides and an Angle opposite to one of them given, to find the Rest. 194
  • Prob. 10. Two Angles and the Side comprehended between them given, to find the Rest. 194
  • Prob. 11. Two Angles and a Side opposite to one of them given, to find the Rest. 195
  • Prob. 12. Three Angles given, to find the Sides. 196
  • Prob. 13. How to let fall a Perpendicular that shall divide any Oblique Spherical Triangle into two Right Angled Spherical Trian­gles. 198
  • The Poetical Stories of the Constellations in Heaven. 200

The First BOOK. Being the first RUDIMENTS of Astronomy & Geography. Or A Description of the Lines, Circles, and other Parts of the GLOBE.

PRAEFACE.

THe Students of all Arts and Sciences have ever proposed a Maxime, whereon (as on an allowed Truth) the whole Science hath dependance: and by so much the more demonstrable that Maxime is, so much the more of Excellency the Science may claim.

This of Astronomy and Geography comes not behind any; for herein we shall only admit (with the Ancients) that the Form of the visible World is Spherical: Neither shall we beg our Ascertion any farther then Occular Appearance will demonstrate: every Mans Ey being his Judge, if he be ei­ther on a Plain field, or at Sea, where nothing can hinder a free inspection of the Horizon.

Vpon good grounds therefore they ascerted the Spherical form of the Whole: and also concluded the Parts to be Round: I meane, very intire Subsistence, as the Stars, Planets, and the Earth. In the Celestial Bodies (as the Stars and Planets) this is also visible; and therefore un-controullable: But that the Earth is Round proves with the unskilfull matter of di­spute; [Page 2] they frequently objecting with S. Austine the words of the Scripture, which say, He hath stretched forth the corners of the Earth; not considering whether those words were spoken as alluding to the amplitude of Gods Omnipotence; or that the Corners were meant Capes of Land, which indeed are stretched forth into the Sea. But that the Earth is Round is proved by divers certain and in­fallible Reasons,

As first, By the Navigations of our Age, Divers able and honest Mariners having Sailed and continued an Easterly Course, have at length arrived (without turning back) to the same place from whence they set forth: witness Magellani­cus, Sr. Francis Drake, Tho. Cavendish, Oliver van­der Noort, W. Schouten, &c.

Secondly, By the length of degrees in every Parallel; for it is found by Dayly observation that the degrees of every Parallel upon the Earth, hold the same proportion to the de­grees of the Equinoctial, as the degrees of the same Parallel upon an Artificial Globe or Sphear do to the degrees of the greatest Circle of the same: This Argument alone is suffici­ent: yet take one more from Visible Appearance: And that is this: The shadow which the Earth and Water together make in the Eclipse of the Moon is alwaies a part of a Cir­cle; therefore the Earth and Water which is the Body sha­dowing must also be a Circular or round Body; for if it were three square, four square, or any other form, then would the shadow which it makes in the Moon be of the same fashion.

Besides, Of all figures the Sphear or Globe is most perfect, most Capacious, and most intire of it self, without either joynts or Angles; which form we may also perceive the Sun, Moon, and Stars to have, and all other things that are bounded by themselves, as Drops of Water, and other liquid things.

But there is another frequent Argument against the Globulus form of the Earth; and that is, That it seems im­possible [Page 3] that the Earth should be round, and yet also Inhabi­ble in all Places: For though we that inhabite on the top of the Earth go with our heads upwards; yet those that inhabite underneath us must needs go with their Heads downwards, like Flyes on a Wall or Ceeling; and so be in danger of falling into the Air.

For Answer hereunto, first, You must understand that in the Center of the Earth there is an Attractive and drawing power, which draws all heavy substances to it: by vertue of which Attractive power, things though loosed from the Earth will again incline and cling to the Earth, and so much the more forcibly, by how much the heavier they are; as a bullet of Lead let fall out of the Air, inclines towards the Earth far more violently and swiftly then a bullet of the same bigness of Wood, or Cork.

Secondly, you must understand that in respect of the whole Vniverse there is no part either upper or under, but all parts of the Earth are alike incompast with Heaven; yet in respect of the Earth, it is Heaven, which we take for the upper part; and therefore we are said to go with our heads up­wards, because our head (of all the parts of our body) is nearest to Heaven.

Now that this Attractive power lies in the Center of the Earth, is proved by this Argument: If the Attractive power were not in the Center, a Plumb-line let fall would not make Right Angles with the Superficies of the Earth; but would eb Attracted that way the Attractive vertue lies, and so make unequal Angles with the Superficies: But by so many Experiments as hath yet been made, we find that a Plumb-line continued, though never so deep, yet it alters no Angles with the Superficies of the Earth; and therefore undoubtedly the Attractive power lies in the very Center, and no where else.

CHAP. I.

I. What a Globe is.

A Globe according to the Mathematical Definition, is a perfect and exact round Body contained under one surface.

Of this form (as hath been proved) consists the Hea­vens and the Earth: and therefore the Ancients with much pains Study and Industry, endeavouring to imitate as well the imagina­ry as the real appearances of them both, have Invented two Globes; the one to represent the Heavens, with all the Constel­lations, fixed Stars. Circles, and Lines proper thereunto, which Globe is called the Celestial Globe; and the other with all the Sea Coasts, Havens, Rivers, Lakes, Cities, Towns, Hills, Capes, Seas, Sands, &c. as also the Rhumbs, Meridians, Parallels, and other Lines that serve to facilitate the Demostration of all manner of Questions to be performed upon the same: and this Globe is called the Terrestrial Globe.

II. Of the two Poles.

Every Globe hath two Poles, the one North, the other South. The North Pole is in the North point of the Globe: The South Pole in the South point.

III. Of the Axis.

From the Center of the Globe both waies, proceeds a line through both the Poles, and continues it self infinitely; which is called the Axis of the World; and is represented by the two wyers in the Poles of the Globe: Upon these two wyers the Globe is turned round, even as the Heavens is imagined to move upon the Axis of the World.

IIII. Of the Brasen Meridian.

Every Globe is hung by the Axis at both the Poles in a Bra­sen Meridian, which is divided into 360, degrees; (or which is all one) into 4 Nineties: the first beginning at the North Pole, is con­tinued from the left hand towards the right till the termination of 90 degrees, and is marked with 10, 20, 30, &c. to 90. from whence the degrees are numbred with 80, 70, 60, &c. to 0. which is in the South Pole: from whence again the degrees are numbred [Page 5] with 80, 70, 60, &c. to 0, and lastly, from 0 the degrees are num­bred with 10, 20, 30, to 90. which is again in the North Pole.

This Brasen Meridian is of great use; for by help of it you may find the Latitude of all Places, the Declination of all the Stars, &c, and rectifie the Globe to any Latitude.

V. Of the Horizon.

The Horizon is a broad wooden Circle, encompassing the Globe; having two notches in it; the one in the North the other in the South point: The notches are made just fit to contain the Bra­sen Meridian that the Globe is hung in: In the bottom or under Plane of the Horizon there stands up a rop or (as it is called) a Bed, in which there is also a notch, into which notch the Brasen Meridian is also let, so lo, as that both it and the Globe may be divided into two equal halfs by the upper Plane of the wooden Ho­rizon. These Notches are as gages to keep the Globe from inclin­ing more to the one side of the wooden Horizon then the other.

Upon the upper Plane of the Horizon is several Circles delinea­ted: as first, the inner Circle, which is a Circle divided into twelve equal parts, viz. into twelve Signes; every Signe having its name prefixed to it; as to the Signe of ♈ is the word Aries; to ♉ the word Taurus, &c. every Signe is again divided into 30 equal parts, which are called Degrees, and every tenth degree is marked with 10, 20, 30.

Next to the Circle of Signes is a Kalender or Almanack, ac­cording to the Old stile used by us here in England, each Moneth being noted with its proper Name; as January, February, March, &c. and every day distinguished with Arithmetical figures, as 1, 2, 3, 4, &c. to the end of the Moneth.

The other Calender is a Calender of the New stile; which is in a manner all one with the Old; only in this Calender the moneth begins ten daies sooner then they do in the other: and to this Ca­lender (because it was instituted by the Church of Rome) there is annexed the Festival daies Celebrated by the Romish Church.

The two other Circles are the Circles of the Winds; the inner­most having their Greek and Latine names; which by them were but twelve; and the outermost having the English Nanes, which for more preciseness are two and thirty.

The use of the upper Plane of the Horizon is to distinguish the Day from the Night; the Rising and Setting of the Sun, Moon, or [Page 6] Stars, &c. and for the finding the Azimuth, and Amplitude, &c.

VI. Of the Quadrant of Altitude.

The Quadrant of Altitude is a thin brass plate, divided into 90. degrees; and marked upwards with 10, 20, 30, 40, &c. to 90. It is rivetted to a Brass Nut, which is fitted to the Meridian; and hath a Screw in it, to screw upon any degree of the Meridian. When it is used it is screwed to the Zenith. Its use

[figure]

is for measuring the Altitudes, finding Amplitudes, and A­zimuths, and discribing Almicantaraths. It would sometimes stand you in good steed if the Plate were longer by the bredth of the Horizon then 90. degrees; for then that length being turned back will serve you instead of an Index, when the Nut is screwed to the Zenith, to cut either the degrees or Daies of either Style, or the Points of the Compass in any of those Circles concentrical to the innermost edge of the Horizon, which the Ey cannot so well judge at.

VII. Of the Hour Circle, and its Index.

The Hour Circle is a smal Brasen Circle, fitted on the Meridi­an, whose Center is the Pole of the world: It is divided into the 24 hours of the Day and Night, and each hour is again divided into halfs and quarters, which in a Revolution of the Globe are all pointed at with an Index, which to that purpose is fitted on the Axis of the Globe.

The use of the hour Circle is for shewing the Time of the se­veral mutations and Configurati­ons of Celestial Appearances.

[figure]

VIII. Of the Nautical Compass, or Box and Needle.

Just under the East point of the Horizon, upon the undermost Plane, is sometimes fixed a Nautical Compass, whose North and South line must be Parallel to the North and South line of the Horizon. The use of it is for setting the Angles of the Globe correspondent to the Angles of the World.

IX. Of the Semi-Circle of Position.

This is a Semi-Circle made of Brass, and divided into 180. degrees, numbred from the Equinoctial on either side with 10, 20, 30, &c. to 90. at the two ends there is an Axis, which is fitted into the two hole, of two smal studs fixed in the North and South points of the upper Plane of the Horizon: upon this Axis it is moved up and down, according to the intent of your operation.

The use of this Circle of Position is, for the finding the twelve Astrological Houses of Heaven; and also for finding the Circle of Position of any Star or Point in Heaven.

Thus much may serve for the lineaments Circumjacent to the body of the Globe. The next discourse shall be

CHAP. II.

Of the Circles, Lines, &c. discribed upon the Superficies of the Globe; beginning with the Terrestrial Globe; and

I. Of the Equator.

THe Equator is a great Circle, encompassing the very middle of the Globe between the two Poles thereof, and divides it into two equal parts, the one the North part, and the other the South part. It is (as all great Circles are divided into 360. equal parts, which are called Degrees. Upon this Circle the Longitude is numbred, from East to West: and from this Circle both waies, viz. North and South the Latitude is reckoned. It is called the E­quator, because when the Sun comes to this line (which is twice in one year, to wit, on the tenth of March, and the eleventh [Page 8] of June) the Daies and Nights are equated, and both of one length.

II. Of the Meridians.

There are infinite of Meridians, for all places lying East or West from one another have several Meridians; but the Meridians deli­neated upon the Terrestrial Globe are in number 36. so that be­tween two Meridians is contained ten degrees of the Equator. From the first of these Meridians (which is divided into twice 90 degrees) accounted from the Equator towards either Pole) is the beginning of Longitude, which upon our English Globes is at the Ile Gratiosa, one of the Iles of the Azores, and numbred in the Equator Eastwards, with 10, 20, 30, &c. to 360. round about the Globe, till it end where it began.

They are called Meridians, because they divide the Day into two equal parts: for when the Sun comes to the Meridian of any Place, it is then Midday, or full Noon.

III. Of the Parallels.

As the Meridians are infinite, so are the Parallels; and as the Meridian lines delineated upon the Globe are drawn through no more then every tenth degree of the Equator, so are the Parallels also delineated but upon every tenth degree of the Meridian; lest the Globe should be too much filled with superfluity of lines, which might obscure the smal names of Places. The Parallel Circles run East and West round about the Globe, even as the Equator; only the Equator is a great Circle; and these are every one less then other, diminishing gradually till they end in the Pole. The Parallels are numbred upon the Meridian with 10, 20, 30, &c. to 90. beginning in the Equator, and ending in the Pole.

They are called Parallels; because they are Parallel to the Equator.

IIII. Of the Ecliptick, Tropicks, and Polar Circles.

These Circles though they are delineated upon the Terrestrial Globe, yet they are most proper to the Celestial; and therefore when I come to the Celestial Globe, I shall define them unto

V. Of the Rhumbs.

The Rhumbs are neither Circles nor straight lines, but Heli­spherical or Spiral lines: They proceed from the point where we stand, and wind about the Globe till they come to the Pole; where at last they loose themselves. They represent the 32 winds of the Compass.

Their use is to shew the bearing of any two places one from another: that is to say, upon what point of the Compass any shoar or Land lies from another.

There are many of them described upon the Globe, for the better directing the ey from one shoar to the other, when you seek after the bearing of any two Lands. Some of them (where there is room for it) have the figure of the Nautical Card drawn about the Center or common intersection, and have (as all other Cards have) for the distinction of the North point, a Flowerde­luce pictured thereon.

They were first called Rumbs by the Portugals; and since used by Latine Authors, and therefore that name is continued by all Writers that have occasion to speak of them.

VI. Of the Lands, Seas, Ilands, &c. Described upon the Terrestrial Globe:

The Land described upon the Globe is bounded with an irregu­lar line, which runs turning and winding into Creeks and Angles, even as the shoar which it represents (doth) For the better di­stinction of Lands, &c, this line is cullered close by one side thereof with divers Cullers, as with red, yellow, green, &c. these cullers distinguish one part of the Continent from the other; and also one Iland from another. That side of the line which incompasses the Cullers, is the bounds of the Land; the other side of the line which is left bare without Cullers, is the limits of the Water.

The Land is either Continents, or Ilands.

A Continent is a great quantity of Land, not interlaced or sepa­rated by the Sea, in which many Kingdomes and Principalities are contained; as Europe, Asia, Affrica, America.

An Island is a part of the Earth, environed round with Wa­ters; as Britain, Java, S. Laurence Isle, Barmudas, &c.

These again are sub-divided into Peninsula, Istmus, Promon­torium.

[Page 10] A Peninsula is almost an Island; that is, a track of Land which being almost encompassed round with Water, is joyned to the firm Land, by some little Istmus; as Molacca in the East-Indies, &c.

An Istmus is a little narrow neck of Land, which joyneth any Peninsula to the Continent; as the Straits of Dariene in Peru, and Corinth in Greece.

Promontorium, is some high Mountain, which shooteth it self into the Sea, the utmost end of which is called a Cape, as that great Cape of Good Hope, and Cape Verde in Africa.

The Water is either Ocean, Sea, Straits, Creeks, or Rivers.

The Ocean is that generall collection of all Waters, which in­vironeth the whole Earth on every side.

The Sea is a part of the Ocean; to which we cannot come, but through some Strait, as Mare Mediterraneum, Mare Balticum, and the like.

These two take their names either from the adjacent places, as the Brittish Ocean, the Atlantick Sea, &c. or from the first disco­vere as Mare Magellanicum; Davis, and Forbishers Staits; &c. Or from some remarkable accident, as Mare Rubrum, from the red colour of the Sands; Mare Aegeum, Pontus Euxinus, and the like.

A Strait, is a part of the Ocean restrained within narrow bounds, and opening a way to the Sea; as the Straits of Gi­bralter, Hellespont, &c.

A Creek is a crooked shoar, thrusting out as it were two armes to imbrace the Sea, as Sinus Adriaticus, Sinus Persi­cus &c.

A River is a small branch of the Sea, flowing into the Land; as Thames, Tiber, Rhine, Nilus &c.

Now that these Lands, Ilands, Towns, Seas, Rivers, &c. may at the first search be found upon the Globe, all Geographers have placed them thereon according to Longitude, and Latitude,

VII. Longitude.

The Longitude is an Arch of the Equator, comprehended be­tween the first Meridian and the Meridian of the Place you in­quire after. It is numbred on the Equator from the West to the [Page] Eastwards, with 10, 20, 30, to 360. degrees, till it end where it began.

VIII. Latitude.

The Latitude is an Arch of the Meridian, comprehended be­tween the Equator and the place enquired after. It is numbred on the Meridian, from the Equator both waies, viz. North and South, till it come to the Poles, or 90 degrees.

Thus much may serve for the description of the Terestrial Globe: I therefore come to treat of the Celestial.

CHAP. III.

Of the Celestial Globe, or the Eighth Sphear, repre­sented by the Celestial Globe: its motion, and of the Circles, Lines, Images, Stars, &c. described thereon.

I. Of the eighth Sphear.

THe eighth Sphear which is the starry Heaven, is represen­ted by the Celestial Globe, because upon the Convex­ity of it all the Stars and visible appearances are placed according to the order that they are situated in the concavity of the eighth Sphear. It is called the eighth Sphear, because between it and us are contained seven other Heavens, or Sphears; as 1. the Moon, 2. Mercury, 3. Venus, 4. the Sun, 5. Mars, 6. Jupiter, 7. Saturn. and eighthly the starry Heaven. The antients have made the Systeme of the world to consist of 2 other Sphears, called the Chiristiline Heaven, and the Primum Mobile, or first Mover: as in the following figure is represented.

[Page 12]

A figure wherein may be seen the Composition of the whole frame of the World.

II. Of the Motion of the eighth Sphear.

There hath bin attributed to the eighth Sphear a twofold mo­tion; the one called its Diurnal Motion, which is made from East to West upon the Poles and Axis of the World: And the o­ther called its Second motion; which is made from West to East upon the Poles and Axis of the Ecliptick.

The Diurnal motion is caused by the violent Motion of the [Page 13] Primum Mobile; for in 24 hours it carries along with it, not only the eighth Heaven or Orb of fixed Stars, but the Orbs of the Sun, the Moon, and all the rest of the Planets. It is called the Diurnal Motion because it is finished in one Day.

The second Motion is unproperly attributed to the eighth Sphear; it being indeed the Motion of the Equinoctiall; tho Au­thors sometimes carelesly mention the one insteed of the other. Therefore in the next Section, where I treat of the Equinoctial, I shall at large explain unto you the nature of this mis-called Second Motion.

III. Of the Equinoctial.

The Equinoctial upon the Celestial Globe, is the same line formerly called the Equator upon the Terrestrial; only with this difference, that the Equator remains fixt upon the Terrestrial Globe, but the Equinoctial upon the Celestial Globe is moveable; (or at least must be imagined to move) contrary to the Diurnal motion from West to East, upon the Poles of the Ecliptick: I say imagined to move, because in the Heavens it doth really move, tho on a material Globe it would be inconvenient to make a moveable Equinoctial, and therefore it hath one fixed: which for this and the next age will sufficiently serve, without much devia­tion from the truth it self.

Now that the difference between the Equator upon the Ter­restrial Globe, and the Equinoctial upon the Celestial, may be proved; and the motion of the Equinoctial be the better under­stood; I shall only bring this example,

All places that were formerly under the Equator, do and will keep the same Longitude, and remain still under the Equator: as may be proved by comparing the Ancient and modern Geogra­phers together: but those Stars that were formerly under the E­quinoctial, do not keep the same Longitude, nor remain under the Equinoctial: because the Equinoctial (as aforesaid) hath a motion from West to East, upon the Poles of the Ecliptick. But the Stars being fixed in their one Sphear, like knots in wood, and therefore move not, are by the Precession of the Equinox left be­hind the Equinoctial Colure, and so are caused to alter their Longitude; as by comparing the Observations of ancient and modern [...] together, it will appear: for about 346 [Page 14] years before Christ, the first Star in the Rams horn was by the Egyptian and Grecian Astronomers observed to be in the Equi­noctial Colure: and 57 years ago, when Tycho observed, it was found to be in 27 degrees 37 minutes of ♈. So that in about 2000 years it is moved forwards 28 degrees, and will according to Tycho's opinion, finish its Revolution in 25412 years: Ac­cording to which motion, I have Calculated this following Table, for finding the Degrees and Minutes of the Equinoctial motion, answerable to any number of years within the said Re­volution.

ye. deg. m years. deg. m.
1 0 0¾ 100 1 25
2 0 1½ 200 2 50
3 0 2½ 300 4 15
4 0 3⅓ 400 5 40
5 0 4¼ 500 7 5
6 0 5 1000 14 10
7 0 5¾ 2000 28 20
8 0 6½ 3000 42 30
9 0 7¼ 4000 56 40
10 0 8½ 5000 70 50
20 0 17 10000 141 40
40 0 34 20000 283 20
60 0 51 25000 354 10
80 1 8 25412 360  

This Table may be of use for finding the Equinoctial posi­tion of any Star, for any year either past, present, or to come. Its use is very easie, for if you desire to know the motion of the Equinox for any number of years, you need but seek your num­ber in the Collumn of years, and against it you have the degrees and minutes of the Equinoctial motion.

But tho the Stars have this motion one way, viz. in Longi­tude, yet do they not at all alter their Latitudes; because the mo­tion of the Equinoctial is made upon the Poles of the Ecliptique.

IIII Of the Ecliptique.

The Ecliptique is a great Circle, lying oblique or aslope from the Equinoctial, making an Angle of 23 ½ degrees with it: It cuts the Equinoctial into two equal parts, and is cut by the E­quinoctial in two opposite points, viz. ♈, and ♎. It divides the Globe into two equal parts, called Hemisphears; the one the Northern and the other the Southern Hemisphear. It is divided into 12 equal parts, which are called the twelve Signes, every part being noted with the Character of the Signes belonging unto it; as unto Aries, ♈: to Taurus, ♉: to Gomini, [...]; and so of the rest. From every one of these 12 divisions proceed both waies viz. North, and South, Circles of Longitude, into the Poles of the Ecliptique. Each of these twelve Signes is divided into 30 equal parts, which are called degrees; and are numbred upon every tenth degree with 10, 20, to 30, and upon may new Celestial Globe, for more preciseness, every degree is again divi­ded into halfs.

It is called the Ecliptique as being derived from the Greek word: [...] which signifies to want light, because in and about it happen all the defects and Eclipses both of the Sun and the Moon.

It is also called the Way of the Sun, because the Sun goes alwaies under it, passing through it in all his Annual Course.

V. Of the Poles of the Ecliptick.

There are two Poles of the Ecliptick, the one the North Pole, the other the South Pole; and are called North or South accor­ding to their position next the North or South Pole of the World. Each it distant from its correspondent Pole of the World 23 degrees 30 minutes.

As on the Terrestrial Globe all the Meridians discribed there­on meet in the Pole of the World, so on the Celestial all the Cir­cles of Longitude drawn through the twelve Signes meet in the Poles of the Ecliptick.

VI. Of the Axis of the Ecliptick.

Through the two Poles of the Ecliptick is imagined to pass a straight line, through the Center of the Plain of the Ecliptick; which is called the Axis of the Ecliptick, upon which the second motion of the Ecliptick is performed: even as the Diurnal motion is performed upon the Axis of the World.

VII. Of the Colures, and Cardinal Points.

There are two great Circles cutting one another at right an­gles in the Poles of the World, which are called the Colures. Each Colure receives an additional name from the point in the Ecliptick that it Cuts; as the one passes from Pole to Pole through the beginning of ♈ and ♎, which being two Equinoctial Signes, name therefore that Colure the Equinoctial Colure: The other passes through the beginning of ♋ and ♑, which are Solsticial Signes, and therefore names that the Solsticial Colure.

These Colures by intersecting one another, divide themselves into four Semi-circles; and these Semi-circles divide the Ecliptick into four equal parts. viz. in ♈, ♋, ♎, and ♑,

The points of the Ecliptick that these intersections pass through, are called the four Cardinal points, and are of great use in A­stronomy; for according to the Suns approach to any of them, the Season of the year is altered into Spring, Summer, Autumn, Winter: as shall be shewed hereafter.

VIII. Of the Tropicks.

There are two smaller Circles Parallel to the Equinoctial, which are called the Tropicks; the one called the Tropick of Can­cer, the other the Tropick of Capricorn: they are distant from the Equinoctial 23 degrees 30 minutes; and therefore are the bounds of the Ecliptick. They receive their names from the Celestial Signe that they are joyned unto; as the one the Tropick of Cancer, because it touches the Signe of Cancer; the other the Tropick of Capricorn, because it touches the Signe of Capricorn.

IX. Of the Circles Arctick and Antarctick.

About the Poles of the World are two smal Circles described; the one called the Arctick, the other the Antartick: That in the North is called the Arctick Circle: that in the South the Antarctick Circle.

They have the same distance from the Poles of the World that the Tropicks have from the Equinoctial Circle, (viz. 23 degrees 30 minutes) and that the Ecliptick hath from the Poles of the World; and therefore run through the Poles of the Ecliptick.

X Of the Images called Constellations, drawn upon the Celestial Globe.

Here I think fit to be beholding to Dr. Hood. for the paines he hath taken in his comment upon the Images and Constelations. He saith, The stars are brought into Constellations, for instructi­ons sake: things cannot be taught without names, to give a name to every star had been troublesome to the Master, and for the Scholler; for the Master to devise, and for the Scholler to re­member: and therefore the Astronomers have reduced many stars into one Constellation, that thereby they may tell the better where to seek them; and being sought, how to express them.

All the Constellations formerly notified by the Antients were in number 48. twelve whereof we call the twelve Signes of the Zodiack, viz. 1 Aries, ♈. 2 Taurus, ♉. 3 Gemini, ♊. 4 Cancer, ♋. 5 Leo, ♌. 6 Uirgo, ♍. 7 Libra, ♎. 8 Scorpio, ♏. 9 Sagit­tarius, ♐. 10 Capricorn, ♑. 11 Aquarius, ♒. 12 Pisces. ♓. One and twenty more are Placed in the North Hemisphear, and are called 1 Ursa minor, 2 Ursa Major, 3 Draco, 4 Cepheus, 5 Bootes, 6 Corona Septentri, 7 Hercules, 8 Lyra, 9 Cygnus, 10 Cassiopeia, 11 Perseus, 12 Auriga, 13 Serpentarius, 14 Serpens Ophiuchi, 15 Sagitta, 16 Aquila, 17 Delphinus, 18 Equiculus, 19 Pegasus, 20 Andromeda, 21 Triangulum. The other 15 are scituated in the South Hemisphear, and called 1 Cetus, 2 Orion, 3 Eridanus, 4 Lepus, 5 Canis Major, 6 Canicula, 7 Argo Navis, 8 Hydra, 9 Crater, 10 Corvus, 11 Centaurus, 12 Lupus, 13 Ara, 14 Corona Austrina, 15 Pisces Austrina. Besides there are 2 other Constellations in the North Hemisphear, viz. Antinous, [Page 18] and Coma Berenices: which because they were not specified by the Ancients are here inserted apart.

Now the Astronomers did bring them into these figures, and not into other, being moved therto by these three reasons: first these Figures express some properties of the stars that are in them; as those of the Ram to bee hot and dry; Andromeda chained, betokeneth imprisonment: the head of Medusa cut off, signifieth the loss of that part: Orion with his terrible and threat­ning gesture, importeth tempest, and terrible effects: The Serpent, the Scorpion, and the Dragon, signifie poyson: The Bull, insinu­ateth a melancholy passion: The Bear inferreth cruelty, &c. Secondly, the stars, (if not precisely yet after a sort) do represent such a Figure, and therefore that Figure was assigned them: as for example, the Crown, both North, and South; the Scorpion and the Triangle, represent the Figure which they have. The third cause, was the continuance of the memorie of some notable men, who either in regard of their singular paines taken in Astronomy, or in regard of some other notable deed, had well deserved of man kind.

The first Author of every particular Constellation is uncertain; yet are they of great antiquity; we receive them from Ptolomte, and he followed the Platonicks; so that their antiquity is great. Moreover we may perceive them to be ancient by the Sciptures; and by the Poets. In the 38 Chapter of Job there is mention made of the Pleiades, Orion, and Arcturus, and Mazzaroth, which some interpret the 12 Signes: Job lived in the time of Abraham, as Syderocrates maketh mention in his Book de Commensurandis locorum distantiis.

Now besides all this, touching the reason of the invention of these Constellations, the Poets had this purpose, viz. to make men fall in love with Astronomy: And to that intent have to eve­ry Costellation invented strange conceited stories, (as you may read at the latter end of this Book) therein imitating Demost­henes, who when he could not get the people of Athens to hear him in a matter of great moment, and profitable for the Com­mom-wealth, he began to tell them a tale of a fellow that sold an Ass; by the which tale, he so brought on the Athenians, that they were both willing to hear his whole Oration, and to put in practice that whereto he exhorted them. The like intent had the Poets in of those Stories: They saw that Astronomy being for [Page 19] commodity singular in the life of man, was almost of all men ut­terly neglected: Hereupon they began to set forth that Art under Fictions; that thereby, such as could not be perswaded by com­modity, might by the pleasure be induced to take a view of these matters: and thereby at length fall in love with them. For commonly you shall note this, that he that is ready to read the Stories, cannot content himself therewith, but desireth also to know the Constellation, or at leastwise some principal Star therein.

There are in Heaven yet twelve Constellations more, posited about the South Pole, which were added by Frederic [...] Ho [...]t­manno, inhabiting on the Island Sumatra who being accommo­dated with the Instruments of that immortal Tycho, hath obser­ved the Longitude and Latitude of those Stars, reduced them into Constellations, and named them as follows, 1 The Crane, 2 The Phenix, 3 The Indian, 4 The Peacock, 5 The Bird of Paradice, 6 The Fly. 7 The Camelion. 8 The South Triangle, 9 The Flying Fish, 10 Dorado, 11 The Indian Fowl, 12 The Southern Serpent.

XI. Of the Number of the Stars.

Although in Heaven there be a very great number of visible Stars, which for their multitude seem innumerable; yet no wise man will from thence infer that they are impossible to be counted: for there is no Star in Heaven that may be seen, but its Longi­tude and Latitude may with meet Instruments for that purpose be exactly found; and being once found, it may have a name allotted it, which with its Longitude and Latitude may be Cata­logized either for the memory of the Observer, or the knowledge of Posterity. Now therefore if any one Star may be observed, they may all be observed; and then may they all have Names given them; which tho to the ignorant it seem uncredible, yet to the sons of God, (as Josephus call Astronomers) who herein participate of their fathers knowledge, it is easie to number the Stars, and call them all by their Names Psal. 97, 4.

But tho all the Stars in Heaven may be numbred and named, yet have not the Ancient Astronomers thought fit to take notice of more then 1025 of the chiefest that are visible in our Horizon, they being sufficient for any purpose that we shall have occasion to apply them unto. Yet of late the industry of Frederick Hout­man [Page 20] aforesaid, hath added to the Catalogue 136 Stars, with their Longitude Latitude and Magnitude, and given Names unto them: which upon my New Globes I have also ascerted, as may be seen about the South Pole thereof. So that with these 1025, observed by the Ancients, and these 136, the whole number of the Catalogue is 1161.

Some other Stars of late have been also observed by Bai [...]rus, among the several Constellations aforesaid; but none of any Con­siderable Magnitude, and therefore I think fit to pass them by, and come to their scituation in Heaven, according to Longitude and Latitude.

XII. Of the Scituation of the Stars:

The Stars are Scituate in Heaven according to their Longitude and Latitude As the Longitude of any Place upon the Terrestrial Longitude of the Stars Globe is an Arch of the Equator, Comprehended between the first Meridian and the Place. So the Longitude of any Star upon the Celestial Globe is an Arch of the Ecliptick, contained between the first point of ♈ and the Star inquired after. But yet because the Ecliptick is divided into twelve Signes, the Longitude of a Star is therefore (in the most Customary account) an Arch of the Ecliptick comprehended between the Semi-circle of Longi­tude passing through the beginning of the Signe the Star is in, and the Semi-circle of Longitude passing through the Center of the Star.

The Latitude of a Star is either North or South: North, if on Latitude of the Stars the North side of the Ecliptick; South, if on the South side of the Ecliptick. As the Latitude of any Place upon the Terrestrial Globe is an Arch of the Meridian, contained between the Equa­tor and the Parallel of the Place, So is the Latitude of any Star upon the Celestial Globe an Arch of a Semi-circle of Longitude, comprehended between the Equinoctial and the Star inquired after.

XIII. Of the Magnitudes of the Stars:

For the better distinction of the several sizes of Stars, they are divided into six several Magnitudes. The biggest and brightest Stars are called Stars of the first Magnitude: Those one degree [Page 21] inferiour in light and bigness are called Stars of the Second Mag­nitude, Those again one degree inferiour to the Stars of the second Magnitude, are called Stars of the Third Magnitude, and so the Stars gradually decrease unto the sixth Magnitude, which is the smalest, some few obscure Stars only excepted, which for their Minority and dimness are called Nebula. These several Magni­tudes of the stars are expressed on the Globe in several shapes, as may be seen in a small Table placed on the Globe for that purpose.

Now for your further satisfaction and delight, I have inserted a Collection of D. Hoods, wherein is expressed the measure of The meas [...]res [...] of the severa Stars every Magnitude, and the proportion it hath, first, to the Diame­ter, and secondly, to the Body of the Earth.

The greatness of any thing (saith he) cannot be better expres­sed then by comparing it to some common measure, whose quan­tity is known: The common measure whereby Astronomers ex­press the greatness of the Stars, is the Earth;

Sometimes they compare them with the Diameter of the Earth, sometimes with the Globe thereof: The Diameter accor­ding to their account which allow but 60 miles to a degree, con­taineth 6822 8/11 miles; and the whole soliditie of the Globe con­taines 165, 042, 481, 283. miles and 79/137. According to Ptolo­me, who allotteth to every degree 62½ miles, the Diameter con­taineth 7159 miles 1/11, and the whole soliditie of the Globe, hath 192, 197, 184, 917, 473/1331 miles.

The proportion of the Diameters of the fixed Stars; Com­pared with the Diameter of the Earth.

The Diameter of a fixed Star of the first Magnitude compared with the Diameter of the Earth hath such proportion to it, as 19 hath to 4: therefore it containeth the Diameter of the Earth 4 times and ¾.

The Diameter of a Star of the second Magnitude is unto the Diameter of the Earth as 269 is to 60: therefore it containeth it 4 ⅙ times.

The Diameter of a fixed Star of the third Magnitude is unto the Diameter of the Earth as 25 unto 6: therefore it containeth it 4 ⅙ times.

The Diameter of a fixed Star of the fourth Magnitude is unto [Page 22] the Diameter of the Earth as 19 unto 5: therefore it containeth it 3 ⅘ times.

The Diam. of a fixed Star of the fifth Mag, is unto the Diameter of the Earth, as 119 unto 36. therefore it containeth it 3 11/36 times.

The Diam. of a fixed Star of the sixth Mag. is unto the Diame [...] of the Earth, as 21 unto 8; therefore it containeth it ⅝ times.

As for the proportions of the cloudie and obscure Stars, they are not expressed because they are but few, and of no great ac­count in respect of their smalness.

The proportions of the fixed Stars compared with the Globe of the Earth, are as follow.

A Star of the first Magnitude is to the Globe of the Earth, as 6859, to 64. therefore it containeth the Globe of the Earth 107 ⅙ times.

A Star of the second Magnitude is to the Globe of the Earth, as 19465109 is to 216000. therefore it containeth it 90 ⅛ times.

A Star of the third Magnitude is to the Globe of the Earth, as 15625 is unto 216: therefore it containeth it 72 ⅓ times.

A Star of the fourth Magnitude is to the Globe of the Earth as 6850 is unto 125: therefore it containeth the Globe of the Earth 54 11/12 times.

A Star of the fifth Magnitude is to the Globe of the Earth, as 1685159: is unto 46656: therefore it containeth the Globe of the Earth 36 ⅛ times.

A Star of the sixth Magnitude is to the Globe of the Earth, as 9261 is unto 512: therefore it containeth the Globe of the Earth 18 1/10 times.

I confess all this may seem matter of incredulity to those whose understanding is swayed by their visual sence; but if they be ca­pable to consider the vast distance of those Huge Bodies, (the Stars) from the face of the Earth, and also the diminutive qua­lity of Distance, their reason will be rectified, and their increduli­ty turn'd into an acknowledgement of the unspeakable wisdom of Almighty God; and they will say with the Psalmist, Great is our Lord, Great is his Power, his Wisdom is infinite. Psal. 147. 5.

The distance of the Stars therefore from the Earth, is accor­ding to M. John Dee's Computation, 20081 ½ Semidiameters of the Earth. The Semidiameter of the Earth containeth of our [Page 23] common miles 3436 4/11, Such miles as the whole Earth and Sea round about is 21600: allowing for every degree of the great­est Circle 60 miles: so that the distance of the Stars from the Earth is in miles 69006540. Now as M. Dee saith, (almost in these same words) if you weigh well with your self this little par­cel of fruit Astronomical; as concerning the bigness and distance of the Stars, &c. and the Huge massiness of the Starry Heaven, you will find your Consciences moved with the Kingly Prophet to sing the confession of Gods Glory; and say, The Heavens De­clare the Glory of God, and the firmament sheweth forth the works of his Hands.

XIIII. Of the Nature of the Stars.

To many of the Principal Stars there is in Planetical Chara­cters prefixed their Planetical Natures. The Astrologers make great use of them for knowing the nature of the Stars: for those Stars that have the character of ♄ adjoined are said to be of the nature of ♄: those that have ♃ adjoined, are of the nature of ♃: and so of the rest. If a Star have the characters of two Planets ad­joined, that Star participates of both their Natures, but most of that Planets whose character is first placed.

The use Astronomers make of those characters, is for knowing that culler of any Star; as if a Star have ♄ adjoined, it is of the cul­ler of ♄; if ♃, it is the culler of ♃, &c.

The fixed Stars are known from the Planets by their conti­nual twinckling; for the Planets never twinckle, but the fixed Stars do.

XV. Of Via Lactea, or the Milky way.

This subject because it is already so fully handled by D r. Hood, that more then he hath written cannot well be said, either of his own oppinion or other mens, I think fit therefore to give you his own words: which are as follow.

VIA LACTEA▪ or Circulus Lacteus; by the Latines so called; and by the Greekes, Galaxia; and by the English, the Milky way. It is a broad white Circle that is seen in the Heaven: In the North Hemisphear, it beginneth at Cancer, on each side the head thereof, and passeth by Auriga, by Perseus, [Page 24] and Cassiopeia, the Swan, and the head of Capricorn, the tayl of Scorpio, and the feet of Centaur, Argo the Ship, and so unto the head of Cancer. Some in a sporting manner, do call it Watling street; but why they call it so, I cannot tell; except it be in re­gard of the narrowness that it seemeth to have, or else in respect of that great High way that lieth between Dover and S. Albons, which is called by our men Watling street.

Concerning this Circle there are sundry opinions: for there is great difference among some writers, both touching the place, matter, and efficient cause thereof. Aristotle dissenteth from all other, both Philosophers and Poets, in the place, matter, and cause of this Circle; saying, that it is a Meteor ingendred in the Air, made of the vapors of the earth, drawn up thither by the heat of the Sun, and there set on fire. But his opinion is of all men confuted.

First, touching the place, it cannot be in the Air; for whatso­ever is in the Air, is not seen of all men, at all times, to be un­der one and the same part of Heaven. If we see it in the South, they that are in the West shall see it under the East side of the Heaven; and they that are in the East, shall see it in the West part of the Heaven; but this Circle is of all men seen alwaies un­der the same part of Heaven, and to be joyned with the same Stars; therefore it cannot be in the Air.

Again, for the matter, it cannot be made of that which A­ristotle nameth (i. e.) the vapours of the earth, because of the long continuance of the thing, and that without any alteration: for it is impossible that any Meteor made of vapours drawn up from the water, or exhalations from the earth, should last so long; as may be seen in blazing Stars; which though they have continued long, as namely, 16. moneths, some more, some less; yet at the length they have vanished away: whereas this Cir­cle hath continued from the beginning unto this day. Besides, put case it were made of these exhalations, Whence will they in­fer the uniformity thereof? The Comets do alter diversly, both in the fashion of their blazing, and also in their several quantities; whereas in this Circle, there is nothing but the same part, alwaies of one form and of one bigness. In the e [...]cient cause therefore he must needs err: for if it be neither in the Air, nor made of the exhalations of the earth, it cannot be caused by the Sun; for the [Page 25] one is the place and the other the matter, wherein, and whereup­on the Sun sheweth his power.

All other, (besides Aristotle) agree in the place, but dif [...]er in the efficient cause thereof: and they are either Philosophers, or Poets. Both these affirm that it is in the Firmament (i. e.) in the eight Sphear; but they disagree in the cause thereof.

The Philosophers (and chiefely Demecritus) affirm the cause of the thing, to be the exceeding great number of Stars in that part of Heaven, whose beams meeting together so confused­ly, and not coming distinctly to the ey, causeth us to imagine such a whiteness as is seen. But the best opinion is this, that this Milky way is a part of the Firmament, neither so thin as the o­ther parts thereof are, not yet so thick as the Stars themselves. If it were as thin as the other parts of the Heaven besides the Stars, then could it not retain the light, but the light would pass through it and not be seen: If it were as thick as the Stars, then would the light be so doubled in it, that it would glister and shine, as the Stars themselves do: but being neither so thin as the one, nor so thick as the other, it becommeth of that whiteness we see.

Bla [...]u saith, This Lactean whiteness and clearness ariseth from a great number of little Stars, constipated in that part of Heaven: flying so swiftly from the sight of our eyes, that we can perceive nothing but a confused light: this the Tubus Diopticus (more lately found out) doth evidently demonstrate to us: by the bene­fit of which little Stars (otherwise inconspicuous to our eyes) are there clearly discerned.

About the Southern Pole are seen two white spots, like little clouds, colured like the via Lactea. One of which is trebble the Latitude of the other; some Mariners call them Nubecula Magellani.

This Milkie way is discribed on the Globe between two tracks of smal Pricks, running through the Images mentioned in the beginning of this Section.

Thus have you the definition of the Globes; with the descripti­on of all the lines, Circles, &c. described thereon. I shall now ex­plain unto you the meaning of Several words of Art, which in the use of them you will meet with, and then come to the Use it self.

And first, what is meant by the word Horizon.

[Page 26] When I spake of the Horizon before, I only mentioned the wooden Horizon or frame about the Globe; which because it represents the Mathematical Horizon, is therefore called the Horizon: but the word Horizon is to be considered more parti­cularly, two manner of waies: as

First, the Natural Horizon.

Secondly, the Mathematical Horizon.

The Natural Horizon is that Appearent Circle which di­vides the Visible part of Heaven from the invissible; it extends it self in a straight line from the Superficies of the Earth, every way round about the place you stand upon, even into the very Circumference of the Heavens. It is onley discerned at Sea, or on plaine ground, that is free from all hinderances of the sight as Hills, Trees, Houses, &c.

The Mathematical Horizon (which indeed is meant in this Treatise, so oft as I shall have occasion to name the word Hori­zon) is a great Circle which divides that part of Heaven which is above us, from that which is under us, precisely into two equal parts: whose Poles are the Zenith and Nadir. In this Circle the Azimuths or Verticle Circles are numbred: and by this Circle our Daies and Nights are measured out unto us: for while the Sun is above the Horizon it is day; and when it is under the Horizon it is Night.

This Circle is represented unto us by the upper Plain of the wooden Horizon: Therefore so oft as you are directed to bring any degree or Star &c. to the Horizon, it must be understood that you must turn the Globe till the degree or Star come just to the upper inner edge of the wooden Horizon.

The Zenith, and Nadir, are two points opposite to one another. The Zenith is that point in Heaven which is directly over our Zenith. Heads: and the Nadir is that point in Heaven which is directly Nadir. under our feet.

The Azimuths or Verticle Circles are great Circles passing through the Zenith, and Nadir, whose Poles are the Zenith and Azimuths, or Verticle Cir­cles. Nadir. And as the Meridians cut the Equator, and all Paral­lels to the Equator at Right Angles, so the Azimuths cut the Horizon and all Almicanthars at Right Angles also. The Azimuths (as the Meridians) are infinite; and are numbred by degrees from the East and West point towards the North and South in the Horizon: as also is the Amplitude.

[Page 27] The Almicanthars are Circles Parallel to the Horizon, Almicanthars, or Circles of Altitude. whose Poles are the Zenith and Nadir. They are also called Cir­cles of Altitude, because when the Sun Moon or any Star, is in a­ny number of degrees above the Horizon, it is said to have so many degrees of Altitude, which degrees of Altitude are num­bred upon the Verticle Circle from the Horizon upwards, to­wards the Zenith. The Almicanthars are also infinite: as Pa­rallels, Meridians and Azimuths are.

The Amplitude is the number of degrees contained between Amplitude. the true East or West point in the Horizon, and the rising or set­ting of the Sun, Moon, or Stars. &c.

The Declination is the number of degrees that the Sun, Moon, Declination. or any Star, is distant from the Equinoctial, towards either Pole: and hath a double Denomination, viz. North Declination, and South Declination: for if the Sun Moon or Star swarve towards the North Pole, they are said to have North Declination; if to­wards the South Pole, South Declination.

The Right Ascension is the number of degrees of the Equi­noctial (accounted from the first point of Aries) which comes Right Ascen­sion. to the Meridian with the Sun Moon or Star, or any other point in Heaven proposed.

The Oblique Ascension is the number of degrees of the Equi­noctial Oblique Ascen­sion. which comes to the East side of the Horizon with the Sun Moon or any Star.

The Oblique Descension is the degrees of the Equinoctial Oblique Des­cension. which comes to the West side of the Horizon with the Sun Moon or any Star.

The Ascensional Difference is the number of degrees after Ascensional Difference. subtraction of the Oblique Ascension from the [...] [...] [...]scen­sion, [...].

So many degrees as you are said to sail towards the Pole, you Raise the Pole. Depress the Pole. are said to Raise the Pole; and so many degrees as you sail from the Pole, you are said to Depress the Pole.

Course, is the point of the Compass you sail upon; as if you sail Course. East-wards, it is an Easterly Course, if West, a Westerly Course &c.

Distance is the number of leagues you have sailed from any Distance. Place, upon any Course.

A Zone is a space of Earth contained between two Parrallels. Zone. The ancient Geographers made five Zones in the Earth. Two Frozen, Two Temperate, and one Burnt Zone.

[Page 28] The two Frozen Zones are those parts of the Globe, compre­hended Frozen Zones. between the North Pole and the Arctick Circle, and the South Pole and the Antarctick Circle; by the Ancients called inhabitable; because the Sun being alwaies far remote from them, shoots its beams Obliquely upon them, which Oblique beams are so very weak, that all their Summer is but a continued Winter, and the Winter (as they thought impossible to be at all indured.

The Temperate Zones are the space of Earth contained be­tween the Arctick Circle and the Tropick of ♋, and the An­tarctick Temperate Zones. Circle and the Tropick of ♑: by the Ancients called Temperate and Habitable; because they are composed of a sweet Mediocrity, between outragious Heat and extremity of Cold.

The Burnt Zone is the space of Earth contained between the Tropick of ♋, and the Tropick of ♑, called by the Ancients Un­habitable; Burnt Zone. because in regard the Sun never moves out of this Zone but darts its Beames perpendicularly upon it, they imagined the Air was so unsufferable Hot, that it was impossible for any to inhabite in this Zone. So that as you see they held the two Tempe­rate Zones only habitable; and the two Frozen Zones and one Burnt Zone, altogether unpossible to be inhabited. But their Suc­cessors either animated by industry, or compeld by necessity, have apparently confuted that Assertion; for at this time many thou­sands can witness that their bloods are not so greasie as to be melted in the Scortching heat of the one, or so watry as to be con­gealed in the Icy frosts of the other.

The Ancients have yet otherwise divided the Earth into four and twenty Northern Climates, and four and twenty Southern Climates. Climates: so that in all there is eight and forty Climates. The Climates are altered according to the half hourly increasing of the longest daies; for in the Latitude where the longest daies are in­creased half an hour longer then they are at the Equator (viz. longer then 12 hours) the first Climate begins; and in the Lati­tude where they are increased an whole hour longer then in the Equator, the second Climate begins; where the daies are increa­sed three half hours longer then in the Equator, the third Cli­mate begins; and so onwards, the Climates alter according as the longest day increases half an hour, till you come to find the longest day 24 hours long

Now the Ancients (in those times) knowing no more then nine Habitable Climates, gave names only to nine. The first [Page 29] they called Dia Meroes, after the name of a famous Inland Iland, which is scituate about the middle of that Climate, and is now called Gueguere. The second Climate they called Dia Syenes, after the name of an eminent Citty in Egypt, lying about the midst of that Climate. The third Dia Alexanderas, after the name of the Metropolitan Citty of Egypt. The fourth Dia Rhodes. The fifth Dia Romes. The sixth Dia Ponton. The seventh Dia Boristheneos, The eighth Dia Ripheos. The ninth Dia Daniam.

These names belong only to the Climates on the North side of the Equator. But those on the South side (in regard of the smal Discoveries those Ages had on that side the Equator) were distinguisht only by the addition of the word Anti, to the same Southerly Climate: as the first Southern Climate (which is that Climate that lies as many degrees to the South-ward as the first doth to the North-ward) they called Anti Meroes. The second Anti Syenes. The third Anti Alexanderas: and so on to the ninth.

In every Climate is included two Parallels, which are of the Parallels. same nature with the Climates, save only that as the Climates al­ter by the half hourly increasing of the longest day, the Parallels alter by the quarter hourly increasing of the longest day.

Furthermore, in respect of the Horizon, we find the Sphear constituted into a threefold Position: as first, into a Direct Sphear, Secondly, a Parallel Sphear, Thirdly, an Oblique Sphear.

A Direct Sphear hath both the Poles of the World in the Direct Sphear. Horizon, and the Equinoctial transiting the Zenith. In a Direct Sphear all the Circles Parallel to the Equator make right angles with the Horizon, and are also divided into two equal parts by the Horizon: and in a Direct Sphear the Sun Moon and Stars are al­waies twelve hours above the Horizon, and twelve hours under the Horizon, and consequently make twelve hours Day, and twelve hours Night.

It is called a Direct Sphear because all the Celestial Bodies, as Sun Moon and Stars &c. by the Diurnal Motion of the Primum Mobile, ascend directly above, and descend directly be­low the Horizon.

They that inhabite under the Equator have the Sphear thus posited; as in the Iland Borneo, Sumaira, Celebes, St. Thomas a great part of Africk, Peru in the West-Indies: &c. as you may [Page 30] see by the Globe it self; if you move the Brasen Meridian through the notch in the Horizon, till the Poles thereof touch the Hori­zon. As in this Figure.

[figure]

A Parallel Sphear hath one Pole of the VVorld in the Zenith, the other in the Nadir, and the Equinoctial line in the Horizon. Parallel Sphear.

In a Parallel Sphear all the Circles Parallel to the Equi­noctial are also Parallel to the Horizon, and in a Parallel Sphear from the 10th of March to the 11th of September (the Sun being then in the Northorly Signes and consequently on the North side the Horizon) there is six Moneths Day in the North, and six Moneths Night in the South: and contrarily from the 11th of September to the 10th of March, (the Sun being then in the Southerly Signes, and therefore on the South side the Horizon) [Page 31] there is six Moneths Day in the South, and six Moneths Night in the North.

It is called a Parallel Sphear, because the Sun Moon or Stars in a Diurnal Revolution of the Heavens, neither ascend higher or descend lower, but alwaies move Parallel to the Horizon.

The Earth is thus Posited under both the Poles, viz. in 90 degrees of Latitude; as may be seen by the Globe, if you turn the Brasen Meridian till either of the Poles be elevated 90 degrees above the Horizon. As in this figure.

[figure]

An Oblique Sphear hath the Axis of the World neither Di­rect Oblique Sphear. nor Parallel to the Horizon, but lies aslope from it.

In an Oblique Sphear all the Celestial Bodies, as Sun Moon or Stars &c. have (in respect of the Horizon) Oblique and un­equal Ascensions and Descensions, and all the lines Parallel to the [Page 32] Equator make unequal Angles with the Horizon, and are cut by the Horizon into unequal parts; for those lines towards the elevated Pole, have a greater portion of a Circle under the Hori­zon then above it: only the Equator because it hath the same Center with the Horizon, doth divide the Horizon into two e­qual parts, and is also divided into two equal parts by the Horizon.

Hence is follows that when the Sun is in any part of the E­cliptick that declines towards the elevated Pole, the Daies in the elevated Hemisphear shall be longer then the Nights: and when the Sun is in any part of the Ecliptick that declines towards the Depressed Pole, the Nights shall be longer then the Daies. But when the Sun is in the Equinoctial, (because whether the Pole be either Raised or Depressed) equal portions remain both above and under the Horizon, therefore the Daies are of the same length with the Nights, and the Nights with the Daies.

Also in an Oblique Sphear, all those Stars that have as great or greater number of degrees of Declination then is the elevated Poles Complement of Latitude to 90, never set or come under the Horizon, and those Stars that have the same Declination a­bout the Depressed Pole never rise.

It is called an Oblique Sphear, because all the Circles of the Sphear move Obliquely about the Horizon.

The Earth is thus Obliquely posited to all those Nations that inhabite under any degree of Latitude either North or South-wards between the Equator and either Pole: as may variously be seen by the Globe, when the Axis lies not on the Horizon, nor the Equator is Parallel to the Horizon. As in this following Figure.

[Page 33]

[figure]

Moreover all Places have their Antipodes, Peraeci and Antae [...]i.

The Antipodes of any Place is the opposite degree on the Antipodes. Globe. As if a Perpendicular were let fall from the Place you stand on, through the Center of the Earth, and continued till it pass quite through the Superficies of the Earth, on the other side; then in the point where the Perpendicular cuts the Superficies of the Earth on the other side, is the Antipodes of that Place.

The Inhabitants of any two Places that are in Antipodes to each other, go with their Feet directly against one another: and have a contrariety in the Seasons of the Year, and Risings, and Settings, of the Sun Moon Stars, and all other of the Heavenly Bodies: so that when with us it is Spring, with them it is Au­tumn; when with us the Sun Rises, in our Antipodes it Sets; and therefore their Morning is our Evening, their Noon our Mid­night, [Page 34] their Evening our Morning; and their Longest Day our shortest.

The Periaeci of any Place is that point in the same Parallel which comes to the Meridian with the Antipodes. Periaeci.

In the Periaeci of any Place, there happens not that Contrariety of Seasons in the Year, that doth in the Antipodes; nor in the Length of Daies: for the Daies in both Places are of equal length: but in the times of the Day, there is the same contrariety, for (though their Spring be our Spring, and therest of their Seasons of the year the same with ours, yet) their Morning is our Evening, their Night our Day, &c.

The Antaeci of any Place is the point under the same Meridi­an that is distant from the Equator on the South side so many de­grees Antaeci. as your Place is distant from the Equator on the North side.

In the Antaeci there happens not that contrariety in the Daies as doth in the Antipodes, but in the Seasons of the Year there is the same contrariety; for in our Antaeci their Morning is our Morning, their Noon our Noon, their Night our Night: but herein is the Difference, their Spring is our Fall, their Summer our VVinter, &c. and their Longest Day our shortest: as in the [...]ntipodes.

The Second Book. Shewing the Practical Use of the GLOBES. Applying them to the Solution of Astronomical and Geographical Problems.

PRAEFACE.

Some Advertisements in Choosing and Using the GLOBES.

1. SEE the Papers be well and neat­ly pasted on the Globes: which you may know, if the Lines and Circles discribed thereon meet ex­actly, and continue all the way even and whole: the lines not swerving out or in, and the Cir­cles not breaking into several Ar­ches; nor the Papers either come short, or lap over one the other.

2. See that the Culler be transparent, and ly not too thick on the Globe; lest it hide the superficial Descriptions.

3. See the Globe hang evenly between the Meridian and Horizon, not inclining more to one side then the other.

4. See the Globe swim as close to the Meridian and Ho­rizon [Page 36] as conveniently it may; lest you be too much puzzeld to find against what point of the Globe any degree of the Ho­rizon or Meridian is.

5. See the Equinoctal line be one with the Horizon, when the Globe is set in a Parallel Sphear.

6. See the Equinoctal line cut the East and West point of the Horizon, when the Globe is set to an Oblique Sphear.

7. See the Degrees marked with 90. and 00, hang exa­ctly over the Equinoctial line of the Globe.

8. See that exactly half the Meridian be above the Ho­rizon, and half under the Horizon: which you may know if you bring any of the Decimal Divisions to the North Side of the Horizon, and find their Complement to 90. inth South.

9. See that when the Quadrant of Altitude is placed at the Zenith, the Beginning of the Graduations reach just to the superficies of the Horizon.

10. See that while the Index of the Hour Circle (by the motion of the Globe) passes from one hour to the other, 15. degrees of the Equator pass through the Meridian.

11. If you have a Circle of Position, see the Graduations agree with those of the Horizon.

12. See that your wooden Horizons be made substantial and strong; for (besides the Inconveniences that thin wood is subject unto, in respect of warping and shrinking) I have had few Globes come to mending that have not had either broken Horizons, or some other notorious fault, occasioned through the sleightness of the Horizons.

In the Using the Globes.

KEep the East side of the Horizon alwaies towards you, unless your Proposition requires the turning of it: which East side you may know by the Word East, placed on the outmost verge thereof. For then have you the gradu­ated [Page 37] side of the Meridian alwaies towards you; the Qua­drant of altitude before you, and the Globe divided exactly into two equal parts.

So oft as I name to, at, of, or under the Meridian, or Horizon, I mean the East side of the Meridian, and Super­ficies of the Horizon: because the East side of the Meridian passes through the North and South points, both of the Globe and Horizon; and agrees just with the middle of the Axis: And the Superficies of the Horizon divideth the Globe exa­ctly into two equal parts.

It you happen to use the Globes on the South side the E­quator, you must draw the wyers out of either Pole, and change them to the contrary Poles; putting the longest wy­er into the South Pole. And because on the other side the Equator the South Pole is elevated, therefore you must ele­vate the South Pole of the Globe above the Horizon; ac­cording to the South Latitude of your Place; as shall be shewed hereafter.

In the working some Problems it will be required that you turn the Globe to look on the West side thereof: which turning will be apt to jog the Ball, so as the degree that was at the Horizon or Meridian, will be moved away, and there­by the Position of the Globe altered. To avoid which incon­venince you may make use of a Quill, thrusting the Feather end between the Ball and the Brazen Meridian, and so wedge it up, without wronging the Globe at all, till your Proposi­tion be answered.

PROBLEME I.

To find the Longitude and Latitude of Places, on the Terrestrial Globe.

SEek the Place on the Terrestrial Globe, whose Longitude and Latitude you would know, and bring that Place to the [Page 38] Brazen Meridian; and see how many degrees of the Equator is cut by the Meridian, from the first general Meridian, (which on my Globes pass through Gratiosa, one of the Isles of the Azores,) for that number of degrees is the Longitude of the Place.

Example.

I desire to know the Longitude of London, and close to the name London I find a smal mark 0 thus, (which smal mark is in some Globes and Maps adorned with the Picture of a Stee­ple, &c.) therefore I do not bring the word London to the Me­ridian, but that smal mark; for that alwaies represents the the Town or Citty sought for: And keeping the Globe steddy in this Position, I examine how many degrees of the Equa­tor are contained between the Brazen Meridian, and the first ge­neral Meridian; which I find to be 24. deg. 00. min. There­fore I say the Longitude of London is 24. degrees 00. min.

For the Latitude.

See on the Brazen Meridian how many degrees are contained between the Equator and the mark for London; which in this Example is 51½: therefore I say London hath 51½ degrees North Latitude.

PROBLEME II.

The Longitude and Latitude being know, to Rectifie the Globe fit for use.

1. WHen you rectifie the Globe to any particular Lati­tude you must move the Brazen Meridian through the notches of the Horizon till the same number of degrees accounted on the Meridian from the Pole (about which the Hour-Circle is) towards the North point in the Horizon (if in North Latitude, and toward the South if in South Latitude) come just to the edge of the Horizon.

Example.

By the former Proposition I found the Latitude of London to be [Page 39] 51½ degrees North Latitude: therefore I count 51½ degrees from the Pole downwards towards my right hand, and turn the Meridian through the notches of the Horizon till those 51½ de­grees comes exactly to the uppermost edge of the North point in the Horizon; and then is the Meridian rectified to the Latitude of London.

2. Next rectifie the Quadrant of altitude, after this manner, Screw the edge of the Nut that is even with the gradua­ted edge of the thin Plate, to 51½ degrees of the Brazen Meri­dian, accounted from the Equinoctial on the Southern side the Horizon, which is just the Zenith of London: and then is your Quadrant Rectified.

3. Bring the degree of the Ecliptick the Sun is in that day, to the Meridian: which you shall learn to know by the next Pro­bleme, and then turn the Index of the Hour Circle to the hour 12. on the South side the Hour Circle, and then is your Hour Circle also rectified fit to use, for that Day.

4. Lastly If you will rectifie the Globe to correspond in all re­spects with the Position and Scituation of the Sphear, you must set the four Quarters of the Horizon. viz. East, West, North, and South, agreeable with the four quarters of the World; which you may do by the Needle in the bottom of the Horizon; for you must turn the Globe so long till the Needle point just to the Flower de luce. Next you must set the Plain of the wooden Horizon parallel to the Horizon of the World; which you may try by setting a common Level on the four Quaters of the Hori­zon. And then positing the degree of the Ecliptick the Sun is in, to the Height above, or depth below the Horizon, the Sun hath in Heaven, (as by the 11th Probleme) your Globe is made Cor­respondent in all points with the frame of the Sphear, for that particular Time, and Latitude.

PROBLEME III.

To find the Place of the Sun in the Ecliptick, the Day of the Moneth being first known.

SEek the Day of the Moneth in the Circle of Moneths upon the Horizon, and right against it in the Circle of Signes is the degree of the Ecliptick the Sun is in.

Example.

Imagine the Day to be given is May 10. therefore I seek on the Horizon in the Circle of Moneths, for May, and find the Moneths divided into so many parts as there is Daies in the Mo­neth; which parts are marked with Arithmetical figures, from the beginning of the Moneth to the end, and denote the number of the Day of the Moneth that each Division represents: there­fore among the Divisions I seek for 10, and directly against it in the Circle of Signes, I find ♉ 29. degrees. Therefore I say May 10. the Suns Place is in 29. degrees of ♉.

But note, that if it be Leap Year, instead of the 10. of May you must take the 11. of May: because February having in a Leap Year 29. Daies, the 29. of February must be reckoned for the first of March, and the first of March for the second of March; the second of March for the third of March; and so throughout the year.

The Leap Year is caused by the six od hours more then 365. daies that are assigned to every common Year: so that in a Re­volution of 4. Years, one Day is gained, which is added to Fe­bruary; and therefore February hath every fourth or Leap Year 29. Daies.

PROBLEME IIII.

To find the Day of the Moneth, the Place of the Sun being given.

AS in the last Probleme it was your task to find on the Horizon the Day of the Moneth first, so now you must first seek the Signe and degree the Sun is in, and against it in the Circle of Moneths you shall see the Day of the Moneth: As against ♉ 29. you have May 10.

PROBLEME V.

The Place of the Sun given, to find its Declination.

HAving by the third Probleme found the Suns Place on the Plain of the Horizon, you must seek the same degree in [Page 41] the Ecliptick, on the Globe; then bring that degree to the Brazen Meridian; and the number of degrees intercepted between the Equinoctial and the degree just-over the degree of the Eclip­tick the Sun is in, is the Declination of the Sun for that Day: and bears its Denomination of North or South, according to its Position either on the North or South side the Equinoctial.

Example.

By the third Probleme aforesaid, of May 10. I find ♉ 29. the Suns Place; Therefore I seek in the Ecliptick Line on the Globe for ♉ 29. and bring it to the East side of the Brazen Meridian, which is the graduated side; and over ♉ 29. I find on the Brazen Meridian 20. deg. 5. min. (numbred from the Equinoctial:) and because ♉ is on the North side the Equinoctial, therefore I say, The Sun hath May 10. North Declination 20. degrees 5. min.

PROBLEME VI.

The Place of the Sun given, to find its Meridian Altitude.

THe Globe rectified, Bring the degree of the Sun to the Meridian, (or which is all one, the degree of the Ecliptick the Sun is in;) and the number of degrees contained be­tween the Horizon and the Suns Place in the Meridian, is the number of degrees that the Sun is Elevated above the Ho­rizon at Noon, or (which is all one) the Meridian Altitude of the Sun.

Example.

To know what Meridian Altitude the Sun hath here at Lon­don, May 10. I bring the Suns Place (found by the third Pro­bleme) to the Meridian, and count on the Meridian the number of degrees contained between the Horizon and the degree just over the Suns Place; which in this Example I find to be 58½▪ Therefore I say the Suns Meridian Altitude May 10. is here at London 58½ degrees.

PROBL. VII.

The Suns Place given, to find the Hour of Sun Rising, and the length of the Night and Day.

THe Globe and Hour Index rectified, Seek the degree the Sun is in on the Globe, and bring that degree to the East­ern Side of the Horizon; and the Index of the Hour Circle will point at the Hour of Sun Rising.

Example.

To know the Hour of Sun Rising here at London, May 10. The Suns Place (as before) is ♉ 29. Therefore the Globe being rectified (as before) I seek ♉ 29. degrees on the Globe, and bring that degree to the East Side of the Horizon; and look­ing on the Index of the Hour Circle, I find it point at 4. a clock and ⅙ part of an hour more towards 5; therefore I say May 10. the Sun rises here at London at ⅙ (which is 12. mi­nutes) after 4 a clock in the Morning.

If you double 4 hours 12. minutes, it gives you the length of the Night, 8 hours 24. minutes. And if you substract the length of the Night 8. hours 24. minutes, from 24. hours, the length of Day and Night; it leaves the length of the Day 15. hours 36. minutes.

PROB. VIII.

To find the Hour of Sun Set.

TUrn the Place of the Sun to the West side of the Horizon, and the Index of the Hour Circle shews on the Hour-Cir­cle the hour of Sun set; which on the 10th of May aforesaid, is [...] parts of an hour after [...] 7. a clock at Night, Viz. the Sun Sets at 48. minutes past 7. a clock.

PROB. IX.

To find how long it is Twilight in the Morning, and Evening.

TWilight is that promiscuous and doubtfull light which ap­pears before the Rising of the Sun in the Morning, and con­tinues after the setting of the Sun in the Evening: It is made by the extension of the Suns beams into the Vapours of the Air, when the Sun is less then 18. deg. below the Horizon: for the Sun ere it Rises, and after it Sets, shoots forth its Beams through the Air, and so illuminates the Vapours of the Air; which il­lumination does by degrees enlighten the Horizon, and spreads through the Zenith, even into the West, ere the Sun Rises; and also continues above the Horizon, afte [...] the Sun sets.

Now though it be Twilight when the Sun is 18. degrees be­low the Horizon; yet the duration of Twilight (is alterable both in respect of Time) and Place: for at such Time at the Sun is farthest distant from any Place, the Twilight shall be greater, then when it is neerest. And in respect of Place, All Places that have great Latitude from the Equator, have longer Twilight than those that are neerer to the Equator: for as Authors say, under the Equator there is no Twilight; when again in ma­ny Climes both Northward and Southward, the Nights are indeed no Nights but only (as it were) a little over-spread with a cloudy Shade; and is either increased or diminished ac­cording to the [...]autation of Meo [...]erological Causes.

Therefore to know the beginning of Twilight in the Morning here at London, May 10; you must (having the Globe re­ctified) turn the degree of the Ecliptick which is opposite to the Place of the Sun till it be elevated 18. degrees in the Quadrant of Altitude above the Horizon in the West; So shall the Index of the Hour-Circle point at the Hour that Twilight begins: Then subtract the Hour and Minute that Twilight begins from the Hour and Minute of Sun Rising, if in the Morning, or substract the Hour of Sun sett from the Hour of Twilight, if at Night; and the remainder is the length of Twilight.

Example.

The Globe Quadrant and Hour-Index being rectified, as be­fore; [Page 44] and the Suns place given, ♉ 29. I seek the opposite degree on the Globe, after this manner▪ I bring ♉ 29. to the Meridian, and observe what degree of the Ecliptik the opposite part of the Meridian cuts; and because I find it cuts ♏ 29. therefore I say ♏ 29. is opposite to ♉ 29. Having found the opposite de­gree, I bring it into the West, and also the Quadrant of Alti­tude, and joyn ♏ 29. to 18. degrees (accounted upwards on the Quadrant) so shall ♉ 29. be depressed 18. degrees in the East Side the Horizon: Then looking what Hour the Hour-In­dex points at in the Hour-Circle, I find it to be, 1. Hor. 8. Min. which shews that Twilight begins at 8. Minutes past 1. a clock in the Morning.

And if you substract 1. Hour 8. Minutes, from 4. Hours 11. Minutes, the time of Sun Rising, found by the 7th. Probleme, it leaves 3. Hours 3. Minutes for the length of Twilight: And if you double 1. Hour 8. Minutes, the beginning of Twilight, it makes 2. Hours 16. Minutes for the intermission of Time between Twilight in the Evening, and Twilight in the Morning. So that May 10. absolute Night is but 2. Hours 16. Minutes long, here at London.

The reason why you bring the degree opposite to the Suns Place to the West, is, because the Quadrant containing but 90. degrees will reach no lower then the Horizon; but this Probleme requires it to reach 18. degrees beneath it: therefore by this help, you have the Proposition Answered, as well as if the Qua­drant did actually reach 18. degrees below the Horizon. This shift you may have occasion to make in some other Problemes.

If you would know when Twilight ends after Sun set; you shall find it by bringing the degree of the Ecliptick opposite to the Place of the Sun to 18. degrees of the Quadrant of Altitude, on the East side the Horizon; for then shall the Index of the Hour-Circle point at 10. Hours 52. Minutes: which shews that it continues Twilight till 52. Minutes past 10. a clock at Night, May 10. here at London.

PROB. X.

The Suns Place given, to find its Amplitude; And also to know upon what point of the Compass it Riseth.

THe Globe &c. rectified: Bring the Suns Place to the East Side the Horizon; and the number of degrees intercepted [Page 45] between the East point of the Horizon and the Suns Place, is the number of degrees of Amplitude that the Sun hath at its Ri­sing; and bears its denomination either of North or South, accord­ing to its inclination to either point in the Horizon.

Or, if you would know upon what point of the Compass the Sun Rises, Look but in the Circle of Winds; and against the Place of the Sun you have the name of the point of the Compass upon which the Sun Riseth.

Examples of both.

May 10. the Suns Place is ♉ 29. There [...]re • the Globe being rectified; I bring ♉ 29. to the East side the Horizon, and find it touch against 33, degrees 20. Minutes from the East point to­wards the North: Therefore I say the Sun hath North Ampli­tude 33, degrees 20. Minutes.

And to know upon what point of the Compass the Sun rises; I keep the Globe to its Position, and look in the Circle of Winds, in the outmost verge of the Horizon, and find the Suns Place against the Wind named North East and by East; Therefore I say May 10. here at London the Sun riseth upon the North East and by East point of the Compass.

PROBL. XI.

The Hour of the Day given, to find the Heigth of the Sun.

THe Globe &c. Rectified. Turn about the Globe till the Index of the Hour-Circle point (in the Hour-Cir­cle) to the Hour of the Day: Then bring the Qua­drant of Altitude to the Suns Place in the Ecliptick, and the degree on the Quadrant which touches the Suns Place, shall be the number of degrees of the Suns Altitude.

Example.

May 10. here at London; At 53. Minutes past 8. a clock in the Morning, I would know the Heigth of the Sun above the Ho­rizon. Therefore I turn about the Globe till the Index of the [Page 46] Hour-Circle come to 53: Minutes past 8. a clock (which is almost 9.) in the Hour-Circle: And keeping the Globe to this Posi­tion, I bring the Quadrant of Altitude to the Suns place, viz. [...] 29. (found by the third Probleme) and because the Suns Place touches upon 40. degrees of the Quadrant, therefore I say May 10. 53. Minutes past 8. a clock in the Morning, here at London, The Sun is just 40. degrees above the Horizon; or which is all one, hath 40. degrees of Altitude.

PROB. XII.

The Altitude [...] Sun, and Day of the Moneth given, to find the Hour of the Day.

AN Hour is the 24th. part of a Day and a Night, or the space of time that 15. degrees of the Equator takes up in An Hour defi­ned. passing through the Meridian; for the whole Equator which contains 360. degrees, passes through the Meri­dian in 24. Hours, therefore 15. degrees which is the 24th. part of 360, pass through in one Hour. These Hours are Vulgarly divided into halfs, quarters, and half quarters; but Mathemati­cally into Minutes, Seconds. Thirds, Fourths, &c. A Minute is the 60th. part of an Hour, so that 60, minutes make an Hour, 30, half an Hour, 15. a quarter of an Hour: A Second is the 60th Minutes, Se­conds, and Thirds, &c. defined. part of a Minute: a third is the 60th part of a Second: a Fourth is the 60th part of a Third: and so you may run on to Fifths, Sixths, Sevenths, &c. if you please. 12. of these Hours make a Day, and 12. more make a Night: so that Day and Night con­tain 24. hours as aforesaid▪ which are Volgarly numbred from Noon with 1, 2, 3, to 12, at Night▪ and then begin again with 1, 2, 3, till 12 at Noon: But by Astronomers they are Numbred from Noon with 1, 2, 3, &c. to 12. at Night; and so forward to 13, 14, 15, till 24; which is just full Noon the next Day. Yet in this Treatise I shall mention the Hours as they are Vulgarly co [...]ted, viz. from [...]. after noon, to 12. at Night, and call the Hours after Midnight by 1, 2, 3, 4, &c. in the Morning, to 12. at Noon again, the next Day. But to the operation.

The Globe, &c. Rectified, Bring the Place of the Son to the Number of degrees of Altitude accounted upon the Quadrant of [Page 47] Altitude, and the Hour-Index shall point at the Hour in the Hour-Circle: yet herein respect must be had to the Fore or After noons Elevation; as shall be shewed in the next Pro­bleme.

Example.

May 10. The Sun is elevated 40. degrees above the Horizon, here at London: Therefore having found the Place of the Sun, by the third Probleme, to be [...]29. I move the Globe and Quadrant till I can joyn the 29. degree of [...] to the 40. deg, upon the Quadrant of Altitude; and then looking on the Hour-Circle, I find the Index point at 53. Minutes past 8. a clock, for the Fore noon Elevation; and at 3. hours 7. Minutes for the After noons Elevation. Therefore if it be Fore-noon, I say, It is 53. Minutes past 8. a clock in the Morning. But if it be After noon I say, It is 7. Minutes past 3. a clock in the After noon.

PROB. XIII.

How to know whether it be Before or After Noon.

HAving made one Observation, you must make a Second a little while after the First; and if the Sun increase in Alti­tude, it is Before Noon: but if it decrease in Altitude, it is After Noon.

Example.

The Sun was at 8. hor. 53. Min. elevated 40. degr. above the Horizon: A little while after (suppose for examples sake aquar­ter of an hour,) viz. at 9. hor. 8. Min. I observe again the heigth of the Sun, and find it 42. degrees high; so that the Altitude is increased 2. degrees; Therefore I say, It is Fore-Noon: But if the Sun had decreased in Altitude, I should have said it had been After-Noon.

How to take Altitudes by the Quadrant, Astrolabe, and Cross-staff.

There are divers Instruments whereby Altitudes may be taken: but the most in use are the Quadrant, Astrolabe, and Cross-staff. A Quadrant is an Instrument comprehen­ded between two Straight lines making a Right Angle, and an [Page 48] Arch discribed upon the Right Angle, as on the Center, con­taining 90. degrees, which is a quarter of a Circle: and therefore the Instrument is called a Quadrant. See this Figure.

[figure]

A prepresents the Center; upon which is fastned a Plumb-line, A B the one side, A C the other side, upon which the Sights are placed: B C the Arch or Quadrant, which is divided into 90. equal parts, and numbred from B to C. D one Sight, E the other Sight: F the Plumbet fastned to the Plumb-line.

When by this Instrument you would observe the heigth of the Sun, you must turn the Center A to the Sun, and let the beams thereof dart in at the hole in the first Sight D, through the hole in the second Sight E; so shall the Plumb-line ly upon the degree in the Limb, of the Suns Elevation: As if the plumb-line ly upon the 20th degree, then shall the Alti­tude be 20. degrees; if on 25. the Altitude shall be 25. degrees: and so for any number of Degrees the thred or Plumb-line lies on, the same number of Degrees is the Altitude of the Sun.

[Page 49] But if it be a Star whose Altitude you would observe; you must hold up the Quadrant, and joyn the Limb to your Cheek bone, and turn the Center towards the Star: then winking with one Ey, look through the holes of the Sights with the other Ey, till you can see the Star through those holes; so shall the Plumb-line (as before in the Sun) hang upon the degree in the Limb of the Stars Elevation.

Another sort of Quadrants is made with a moveable Index, as is represented in this Figure.

[figure]

A is the Center, A Band A C the two sides, B C the Limb, D E two Sights fixed upon a moveable Index or Label; F G two other Sights, for observing the Horizon.

When by this Quadrant you would observe an Altitude, the side B A must be parallel to the Horizon, and the Index must be mo­ved till the Object (be it either the Sun Moon or any Star) be seen through the holes or slitts of the Sights placed on the Index; for then the Arch D B shall be the Elevation required. You [Page 50] may know when the side B A is parallel to the Horizon, by ob­serving the parting of Heaven from the Earth through the Sights on the Side B A.

To take Altitudes by the Astrolabe.

The Astrolabe is a round Instrument, flat on either side, upon one of the flats or Plains is discribed a Circle as B C D E, divided into 360, equal parts or degrees, numbred from the line of Level B A C, with 10, 20, 30, &c. to 90. in the Per­pendicular D C. Upon the perpendicular is fastned a Ring as F, so as the Instrument hanging by it, the line of Level may hang pa­rallel to the Horizon. Upon the Center is a moveable Label or Ruler, as G H, whereupon is placed two Sights as I K.

[figure]

If you desire further instructions for making this Instrument, you may peruse M r Wright in his Division of the whole Art [Page 51] of Navigation, annexed to his Correction of Errors: where he also shews the use of it at large; which in brief is as follows.

You must hold the Astrolabe by the Ring in your left hand, and turning your right side to the Sun, lift up the Label with your right hand, till the beams of the Sun entring by the hole of the uppermost Vane or Sight, doth also pierce through the hole in the nethermost Vane of Sight; and the deg. and part of deg. that the Label lies on is the height of the Sun above the Horizon.

But if it be a Star you would observe; you must use the A­strolabe as you were directed to use the Quadrant, holding it up to your Cheek bone, and looking through the Sights, &c.

To take Altitudes by the Cross-staff.

This Instrument consists of a Staf about a yard long, and three quarters of an inch square: Upon it is fitted a Vane, (or sometimes two, or three,) so as it may slide pretty stiff upon the Staff, and stand at any of the Divisions it is set to.

[figure]

[Page 52] The making is taught by M r Wright, aforesaid: But the use is as follows.

You must put that end of the Cross-staff which is next 90. degrees to your Cheek bone, upon the outter corner of your Ey, and holding it there steddy, you must move the Vane till you see the Horizon joyned with the lower end thereof, and the Sun or Star with the higher end; then the degree and part of degree which the Vane cutteth upon the Staff, is the height of the Sun or Star.

Some of these waies for taking Altitudes have been formerly taught by others, that have treated upon the Use of Globes: and therefore because some would be apt to think this Treatise un­compleat if I did not shew these waies also, I have thought fit to insert them: Yet the same things may be performed by the Globe alone, without troubling your self with multiplicity of In­struments; if your Globe be made with a hollow Axis; for then if the Globe stand Horizontal, you shall by Observing the Object through the Axis have the degree of Elevation, noted by the superficies of the Horizon.

PROB. XIV.

To observe with the Globe the Altitude of the Sun.

PLace the Globe so that the upper plain of the Horizon may stand parallel to the Plain of the Horizon of your Place; as was taught by the Second Probleme; then turn the North Pole towards the Sun, and place it higher or lower, by moving the Meridian through the notches of the Horizon, till the beams of the Sun pierce quite through the Axis of the Globe: So shall the arch of the Meridian com­prehended between the Pole and the Horizon, be the number of Degrees that the Sun is elevated above the Ho­rizon.

Example.

March 20. just at noon, here at London, I would observe the Meridian Altitude of the Sun. Therefore placing the Ho­rizon Horizontal, as by the Second Probleme: I turn the North [Page 53] Pole towards the Sun, and move it with the Meridian upwards or downwards, either to this side or that, till I can fit it to such a Position that the Sun Beams may dart quite through the Axis of the Globe; which when it does, I look on the Meri­dian and find 42. degrees 25. min. comprehended between the Pole and the superficies of the Horizon; Therefore I say the Meridian Altitude of the Sun March 20. here at London, is 42. degrees 25. min.

PROB. XV.

To find the Elevation of the Pole, by the Meridian Alti­tude of the Sun, and Day of the Moneth given.

THe Day of the Moneth is March 20. By the 4th Prob. you may find the place of the Sun to be ♈ 10. Therefore bring the Place of the Sun to the Meridian, and elevate it above the Horizon the same number of degrees it hath in Hea­ven; so shall the arch of the Meridian comprehended between the Pole and the Horizon, be the elevation of the Pole, in your Place.

Otherwise.

The Day of the Moneth given is March 20. so that by the fourth Prob. you have the Suns Place ♈ 10; and by the fifth, the Declination of the Sun 3. 55. North: therefore the Declination being North, and you on the North side the Equator; you must substract 3. 55. from the Meridian Altitude 42. 25. and there remains 38, 30. for the heighth of the Equinoctial above the Horizon; but if your Declination had been South, you must have added 3 55. to the Meridian Altitude, and the Sum would have been the Elevation of the Equinoctial. Having the Elevation of the Equinoctial, you may easily have the Elevation of the Pole; for the one is alwaies the Complement of the other to 90. Thus the Height of the Equinoctial 38. 30. subtracted from 90. leaves 51. 30. for the Elevation of the Pole, here at London. And thus it follows, that the Latitude of any Place from the Equinoctial, is alwaies equal to the Elevation of the [Page 54] Pole: for between the Zenith and the Equinoctial is contained the Complement of the Heighth of the Equinoctial above the Horizon to 90.

PROB. XVI.

To take the Altitude of any Star above the Horizon; by the Globe.

THe Horizon of the Globe set parallel to the Horizon of the World, as before: Turn the North Pole towards the Star, and when you can see the Star through the Axis, the Northern notch of the Horizon will cut the degree of Eleva­tion on the Meridian.

Example.

April 19. at 11. a clock at Night, I would observe the Alti­tude of Spica Virgo: Therefore I set the Horizon parallel to the Horizon of the World, as by the Second Probleme, and turn the Northern Pole till it point towards the Star: Then looking in at the South Pole of the Globe through the Axis, I shall see the Star, and have on the Meridian the Question resolved. But if it point not exactly, then I move the North Pole upwards or downwards, either to the right hand, or to the left, according as I may find occasion, till I can see the Star through the Axis: and then the edge of the notch in the Horizon cuts 28. degrees 57. min. on the Brazen Meridian. Therefore I say April 19. at 11. a clock at Night, here at London, the Altitude of Spica [...] is 30. degrees above the Horizon.

PROB. XVII.

By the Meridian Altitude of any Star given, to find the Height of the Pole.

JOyn the Star to the Meridian, and place it to the Altitude observed; so shall the number of degrees intercepted be­tween the Pole and the Horizon, be the Elevation of the Pole.

Example.

Spica Virgo is observed to have 28. degrees 57. min Meri­dian Altitude; therefore I bring Spica Virgo to the Meridian, and raise it or depress it higher or lower as I find occasion, till it is just 28. degrees 57. min. above the Horizon: Then I count the number of degrees between the Pole and the Horizon, and find them 51½. Therefore I say the Elevation of the Pole is here at London 51½. Yet note, If the Star whose Altitude you observe have fewer number of degrees of Declination from the Pole, then the Elevation of the Pole, you may be apt to mistake in its coming to the Meridian; for those Stars never set; and there­fore are twice Visible in the Meridian in 24. hours, once above the Pole, and once under the Pole.

If your Star have greater Altitude then the North Star, it is above the Pole; but if it have less, it is below the Pole: so that if you know but whether it be above or below, it is enough; for so you may accordingly raise it to the Altitude on the Me­ridian it hath in Heaven, and joyn it to the Meridian either above or beneath the Pole, as the Star is placed in Heaven: and then the arch of the Meridian comprehended between the Pole and the Horizon, is the Elevation of the Pole, as aforesaid.

Otherwise.

Having the Meridian Altitude of the Star, you must find its Declination by the 27. Probleme: and if the Declination be South, and you on the North side the Equator, you must ad the Declination to the Meridian Altitude, and the sum of both makes the Altitude of the Equinoctial: But if the Declination be North, and you on the North side the Equator, you must substract the Declination from the Meridian Altitude, (as was taught by the 15. Prob. in the Example of the Sun) and the remainder is the Altitude of the Equinoctial Then (as was taught by the 15 Probleme aforesaid) substract the Altitude of the Equinoctial from 90, the Remainder is the Elevation of the Pole in your Place.

Example.

By the last Probleme the Meridian Altitude of Spica Virgo was 28 degrees 57 min, and the Declination of Spica by the 27th Probleme is found 9. degrees 33. min. South: therefore because the Declination is South, I ad 9. degrees 33. min. to the Meridian Altitude, which makes 38. deg. 30. min. for the Ele­vation of the Equinoctial: which 38. deg. 30. min. substracted from 90. leaves 51. degrees 30. min. for the Elevation of the Pole here at London.

PROB. XVIII.

Another way to find the Height of the Pole by the Globe; if the Place of the Sun be given: and also to find the Hour of the Day, and Azimuth, and Almican­tar of the Sun.

THis must be performed by help of a Spherick Gnomon, (as Blaew calls it,) which is a small Pin or Needle fix­ed perpendicularly into a smal Basis with an hollow concave bottom, that it may stand upon the convexity of the Globe. Therefore the Horizon of the Globe being set parallel to the Horizon of the World, (as by the Second Pro­bleme) the Spherick Gnomon must be set exactly upon the Place of the Sun; and then turning the Globe about (upon its Axis) either from East to West, or contrarily from West, to East; or else by the Meridian, through the notches of the Horizon, till the Spherick Gnomon cast no shadow on any side thereof; you have on the Meridian in the North point of the Horizon the number of degrees that the Pole is elevated above the Ho­rizon.

Example.

Imagine the four Quarters of the Horizon of the Globe cor­respond with the four Quarters of the Horizon of the World; and the Plain of the Horizon of the Globe is parallel to the Plain of the Horizon of the World: The Suns Place is ♉ 29¼, [Page 57] which I find on the Globe, and place the Spherick Gnomon thereon; Then at a guess I move the Globe both on its Axis, and by the Meridian, (as neer as I can) so as the Spherick Gnomon may cast no shadow; yet if it do, and the shadow fall to­wards the North Pole; then I elevate the North Pole more, till the shadow fals just in the middle of it self: but if the shadow fall downwards, towards the South Pole, then I depress the North Pole: If the shadow fall on the East side, I turn the Globe on its Axis more to the West; and if the shadow fall to the West, I turn the Globe more into the East: and the degree of the Meridian which the North point of the Horizon touches, is the degree of the Poles Elevation: which in this Example is 51½. the Latitude of the City of London.

By this Operation you have also given the Hour of the Day in the Hour-Circle, if you keep the Globe unmoved: and the Azimuth, and Almicantar, if you apply but the Quadrant of Altitude to the Place of the Sun, as by the 22, and 23. Problemes.

PROB. XIX.

To observe by the Globe the Distance of two Stars.

YOu must pitch upon two Stars in the Meridian; and ob­serve the Altitude of one of them first, and afterwards the Altitude of the other: Then substract the lesser Altitude from the greater, and the remainder shall be the distance re­quired.

Example.

March 7. at 11. a clock at Night here at London, I see in the Meridian the two Stars in the foremost Wheels of the Waggon, in the Constellation of the Great Bear, called by Sea-men the Pointers, (because they alwaies point towards the Pole-Star.) Therefore to observe the distance between these two Stars, I first observe (as by the last Probleme) the Altitude of the most Northern to be 77. degree 59. minutes, and set down that number of Degrees and minutes with a Pen and Ink on a Paper, or with a peece of Chalk or a Pencil on a Board: and afterwards I observe the Altitude of the other Star which is un­der [Page 58] it, as I did the first, to be 83. deg. 21. min. and set that number of degrees and minutes also down, under the other number of degrees and minutes: Then by substracting the lesser from the greater, I find the remainder to be 5. degrees 22. min. which is the distance of the two Stars in the Great Bear, called the Pointers.

PROB. XX.

How you may learn to give a guess at the number of degrees that any two Stars are distant from one another; or the number of degrees of Altitude the Sun or any Star is elevated above the Horizon: only by looking up to Heaven, without any Instru­ment.

BEtween the Zenith and the Horizon is comprehended an Arch of a Circle containing 90. degrees; so that if you see any Star in or neer the Zenith, you may know that Star is 90. or neer 90. degrees high; and by so much as you may conceive it wants of the Zenith, so much you may guess it wants of 90. degrees above the Horizon. By this Rule you may guess at an Arch of Heaven containing 90. degrees, or at an Arch of Heaven containing 45. degrees; if by your ima­gination you divide the whole Arch into two equal parts, for then shall each of them contain 45. degrees; And if by your imagination you divide the Arch of 90. into 3. equal parts, each division shall contain an Arch of 30. degrees, &c. But this way is a little too rude for guessing at Stars elevated but few degrees, or for Stars distant but few degrees from one another. Therefore that you may learn to guess more precisely at Distances in Hea­ven, you may either with a Quadrant, Astrolabe, or the Globe; find the exact distance of any two known Stars that are but few degrees asunder, and by a little revolving the distance of those Stars in your fancy, you may at length so imprint their distance in your memory, that you may readily guess the distance of other Stars by the distance of them.

Example.

You may find either by the Globe, Quadrant, or As [...]rotabe, [Page 59] (for they all agree) 3. degrees comprehended between the first Star in Orions Girdle, and the last; therefore by a little [...] ­nating upon that distance, you may imprint it in your fancy for 3. degrees, and so make it applicable to other Stars, either of the same distance, or more, or less: And the Pointers (by the last Probleme) are distant from one another 5. degrees and almost an half: These are alwaies above our Horizon, and therefore may alwaies stand as a Scale for five and an half degrees; So that by these for 5½ degrees, and those in Orions Girdle for 3. degrees, and others observed, either of greater or lesser distance, you may according to your own Judgement shape a guess, if not exactly, yet pretty neer the matter of Truth, when you come to other Stars. Thus you may exercise your fancy upon Stars found to be 10. or 15. degrees asunder, or more, or less; and with a few experiments of this nature enure your Judgement to guess di­stances, and enable your memory to retain your Judgement.

This way of guessing will be exact enough for finding the Hour of the Night by the Stars, for most common Uses; or the Hour of the Day, by guessing at the Altitude of the Sun; if after you have guessed at the Altitude, you shall work as was taught by Prob. 12. for the Hour of the Day: and as shall be taught in the next Probleme, for the Hour of the Night.

PROB. XXI.

The Day of the Moneth, and Altitude of any Star given, to find the Hour of the Night.

THe Globe, Quadrant, and Hour Index rectified: Bring the Star on the Globe to the same number of Degrees on the Quadrant of Altitude that it hath in Heaven: So shall the Index of the Hour-Circle point in the Hour-Circle at the Hour of the Night.

Example.

March 10. the Altitude of Arcturus is 35. degrees above the Horizon, here at London: Therefore having the Globe, [Page 60] Quadrant and Hour Index rectified, I bring Arcturus on the Globe to 35. degrees on the Quadrant of Altitude: And then looking in the Hour-Circle, I find the Index point at 10. a clock; which is the Hour of the Night.

PROB. XXII.

The Place of the Sun, and Hour of the Day given, to find its Azimuth in any Latitude assigned.

THe Globe, &c. rectified to your Latitude: Turn the Globe till the Index of the Hour-Circle come to the given hour; and bring the Quadrant of Altitude to the Place of the Sun: so shall the number of degrees contained between the East point of the Horizon and the degree cut by the Quadrant of Altitude on the Horizon, be the number of degrees of the Suns Azimuth, at that time.

Example.

May 10. at 53. minutes past 8. a clock in the Morning, I would know the Azimuth of the Sun: Therefore (the Globe being first rectified) I turn about the Globe till the Index of the Hour-Circle point to 53. minutes past 8. a clock, or which is all one, within half a quarter of an hour of 9; then I move the Quadrant of Altitude to the degree the Sun is in that Day, and there let it remain till I see how many degrees is contained be­tween the North point and the Quadrant; which in this Ex­ample is 108. deg. 25. min. And because this distance from the North, exceeds 90. degrees; therefore I substract 90. de­grees from the whole, and the remains is 18. degrees 25. min. for the Azimuthal distance of the Sun from the East point towards the South. But if it had wanted of 90. degrees from the North point, then should the Complement of 90. have been the Azimuthal distance of the Sun from the East point.

PROB. XXIII.

The Place of the Sun, and hour of the Day given, to find the Almicantar of the Sun.

THe Almicantars of the Sun is upon the matter the same thing with the Altitude of the Sun: only with this di­stinction. The Almicantars are Circles parallel to the Horizon, discribed by the degree of the Quadrant of Altitude upon the Zenith as its Center, by turning the Qua­drant round about the Globe till it comes again to its first Place: But the Altitude is an Arch of the Vertical Circle, comprehen­ded between the Horizon and any point of the Globe assigned. Their agreement consists in this; When the Sun or any Star ha [...] any known Almicantar, they are said to have the same number of degrees of Altitude; As if the Sun be in the 20th Almican­tar; he hath 20 degrees of Altitude; if in the 30th Almicantar, he hath 30. degrees of Altitude, &c. Now because the Opera­tion is the same for finding the Altitude and Almicantar, I shall refer you to the 11th Probleme; which shews you how to find the Altitude or Heighth; and by consequence the Almicantar.

PROB. XXIV.

The Place of the Sun given, to find what Hour it comes to the East, or West, and what Almicantar it then shall have.

THe Globe, Quadrant, and Hour Index rectified, Bring the Quadrant of Altitude to the East point in the Horizon, if you would know what hour it comes to the East; or to the West point, if you would know what hour it comes to the West: Then turn about the Globe till the place of the Sun come to the Quadrant of Altitude; and the Index of the Hour Circle shall point at the hour of the Day: which on the Day aforesaid will be 7. hor. 7 min. in the Morning, that the Sun commeth to the East, and 4 hor. 53. min. after noon, that the Sun commeth to the West. And if you then count the number of degrees from [Page 62] the Horizon upwards on the Quadrant of Altitude, it will shew you the Almicantar of the Sun for that time; which will both Morning and Evening be 15, deg. 30. min. as was taught you by the last Probleme.

PROB. XXV.

To know at any time what a clock it is in any other Part of the Earth.

THe difference of Time is reckoned by the access and pro­gress of the Sun: for the Sun gradually circumvolving the Earth in 24. hours, doth by reason of the Earths rotundity en­lighten but half [...] at one and the same moment of Time; as shall be shewed hereafter: so that hereby it comes to pass, that when with us here in England it is 6. a clock in the Morning, with those that have 90. degrees of Longitude to the Westward of us, it is yet Midnight: with those that have 180. degrees of Longitude from us, it is Evening; And with those that have 90. degrees of Longitude to the Eastwards, it is Noon. So that those to the Eastward have their Day begin sooner then ours: But to the Westward their Day begins after ours. Therefore that you may know what Hour it is in any Place of the Earth, of what distance soever it be, you must first Bring the Place of your own Habitation to the Meridian, and the Index of the Hour Circle to 12. on the Hour Circle; Then bring the other Place to the Meridian, and the Arch of the Hour Circle comprehended between the hour 12. and the In­dex, is the difference in Time between the two Places.

Example.

London in England, and Surat in the East Indies: First I bring London to the Meridian, and turn the Index of the Hour-Circle to 12; then I turn the Globe Westward, because London [...]s Westward of Surat, till Surat come to the Meridian; and see at what Hour the Index of the Hour Circle points, which in this Example is 5. hor. 54. minutes: And because Surat lies to the Eastward of us so many degrees, therefore as was said before, [Page 63] their Day begins so much before ours: So that when here at London it is 6. a clock in the Morning, at Surat it will be 11. a clock 54. minutes; when with us it is 12. a clock, with them it will be 5 a clock 54. minutes afternoon.

If you would know the difference of Time between London and Jamaica; Working as before, you may find 5. hor. 15. min. But Jamaica is to the West of London; therefore their Day begins 5. hor. 15. min. after ours: so that when with us it is Noon, with them it will be but three quarters of an hour past 6. a clock in the Morning: and when with them it is Noon, with us it will be one quarter past 5. a clock after Noon, &c.

Or you may yet otherwise know the difference of Time, if you divide the number of Degrees of the Equinoctial that pass through the Meridian while the Globe is moved from the first Place to the second, by 15. so shall the product give you the dif­ference of hours and minutes between the two Places: as you will find if you try either of these Examples, or any other.

PROB. XXVI.

To find the Right Ascension of the Sun, or Stars.

THe Right Ascension of any point on the Globe is found by bringing the point proposed to the Meridian, and counting the number of degrees comprehended between the Vernal Colure, and the Meridian.

Example, for the Sun.

June 1. I would know the Right Ascension of the Sun: His Place found, as by the third Probleme, is ♊ 20. Therefore I bring ♊ 20. to the Meridian; and then the Meridian cuts the Equinoctial in 79. degrees 15. minutes, accounted from the Ver­nal point ♈: Therefore I say the Right Ascension of the Sun June 1. is 79. deg. 15. Minutes.

Example, for a Star.

I take Capella, alias Hircus, the Goat on Auriga's sholder, [Page 64] and bring it to the Meridian; and find the Meridian cut the Equinoctial (counting as before from the Vernel point ♈) in 73. degrees 58. minutes: Therefore I say, the Right Ascension of Hircus is 73. degrees 58. min. Do the like for any other point of the Globe proposed.

PROB. XXVII.

To find the Declination of the Sun, or Stars.

THe Declination of any point on the Globe is found by bringing the point proposed to the Meridian, and counting the number of degrees comprehended on the Meridian between the Equinoctial and the point proposed: and bears its Denomi­nation of North or South, according as it is scituate on the North or South side the Equinoctial.

Example, for the Sun.

June 1. I would know the Declination of the Sun. His Place found, as before, i [...] ♊ 20. Therefore I bring ♊ 20. to the Me­ridian; and find 23. degrees 8. min. comprehended on the Me­ridian between the Equinoctial and ♊ 20. and because ♊ is on the North side the Equinoctial; Therefore I say, June 1. The Sun hath North Declination 23. degrees 8. minutes.

Example, for a Star.

I take Hircus aforesaid, and bring it to the Meridian, and find 45. degrees 40. minutes comprehended on the Meridian between the Equinoctial and the Star Hircus. And because Hircus is on the North side the Equinoctial; Therefore I say, Hircus hath North Declination 45. degrees 40. min. Do the like for any other point on the Globe proposed.

But Note, The Right Ascension and Declination of the Sun al­ters dayly; for in twelve Moneths he runs through every degree of Right Ascension, and in three Moneths to his greatest Decli­nation: But the Right Ascension and Declination of the Stars is scarce perceiveable for some Years: Yet have they also an alter­ation of Right Ascension and Declination: For, those Stars [Page 65] that have but few degrees of Right Ascension, will in process of Time have many; and those Stars between the Tropick that have North Declination, will in length of Time have South De­clination; and the contrary (as shall be more fully shewed hereafter:) For, the Stars moving upon the Poles of the Eclip­tick go forwards in Longitude one whole Degree in 70½ Years (as hath been shewed before, Book 1. Chap. 3. Sect. 3.) and so alter both their Right Ascension, and Declination; as may be seen by this following Table of Right Ascensions and Declina­tions of 100. of the most eminent fixed Stars, Calculated by Tycho Brahe, for the Years 1600. and 1670. which I have in­serted; partly, because by it you may see the differences of their Right Ascensions and Declinations in 70½ Years; and partly to Accomodate those that may have occasion to know their Right Ascensions and Declinations neerer than the Globe can shew them.

A Table of the Right Ascensions and Declinations of 100. Select fixed Stars; Calculated by Tycho Brahe, for the Years 1600, and 1670. As also their Difference of Right Ascensions and Declinations, in 70. Years.

  1600   Differentia. 1900
Names of the Stars. R. Asc. Declin.   R. As. Decl. R. Asc. Declin.
Scedir, in Casssopeae. 4 36 54 21 N 1 22 34 S 5 58 54 55
The Pole Star. 5 47 87 9½ N 3 59 34 S 9 46 87 43½
Southern in the whales tail. 5 51 20 12 S 1 17 34 N 7 8 19 38
Cassiopeae's Belly. 8 21 58 33 N 1 27 34 S 9 48 59 7
Girdle Andromeda. 11 50 33 32 N 1 23 33 S 13 13 34 5
Knee of Cassiopeae. 15 3 58 7 N 1 35 33 S 16 38 58 40
1. in ♈ horn. 22 56 17 19 N 1 23 31 S 24 19 17 50
Whales belly. 22 59 12 16 S 1 15 31 N 24 14 11 45
2. in ♈ horn. 23 10 18 50 N 1 22 31 S 24 32 19 31
South foot of Andromeda. 24 55 40 23 N 1 29 30 S 26 24 40 53
[Page 66]In the Knot in the line ♓. 25 22 0 50 N 1 18 30 S 26 40 1 20
* Star in ♈ head. 26 23 21 33 N 1 25 30 S 27 38 22 3
* In the wtales jaw. 40 25 2 29 N 1 15 25 S 41 40 2 54
Caput Medusae 40 38 39 22 N 1 37 25 S 42 15 39 47
* In Persons side. 44 2 48 22 N 1 28 21 S 45 30 48 43
* In the Pletades. 50 57 22 49 N 1 29 21 S 52 26 23 10
In the Nostrils of ♉. 59 16 14 37 N 1 25 17 S 60 41 14 54
North Ey of ♉. 61 21 18 14 N 1 24 17 S 62 45 18 31
Aldebaran. 63 16 15 38 N 1 26½ 15 S 64 43 15 53
Hircus, Capella. 71 49 45 30 N 1 49 10 S 73 38 45 40
* Orions foot, Rigel. 73 51 8 43 S 1 15 9½ S 75 7 8 33½
North Horn ♉. 75 16 28 12 N 1 37 8 S 76 53 28 20
Orions left sholder. 75 58 5 55 N 1 19 3 S 77 17 6 3
Belly of the Hare 77 48 71 6 S 1 5 7 N 78 53 20 59
1. In Orions Girdle 77 58 [...] 39 S 1 17 7 N 79 15 0 32
Uppermost in Orions face 78 21 9 36 N 1 22 7 S 79 41 0 43
South Horn ♉. 78 26 20 51 N 1 31 7 S 79 57 20 58
2. In Orions Girdle. 79 1 1 30 S 1 17 6 N 80 18 1 24
Last in Orions Girdle. 80 10 2 12 S 1 16 5 N 81 26 2 7
Auriga's right Sholder. 82 40 44 50 N 1 55 4 S 84 35 44 54
Orions right Sholder. 83 26 7 16 N 1 22 4 S 84 48 7 20
* Foot ♊. 93 38 16 40 N 1 28 2 N 95 6 16 38
Great Dog Sirius. 96 53 16 11 S 1 7 4 S 98 0 16 15
Head of Castor, the first Twin. 107 9 32 41 N 1 44 11 N 108 53 32 30
The little Dog, Procyon. 109 37 6 12 N 1 20 12 N 110 57 6 0
Head Pollux, second Twin. 110 13 28 55 N 1 34 12 N 111 47 28 43
* In the Stern of the 117 39 23 11 S 1 4 15 S 118 43 23 26
Praesepe ♋ 124 20 21 2 N 1 28 19 N 125 48 20 43
Northern Asse ♋ Ship. 124 58 22 51 N 1 30 20 N 126 28 22 31
Southern Asse ♋ 125 27 19 35 N 1 27 20 N 126 54 19 15
The Heart of Hydra. 137 1 6 57 S 1 15 25 S 138 16 7 22
South of 3. in neck ♌ 146 22 18 42 N 1 28 28 N 147 50 18 14
Lions Heart, Basiliscus. 146 45½ 13 53½ N 1 53½ 28½ N 148 8 13 25
North of 3. in neck ♌ 148 33 25 23 N 1 23 29 N 150 1 24 54
Middle of 3. in neck ♌ 140 [...] 21 50 N 1 50 29 N 150 51 21 21
[Page 67]First lowest in [...] Vrsa Ma [...]. 159 12 58 31 N 1 37 32 N 160 49 57 59
First upper in □ Dubbe 159 37 63 54 N 1 41 32 N 161 18 63 22
* back ♌. 163 10 22 43 N 1 27 34 N 164 37 22 9
Lions tail. 172 9 16 49 N 1 19 34 N 173 28 16 15
following lowest in □ Ursa Major. 173 3 55 57 N 1 23 34 N 174 26 55 23
Uppermost following in □. 178 50 59 15 N 1 20 34 N 180 10 58 41
Girdle [...]. 188 53 5 37 N 1 18 34 N 190 11 5 3
Rump Ursa Major, Aliot. 189 1 58 10 N 1 19 33 N 190 10 57 37
Vindemiatrix, ♍. 190 36 13 8 N 1 17 33 N 191 53 12 35
Spica ♍. 196 4 9 1 S 1 19½ 32½ S 197 23½ 9 33½
Middle tail Ursa Major. 196 54 57 3 N 1 3 32 N 197 57 56 31
End Tail Urs. Major. 202 54 51 22 N 1 2 31 N 203 56 50 51
Arcturus. 209 23½ 21 18½ N 1 11 29½ N 210 34½ 20 49
Left Sholder of Bootes. 214 2 40 3 N 1 2 27 N 215 4 39 36
South Scale ♎. 217 14½ 14 18 S 1 23 27 S 218 37½ 14 45
North Scale ♎. 223 54½ 7 50 S 1 21½ 24 S 225 16 8 14
* Northern Crown. 229 26 28 6 N 1 5 21 N 230 31 27 45
* Serpents neck. 231 12 7 46 N 1 15 21 N 232 27 7 25
Northern of 3. * in front ♍. 235 34 18 38 S 1 28 19 S 237 2 18 57
Lest hand Ophiucus. 238 25 2 37 S [...]1 23 18 S 239 48 2 55
Heart [...]. Antares, 241 18 25 26 S 1 32 16 S 242 50 25 42
Right Shold▪ Hercules. 243 15 22 27 N 1 5 15 N 244 20 22 12
Left knee of Ophiucus. 243 49 9 39 S 1 23 15 S 245 12 9 54
Right knee of Ophiucus. 251 50 15 7 S [...]0 50 10 S 252 40 15 17
Head of Hercules. 254 6 14 55 N 1 8 8 N 255 14 14 47
Left Sholder of Hercules. 254 40 25 22 N 0 52 8 N 255 32 25 14
Head of Ophiucus. 259 5 12 56 N 1 11 7 N 260 16 12 49
Right Sholder of Ophiucus. 260 56 4 49 N 1 13 5 N 262 9 4 44
* head of the Dragon. 266 52 51 37 N 0 35 2 N 267 27 51 35
* Lyrae. 275 52 38 28 N [...]0 50 4 S 276 42 38 32
Most Eastern in Head ♐. 281 32 21 35 S 1 31 8 N 283 3 21 27
Vultures tail. 281 47 13 20 N 1 13 8 S 283 0 13 28
In the Swans Beak. 288 40 27 10 N 1 1 11 S 289 41 27 21
* in Vulture. 292 49 7 54 N 1 17 13 S 294 6 8 7
In the Swans North wing. 293 10 44 12 N 0 48 14 N 293 58 44 26
[Page 68]Upper horn ♑. 289 57 13 40 S 1 25 16 N 300 22 13 24
Lower horn ♑. 299 39 15 57 S 1 27 17 N 301 6 15 40
In the Swans breast. 302 1½ 39 1 N 0 53½ 18 S 302 55 39 19
Left hand of ♒. 306 32 10 53 S 1 16 19 N 307 48 10 34
Swans Tail. 306 57 43 53½ N 0 51½ 20½S 307 49 44 14
In the Swans South wing 307 31 32 30 N 1 0 21 S 308 31 32 51
Left Sholder ♒. 317 37 7 15 S 1 21 26 N 318 58 6 49
1. In tail ♑. 319 28 18 21 S 1 26 26 N 320 54 17 55
In Cepheus Girdle. 320 46 68 50 N 0 22 26 S 321 8 69 16
In Pegasus mouth. 321 10 8 5 N 1 18 26 S 322 28 8 31
2. in tail ♑. 321 16 17 51 S 1 25 27 N 322 41 17 24
Right Sholder of ♒. 326 19 2 13 S 1 20 29 N 327 39 1 44
Fomahant, ♒. 338 46 31 39 S 1 25 31 N 340 11 31 8
Scheat. P [...]gasus. 241 9 25 56 N 1 12 32 S 342 11 26 28
Marchab, Pegasus. 341 15 13 5 N 1 15 32 S 342 30 13 37
Mouth of Southern fi [...]h. 344 9 1 7 N 1 17 33 S 345 26 1 40
Head of Andromeda. 356 59 26 54 N 1 17 34 S 358 16 27 28
* Cassiopeae's chair. 357 5 56 58 N 1 15 34 S 358 20 57 32
End of Pegasus wing. (tail. 358 14 12 58 N 1 16 34 S 359 30 13 32
Northern in the wh [...]les 359 49 11 1 S 1 18 34 S 1 7 10 27

The Vse of this Table.

The first Collumne on the left hand is the names of the Stars. The Second Collumne shews the degrees and minutes of Right Ascension, for the Year 1600. The third the Declination for the same Year. The fourth shews whether the Declination be North or South; N stands for North, S for South. The fifth shews the difference in degrees and minutes of Right Ascension of the Stars, between the Years 1600▪ and 1670. The sixth shews the Difference of Declination; and whether it be North, or South. The seventh shews the Right Ascension in degrees and minutes, for the Year 1670. The eighth shews the D [...]clination in degrees and minutes for the same Year.

By this Table you may perceive the fixed Stars increase in Right Ascension, till they come to the Vernal Colure; from [Page 69] whence the number of their Right Ascension is reckoned: and by the Collumne of their Difference of Right Ascension, you may see how much they increase in 70. Years▪ And if you would know how much they increase for any other number of Years, you must find what proportion they have to 70, and the same proportion the Difference of the Right Ascension of the Stars will have to the Difference in the Table.

Example.

I would know the Difference of Right Ascension the Pole-Star will have in 35. Years. I find in the fifth Collumne the Difference of Right Ascension of the Pole Star to be 3. degrees 59. min. Therefore by the Rule of Proportion. I say, If 70. Years give 3. degrees 59. min. 35. Years shall give 1. degree 59½▪ min: and so proportionably for any other number of Years.

Though this Rule serves for finding the Difference of Right Ascension of any Star; Yet it will not serve for finding the Difference of any Stars Declination. For the Stars on the North side the Equinoctial between the Hyemnal and Solsticial Colures, and on the South side the Equinoctial between the Solsticial and Hyemnal Colures, increase in Declination. But the Stars on the South side the Equinoctial between the Hyem­nal and Solsticial Colures, and on the North side the Equino­ctial between the Solsticial and Hyemnal Colures, Decrease in Declination: as you may yet more plainly see by the Globe, if you bring 66½ deg. of the Meridian to the North side of the Ho­rizon, and screw the Quadrant of Altitude to 66½ degrees in the Zenith, and Declination of the Pole of the Ecliptick; and bring the Hyemnal Colure to the Meridian; for so shall the Pole of the Ecliptick be joyned with the center of the Quadrant of Altitude, and the Ecliptick with the Horizon; and all the Circles that the several degrees on the Quadrant make in a Re­volution from West to East upon the Poles of the Ecliptick, re­present the great Revolution of every Star that each degree on the Quadrant cuts. And thus demonstratively will be represen­ted the progress of the fixed Stars through every degree of Lon­gitude, and by consequence the alteration of their Right Ascen­sion, and Declination. For, Imagining that degree of the Qua­dra [...]t [Page 70] of Altitude to be the Star, which just reaches the Star; you may by turning about the Quadrant, see how Obliquely the Star (or the degree representing the Star) either moves about, or cuts the Equinectial, and all Circles parallel to the Equinoctial; and thereby observe it sometimes to incline in mo­tion to, and other times to decline in motion from the Equi­noctial. But how long time it will be [...]re the Star inclines to, or declines from the Equinoctial, you may know by finding the distance of Longitude in degrees it hath from either the Solsticial or Hy [...]mnal Colure; and with respecting the forego­ing Rules in its Position, you may by the Table in Book 1, Chap. 3. Sect. 3. satifie your self.

Example.

The most Northerly Star in the Girdle of Orion doth yet de­crease in Declination. But I would know how long it shall de­crease; Therefore by the 32. Probleme, I find the Longitude of that Star to be for the Year 1670. 77. deg. 51. min. which subducted out of 90, (the distance of the Solsticial Colure from the Equinoctial,) leaves 12. 9, for the distance of that Star from the Solsticial Colure. Therefore by the Table aforesaid, I find what number of Years answers to the motion of 12. deg. 9. min. And because I cannot find exactly the same number of degrees and minutes in the Table, I take the number neerest to it; which is 14. degrees 10. minutes, and that is the motion of the Ecliptick in 1000. Years. But because this 14. degrees 10. minutes is 2. degrees 1. minute too much, I seek 2. degrees, 1. min. in the Table, and the number of Years against it I would subduct from the number of Years against 14, deg, 10. min. and the remainder would be the number of Years required: But 2. deg. 1. min. I cannot find neither, therefore I must take the number of degrees and minutes neerest to it, which is 2. deg. 50. min. and that yeelds 200. Years; which subducted out of 1000. leaves 800. Years. But because this is also too much by the motion of 49. min. Therefore I seek for 49. min. in the Table, and subduct the number of Years against it from 800, and the remainder would be the number of Years required. But 49. min. is not in the Table neither, Therefore I take the neerest to it, which is 51. min. and that yeelds 60. Years; which sub­ducted out of 800. leaves 740. But this is likewise too much by [Page 71] the motion of two min. Therefore I seek 2. min. in the Table, but cannot find it neerer then 2½, and against it I find 3. Years, which 3. Years I subduct out of 740, and the Remainder is 737. the number in Years required. You may if you please for exactness, subduct for the ½ min. 8. Moneths; so have you 736, Years 4. Moneths, for the Time that the most Northerly Star in the Girdle of Orion will decrease in Declination after the Year 1670. which will be till An. Dom. [...]406. after which time it will increase in Declination for 12706. Years together, till it come to have 47. degrees 8. min. of Declination: at which time it will be in or very neer the place of the most Southerly Star of the Southern Crown; and that Star in its place.

And thus the Pole Star is now found to increase in Declina­tion, and will yet this 421 Years: after which time it will de­crease in Declination for 12706 Years together, till it come to be within 42. degrees 42. minutes of the Equinoctial, in the void space now between Draco and Lyra; at which time Lyra will be almost as neer the Pole, as the Pole Star now is; and then the most proper to be the Northern Pole Star: And the last Star in the Stalk of the Doves mouth will be then very neer the Southern Pole, and therefore most fit to be the Sou­thern Pole-Star.

PROB. XXVIII.

The Place of the Sun or any Star given, to find the Right Descension, and the Oblique Ascension, and the Oblique Descension.

BRing the Place of the Sun or the Star to the Meridian un­der the Horizon, and the degree of the Equator that comes to the Meridian with it is the Degree of Right Descension.

For the Oblique Ascension.

Bring the Place of the Sun or the Star to the East side the Horizon, and the degree of the Equator cut by the Horizon, is the Degree of Oblique Ascension of the Sun or Star.

For the Oblique Descension.

Bring the Place of the Sun or Star to the West side the Hori­zon, and the degree of the Equinoctial cut by the Horizon is the Degree of Oblique Descension. They need no Examples.

PROB. XXIX.

Any Place on the Terrestrial Globe being given, to find its Antipodes.

BRing the given Place to the Meridian, so may you (as by the first Probleme) see its Longitude and Latitude; then turn about the Globe till 180. degrees of the Equator pass through the Meridian; and keeping the Globe to this Po­sition, number on the Meridian 180. degrees from the Latitude of the given Place: and the point just under that degree is the Antipodes.

Example.

I would find the Antipodes of Cuida Real, an Inland Town of the West Indies, which lies upon the River Parana, an Arm of Rio de la Plata: Therefore I bring Cuida Real to the Me­ridian, and find (as by the first Probleme) its Latitude 23. 50: South; and its Longitude 333. degrees: Then I turn about the Globe till 180. degrees of the Equator pass through the Me­ridian; and keeping the Globe to that position, I number so many degrees North Latitude as Parana hath South, viz. 23, 50, and just under that degree I find Lamoo, a Town lying upon the Coast of China, in the Province of Quancij: Therefore I say Lamoo is just the Antipodes of Cuida Real.

Another way.

Bring the given Place to the North or South point of the Ho­rizon, and the point of the Globe denoted by the opposite point of the Horizon, is the Antipodes of the given Place.

PROB. XXX.

To find the Perecij of any given Place, by the Terrestrial Globe.

BRing your Place to that side the Meridian which is in the South notch of the Horizon, and follow the Parallel of that Place on the Globe till you come to that side the Meridian which is in the Northern notch of the Horizon; and that is the Perecij of your Place.

PROB. XXXI.

To find the Antecij of any given Place, upon the Terrestrial Globe.

BRing your Place to the Meridian, and find its Latitude by the first Probleme; If it have North Latitude, count the same number of degrees on the Meridian from the Equator Southwards; But if it have South Latitude, count the same number of degrees from the Equator Northwards: and the point of the Globe directly under that number of degrees is the Antecij of your Place.

PROB. XXXII.

To find the Longitude and Latitude of the Stars, by the Coelestial Globe.

THe Quadrant of Altitude will reach but 90. degrees, as was said Prob. 9. Therefore if the Star you enquire after be on the North side the Ecliptick, you must elevate the North Pole 66½ degrees above the North side the Horizon: If on the South side the Ecliptick, you must elevate the South Nole 66½ degrees above the South side the Horizon: Then bring the Solsticial Colure to the Meridian on the North side the Horizon, and screw the Quadrant of altitude to the Zenith, which will be in 23½ degrees from the Pole of the World: So shall the Eclip­tick ly in the Horizon, and the Pole of the Ecliptick also ly under the Center of the Quadrant of Altitude (as was [Page 74] shewed Prob. 27.) Now to find the Longitude of any Star, do thus Turn the Quadrant of Altitude about till the graduated edge of it ly on the Star; and the degree in the Ecliptick that the Quadrant touches is the Longitude of that Star.

Example, for a Star on the North side the Ecliptick.

I would know the Longitude of Marchab, a bright Star in the wing of Pegasus: I find it on the North side the Ecliptick, Therefore I elevate the North Pole, and placing ♋ on the North side the Meridian, I screw the Quadrant of Altitude to the Zenith, as aforesaid: Then laying the edge of the Quadrant of Altitude upon that Star, I find that the end of it reaches in the Ecliptick to ♓ 18. 56. Therefore I say, the Longitude of Marchab is ♓. 18. 56.

For the Latitude of a Star.

The Degree of the Quadrant of Altitude that touches the Star is the Latitude of the Star.

Example.

The Globe and Quadrant posited as before, I find 19. deg. 26. min. (accounted upwards on the Quadrant) to touch Marchab aforesaid: Therefore I say, the Latitude of Marchab is 19. deg. 26. min.

And thus by elevating the South Pole and placing the Globe and Quadrant of Altitude as aforesaid, I shall find Canicula have 15. degrees 57. min. South Latitude, and 21. degr. 18. min in ♋, Longitude.

PROB. XXXIII.

To find the Distance between any two Places, on the Ter­restrial Globe.

THis may be performed either with the Quadrant of Al­titude, or with a pair of Compasses: with the Qua­drant of Altitude, [...]: Lay the lower end thereof to one Place, and see what degree reaches the other Place, for [Page 75] that is the number of degrees between the two Places. If you multiply that number of Degrees by 60 the Product shall be the number of English Miles between the two Places.

Example.

I would know the distance between London and the most Easterly point of Jama [...]ca; I lay the lower end of the Quadrant of Altitude to Jamaica, and extending the other end towards London, I find 68½. deg. comprehended between them: Therefore I say 68½ is the number of degrees comprehended between Lon­don and Jamaica.

If you would find the Distance between them with your Compasses, you must pitch one foot of your Compasses in the East point of Jamaica, and open your Compasses till the other foot reach London; and keeping your Compasses at that Di­stance apply the feet to the Equinoctial line, and you wil find 68½ degree comprehended between them: as before.

If you multiply 68½. by 60, is it gives 4110. English miles.

If you multiply it by 20, it gives 1370. English Leagues.

If you multiply it by 17½, it gives 1199. Spanish Leagues.

If you multiply it by 15, it gives 1054 Dutch Leagues.

PROB. XXXIV.

To find by the Terrestrial Globe upon what point of the Compass any two Places are scituate one from another.

FInd the two Places on the Terrestrial Globe, and see what [...]umb passes through them; for that is the point of the Compass they bear upon.

Example.

Bristol and Bermudas are the Places: I examine what Rhumb passes through them both: and because I find no Rhumb to pass immediately through them both, Therefore I take that Rhumb which runs most Parallel to both the Places; which in this Example is the tenth Rhumb counted from the North towards the left hand; and is called as you may see by this following [Page 76] Figure West South West; Therefore I say Bermudos lies scituate from Bristol West South West; and by contraries Bristol lies cituate from Bermudas East North East.

[figure]

PROB. XXXV.

To find by the Coelestial Globe the Cosmical Rising and Setting of the Stars.

WHen any Star Rises with the Sun, it is said to Rise Cosmically.

And when any Star Sets when the Sun Rises, it is sa [...]d to Set Cosmically.

To find these, Rectifie the Globe to the Latitude of your [Page 77] Place, and bring the Place of the Sun to the East side the Ho­rizon; and the Stars then cut by the Eastern Semi-Circle of the Horizon, Rise Cosmically; and those Stars cut by the Western Semi-Circle of the Horizon, Set Cosmically.

Example.

Novemb. 9. I would know what Stars Rise and Set Cosmi­cally▪ here at London. The Suns Place found, as by the third Probleme is [...] 27. Therefore I bring [...] 27. to the East side the Horizon, and in the Eastern Semi-Circle I find Rising with the Sun the right Wing of Cygnus, the Star in the end of A­quila's tail, Serpentarius and Centaurus: Therefore these Con­stellations are said to the Cosmically. In the Western Semi-Circle of the Horizon I find Setting Andromeda, the Triangle, Tau­rus, Orion, (anis Major, and Argo Navis; Therefore I say, these Constellations Set Cosmically.

PROB. XXXVI.

To find by the Coelestial Globe the Acronical Rising and Setting of the Stars.

THe Stars that Rise when the Sun Sets, are said to Rise A­cronically. And,

The Stars that Set with the Sun, are said to Set Acronically.

To find these, Rectifie the Globe to the Latitude of your Place, and bring the Place of the Sun to the West side the Hori­zon; and the Stars then cut by the Eastern Semi-Circle of the Horizon, Rise Acronically: And those Stars cut by the Western Semi-Circle of the Horizon, Set Acronically.

Example.

November 9. I would know what Stars Rise and Set Acro­nically here at London. The Suns Place as before, is [...] 27. Therefore I bring [...] 27. to the West side the Horizon; and in the Eastern Semi-Circle I find Rising the Southern Fi [...]h, Foma­hant, Ce [...]us, Taurus, Auriga, and the Feather in Castor's Cap. Therefore these Constellations are said to Rise Acronically. In [Page 78] the Western Semi-Circle of the Horizon I find Setting the Lyons tail, Virgo, Scorpio, and Sagittarius, Therefore I say, these Con­stellations Set Acronically.

PROB. XXXVII.

To find by the Coelestial Globe the Heliacal Rising, and Setting of the Stars.

WHen a Star formerly in the Suns Beams gets out of the Suns Beams it is said to Rise Heliacally. And.

When a Star formerly out of the Suns Beams, gets into the Suns Beams, it is said to set Heliacally.

A Star is said to be in the Suns Beams, when it is made in­conspicuous by reason of its neerness to the Suns Light. The Bigger Stars are discernable more neer the Suns Light, then the Lesser are: For, Stars of the first Magnitude may (accor­ding to the received Rules of ancient Authors) be seen when the Sun is but 12. degrees below the Horizon but Stars of Second Magnitude cannot be seen unless the Sun be 13. degrees below the Horizon: Stars of the third Magnitude require the Sun to be 14. degrees below the Horizon ere they can be seen; of the fourth Magni [...]ude 15. degrees. of the fifth Magnitude 16. de­grees of the sixth Magnitude 17 degrees; the Nebulous ones 18. degrees. Yet this Rule is not so certain but that either clear or cloudy weather may alter it. Read more of this subject in M r Palmer on the Plamsphear. Book 4. Chap. 20

Now to find the Time that any Star shall Rise Heliacally. Do thus Rectifie the Globe and Quadrant of Altitude to your Latitude. Then bring the given Star to the East side the Horizon, and turn the Quadrant of Altitude into the West side, and see what degree of the Ecliptick is elevated so many degrees above the Horizon as the Magnitude of the Star you enquire after re­quires, according to the foregoing Rules; for the opposite degree of the Ecliptick is the degree the Sun shall be in when that Star Rises Heliacally. Having the degree of the Ecliptick the Sun is in, you may find the Day of the Moneth, by the 4th Pro­bleme.

Example.

I would know when Cor Leonis shall Rise Heliacally here at London: Therefore I Rectifie the Globe and Quadrant of Altitude for London, and bring Cor Leonis to the East side the Horizon, and turn the Quadrant of Altitude into the West; and because Cor Leonis is a Star of the first Magnitude, therefore I see what degree of the Ecliptick is elevated in the West side the Horizon 12. degrees on the Quadrant of Altitude, and find ♓ 9. deg. Now the degree of the Ecliptick opposite to ♓ 9. is [...] 9. Therefore I say, when the Sun comes to [...] 9. degrees (which by the 4th Probleme I find is August. 23.) Cor Leonis shall Rise Heliacally.

For the Heliacal Setting.

The Globe, &c. Rectified, as before: Bring the Star to the West side the Horizon, Then see what degree of the Ecliptick is elevated on the Quadrant of Altitude so many degrees as the Stars Magnitude requires; for when the Sun comes to the oppo­site degree of the Ecliptick that Star shall set Heliacally.

Example.

I would know when Bilanx a Star in the Beam of the Scales, will Set Heliacally here at London. The Globe and Qua­drant Rectified, I bring Bilanx to the West side the Horizon, and turn the Quadrant of Altitude into the East; Then I exa­mine what degree of the Ecliptick is elevated 13. degrees of the Quadrant of Altitude (because Bilanx is a Star of the second Magnitude) and find ♉ 4½. opposite to ♉ 4½. is [...] 4½. Therefore I say, When the Sun comes to [...] 4½. (which by Probleme 4. will be October 18) Bilanx shall set Heliacally.

PROB. XXXVIII.

To find the Diurnal and Nocturnal Arch of the Sun, or Stars, in any given Latitude.

THe Semi-Diurnal Arch is the number of degrees of the E­quator that passes through the Meridian whiles the Sun or [Page 80] any Star is ascending above the East side the Horizon to the Me­ridian. To know the number of degrees it contains, Rectifie the Globe to the given Latitude, and bring the Place of the Sun or Star to the East side the Horizon, and note what number of de­grees of the Equinoctial is then cut by the Meridian: Then re­move the Place of the Sun or Star to the Meridian, and see again what number of degrees of the Equinoctial is then cut by the Meridian, and substract the former from the latter, and the remainder shall be the number of degrees of the Sun or Stars Semi-Diurnal Arch. But Note, If the Equinoctial point ♈ pass through the Meridian while the Sun or Star is turned from the East side the Horizon to the Meridian, then you must substract the number of degrees of the Equinoctial cut by the Meridian when the Sun or Star is at the East side the Horizon from 360. degrees, and to the remainder ad the number of degrees of the Equinoctial that comes to the Meridian with the Place of the Sun or Star, and the Sum of them both is the number of degrees of the Sun or Stars Semi-diurnal Arch; which being doubled is the number of degrees of the whole Di­urnal Arch: and which being substracted from 360, given the Nocturnal Arch.

Example, of the Sun.

Having Rectified the Globe, I would May 10. know the Diurnal Arch of the Sun: His Place found by Prob. 3. is 8 29. Therefore I bring ♉ 29. to the Fast side the Horizon, and find then at the Meridian 299. degrees 30. min. of the Equi­noctial; then I turn the Place of the Sun to the Meridian, and find 56. deg. 30. min. of the Equinoctial come to the Meridian with it. Here the Equinoctial point ♈ passes through the Me­ridian while the Sun moves between the Horizon and the Meri­dian; Therefore as aforesaid, I substract the first number of degrees and minutes viz. 299. deg. 30. min. from 360. degrees, and there remains 60▪ degr. 30. min. for the number of degrees and minutes contained between the degree of the Equinoctial at the Meridian and the Equinoctial point ♈; and to this 60. deg. 30. min. I ad the second number of degrees and minutes, viz. 56. deg. 30. min. the number of degrees and minutes between the point ♈ and the deg. of the Equinoctial at the Meridian, and they make together 117. degrees, for the Suns Semi diurnal [Page 81] Arch; By doubling of which, you have 234. degrees, for the Suns Diurnal Arch; And by substracting 234. (the Diurnal Arch) from 360. you have 126. degrees, for the Suns Noctur­nal Arch.

Example, for a Star.

I take Sirius, a bright Star in the Great Dogs mouth. The Globe rectified, as before; I bring Sirius to the East side the Hori­zon, and find then 29. degrees 30 minutes of the Equinoctial at the Meridian, then I turn Sirius to the Meridian and find 97. degrees 38 minutes of the Equinoctial come to the Meridian with it: Therefore I substract the first number viz. 29. degrees 30. minutes, from the second, 97. 38, and the remains is 68. de­grees 8 minutes, for the Semi-diurnal Arch of Sir [...]us.

His Nocturnal Arch you may find as before.

PROB. XXXIX.

To find the Azimuth and Almicantar of any Star.

THis Probleme is like the 22, and 23. Problemes, which shew the finding the Azimuth and Almicantar of the Sun; only, whereas there you were directed to bring the degree of the Sun to the Quadrant of Alti­tude, you must now bring the Star proposed to the Quadrant of Altitude; and by the Directions in those Problemes the resolu­tion will be found.

PROB. XL.

To find the Hour of the Night, by observing two known Stars in one Azimuth, or Almicantar.

REctifie the Globe Quadrant and Hour Index. Then find the two known Stars on the Globe; and if the two Stars be in one Azimuth, turn about the Globe and Quadrant of Altitude till you can fit the two Stars to ly under the graduated edge of the Quadrant of Altitude: so shall the Index of the Hour-Circle p [...]int at th [...] Hour of the Night. If [Page 82] the two Stars be in one Almicantar, Turn the Globe forward or backward till the two Stars come to such a Position that by moving the Quadrant of Altitude, the same degree on it will ly on both the Stars; so shall the Index of the Hour-Circle point at the Hour of the Night.

PROB. XLI.

The Hour given that any Star in Heaven comes to the Me­ridian, to know thereby the Place of the Sun, and by con­sequence the Day of the Moneth, though it were lost.

BRing the Star proposed to the Meridian, and turn the In­dex of the Hour-Circle to the Hour given, Then turn a­bout the Globe till the Index point at the Hour of 12, for Noon; and the Place of the Sun in the Ecliptick shall be cut by the Meridian.

Example.

March 7. at 11, aclock at Night the Pointers come to the Meridian of London. Therefore I place the Pointers on the Cae­lestial Globe under the Meridian, and turn the Index of the Hour-Circle to 11. past Noon, afterwards I turn back the Globe till the Index point to 12. at Noon; Then looking in the Eclip­tick, I find the Meridian cuts it in ♓ 26. 45. minutes; Therefore I say, when the Pointers come to the Meridian at 11. a clock at Night, the Place of the Sun is ♓ 26. 45. Having thus the Place of the Sun, I may find the Day of the Moneth by the fourth Probleme; and so either know the Day that the Pointers come to the Meridian at 11. a clock at Night, or at any other Hour given.

The Day of the Moneth might also be found by the Declina­tion and the Quarter of the Ecliptick the Sun is in, given: For the Meridian will cut the degree of the Suns Place in the Eclip­tick in the Parallel of Declination: So that having respect to the Quarter of the Ecliptick, you'le find the Suns Place; and having the Suns Place, you may as aforesaid find the Day of the Moneth.

PROB. XLII.

The Day of the Moneth given, to find in the Circle of Let­ters on the Plain of the Horizon, the Day of the Week.

THe seven Daies of the Week were by the Idolatry of the ancient Roman Heathenish Times Dedicated to the Ho­nour of seven of their Gods, which we call Planets. The first is the most eminent, and therefore doubtless by them set in the first Place, called Dia Solis, or the Suns Day: The second Dia Lu­na, the Moons Day: The third Dia Martis, the Day of Mars: by us called Tuesday: The fourth Dia Mercurius, Mercuries Day: by us called Wednesday; from Woden, an Idol the Saxons Worshipt, to whose Honour they Dedicated that Day, and is by all those Germain Nations still called Wodensdagh: The fifth Dia Jovis, Jupiter or Joves Day: which doubtless the Saxons (from whom probably we receive it) called Donder-dagh, be­cause Jupiter is the God of Thunder; and we either by corrup­tion or for shortness, or both, call it Thursday: The sixth Dia Veneris, the Day of Venus: but the Saxons transferring her Honour to another of their Goddesses named Fria, called it Fri­dagh: and we from them call it Fryday: The seventh is Dia Saturnis, Saturus Day.

The same Day of the Moneth in other Years happens not on the same Day of the Week, therefore the Dominical Letter for one Year is not the same it is the next: Now because you can­not come to the knowledge of the Day of the Week unless you first know the Sundaies Letter, therefore have I in Prob. 5 [...] inser­ted a Table of M r Palmers, by which you may find the Domini­cal or Sundaies Letter for ever; and having the Dominical Letter you may in the Circle of Letters on the Horizon find it neer the day of that Moneth, and count that for Sunday, the next under it for Monday, the next under that for Tuesday, and so in order, till you come to the Day of the Moneth.

Example.

I would know what Day of the Week June 1. Anno 1658. Old Style, falls on; I find by the Table aforesaid the Dominical [Page 84] Letter is C, then I look in the Calender of Old Style for June 1. and against it I find Letter E, which because it is the second Let­ter in order from C, therefore it is the second Day in order from Sunday, which is Tuesday.

PROB. XLIII.

The Azimuth of any Star given, to find its Hour in any given Latitude.

THe Hour of a Star is the number of Hours that a Star is distant from the Meridian. To find which, Rectifie the Globe and Quadrant of Altitude, and bring the Star proposed to the Meridian, and the Index of the Hour-Circle to 12. Then place the lower end of the Quadrant of Altitude to the given A­zimuth in the Horizon, and turn the Globe till the Star come to the graduated edge of the Quadrant of Altitude; so shall the Index of the Hour-Circle point at the Hour of the Star. Only this caution you must take; If the Star were turned from the Meri­dian towards the Eastern side of the Horizon, you must substract the number of Hours the Index points at from 12. and the re­mainder shall be the Hour of the Star. But if the Star were turn­ed from the Meridian towards the West side the Horizon, the Hour the Index points at is (without more adoe) the Hour of the Star.

PROB. XLIV.

How you may learn to know all the Stars in Heaven, by the Coelestial Globe.

REctifie the Globe, Quadrant, Hour-Index and Horizon, as by Prob. 2. Then turn about the Globe till the In­dex of the Hour-Circle point at the Hour of the Night on the Hour-Circle. Then if every Star on the Globe had a hole in the midst, and your Ey were placed in the Center of the Globe; you might by keeping your Ey in the Center and look­ing through any Star on the Globe see its Ma [...]ch in Heaven: that is, the same Star in Heaven which that Star on the Globe repre­sents: for from the Center of the Globe there proceeds a straight [Page 85] line through the Star on the Globe, even to the same Star in Hea­ven. Therefore those Stars that are in the Zenith in Heaven, will then be in the Zenith on the Globe; those that are in the East in Heaven, will be in the East on the Globe; those in the West in Heaven, in the West on the Globe; and those Stars that are in any Altitude in Heaven, will at the same time have the same Altitude on the Globe; So that if you see any Star in Heaven whose Name you desire to know, you need but observe its Azimuth and Altitude, and in the same Azimuth and Alti­tude on the Globe, you may find the same Star: and if it be an eminent Star, you will find its Name adjoyned to it.

Example.

December 10. at half an hour past 9. a clock at Night, here at London, I see two bright Stars at a pretty distance one from ano­ther in the South; I desire to know the Names of them; There­fore having the Globe rectified to the Latitude of London, and the Quadrant of Altitude screwed to the Zenith, the Hour-Index also Rectified, and the Horizon posited Horizontally, as by Prob. 2. I observe the Altitude of those Stars in Heaven, (either with a Quadrant, Astrolabe, Cross-staff, or the Globe it self, as hath been shewed Prob. 13, 16.) to be, the one 78. degrees, the o­ther 42, degrees above the Horizon. Therefore having their Altitudes, I count the same number of degrees as for the first 78. upon the Quadrant of Altitude upwards, and turn it into the South, under the Meridian, and see what Star is under 78. de­grees, for that is the same Star on the Globe which I saw in Heaven. Now at the first examination of the Globe you may see that that Star is placed in the Ey of that After time which is called Caput Medusa, and indeed, that being the only Star of Note in that Constellation, bears the Name of the whole Con­stellation. The other Stars about it you may easily know by their Scituation. As, Seeing two little Stars to the Westwards of that Star in Heaven, you may see on the Globe that the hithermost is in the other Ey of Caput Medusa, and the furthermost in the Hair or Snakes of the same Asterisme. Looking a little to the Southwards of those Stars in Heaven, you may see two other smal Stars a little below those in the Eyes; Therefore to know those also, you may look on the Globe, and see that there is one on the [Page 86] Nose, and another Starre in the Cheek of Caput Medusa

In like manner for the second Star in the Meridian, which is 42 degrees above the Horizon: If you move the Quadrant of Altitude (as before) to the South or Meridian, and count 42 de­grees upon the Quadrant of Altitude, you will find a Star of the second Magnitude in the Mouth of the Whale: Therefore you may say, that Star in Heaven is in the Mouth of the Whale: and because close to it on the Globe is written Menkar, Therefore you may know the name of that Star in Heaven is Menkar.

In the South East and by South 56 degrees above the Hori­zon, I [...]ee a very bright Star in Heaven; therefore I bring the Quadrant of Altitude to the South East and by South point in the Horizon, and find under 56 degrees of the Quadrant of Alti­tude a great Star, to which is prefixed the name Occulus Tau­rus; Therefore I say, the name of that Star in Heaven is Oc­culus Taurus.

In the South East in Heaven you may see three bright Stars ly directly in a straight line from one another, the middlemost whereof is 25. degrees or thereabouts above the Horizon, there­fore bring the Quadrant of Altitude to the South East point of the Horizon, and about 25 degrees above the Horizon you will see the same great Stars on the Globe, in the Girdle of Orion: There­fore those Stars are called Orions Girdle.

At the same time South East and by East you have about 10 degrees above the Horizon the brightest Star in Heaven, called Sirius, in the Mouth of the Great Dog; Canicula a bright Star in the Little Dog East and by South, about 25 degrees above the Horizon: Cor Leonis just Rising East North East: you have also at the same time on the East side the Horizon, the Twins, Auriga, the Great Bear; and divers other Stars, eminent both for their splendor and Magnitude.

In the West side the Horizon you have South West and by West about 4 degrees above the Horizon a bright Star in the Right Leg of Aquarius: and all along to the Southwards in Cetus the Whale, you have other eminent bright Stars: More upwards towards the Zenith you have a bright Star in the Line of the two Fishes: Higher yet, you have the first Star in ♈, an eminent Star, because the first in all Catalogues that we have cognizance of; and therefore probably in the Equinoctial Colure when the Stars were first reduced into Constellations: yet more [Page 87] neer the Zenith you have a bright Star in the Left Leg of An­dromeda: From thence towards the North, you find other very eminent bright Stars in Cassiopea, Cepheus, Ursa Minor, in the Tail whereof is the Pole Star: and Draco: Hecules: where you turn back, to Lyra, Cygnus, Pegasus, the Dolphin, &c. all which, or any other, you may easily know by their Altitude a­bove the Horizon, and the point of the Compass they bear upon.

Thus knowing some of the most eminent Fixed Stars, you may by the Figure of the rest come to the knowledge of them also. For Example, Looking towards the North North East in Heaven, you may see seven bright Stars constituted in this Figure; There­fore looking towards the same Quarter on the Globe, you may (without taking their Altitude) see the same Stars lying in the same Figure in the hinder parts of the Great Bear; from whence you may con­clude, that those Stars in Heaven are scitu­ate in the hinder parts of the Asterisme called Ursa Major.

[figure]

Yet nevertheless you may see some Stars of Note in Heaven, which you shall not find on the Globe, and those in or neer about the Ecliptick: They are called Planets, and cannot be placed on the Globe, unless it be for a particular Time, with Black Lead, or some such thing that may be rubbed out again: Because they having a continual motion alwaies alter their Places. Of those there are five in number, besides the Sun and Moon, which are also Planets, though they shew not like Stars. These five are called Saturn, Jupiter, Mars, Venus, Mercury; yet Mecury is very rarely seen: because he never Rising above an Hour before the Sun, or Setting above a Hour after, for the most part hath his light so overspread with the dazelling Beams of the glittering Sun, that sometimes when he is seen he seems rather to be a More in the Suns Beams, then a Body en­dowed with so much brightness as Stars and Planets seem to be.

Now there are divers waies (by some of which you may at all times) know those Planets from the Fixed Stars: as first, Their not twinkling, for therein they differ from fixed Stars; be­cause they most commonly do twinkle, but Planets never; unless it be ♂ Mars; and yet he twinkles but very seldom neither.

Secondly, They appear of a considerable Magnitude, as ♃ [Page 88] sometimes appears greater ly far then a Star of the first Magni­tude; and ☿ many times bigger then he. They are both glitter­ing Stars, of a bright Silver collure; but ♀ most radient, especially when she is in her Perigeon. ♂ appears like a Star of the second Magnitude; and is of a Copperish colloure. ♄ shewes like a Star of the third Magnitude, and is of a Leaden Collour; and he (of all the others,) is most difficult to be known from a fixed Star; partly because of his minority, and partly because of the slowness of his motion. ☿ is very seldom seen (as aforesaid) unless it be in a Morning when he Rises before the Sun, or in an Evening when he Sets after the Sun: He is of a Pale Whitish Collour, like Quick silver, and appears like a Star of the third Magnitude. He may be known by the Company he keeps, for he is never above 29. degrees distant from the Sun.

Thirdly, The Planets may be known from fixed Stars by their Azimuths and Altitudes observed: (as hath been taught before) for if when you have taken the Azimuth and Altitude of the Star in Heaven you doubt to be a Planet, and you find not on the Globe in the same Azimuth and Altitude a Star appearing to be of the same Magnitude that that in Heaven appears to be, you may conclude that that in Heaven is a Planet. Yet notwithstanding it may happen that a Planet may be in the same degree of Longitude and Latitude in the Zodiack that some eminent fixed Star is in; as in the degree and minute of Longitude and La­titude that Cor Leonis, or the Bulls Ey, or Scorpions heart is in, and so may eclipse that Star, by being placed between us and it: But that happens very seldom and rarely; but if you doubt it▪ you may apply your self to some other of the precedent and subse­quent Rules here set down for knowing Planets from fixed Stars.

The fourth way is by shifting their Places; for the Planets having a continual motion, do continually alter their Places: as ♂ moves about half a degree in a day: ♀ a whole degree; but ♃ and ♄ move very slowly; ♃ not moving above 5. mi­nutes, and ♄ seldom above 2. minutes. Yet by their motions alone the Planets may be known to be Planets, if you will precisely ob­serve their distance from any known fixed Star in or near the E­cliptick as on this Night, and the next Night after observe whether they retain the same distance they had the Night before; which if they do, then are they fixed Stars; but if they do not then are they Planets: yet this Ca [...]on is to be given you in this Rule also, [Page 89] That the Planets sometimes are said to be Stationary, as not al­tering 1. minute in Place, forwards, or backwards in 6. or 7. daies together. Therefore, if you find cause to doubt whether your Star be a Planet, or a fixed Star, you may for the help of your understanding confer with some of the former Rules, unless you are willing to wait 8 or 9 daies longer, and so by observation of its motion resolve your self, Or,

Fifthly, you may apply your self to an Ephemeris for that Year, and see if on that day you find any Planet in the degree and minute of the Zodiack you see the Star you question in Heaven; and if there be no Planet in that degree of the Zodiack, you may conclude it is no Planet, but a fixed Star.

PROB. XLV.

How to hang the Terrestrial Globe in such a position that by the Suns shining upon it you may with great delight at once behold the demonstration of many Principles in A­stronomy, and Geography.

TAke the Terrestrial Ball out of the Horizon, and fasten a thred on the Brazen Meridian to the degree of the La­titude of your Place; by this thred hang the Globe in a place where the Suns Beams may have a free access to it; Then direct the Poles of the Globe to their proper Poles in Heaven, the North Pole to the North, and the South Pole to the South; and with a thred fastned to either Pole, brace the Globe, so, that it do not turn from his position: then bring your Habitation to the Meridian; so shall your Terrestrial Globe be Rectified to correspond in all respects with the Earth it self; even as in Prob. 44. the Celestial Globe doth; the Poles of the Globe, to the Poles of the World; the Meridian of the Globe, to the Meridian of the World; and the several Regi­ons on the Globe made Correspondent to the same Regions on the Earth: So that with great delight you may behold,

1. How the counterfeit Earth (like the true one) will have one Hemisphear Sun shine light, and the other shadowed, and as it were dark. By the shining Hemisphear you may see that it is Day in all Places that are scituate under it; for on them the Sun doth shine; and that it is Night at the same time in those Places [Page 90] that are situate in the shadowed Hemisphear; for on them the Sun doth not shine; and therefore they remain in darkness.

2. If in the middle of the enlightned Hemisphear you set a Spherick Gnomon Perpendicularly, it will project no shadow, but shews that the Sun is just in the Zenith of that Place; that is, di­rectly over the heads of the Inhabitants of that Place: and the point that the Spherick Gnomon stands on, being removed to the Meridian, shews the Declination of the Sun on the Meridian for that Day.

3. If you draw a Meridian line from one Pole to the other, in all Places under that line, it is Noon: in those Places scituate to the West, it is Morning; for with them the Sun is East: and in those Places scituate to the East, it is Evening; for with them the Sun is West.

4: Note the degree of the Equator where the enlightned He­misphear is parted from the shadowed; for the number of de­grees of the Equator intercepted between that degree and the Meridian of any Place, converted into Hours (by accounting for every 15. degrees 1. Hour) shews, if the Sun be Eastwards of that Place, how long it will be ere the Sun Rises, Sets, or comes to the Meridian of that Place: or if the Sun be Westward of that Place, how long it is since the Sun Rose, or Set, or was at the Meridian of that Place.

5. The Inhabitants of all Places between the enlightned and shadowed Hemisphear, behold the Sun in the Horizon: Those Westwards of the Meridian Semi-Circle drawn through the mid­dle of the enlightned Hemisphear behold the Sun Rising: Those in the East, see it Setting.

6. So many degrees as the Sun reaches beyond either the North or South Pole, so many degrees is the Declination of the Sun, either Northwards or Southwards: and in all those Places comprehended in a Circle described at the termination of the Sun-shine, about that Pole, it is alwaies Day, till the Sun decrease in Declination: for the Sun goes not below their Horizon: as you may see by turning the Globe about upon its Axis: and a the opposite Pole at the same distance, the Sun-shine not reach­ing thither, it will be alwaies Night, till the Sun decrease in Declination: because the Sun Rises not above their Horizon.

7. If you let the Globe hang steddy, you may see on the East side of the Globe, in what Places it grows Night; and on the [Page 91] West side the Globe how by little and little the Sun encroaches upon it; and therefore there makes it Day.

8. If you make of Paper or Parchment a narrow Girdle, to begirt the Globe just in the Equinoctial, and divide it into 24. e­qual parts, to represent the 24. hours of Day and Night, and mark it in order with I, II, III, &c. to XII. and then be­gin again with I, II, III, &c. to the other XII. you may by placing one of the XII s. upon the Equinoctial under the Meridian of your Place, have a continual Sun-Dyal of it, and the hour of the Day given on it, at once in two places; one by the parting the enlightned Hemisphear from the shadowed on the Eastern side, the other by the parting the enlightned Hemisphear from the shadowed on the Western side the Globe. Much more might be said on this Probleme: But the Ingenuous Artist may of himself find out diversities of Speculations: therefore I forbear.

PROB. XLVI.

To know by the Terrestrial Globe in the Zenith of what Place of the Earth the Sun is.

THis may be performed by the former Probleme in the Day time, if the Sun shines: but not else. But to find it at all times, do thus. Bring the Place of your Habitation to the Meri­dian, and the Index of the Hour-Circle to 12; Then turn the Globe Eastwards, if Afternoon, or Westwards, if Before Noon, till the Index of the Hour-Circle pass by so many Hours from 12. as your Time given is, either before or After-Noon: so shall the Sun be in the Zenith of that Place where the Meridian intersects the Parallel of the Suns Declination for that Day.

Example.

May 10 at ¾ of an hour past 4. a clock After Noon▪ I would know in what Place of the Earth the Sun is in the Ze­nith. My Habitation is London. Therefore I bring London to the Meridian, and the Index of the Hour-Circle to 12. and because it is After Noon: I turn the Globe Eastwards, till the Index passes through 4 hours and 3 quarters, or (which is all one) till 70 degrees 15 minutes of the Equator pass through the Me­ridian. [Page 92] Then I find by Prob. 5. the Suns Declination is 20. de­grees 5. minutes which I find upon the Meridian, and in that Place just under that degree and minute on the Globe, the Sun is in the Zenith: which in this Example is in the North East Cape of Hispaniola.

Having thus found in what Place of the Earth the Sun is in the Zenith. Bring that Place to the Meridian, and Elevate its respective Pole according to its respective Elevation; so shall all Places cut by the Horizon have the Sun in their Horizon: Those to the Eastwards shall have the Sun Setting; those to the Westward shall have it Rising in their Horizon: those at the Intersection of the Meridian and Horizon under the Elevated Pole, have the Sun in their Horizon at lowest, but Rising; those at the Intersection of the Meridian and Horizon under the Depressed Pole, have the Sun in their Horizon at highest, but Setting. Thus in those Countries that are above the Horizon it is Day-light, and in those but 18 degrees below the Horizon, it is Twilight: But in those Countries further below the Horizon it is at that time dark Night: And those Countries within the Parallel of the same number of degrees from the Elevated Pole that the Suns Declination is from the Equinoctial, have the Sun alwaies above the Horizon, till the Sun have less Respective Declination then the Elevated Pole; and those within the same Parallel of the Depressed Pole have the Sun alwayes below their Horizon, till the Sun inclines more towards the Depressed Pole; As you may see by turning about the Globe; for in this position, that portion of the Globe intercepted between the Ele­vated Pole, and the Parallel Circle of 20. degrees 5. minutes from the Pole doth not descend below the Horizon: neither doth that portion of the Globe intercepted between the Depressed Pole and the Parallel Circle within 20. degrees 5. minutes of that Pole, ascend above the Horizon.

PROB. XLVII.

To find in what different Places of the Earth the Sun hath the same Altitude, at the same time.

FInd by the former Probleme in what Place of the Earth the Sun is in the Zenith, and bring that Place on the [Page 93] Globe to the Zenith, and on the Meridian [there] screw the Quadrant of Altitude, and turn it about the Horizon, de­scribing degrees of Almicantars thereby, as by Prob. 23. and all those Countries in any Almicantar on the Globe shall have the Sun Elevated the same number of degrees above their Horizon. Thus those Countries in the tenth Almicantar shall have the Sun Elevated 10. degrees above their Horizon; those in the 20 th Almicantar shall have the Sun Elevated 20 degrees above their Horizon; those in the 30 th, 30. degrees &c. So that you may see, when the Sun is in the Zenith of any Place, All the Countries or Cities in any Almicantar have the Sun in one heighth at the same time above their Horizon. But to find in what different Places the Sun hath the same heighth at the same time, as well Before or After Noon, as at Full Noon; and that in Countries that have greater Latitude then the Suns greatest Declination, (and therefore cannot have the Sun in their Zenith,) requires another Operation.

Therefore, Elevate its respective Pole according to your re­spective Latitude; and let the Degree of the Brazen Meridian which is in the Zenith represent your Habitation, and the degree of the Ecliptick the Sun is in represent the Sun: Then bring the Sun to the Meridian, and the Index of the Hour-Circle to 12, and turn the Globe Eastwards, if Before Noon, or Westwards, if After Noon, till the Index point to the Hour of the Day: Then place the lower end of the Quadrant of Altitude to the East point of the Horizon, and move the upper end (by sliding the Nut over the Meridian) till the edge of the Quadrant touch the place of the Sun: Then see at what degree of the Meridian the upper end of the Quadrant of Altitude touches the Meridian and substract that number of Degrees from the Latitude of your Place, and count the number of remaining degrees on the Meridi­an, on the contrary side the degree of the Meridian where the up­per end of the Quadrant of Altitude touches the Meridian, and where that number of degrees ends on the Meridian, in that La­titude and your Habitations Longitude, hath the Sun the same heighth at the same time.

Example.

May 10. at 53. minutes past 8. a clock in the Morning I [Page 94] would know in what Place the Sun shall have the same Alti­tude it shall have at London, London's Latitude found by Prob. 1. is 51½ degrees Northwards: And because the Elevation of the Pole is equal to the Latitude of the Place (as was shewed Prob. 15.) Therefore I Elevate the North Pole 51½ degrees, so shall 51½ degrees on the Meridian be in the Zenith: This 51½ degrees on the Meridian represents London. The Suns Place found by Prob. 3. is ♉ 29. Therefore I bring ♉ 29 to the Meridian, and the Hour Index to 12. on the Hour Circle: Then I turn the Globe Eastwards (because it is before Noon) till the Index point at 8. hours 53 minutes on the Hour-Circle, and place the lower end of the Quadrant of Altitude to the East point in the Horizon, and slide the upper end either North or Southwards on the Meridian till the graduated edge cut the degree of the Ecliptick the Sun is in: Then I examine on the Meridian what degree the up­per end of the Quadrant of Altitude touches; which in this example, I find is 38½ degrees. Therefore I substract 38½ from 51½ Londons Latitude, and there remains 13. Then counting on the Meridian 13. degrees backwards, from the Place where the Quadrant of Altitude touched the Meridian, I come to 25½ on the Meridian, Northwards. Therefore I say, In the North Latitude of 25½ degrees, and in the Longitude of Lon­don (which is in Africa, in the Kingdom of Numidia) the Sun May 10. at 53. minutes past 8. a clock in the Morning hath the same Altitude above the Horizon it hath here at London.

The Quadrant of Altitude thus applyed to the East point of the Horizon makes right angles with all points on the Meridian, even as all the Meridians proceeding from the Pole, do with the Equator: therefore the Quadrant being applyed both to the East point, and the Suns Place, projects a line to intersect the Me­ridian Perpendicularly in equal degrees; from which intersection the Sun hath at the same time equal Heighth, be the degrees few or many; for those 5. degrees to the Northwards of this in­tersection, have the Sun in the same heighth that they 5 degrees to the Southwards have it: and those 10, 20, 30. degrees, more, or less, to the Northwards, have the Sun in the same heighth that they have that are 10, 20. 30. degrees more or less to the Southwards: So that this Prob. may be performed ano­ther way more easily, with your Compasses, Thus: Having first rectified the Globe, and Hour Index, Turn about the Globe till [Page 95] the Hour Index point to the Hour of the Day; Then pitch one foot of your Compasses in the Suns Place, and extend the other to the degree of Latitude on the Meridian, which in this exam­ple is 51½ degrees North; then keeping the first foot of your Compasses on the degree of the Sun, turn about the other foot to the Meridian, and it will fall upon 25½. as before.

Blaew commenting upon this Probleme, takes notice how grosly they ere that think they can find the heighth of the Pole at any Hour of the Day, by the Suns height: because they do not consider that it is impossible to find the Hour of the Day, unless they first know the height of the Pole.

PROB. XLVIII.

To find the length of the Longest and Shortest Artificial Day or Night.

THe Artificial Day is that space of Time which the Sun is above the Horizon of any Place: and the Artifici­al Night is that space of Time which the Sun is under the Horizon of any Place. They are measured in the Hour Circle, by Hours and Minutes.

There is a constant unequallity of proportion in the Length of these Daies and Nights; which is caused both by the alteration of the Suns Declination, and the difference of the Poles Elevation.

Those that inhabite on the North side the Equator have their longest Day when the Sun enters ♋; and those that inhabite on the South side the Equator, have their longest Day when the Sun enters ♑. But to know how long the longest Day is in any North or South Elevation, Raise the North or South Pole ac­cording to the Elevation of the Place, and bring ♋ for North Elevation, or ♑ for South Elevation to the Meridian, and the Index of the Hour Circle to 12. Then turn the Globe about till ♋ for North Elevation, or ♑ for South Elevation, come to the West side the Horizon and the number of Hours and mi­nutes pointed at on the Hour Circle, doubled, is the number of Hours and minutes of the Longest Day.

The length of the Night to that Day is found by substracting the length of the day from 24. for the remainder is the length of the Night.

[Page 96] The shortest Day in that Latitude is the length of the shortest Night, found as before. And the longest Night is of the same length with the longest Day.

Example.

I would know the length of the longest Day at London. There­fore I Elevate the North Pole 51½ degrees, and bring ♋ to the Meridian, and the Index of the Hour Circle to 12. Then I turn ♋ to the Western side the Horizon, and find the Index point at 8. hours 18. minutes, which being doubled makes 16. hours 36. minutes, for the length of the longest Day here at London.

PROB. XLIX.

To find how much the Pole is Raised, or Depressed, where the longest Day is an Hour longer or shorter then it is in your Habitation.

REctifie the Globe to the Latitude of your Place; and make a prick at that point of the Tropick which is at the Meri­dian; I mean at the Tropick of ♋, if your Habitation be on the North side the Equator; or ♑, if your Habitation be on the South side the Equator: And if you would know where the longest Day is just an hour longer then it is at your Habitation, turn the Globe to the Westward till 7½ degrees of the Equato [...] pass through the Meridian, and make there another prick on the Tropick: Then turn about the Globe till the first prick come to the Horizon; and move the Meridian through the notches of the Horizon till the second prick on the Tropick come to the Ho­rizon; so shall the arch of the Meridian contained between the Elevation of your Place, and the Degree of the Meridian at the Horizon, be the number of Degrees that the Pole is Elevated higher then it is in your Latitude.

Example.

I would know in what Latitude the longest Day is an Hour longer then it is at London. Therefore I Rectifie the Globe to 51½ deg. and where the Meridian cuts the Tropick of ♋ I make [Page 97] a prick; then I note what degree of the Equator is at the Meri­dian, and from that degree on the Equator count 7½ degrees to the Eastwards, and bring those 7½ degrees to the Meridian also; and again where the Meridian cuts the Tropick of ♋ I make ano­ther prick, so shall 7½ degrees of the Tropick be contained be­tween those [...] pricks. Then I turn the Globe about, till the first prick comes to the Horizon, and (with a Quill thrust be­tween the Meridian and the Ball) I fasten the Globe in this posi­tion: Afterwards I move the Meridian through the [...] of the Horizon, till the second prick rises up to the Horizon, and then I find 56½ degrees of the Meridian cut by the Superficies of the Horizon: Therefore I say, In the Latitude of 56½ de­grees, the longest Day is an Hour longer then it is here at Lon­don.

But if you would know in what Latitude the Dayes are an Hour shorter, you must make your second prick 7½ degrees to the Westwards of the first, and after you have brought the first prick to the Horizon, you must depress the Pole till the se­cond prick descends to the Horizon: so shall the degree of the Meridian at the Horizon, shew in what Elevation of the Pole the Daies shall be an Hour shorter.

By this Probleme may be found the Alteration of Climates: for (as was said in the Definition of Climates, Book 1. fol. 28.) Climates alter according to the half-hourly increasing of the Longest Day: therefore the Latitude of 56½ degrees having its Daies increased an whole Hour) is distant from the Latitude of London by the space of two Climates.

PROB. L.

The Suns Place given, to find what alteration of Declina­tion be must have to make the Day an Hour longer, or shorter: And in what number of Da [...]es it will be.

REctifie the Globe to the Latitude of the Place, and b [...]ing the Suns place to the East side the Horizon, and note against what degree of the Horizon it is: then bring one of the Colures to intersect the Horizon in that degree of the Horizon, and at the point of Intersection make a prick in the Colure; and observe what degree of the Equator is then at the Meridian: Then turn the Globe Westward, if the Daies shorten; but Eastwards, if [Page 98] they lengthen, till 7½ degrees of the Equator pass through the Meridian, and where the Horizon intersects the same Colure, make another prick in the Colure: Afterwards bring the Colure to the Meridian, and count the number of degrees between the two pricks, for so many degrees must the Suns Declination alter to lengthen or shorten the Day an Hour.

Example.

The Suns Place is ♉ 10. I would know how much he must alter his Declination before the Day is an Hour longer here at London. Therefore I rectifie the Globe to the Latitude of London, and bring ♉ 10. to the East side the Horizon, and find it against 24½ degrees from the East point: therefore I bring one of the Colures to this 24½ degrees, and close by the edge of the Horizon I make a prick with black lead, in the Colure: then keeping the Globe in this position, I look what degree of the E­quator is then at the Meridian, and find 250¼, and because the Daies lengthen, I turn the Globe Eastwards, till 7½ degrees from the foresaid 250¼ pass through the Meridian: then keeping the Globe in this position I make another prick in the Colure, and bringing this Colure to the Meridian, I find a little more then 5 degrees of the Meridian contained between the two pricks: therefore I say, when the Sun is in ♉ 10. degrees, he must alter his Declination a little more then 5 degrees, to make the Day an Hour longer.

Now to know in what number of Daies he shall alter this Declination, you must find the Declination of the two pricks on the Colure as you found the Suns Declination by Prob. 5. and the Arch of the Ecliptick that passes through the Meridian while the Globe is turned from the first pricks Declination to the second pricks Declination, is the number of Ecliptical de­grees that the Sun is to pass while he alters this Declination: and the degree of the Ecliptick then at the Meridian is (with respect had to the Quarter of the Year) the place the Sun shall have when its Declination shall be altered so much as to make the Day an Hour longer

Thushaving the Suns first place given, and its second place found▪ you may by finding those two places on the Plain of the Horizon, also find the number of Daies comprehended between them, as you are taught by the fourth Probleme.

[Page 99] This Probleme thus wrought for different Times of the Year, will shew the falacy of that Vulgar Rule which makes the Day to be lengthned or shortned an Hour in every Fifteen Daies: when as the lengthning or shortning of Daies keeps no such equality of proportion: for when the Sun is neer the Equinoctial points the Daies lengthen or shorten very fast: but when he is neer the Tropical points, very slowly.

PROB. LI.

Of the Difference of Civil and Natural Daies, commonly called the Equation of Civil Daies. And how it may be found by the Globe.

THe Civil Day is that space of Time containing just 24. Hours, reckoned from 12 a clock on one Day to 12 a clock the next Day; in which space of Time the E­quinoctial makes upon the Poles of the World a Di­urnal Revolution. The Natural Day is that space of Time wherein the Sun moveth from the Meridian of any Place to the same Meridian again. These Daies are at one time of the Year longer then at another; and at all Times longer then the Civil Daies. There is but smal discrepancy between them, yet some there is, made by a two-fold Cause. For first, The Suns Appa­rent motion is different from his true motion; He being much slower in his Apogeum then he is in his Perigeum: For when the Sun is in his Apogeum he scarce moves 58 minutes from West to East in a Civil Day, but when he is in his Perigeum he moves above 61 minutes in a Civil Day: and therefore increases his Right Ascension more in equal Time.

The second Cause is the difference of Right Ascensions answe­rable to equal parts of the Ecliptick: for about ♋ and ♑ the diffe­rences of Right Ascensions are far greater then about ♈ and ♎: for about ♈ and ♎ the Right Ascension of 10. degrees is but 9. degrees 11. minutes; but about ♋ and ♑ the Right Ascension of 10 degrees will be found to be 10. degrees 53. minutes, as by the Globe will appear.

But because of the smalness of the Globes graduation▪ you can­not actually distinguish to parts neer enough for the solution of this Probleme, if you should enquire the difference in length of two single Daies; it will be requisite to take some number of [Page 100] Daies together; Suppose 20. Therefore find by Prob. 3. the Places of the Sun for the beginning and ending of those Daies you would compare; and find the Right Ascensions answerable to each place in the Ecliptick; and also the differences of Right Ascensions answerable to the Suns motion in each number of Daies: Then compare the differences of Right Ascensions toge­ther; and by substracting the lesser from the greater, you will have the number of degrees and minutes of the Equator that have passed through the Meridian more in one number of Daies then in the other number of Daies: which degrees of the Equa­tor converted into Time, is the number of minutes that the one number of Daies is longer then the other number of Daies.

Example.

I would know what difference of Time there is in the length of the first 20. Daies of December, and the first 20, Daies of March. I find by Prob. 3. the Suns place December 1, is [...] 19. 45. at the end of 20 Daies. viz. on the 21 Day his place is [...] 10. 11. The Suns place March 1. is ♓ 21. 16. at the 20. Daies end, viz. March 21, his place is ♈ 11. 3.

I find by Prob. 26. the Right Ascension answerable to ♐ 19. 45 is 258. 10.
♑ 10. 11 280. 25.
♓ 21. 16 352. 00.
♈ 11. 3 9. 40.

and the difference of Right Ascensions contained between the first Day in each Moneth, and the 21 of the same Moneth, by substracting the lesser from the greater is for

258. 10. And for 352. 00.
280. 25. 9. 40.
22. 15 17. 40.

But note, because the Vernal Colure, where the degrees of Right Ascension begin and end their account, is intercepted is the Arch of the Suns motion from the first to the 21. of March, therefore instead of substracting the lesser number of degrees of Right Ascension from the greater, viz. 9. 40 from 35. 2. I do for finding the difference of the Right Ascensional arch of the Suns motion in those 20 Daies, sustract the foresaid 352 degrees from 360, and the remains is 8. which is the difference of Right As­cension from ♓ 21, 16. to the Equinoctial Colure: to which 8 [Page 101] adding 9 degrees 40 minutes, the Right Ascension from the E­quinoctial Colure. to ♈ 11. 3. it makes 17 degrees 40. minutes for the difference of Right Ascensions between ♓ 21, 16. and ♈ 11. 3 Then I find the difference of this Difference of Right Ascension, by substracting the less from the greater, viz. 17. 40. from 22. 15. and the remains is 4. degrees 35. minutes, for the number of degrees and minutes of the Equator that pass through the Meridian in the first 20 Daies in the Moneth of December more then in the first 20 Daies of the Moneth of March: which 4. degrees 35. minutes converted into Time, gives 19. minutes, that is, a quarter of an Hour and 4 minutes that the first 20 Daies of December aforesaid, are longer then the first 20 Daies of March.

PROB. LII.

How to find the Hour of the Night, when the Moon shines on a Sun Dyal, by help of the Globe.

REctifie the Globe, and find by Prob. 54. or an Ephemeris, the Moons place at Noon: Bring it to the Meridian, and the Index of the Hour Circle to 12. and turn about the Globe till the Index of the Hour Circle points to the same Hour the shade of the Moon falls on, on the Sun Dyal. Then by Prob. 3. find the Suns place at Noon, and see how many degrees of Right Ascension are contained between the Suns place and the degree of the Equator at the Meridian, when the Index of the Hour Cir­cle is brought to the Hour the Moon shines on in the Sun Dyal; for those number of degrees converted into Time, shall be the Time from Noon, or the Hour of the Night. Only note, Respect must be had to the motion of the Moon from West to East, for so swift is her mean motion, that it is accounted to be above 12. degrees in 24. Hours; that is 6 degrees in 12 Hours, 3 degrees in 6 Hours, &c. and this also converted into Time, as aforesaid, you must add proportionably to the Time found from Noon; and the sum shall give you the true Hour of the Night.

Example.

Here at London, I desired to know the Hour of the Night Ja­nuary 6. this present Year 1658. The Moons place found by [Page 102] an Ephemeris, or for want of an Ephemeris, by Prob. 54. is in ♊ 21. degree 22, minutes; Therefore I rectified the Globe to Lon­dons Latitude, and brought ♊ 21. 22. minutes to the Meridian, and the Index of the Hour Circle to 12. then by Prob. 3. I found the Suns place in ♑ 26. degrees 46. minutes, and by Prob. 26. I found his Right Ascension to be 300 degrees; Then I turned about the Globe, till the Index of the Hour Circle pointed at 10 Hours, and at the degree of the Equator at the Meridian I made a prick; then I counted the number of degrees of the Equater contained between the foresaid 300 deg. and this prick and found them 111¼ degrees which converted into Time, by allowing 15 degrees for an Hour, gives 7 hours, 25 minutes, Time from Noon: which if the Moons motion were not to be considered, should be the immediate Hour of the Night: But by the Rule a­foresaid, the Moons motion from West to East, in 7 hours 25 mi­nutes is 3 degrees 42 minutes, and this 3 degrees 42 minutes be­ing converted into Time, is 14 minutes more, which being added to 7 hours 25 minutes: make 7 hours 39 minutes, for the true Hour of the Night.

PROB. LIII.

To find the Dominical Letter, the Prime, Epact, Easter Day, and the rest of the Moveable Feasts, for ever.

THough these Problemes cannot be performed by the Globe, because of the several changes, and irregular accounts that their Rules are framed upon, yet because they are of frequent and Vulgar use, and for that the so­lution of many other Questions will have dependency on the knowledge these; Therefore I have thought fit here to inserte this Table of M r Palmers, by which you may find them All.

I shall not insist upon the Reasons of the several changes of Letters, and Numbers, Himself having already very learnedly handled that subject, in his Book of the Catholick Planisphear, Book 1. Chapter 11. (to which I refer you) Neither shall I need to give you any other Instructions for finding what is here proposed, then what himself hath given in his fourth Book, Chap­ter 66, and part of 67. Therefore take it as he there delivers it.

[Page 103] An Example, shall serve here instead of a Rule. For the Year 1657. I would know all these: wherefore I seek the Year 1657. in the Table of the Suns Cycle, and over against it, I find 14. for the Year of the Cycle of the Sun, and D for the Dominical Letter. And note here, that every Leap-year hath 2 Dominical Letters (as 1660, hath A G) and the first (viz. A) serveth that Year till February 25, and the second (G) for the rest of the Year. And note that these Letters go alwayes backwards when you count forwards (as B A, then G F, &c. not F G, and, then A B) as you may see by the Table.

Then in the Table of the Cycle of the Moon, I have for the Year 1657. the Prime 5. the Epact 25. Those had, I go to the Table for Easter, and seek there in the first rank the Prime 5, and

[figure]

[Page 104] under it in the middle rank stands E; that is not my Dominical Letter; therefore I seek not backward, but alwayes forward in the middle rank, till I come to my Dominical Letter D. and under it I find in the third rank March 29. upon which Easter day falls this Year 1657. The rest of the moveable Feasts may be had by their distances from Easter, which are alwayes the same. One­ly for Advent Sunday, remember that the next Sunday after November 26 is Advent Sunday. Read Book 1. 11. and that will sufficiently instruct you with this Example.

To find the Age of the Moon.

Remember first that the Epact begins with March, which must be here accounted the first Moneth: Then if you add to the Epact the number of the Moneth current, and the number of the day of the Moneth current, the sum or the excess above 30, is the Moons age.

Example. January 20. 1656. According to the accompt of the Church of England, (who begin the Year with March 25. which was the Equinoctial day about Christ time) the Epact is 14. January is the 11 th Moneth, and the 20 th day is proposed; now add 14. 11. and 20. together, they make 45. out of which I take 30. and there remains 15, the Moons age.

PROB. LIV.

The Age of the Moon given, to find her place in the Eclip­tick according to her mean motion.

THis Probleme may be performed exact enough for Com­mon uses by the Globe, but in regard it only shews the Moons place in the Ecliptick according to her meat motion, it will often fail you some few degrees of her true Place. The work is thus,

First set figures to every twelth degree of the Equinoctial, ac­counted from the Equinoctial Colure, marking them with 1, 2, 3, 4. &c. to 30 which will end where you began viz. at the E­quinoctial Colure again: so shall the Equinoctial be divided into 30 equal parts, representing the 30 Dayes of the Moons Age These figures (to distinguish them from the degrees of the Equator) were best be writ with Red Ink.

[Page 105] When you would enquire the Moons Place, Elevate the North Pole 90 degrees, that is, in the Zenith, so shall the Equator ly in the Horizon: Then bring the Equinoctial Colure against the Day of the Moneth in the Horizon, so shall the Moons Age written in Red figures, stand against the Signe and degree in the Horizon that the Moon is in at that Time.

Example.

September 28. 1658. I would know the Moons place in the Ecliptick, she being then 12 Daies old. Therefore I Elevate the North Pole 90 degrees above the Horizon, and turn the Globe about till the Equinoctial Colure come to September 28. in the Circle of Daies on the Horizon; then looking against what Signe and degree of the Ecliptick Circle in the Horizon the 12 th division in Red figures stands, I find ♓ 9. which is the Signe and degree the Moon is in, according to her mean Motion.

This Probleme may be applyed to many Uses: for, having the Moons Place you may find the Time of her Rising, Southing, Setting, and Shining &c. by working with her, as you were taught to work with the Sun, in several fore-going Problemes, proper to each purpose.

PROB. LV.

Having the Longitude and Latitude, or Right Ascension and Declination of any Planet, or Comet, to place it on the Globe, to correspond with its place in Heaven.

PLanets and Comets cannot be placed on the Globe so as their places will long retain correspondence with their places in Heaven; Because as was said Chap. 44. they have a continual motion from West to East upon the Poles of the Ecliptick: yet never-the-less you may by having their Longitude and Latitude, or Right Ascension and Declinati­on, for any set Time, place a Mark for them on the Globe, either with Ink if your Globe be Varnisht, for then you may with a wet finger wipe it off again; or with Black-lead, if it be not Var­nisht, and then you may rub it out again with a little White [Page 106] Bread: which Mark for that Time, will as effectually serve you to work by, as any of the Fixed Stars placed on the Globe will do.

Therefore if the Longitude and Latitude of any Planet, or Comet, be given; Do thus, Elevate the North Pole, if the La­titude given be North; but if the Latitude given be South, E­levate the South Pole 66 ½ degrees; and place the Pole of the Ecliptick in the Zenith, and over it screw the Quadrant of Alti­tude: so shall the Ecliptickly in the Horizon; and the Qua­drant of Altitude being turned about the Horizon shall pass through all the Degrees of Longitude: Then find the point of given Longitude in the Ecliptick, and bring it to the Quadrant of Altitude, and hold it there: Then count upwards on the Quadrant of Altitude the number of degrees and minutes of gi­ven Latitude, and at the point where the number ends, close to the Quadrant of Altitude, make a smal Prick, and that Prick shall represent the Planet or Comet you were to place on the Globe.

If it be the Right Ascension and Declination of a Planet or Comet that is given; you must find the degree and minute of Right Ascension on the Equinoctial, and bring it to the Meridian, and keep the Globe there steddy; then find the degree and mi­nute of Declination on the Meridian, and under that degree and minute on the Globe make a Prick, and that Prick shall repre­sent the Planet, or Comet, as aforesaid,

If it be ♄ or ♃ that this Prick is to represent, it may stand on the Globe sometimes a Week or a Fortnight, without much difference from the Planets place in Heaven. But if the Prick were to represent the other Planets, you must (in regard of their swift motion) alter it very often, especially for the Moon; for so swift is her motion, that in every two Hours she alters about a degree in Longitude.

Having thus placed this Mark on the Globe, you may find out the Time of its several Positions, and Aspects, if you work by it as you are directed to work by the Sun, in the several re­spective Problemes throughout this Book.

The End of the Second Book.

The Third BOOK, Being the Practical Use of the GLOBES. Applyed to the Solution of Problemes In the Art of NAVIGATION.

PRAEFACE.

BEcause the Art of Navigation consists aswell in the knowledge of Astronomical and Geographical Problemes, as in Problemes meerly Nautical; Therefore I must desire the Artist to seek in the last Book such Problemes as are only Astronomical or Geographi­cal. For my Designe is here to collect such Problemes as are only used in the Art of Navigation, some few particulars ex­cepted, as for finding Latitude, Longitude, Course; Di­stance, &c. Which though they are handled in than Book, yet for their exceeding Vtility in the Art of Navigation, and for that what there is given, cannot alwayes be had to work by; therefore in this Book I have mentioned divers other Observations, which being made or had, you may by the Rules proper for each Observation find what shall be pro­posed.

PROB. I.

The Suns Amplitude and Difference of Ascension gi­ven, to find the Heigth of the Pole, and Declination of the Sun.

ELevate the Pole so many degrees as the Difference of the Suns Ascension is, and screw the Quadrant of Altitude to the Zenith, and bring the first point of ♈ to the Me­ridian, then number on the Quadrant of Altitude up­wards the complement to 90. of the Suns Amplitude, and move the Quadrant of Altitude till that number of degrees cuts the E­quator; So shall the Quadrant cut in the Horizon the degree of the Pole Elevation; and in the Equator the degree of the Suns Declination.

Example.

The difference of Ascension is 27. degrees 7. minutes. There­fore I Elevate the Pole 27. degrees 7. minutes above the Hori­zon, and screw the Quadrant of Altitude to 27. degrees 7. mi­nutes, which is in the Zenith: then I bring the first point of ♈ to the Meridian, and number on the Quadrant of Altitude up­wards 56. degrees 40. minutes, the Complement of the Suns Amplitude, and bring that degree to the Equator; then I see in what degree of the Horizon the Quadrant cuts the Horizon, and find 51 ½, which is the Elevation of the Pole: then looking in what degree of the Equator the Quadrant of Altitude cuts the Equator, I find 20 degrees, 5 min. which is the Declination of the Sun at the same Time.

PROB. II.

The Suns Declination and Amplitude given, to find the Poles Elevation.

ELevate the Pole so many degrees as the Complement of the Suns Amplitude is; and screw the Quadrant of Altitude [Page 109] in the Zenith, and bring the first point of ♈ to the Meridian: Then count on the Quadrant of Altitude to the Degree of the Suns Declination, and bring that degree to the Equinoctial; and the degree of the Equinoctial cut by that degree of the Quadrant of Altitude, is the degree of the Poles Elevation.

Example.

The Suns Amplitude is 33. degrees 20. minutes, his Decli­nation is 20 degrees 5 minutes, his Complement of Amplitude to 90. is 56 degrees 7 minutes. Therefore I Elevate the Pole 56. degrees 7 minutes above the Horizon, and screw the Quadrant of Altitude to 56 degrees 7 minutes which is in the Zenith: Then I bring the first point of ♈ to the Meridian, and number on the Quadrant of Altitude upwards 20. deg. 5 min. for the Suns Declination, this 20 th degree 5 minutes, I bring to the Equi­noctial, and find it cut there 51 ½. degrees, for the Heigth of the Pole.

PROB. III.

The Suns Declination and Hour at East given, to find the Heigth of the Pole.

ELevate the Pole so many degrees as the Suns Declination is, and screw the Quadrant of Altitude in the Zenith: Then convert the Hours or minutes past 6. given into degrees; by allowing 15 degrees for every Hour of Time, and for every minute of Time 15 minutes of a Degree; and number those degrees or minutes in the Horizon from the East Southwards; so shall the Degree of the Quadrant of Alti­tude cut by the Equator be the Complement of the heigth of the Pole.

Example.

The Suns Declination is 20 deg. 5 min. Therefore I Elevate the Pole 20 degrees 5 minutes, and also screw the Quadrant of Altitude to [...]0 degrees 5 minutes which is in the Zenith: the Hour the Sun comes to be at East is 8 a clock 53 minutes, that is, 1 Hour 7 minutes after 6. Therefore I convert 1 Hour 7 mi­nutes [Page 110] into Degrees, as before, and it gives 16 degrees 50 mi­nutes; which number of degrees and minutes I count from the East point Southwards, and thither I bring the Quadrant of Al­titude: Then I look in what degree of the Quadrant of Alti­tude, the Equator cuts, and find 38 ½, which is the Complement of the Poles Heigth, viz. 51 ½ degrees for the Heigth of the Pole.

In this Probleme the Declination of the Sun and Elevation of the Pole bears the same Denomination of either North or South, for when the Declination and the Elevation are different the Sun cannot come to the East point.

PROB. IIII.

The Declination of the Sun and his Altitude at East gi­ven, to find the Heigth of the Pole.

ELevate the Pole to the Complement of the Suns Altitude, and screw the Quadrant of Altitude to the Zenith: Then bring the Equinoctial point ♈ to the Meridian, and number on the Quadrant of Altitude the degrees of the Suns Declination, and bring that degree to the Equinoctial, and note the degree it cuts; for its Complement to 90 is the Heigth of the Pole.

Example.

May 10. The Suns Declination is 20 degrees 5 minutes; His Altitude at East is 25 degrees 55 minutes here at London: I en­quire the Heigth of the Pole. Therefore I substract 20. 5 min. from [...]0 the remains is 69 deg. 55 min. for its Complement; wherefore I bring 69 deg. 55 min. of the Meridian to the Horizon; and to 69 deg. 55 min. which is in the Zenith, I screw the Quadrant of Alti­tude then I bring ♈ to the Meridian, and count on the Quadran: of Altitude upwards 20 deg. 5 min, and move it about the Equi­noctial till those 20 deg. 5 min. touch the Equinoctial, which I find to be in 38 ½ degrees, Therefore I substract those 38 ½ from 90, and the remains is 51 ½ degrees, Therefore I say the Pole here at London is Elevated 51 ½ degrees.

The Declination and the Elevation is alwaies the same, either North or South, for when they alter their Denomina ions the Sun at East can have no Altitude, neither can it indeed reach the [Page 111] East point: and therefore in this example, because the Declina­tion of the Sun is North, it is the North Pole that is Elevated here at London.

To perform the same otherwise, with a pair of Compasses.

Take off with your Compasses from the Equator or Qua­drant of Altitude the number of degrees of Altitude observed, and place one foot at the beginning of ♈ on the inner edge of the Horizon, and extend the other directly upwards towards the Ze­nith: Then move the Brazen Meridian through the notches of the Horizon till the other point of your Compasses (respecting the Zenith) reach the Parallel of the Suns Declination: So shall the number of degrees on the Meridian be the number of degrees that the Pole is Elevated above the Horizon; and is ei­ther North or South according as the Suns Declination is: as before.

This may yet otherwise be performed with the Quadrant of Altitude, by taking the Nut off the Meridian, and laying the edge of its Index (specified in Chap. 1. Sect. 6. of the first Book) exactly on the East line of the Horizon: for when that lies straight between the point of East on the outer Verge of the Ho­rizon, and the beginning of ♈ in the inner Verge of the Horizon, then shall the upper end of the Quadrant of Altitude point di­rectly to the Zenith: and if then you turn the Meridian through the notches of the Horizon till the Suns Altitude on the Qua­drant of Altitude cut the Parallel of Declination, you will have on the Meridian the heigth of the Pole: as before.

PROB. V.

By the Suns Declination and Azimuth at 6. of the Clock given, to find the Heigth of the Pole, and Almicantar at 6.

ELevate the Pole so many degrees as the Suns Azimuth is at 6. and screw the Quadrant of Altitude in the Zenith, and bring the first point of ♈ to the Meridian: Then number on the Quadrant of Altitude upwards the Complement of the Suns Declination, and bring that degree to the Equator: So shall the [Page 112] degree of the Horizon cut by the Quadrant of Altitude be the Complement of the Poles Elevation; and the degree of the Equa­tor cut by the Quadrant of Altitude shall be the Almicantar of the Sun at 6. of the clock.

Example.

The Suns Azimuth at 6 is 12¾ degrees: Therefore I Elevate the Pole 12¾, and screw the Quadrant of Altitude to 12¾ de­grees which is in the Zenith: Then I bring the first point of ♈ to the Meridian; The Suns Declination is 20 degrees 5 mi­nutes. Therefore I number on the Quadrant of Altitude 69 deg. 55 min. which is the Complement of 20 deg. 5 min. to 90. this 69 deg. 55 min. on the Quadrant of Altitude I bring to cut the Equator, and find when 69 deg. 55 min, cuts the Equator, that the Quadrant of Altitude cuts the Horizon, in 38½ deg. which is the Complement of the Poles Elevation: and at the same time the Quadrant of Altitude also cuts the Equator in 15½ degrees which is the Almicantar or Altitude of the Sun at 6. a clock.

PROB. VI.

By the Hour of the Night and a known Star Observed Ri­sing or Setting, to find the Heigth of the Pole.

REctifie the Hour Index, by Prob. 2. of the former Book; and turn the Globe Westwards till the Hour Index points at the Hour of the Night; fasten the Globe there, and turn the Meridian through the notches of the Horizon till the know [...] Star come to the East side the Horizon, if the Star be Rising, [...] the West if it be Setting; so shall the degrees of the Poles El [...] ­vation be cut by the Horizon under the Elevated Pole; and [...] North or South according as the Elevated Pole of the Globe [...]

PROB. VII.

Two Places given in the same Latitude, to find [...] Difference of Longitude.

BRing the first Place to the Meridian, and note the number of degrees of the Equinoctial that comes to the Meridan [Page 113] with it; then Bring the other place to the Meridian and note the number of degrees of the Equator that comes to the Meridian with it: and by substracting the lesser number from the greater you have the difference of Longitude, This needs no Example.

PROB. VIII.

Two Places given in the same Longitude, to find the Dif­ference of Latitude.

BRing the Places to the Meridian, and the degrees of the Meridian over the two Places is the Latitudes of them both, and by substracting the lesser number of degrees from the greater you will have the difference of Latitude.

PROB. IX.

Course and Distance between two Places given, to find their Difference in Longitude and Latitude.

SEek the Rhumb you have failed upon, as in Prob, 34, of the last Book, and upon that Rhumb make a mark for the Place you departed from; then with your Compasses take off from the Equinoctial the number of Leagues you have failed upon that Rhumb, by allowing a degree for every 20. Leagues and place one foot of your Compasses upon that mark, and where the other foot falls on that Rhumb make a second mark; then by bringing the first mark to the Meridian, you will see on the Meridian the Latitude of that mark, and in the Equa­tor the Longitude as in Prob. 2. of the last Book: and by bringing the second mark also to the Meridian, you will as before, find the Longitude and Latitude of the second mark also. Then by sub­stracting the lesser Latitude from the greater Latitude, and the lesser Longitude from the greater Longitude, you will have the difference remaining, both of Longitude and Latitude you are a­rived into.

PROB. X.

To find how many Miles are contained in a Degree of any Parallel.

EVery Degree of the Equinoctial contains 20. English Leagues and every League 3. English Miles: But in e­very Parallel to the Equinoctial, the Degrees diminish more and more even to the Pole, where they end in a point. Therefore a Degree in any Parallel cannot contain so many Miles as a De­gree in the Equinoctial. Now that you may know how many Miles are contained in a Degree of any Parallel to the Equi­noctial. Do thus, Measure with your Compasses the width of any number of Degrees in any given Parallel; suppose (for Exam­ples sake) 10. Degrees in the Parallel of 51½; Examine in the E­quator, how many Degrees of the Equator they will make, and you will find 6⅕. Therefore 1. Degree in the Equator making 60 Miles 6. Degrees makes 360, to which add for the [...] part 12 Miles, makes [...]72 Miles, to be the Measure of 10 Degrees in the Parallel of 51½. So that by dividing 372. by 10. you have [...]7 Miles for the length of a Degree, from East to West in the Parallel of 51½ Degrees.

PROB. XI.

The Rhumb you have sailed upon, and the Latitudes you de [...]arted from, and are arived to, given, to find the Difference of Longitude, and the number of Leagues you have Sailed.

FIrst seek the Rhumb you have sailed on, and pass it through the Meridian till it cuts in the Meridian the La­titude you departed from; and keeping the Globe there sted [...]y make a mark close by the Meridian, under that Latitude and in that Rhumb on the Globe, and note in the E­quinoctial the degree of Longitude at the Meridian: then pass that Rhumb through the Meridian again, till it cuts in the Meridian the Latitude you are arived to; and in that Rhumb and Latitude make on the Globe another mark, and examine in the Equinoctial [Page 115] the Longitude of the second mark; for the difference between the first and second mark, is the difference of Longitude. Then o­pen your Compasses to one Degree of the Equinoctial, and by measuring along in the Rhumb count how many times that Di­stance is contained between the two points in that Rhumb: for so many times 20. Leagues is the Distance you have sailed.

Example.

I sail upon the North West Rhumb from the Latitude of 1 [...] ▪ degrees, into the Latitude of 30. degrees 40. minutes. There­fore I find the North West Rhumb▪ and turn the Globe through the Meridian till this Rhumb cut the Meridian in the first Lati­tude, viz. in 10. degrees and directly under 10. degrees upon the Rhumb I make a prick, and also find 10 degrees 3 minutes, of the Equator at the Meridian, for the Longitude of the First Place. Then I turn the Globe again through the Meridian, till the same Rhumb cut the Meridian in the second Latitude. viz in 30 degrees 40 minutes, and directly under those 30 degrees 40 minutes upon the same Rhumb, I make another prick, which re­presents the Place I am arrived to: I examine the Longitude of this prick, as before, and find it 32 degrees 10 minutes. Therefore I substract the first Longitude, viz. 10 degrees 3 mi­nutes from the second Longitude, viz. 32 degrees 10 minutes, and there remains 22 degrees 7 minutes, for the Difference of Longitude.

Then for examining the Distance I open my Compasses to 1. degree on the Equinoctial and measure upon the Rhumb how oft that Distance is contained between the two pricks, and find 29¼, that is, 29 degrees 15 minutes, which multiplyed by 2 [...]. gives 585, for the number of Leagues failed upon that R [...]umb.

The reason why I open the Compasses no wider then to 1 de­gree, is because the Rhumbs being Circular or [...] lines the distance on them may be measured more exactly by often count­ing that 1 degree in them the [...] if the [...] had bin op [...]red to many degrees. Thus if the Compasses had been opened wide enough to reach between the two pricks aforesaid. I should not have had above 583 Leagues for the distance between the two Places: neither is there indeed more great Circle distance between them; But I sailed upon a Rhumb, that is, I follow [...]d [Page 116] the Course of a Circular winding line, and so fetcht a Compass about to come to these two pricks; and therefore I have in truth sailed 585. Leagues. For the segment of a Rhumb between two Places is alwaies greater then a straight line drawn betwixt them; yea sometimes by half or more in Places neer either Pole.

Note, If you be not very curious in opening your Compasses to this smal distance, you may in oft turning them about upon the Rhumb commit error in your measuring: therefore when you have taken the Distance of one degree, try if you neither gain or loose any thing in measuring 10, or 20. degrees of the Equi­noctial by them: for then your Compasses are opened to a width exact enough for your purpose.

PROB. XII.

The Longitudes and Latitudes of two Places given, to find Course, and Great Circle distance between them.

FInd on the Globe the Longitudes and Latitudes given, and make pricks to either Longitude and Latitude: If any Rhumb pass from one place to the other, that is (without more a doe) the Rhumb sought. But if no Rhumb pass through; Take the Rhumb that runs most Parallel to the two pricks: for that shall be the Rhumb or the neerest Rhumb that these two pricks Bear on. An Example of this, see in Prob. 34. of the Last Book: And the Great Circle Distance between these two pricks, you may find as by Prob, 33. of the same Book.

PROB. XIII.

The Latitude you departed from, and the Latitude you are arrived to, and the number of Leagues you have sailed given, to find the Rhumb you have sailed on, and diffe­rence of Longitude.

MAke a prick on the Globe in the Latitude you departed from: then open your Compasses to the number of Leagues you have sailed, by taking for every 20. Leagues 1. degree of the Equator, half a degree for [Page 117] 10 Leagues, a quarter of a Degree for 5 Leagues, and so propor­tionably for any other number of Leagues: Place one foot of your Compasses in the prick made for the Latitude you departed from, and extend the other towards the Latitude you are arived to, and discribe an occult Arch; Turn the Globe till this occult Arch come to the Latitude on the Meridian, and where the Latitude cuts this occult arch make another prick to represent the Latitude you are arived to; so shall the Rhumb passing through those two pricks (or that is most Parallel to those two pricks) be as in the last Prob. the Course or the Rhumb those two pricks Bears on.

The difference of Longitude you may find as by Prob. 11.

PROB. XIV.

To find by the Globe the Variation of the Needle; com­monly called the Variation of the Compass.

OBserve by a Compass whose wyer is placed just under the Flower deluce, what point of the Compass the Sun Rises or Sets on, Morning, or Evening: Then exa­mine by Prob: 10. of the second Book, what degree of the Horizon the Sun Rises or Sets on by the Globe also; and if the Rising or Setting be the same, both on the Globe and Com­pass, there is no Variation in your Place, But if there be difference between the Rising or Setting by the Compass and the Globe, then is there Variation in your Place.

If the point the Sun Rises upon in the Compass be neerer the North point, then the point the Sun Rises upon by the Globe, the Variation is Westwards.

If the point the Sun Sets upon in the Compass be neerer the North then the point it Sets upon by the Globe, the Variation is Eastwards.

If the point the Sun Sets upon in the Compass be further from the North point, then the point the Sun Sets upon by the Globe, the Variation is Westwards.

If the point the Sun Rises upon in the Compass be further from the North point then the point the Sun Rises upon by the Globe, the Variation is Eastwards. And so many degrees as there is between the point of Rising or Setting found by the Compass, and the point of true Rising or Setting found by the Globe, so [Page 118] many degrees is the Variation from the North towards the East, or West point.

Otherwise, when the Sun hath Altitude.

Having the Altitude of the Sun; find by Prob. 22. of the second Book, its Azimuth: Then examine by a Compass whe­ther the true Azimuth found by the Globe, agree with the A­zimuth found by a Nautical Compass: If they agree there is no Variation: But if the Azimuth of the Compass before Noon be neerer the North then the true Azimuth found by the Globe, the Variation is Westwards.

If the Azimuth by the Compass Afternoon be neerer the North, the Variation is Eastwards.

If the Azimuth by the Compass Afternoon be further from the North, the Variation is Westwards,

If the Azimuth by the Compass before Noon be further from the North, the Variation is Eastwards.

And this Variation shall be as aforesaid so many degrees as there is between the Azimuth Observed by the Compass, and the true Azimuth, Observed by the Globe.

PROB. XV.

To keep a Journal by the Globe.

BY some of these foregoing Problemes you may Dayly (when Observations can be made find both the Longitude and Latitude on the Globe of the Places you are arived to, and also the Way the Ship hath made, and make pricks on the Globe in their proper Places for every Da [...]s Journey, so truly and [...] naturally that if you kept your reckoning aright you may be sure you cannot miss any thing of the truth it self; and that with less trouble and greater advantage, then keeping a Book of every Daies Reckoning.

PROB. XVI.

To Steer in the Night by the Stars.

REctifie the Globe and Hour Index as by Prob. 2. of the last Book, and turn about the Globe till the Index of the Hour Circle points to the Hour of the Day or Night: Then turn the Globe till the Difference of Longitude between the Place you depart from, and the Place you sail to pass through the Meridian and if any Star in the Latitude of the Place you sail To come to the Meridian, or neer the Meridian with the degree of the difference of Longitude, that Star is at that time in or neer the Zenith of that Place you sail to: and by finding the same Star in Heaven, as by Prob, 44. of the last Book you may direct your ship towards that Star, and fail as confidently (saies M r Blagrave) as if Mercurie were your Guide. But because this Star moves from the Zenith of this Place you must often examine what Star is come to the Zenith, and so often charge the Star you Steer by, as the length of your Voyage may require.

PROB. XVII.

How to platt on the Globe a New Land, never before Dis­covered.

THese two following Problemes are 2. Chapters of M r Wrights, delivered by him as follows.

It may sometimes fall out in new Discoveries, or when your Ship by means of a Tempest is driven out of her right Course, that you shall come to the sight of some Isle, Shoald, or new Land, whereof the Mariner is utterly ignorant: And to make some relation of the same. or to go unto it some o­ther time, if you desire to set it down on your Globe in the true place, you may do it after this manner: So soon as you have sight thereof, mark it well first with your Compass, observing diligently upon which Point thereof it lieth, And secondly, you must there take the heigth of the Sun, or of the Pole-star, as you were taught Prob. 13. of the second Book, that you may know [Page 120] in what Point your Ship is, and that point you must call the First Point; which being so done, your Ship may sail on her Course all that day, till the day following, without losing her Way: and the next day mark the Land again, and see upon what Point it li­eth; and then take your heigth, and with it cast your Point of Traverse once again; and that you may call your second Point. Then take a pair of Compasses, and placing one foot upon the First Point, and the other upon the Rhumb towards which the Land did Bear, when you Cast your First Point: set also one foot of another pair of Compasses in the second Point, and the other foot upon the Rhumb upon which the Land lay when you cast your second Point; and these two Compasses thus opened, you must move by their Rhumbs, till those two feet of both Com­passes do meet together, which were moved from the foresaid two Points: and where they do so meet together, there may you say is the Land which you Discovered; which Land you may point out with the In lets and Out-lets, or Capes and other Signes, which you saw thereupon. And by the graduation you may see the Latitude thereof; that thereby you may find it, if a any time after you go to seek for it.

PROB. XVIII.

Seeing two known Points or Capes of Land, as you sail [...] ­long, how to know the distance of your Ship from them▪

PItch one foot of one pair of Compasses upon one of the two foresaid Capes, and the other foot upon the Rhum [...] which in this Compass pointeth towards that Cape. [...] in like manner shall you do with another pair of Com­passes, placing one foot thereof upon the other known Cape, [...] the other foot upon the Rhumb, which stretcheth towards [...] said second Cape; and moving the two Compasses (so opened) by these two Rhumbs off from the Land, the very same Point where the two feet which came from the two Capes do meet, you may affirm to be the very Point where your Ship is. And then measuring by the degrees of the Equinoctial, you may see what distance there is from the said Point to either of the fore­said Capes, or to any other place, which you think good, for it is a very easie matter, if you know the point where your Ship is,

PROB. XIX.

Of Tides, and how by help of the Globe you may in general judge of them.

DIvide the Equinoctial into 30 equal parts, as was directed in Prob. 54. of the last Book. These 30. equal parts represent the 30. daies of the Moons Age.

Then on the North and South point of the Com­pass in the outmost Verge of the Horizon, Write with red Ink 12. From the North Eastward, viz. at the Point North and by East, Write 11 ¼. At the next point to that the same way, viz. North North East, Write 10 ½. At the next, viz. North East and by North, Write 9 ¾. And so forward to every point of the Compass; reba­ting of the last hour ¾ till you come to 12. in the South; where you must begin again to mark that Semi-Circle also in the same order you did the last. In this Circle is then represented the Points of the Compass the Sun and Moon passeth by every Day; and the Figures annexed represent the twice 12. hours of Day and Night.

Having thus prepared your Globe and Horizon, you may by having the Moons Age, and the point of the Compass on which the Moon maketh full Sea at any Place given, find at what Hour of Day or Night it shall be high Tide in the same Place. Thus,

It is a known Rule that a North and South Moon makes high water at Margarate. Therefore Bring the first point of ♈ to the North or South point in the Horizon, and Elevate the North Pole into the Zenith: Then count in the Equinoctial the Daies of the Moons Age numbred in red figures; and the Hour and minutes written in red figures annexed to the names of the Windes) that stands against the Moons Age shall be the Hour of High Tide on that Day or Night at Margarate.

The End of the Third Book,

The Fourth BOOK, Shewing the Practical Use of the GLOBES: Applying them to the Solution of Astrological Problemes.

PRAEFACE.

THe Practise of Astrology is grounded upon a two-fold Doctrine. The first, for erecting a Figure of Heaven, placing the Planets in it, finding what As­pects they bear each other, and in what Places they are con­stituted, &c. and this we call the Astronomical part of A­strology.

The second is, how to judge of the events of things by the Figure erected: and this is indeed the only Astrological part.

The first of these I shall briefly handle; because what there­in is proposed may be performed by the Globe, both with speed, ease, delight, and demonstration. The second I shall not meddle with, but refer you to the whole Volumnes alrea­dy written upon that Subject.

PROB. I.

To Erect a Figure of the 12 Houses of Heaven.

BEfore you erect a Figure of the 12 Houses of Heaven it will be requisite you place the Planets, ☊, and ☋, according to their Longitude and Latitude upon the Globe, as was directed in Prob. 55. of the second Book: for then, as you divide the Houses of your Figure by the Circle of Position, you may by inspection behold in what Houses the Planets are scituated, and also see what fixed Stars they are applying to, or separating from. But to the matter.

There is disagreement between the Ancient and Modern A­strologers, about erecting a Figure of Heaven. M r Palmer in his Book of Spherical Problemes Chap. 48. mentions four seve­ral waies, and the Authors that used them; whereof one of them is called the Rational way used by R [...]giomontanus; and now gene­rally practised by all the Astrologers of this Age. This way the face of Heaven is divided into twelve parts, which are called the twelve Houses of Heaven numbered from the Ascendent or angle at East downwards, with 1, 2, 3, &c, As in the following Figure.

In a Direct Sphear, viz. under the Equator these twelve Houses are twelve equal parts: but in an Oblique Sphear they are unequal parts, and that more or less according to the quanti­ty of the Sphears obliquity.

These twelve Houses are divided by 12. Semi-Circles of Po­sition; which are Semi-Circles passing from the two intersections of the Horizon and Meridian through any Star, degree, or point in the Heavens.

Four of these Houses are named Cardinals. The first and most eminent of these Cardinals is the first House, or the Angle of East, called the Ascendent; where the Semi-Circle of P [...]sition is the same with the Eastern Semi-Circle of the Horizon. The se­cond Cardinal is the tenth House, or the Angle of South; called Medium Caeli, or Culmen Caeli; where the Semi-Circle of Position is the same with the Semi-Circle of the Meridian above the Horizon. The third Cardinal is the seventh House, or the An­gle of West; called the Descende [...]; where the Semi-Circle of Position is the same with the Western Semi-Circle of the Hori­zon. [Page 124]

[figure]

The fourth Cardinal is the fourth House, or Angle of North; called Imum Caeli; where the Semi Circle of Position is the same with the Semi-Circle of the Meridian under the Ho­rizon.

The degrees and minutes of the Ecliptick upon the Cusps of these four Houses (that is, upon the beginning of these Houses) are found all at once only by bringing the Rising degree of the E­cliptick to the Horizon: (for the Horizon represents the Cusp of the Ascendent:) and then shall the Meridian cut the degree of the Ecliptick on the Cusp of the tenth House. The Western Semi-Circle of the Horizon shall cut the degree of the Ecliptick on the Cusp of the Seventh House: and the Semi-Circle of the Meri­dian under the Horizon shall cut the degree of the Ecliptick on the Cusp of the fourth House.

If you have the day of the Moneth, you may by Prob. 3. of [Page 125] the second Book find the Suns Place; and if you have the Hour of the Day you may by first rectifying the Globe, as by Prob. 2. of the same Book, turn about the Globe till the Index of the Hour-Circle point to the same Hour in the Hour-Circle, and you will then at the Eastern Semi-Circle of the Horizon have the de­gree of the Ecliptick that is Rising, and by Consequence (as afore­said) all the Cardinal points in their respective places.

Now to find what degree of the Ecliptick occupies the Cusps of the other eight Houses of Heaven; Do thus, The Globe rectified, as aforesaid, Move the Semi-Circle of Position up­wards till 30 degrees of the Equator shall be contained be­tween it and the Eastern Semi-Circle of the Horizon; so shall the Semi-Circle of Position cut in the Ecliptick the degree and minute of the Ecliptick on the Cusp of the twelfth House; and its opposite degree and minute in the Ecliptick shall be the Cusp of Opposite de­grees and mi­nutes of the Ecliptick pos­sess the Cusps of opposite Houses. the sixth House, (for you must note that if you have but the de­gree and minute of the Ecliptick upon the Cusps of six of the Houses, the opposite degrees and minutes of the Ecliptick shall immediately possess the Cusp of every opposite House.)

Then move the Circle of Position over 30. degrees more of the Equinoctial, so shall the degree of the Ecliptick cut by the Circle of Position be the degree of the Ecliptick, upon the Cusp of the eleventh House; and its opposite degree in the Ecliptick shall be upon the Cusp of the fifth House. The degree of the Ecliptick upon the Cusp of the tenth and fourth Houses was found as before. Then remove the Circle of Position to the Western side of the Meridian, and let it fall towards the Horizon till 30. degrees of the Equator are contained between the Meri­dian and it, so shall the degree of the Ecliptick cut by the Semi-Circle of Position be the degree of the Ecliptick on the Cu [...]p of the Ninth House; and the opposite degree of the Ecliptick shall be upon the Cusp of the third House. Let the Semi-Circle of Position fall yet lower, till it pass over 30. degrees more of the Equator, so shall the degree of the Ecliptick cut by the Semi-Circle of Position be the degree of the Ecliptick on the Cusp of the eighth House; and the opposite degree of the Ecliptick shall be upon the Cusp of the second House. The degrees of the Ecliptick on the Cusp of the seventh House, and Ascendent, were found as before.

Example.

I would erect a Figure of Heaven for July 27. 5. hours o [...] mi­nutes Afternoon, 1658. in the Latitude of London, viz. 51½ de­grees, North Latitude.

I first place the Planets, ☊, and ☋, on the Globe, as by Prob. 55. of the Second Book was directed: yet not exactly as I find them in the Ephemeris, for that shews only their place in the E­cliptick at Noon: Therefore I consider how many degrees or minutes each Planets motion is in a whole Day or 24. Hours, by substracting the Ecliptical degrees and minutes of the Planets place that Day at Noon from the Ecliptical degrees and mi­nutes of the Planets place the next Day at Noon: or contrarily if the Planet be Retrograde: for the remains of those degrees and minutes is the motion of the Planet that Day; Therefore propor­tionably to that motion I place the Planet forward in the Eclip­tick: (or backward if it be Retrograde:) As if the Sun should move forward 1 degree, that is 60 minutes in a whole Day, or 24 Hours, then in 12 hours he should move 30 minutes, in 6 hours 15 minutes, in 4 hours 10 minutes, in 1 hour 2½ minutes, and so proportionably for any other space of Time: which I con­sider before I place the Planets on the Globe.

Having thus placed the Planets on the Globe, I Elevate the North Pole 51½ degrees above the Horizon, and find the Suns place by Prob. 3. Book 2. to be in ♌ 14. degrees 9. minutes, Therefore I bring ♌ 14. degrees 9. minutes to the Meridian, and the Index of the Hour-Circle to 12. Then I turn the Globe Westwards, because it is Afternoon, till the Index point to 5. Hours afternoon, and with a quill I fasten the Globe in this posi­tion: Then I examine what degree of the Ecliptick is at the As­cendent or Horizon, and find [...] 27. 47. to which Sig [...] degree and minute [...] 27, 47. is opposite, and therefore, as aforesaid upon the Cusp of the Seventh House: Lifting up the Circle of Position till it pass over 30 degrees of the Equator from the Horizon up­wards I find [...] 7. 5. cut by it in the Ecliptick, which is the Signe degree and minute upon the Cusp of the twelfth House, and its opposite Signe degree and minute is [...] 7. 5. which is upon the Cusp of the sixth House: Then lifting up the [...]ircle of Position again till it pass over 30 degrees more of the Equinoctial, I find [Page 127] cut by the Circle of Position [...] 21. 18. which is the Signe de­gree and minute upon the Cusp of the eleventh House; and its op­posite Signe degree and minute is ♉ 21. 18. which is upon the Cusp of the fifth House: [...] 3. [...]0. is at the Meridian, which is the Cusp of the tenth House, and the Signe degree and minute oppo­site to it is ♍ 3. 20. which is on the Cusp of the fourth House. Then taking the Semi-Circle of Position off its Poles, I place it on the West side the Meridian, and let it fall towards the Horizon till it pass over 30 degrees of the Equator from the Meridian, and find the Circle of Position cut the Ecliptick in ♎ 1. 9. which is the Signe degree and minute on the Cusp of the ninth House; op­posite to ♎ 1. 9. is [...] 1. 9. therefore ♈ 1. 9. is upon the Cusp of the third House: Letting the Circle of Position fall yet lower till it passes over 30 degrees more of the Equator, I find it cut the Ecliptick in ♌ 6. 47. which is the Signe degree and minute up­on

[figure]

[Page 128] the Cusp of the eighth House; and its opposite Signe degree and minute is ♒ 6, 47. which is upon the Cusp of the second House. So have you a Figure of the Face of Heaven: which if you have future use for, you may set down the several charracters in the proper places of a Figure, as they are on the other side the leaf,

PROB. II.

To Erect a Figure of Heaven according to Campanus.

REgiomontanus as aforesaid makes the beginning of every House to be the Semi Circle drawn by the side of the Se­mi Circle of Position according to the succession of every 30 th degree of the Equator from the Horizon But Camp [...] make it to be the Semi-Circle drawn by the side of the Semi-Circle [...] Position according to the succession of every 30 th degree of [...] Prime Verticle, or East Azimuth; which is represented by the Quadrant of Altitude placed at the East point.

The four Cardinals are the same, both according to Regiomon­tanus, and Campanus: but the other eight Houses differ: There­fore when you would find them according to Campanus; Rectifie the Globe and Quadrant of Altitude, and bring the lower end [...] the Quadrant of Altitude to the East point in the Horizon: Then count from the Horizon upwards 30 degrees o [...] the Quadrant [...] Altitude, and bringing the Circle of Position to those 30 degree [...] examine where the Circle of Position cuts the Ecliptick, which [...] the aforesaid time is in [...] 29. 40 for that degree and minute upon the Cusp of the twelfth House, and its opposite degree [...] minute in the Ecliptick viz. ♉ 29. 40. is upon the Cusp of [...] sixth House: Lift up the Circle of Position 30 degrees high [...] upon the Quadrant of Altitude (viz. to 60 degrees) and [...] Circle of Position will cut the Ecliptick in [...] 15. degrees for the Cusp of the eleventh House, and its opposite degree and mi­nute in the Ecliptick viz. ♉ 15. is upon the Cusp of the first House. The degree and minute of the Ecliptick on the Cusp [...] the Tenth and Fourth Houses is at the Meridian.

Then transfering the Circle of Position to the West side of the Meridian and the Quadrant of Altitude to the West point in the Horizon, Let the Semi-Circle of Position fall 30 degrees from the Meridian on the Quadrant of Altitude, and it will cut in the E­cliptick [Page 129] ♎ 16 degrees, for the Cusp of the ninth House, and its op­posite degree and minute in the Ecliptick viz. ♈ 16. is upon the Cusp of the third House: Let fall the Circle of Position 30 de­grees lower on the Quadrant of Altitude, and it will cut the E­cliptick in [...] 2 degrees, for the Cusp of the eight House, and its opposite degree viz. ♓ 2. degrees is on the Cusp of the second House: The Cusps of the Seventh and Ascendent is the same with Regiomontanus viz. [...] 27. 47, and ♐ 27. 47. The Fi­gure follows.

[figure]

PROB. III.

To find the length of a Planetary Hour.

AStrologers divide the Artificial day (be it long or short) into 12 equal parts, and the Night into 12 equal parts: These parts they call Planetary Hours. The [Page 130] first of these Planetary Hours takes its denomination from the Planetary Day; and the rest [...]re named orderly from that Planet according to the succession of the Planetary Orbs: As if it be Munday that is, the Moons day, (as by Prob. 42, of the second [...]ook) the Planet reigning the first Hour shall be [...], the Planet ruling the second Hour shall be ♄, the third Planetary Hour shall be [...], the fourth [...], the fifth ☉, the sixth ♀, the seventh: Thee begin again with [...] for the eight Planetary, [...] for the ninth and so through the whole Day and Night, till the Sun Rise again the next Day.

The length of this Planetary Hour is found by the Globe, thus: The Globe rectified; Bring the Suns place to the East side the Horizon and make a prick at the degree of the Equator that comes to the Horizon with it. Then remove the Suns place to the Meridian, and count the number of degrees of the Equator comprehended between that prick and the degree now at the Horizon; and divide that number of degrees and minutes by 6. because there is 6 Planetary H [...]urs past since Noon; and the Q [...]tient shall shew the number of d [...]g [...]s and minutes that pass through the Meridian in one Planetary Hour.

Example.

J [...]ly 27. 1658. I would know the length of the Planetary [...] here at Lonaon: I Rectifie the Globe, and bring the Sun▪ place viz ♌ [...]. 50. to the Eastern side the Horizon and find 115 degrees of the Equator come to the Horizon with it; to this 115 degrees I make a prick: Then I turn the Suns place to the Meridian and find 22 [...] degrees of the Equator at the Horizon, Therefore I either count the number of degrees between the pricks and the degree of the Equator at the horizon, or else sub­ [...]r [...]ct the [...] from the greater but both waies I find 111 de­g [...]ees of the Equator to pass through the Meridian (or the Hori­zon in six Planetary Hours Therefore dividing 111. by 6. I [...] [...]. degrees [...]0 minutes of the Equator to pass through the M [...]an in one Planetary Hour: which 18. degrees 30 minutes reduced into Time yeelds 72. minutes, by accounting for every 15. degrees one Hour for 1. degree 4. minutes, and for half a degree [...]. minutes of Time and so proportionably▪ so that the le [...]g [...]h of a Planetary Hour, July 27 is 1 co [...]on Hour and [...]4 minute, here at London.

PROB. IV.

The length of a Planetary Hour known, to find what Pla­net Reigneth any green Hour of the Day, or Night.

THe Globe Rectified as in the last Probleme, Turn about the Globe till the Index of the Hour Circle points to the Hour of the Day in the Hour Circle. Then count the number of degrees comprehended between the de­gree of the Equator at the Horizon and the prick in the Equa­tor, made as in the last Probleme, and reduce that number of de­grees into minutes of Time, by re [...]koning 4. minutes of Time for every degree of the Equator. Reduce also the number of de­grees and minutes that pass through the Meridian in one Plane­tary Hour into minutes by allowing (as aforesaid 4. minutes for e­very degree, and then divide the [...] [...] by the second and the Quotient shall be the number of [...] [...] since Sun Rising Having the number of Planetary Hours since Sun Ri­sing R [...]ckon the first Planetary H [...]ur by the [...]ame of that Pla­net that bears the denomination of the Day the second Planeta­ry Hour by the Planet succeeding that in order [...]he th [...]d by the next in order and so for all the rest [...] you c [...]me to the last Pla­net viz. [...]; and then begin again with [...], and so [...] [...] &c. [...] you have [...] so many Planets as there are Planetary Hours si [...]ce M [...]ing. and that Planet the number ends on shall be the Planet Reigning that Planetary Hour.

Example.

July 27. 1658. aforesaid, I would know what Planet Rules at 5 a clock past Noon: The length of the Planetary Hour this Day [...]ound by [...]he last Probleme▪ is 1. hour 14. minutes▪ There­fore the Globe Rectified. I bring the Index of the Hour Circle to the Hour of the Day viz. 5 a clock in the Hour-Circle, and then count the number of degrees between the Prick made, as by the last Probleme and the degree of the Equator at the Hori­zo [...]; and find them 187. which I reduce into minutes, by allow­i [...]g for every degree 4 minutes; and that gives 748 minutes. This [...] minu [...]es I divide by the minutes contained in one Planeta­ry [Page 132] Hour this Day, viz. by 72. and find 10. hours 8. minutes; which shews there are 10. Planetary Hours and 8. minutes past and gon since Sun Rising. Therefore ♂ being the Planet after whose name the Day is called viz. Dia Martis, ♂ is as afore­said, the Ruler of the first Planetary Hour: From him I count the Planet succeding, which is ☉ for the second Hour; from ☉ I count the Planet succeding, which is ♀ for the third Hour, and so on to ♀, and ☽: and then I begin the Round again with ♄, ♃, ♂, and ☉, till I come again to ♀, which is the tenth Planetary Hour since Sun Rising▪ and the minutes remaining being 8. shews that there is 8. minutes past since she began to Reign.

PROB. V.

To find Part of Fortune by the Globe.

COunt the number of degrees and minutes contained be­tween the Suns place and the Moons place, begining at the Suns place and counting according to the succession of Signes till you come to the Moons place: and having found that number of degrees and minutes, add them to the num­ber of degrees and minutes Ascending, reckoned from the first point of ♈. If the sum exceed 360, east away 360, and the re­mainder shall be the number of degrees and minutes from the first point in [...], in which Part of For [...]ne falls. But if it do not exceed 360, you have already the number of degrees and minutes from the first point of ♈ in which you must place Part of Fortune.

Example.

I would find the place of Part of Fortune for the time of ou [...] Figure: I seek the two pricks representing ☉ and [...], and find ☉ in ♌ 14. 9. and ☽ in ♏ 19. 44. therefore counting from the Suns place to the Moons place according to the succession of Signes, I find 95. degrees 35. minutes, contained between them: This 95. degrees 35. minutes I add to 267. degrees 47. minutes, the degree and minute contained between the first point of ♈ and the Ascendent; and they make together 363. degrees 22. minutes. This exceeds 360. therefore I cast away 360. and the remains are 3 degrees 22. minutes, for the place in the E­cliptick of Part of Fortune, reckoned from the first point of ♈▪ [Page 133] Therefore this character ♁ which represents Part of Fortune, I set in its proper place of the Figure, as I did the Planets.

PROB. VI.

To find in what Circle of Position any Star, or any degree of the Ecliptick is.

CIrcles of Position are numbred from the Horizon up­wards, upon the Quadrant of Altitude placed at the East or West point of the Horizon, Therefore when you would find what Circle of Position any Star or degree of the E­cliptick is in, Rectifie the Globe and Quadrant of Altitude, and bring the lower end of the Quadrant of Altitude to the East or West point of the Horizon, and lift up the Circle of Position till it come to the Star or degree of the Ecliptick proposed: and the number of degrees the Circle of Position then cuts in the Qua­drant of Altitude is the number of the Circle of Position that the Star or degree of the Ecliptick is in. If the Star or degree of the Ecliptick be under the Horizon, turn the Globe about till 180, degrees of the Equator pass through the Meridian, then will the Star or degree of the Ecliptick be above the Horizon: Lift up then the Circle of Position (as before) to the Star or degree of the Ecliptick and the number of degrees of the Quadrant of Al­titude the Circle of Position cuts on the East side, is the number of Circles of Position the Star was under the Horizon on the West side: Or so many degrees as the Circle of Position cuts on the Quadrant of Altitude in the West side the Horizon is the number of the Circles of Position the Star or degree of the Ecliptick was under the Horizon on the East side.

PROB. VII.

To find the Right Ascensions, the Oblique Ascensions, and the Declinations of the Planets.

EXamine the Right Ascensions and Declinations of those pricks made to represent each Planet, in Prob. 1. of this Book; and work by them as you were directed to work by the Sun, in Prob. 26, 27, 28. of the second Book,

PROB. VIII.

How to Direct a Figure, by the Globe.

TO Direct a Figure is to examine how many degrees of the Equinoctial are moved Eastwards or Westwards, while a­ny Planet or Star in one House comes to the Cusp or any other point of any other House.

When you would Direct any Promittor to any Hylegiacal point examine the degree of the Equator at the Meridian; then turn about the Globe till the Promittor come to the Hylegiacal point, and examine again the degree of the Equator at the Meri­dian: and by substracting the lesser from the greater you will have the number of Degrees that passed through the Meridian whiles the place of the Promittor was brought to the Hy [...]g [...] ­cal point: and that number of degrees shall be the Arch of D [...] ­rection.

Example.

I would Direct the Body of the Moon in our Figure afore­said to Medium C [...], or the tenth House: I find by the Globe 20 [...]. degr [...]es 30. minutes of the Equator at the Meridian with the [...]eath House and turning the Globe till the prick made to represent the Moon come to the Meridian. I find 227, degrees 20, minutes of the Equator come to the Meridian with it. There­fore I [...] the lesser from the greater viz. 2 [...]3 degrees 3▪ minutes from 227. degrees 2 [...]. minutes, and have remaining 2 [...] ▪ degrees 50 minutes.

This [...]. degrees 50. minutes shews that 23. Years 1 [...]. Moneths must expire ere the Effects promised by the Moons pre­sent position shall opperate upon the signification of the [...] House.

If the Body of the Moon had been Directed to any other point the [...] [...] Meridian or Horizon; you must have Elevated the Circle of [...] [...] the point proposed; and have under-propped it to that [...], and [...] ▪ have turned about the Globe till the prick [...] the Moon, had come to the Circle of Position; and then [...] degrees of the Equator that should have passed [Page 135] through the Meridian whiles this motion was making, should be the number of degrees of Direction; and signifie in Time as fore­said,

PROB. IX.

Of Revolutions: and how they are found by the Globe.

BY Revolution is meant the Annual Conversion of the Sun to the same place he was in at the Radix of any Business. When you would find a Revolution by the Globe, first find the Right Ascension of M [...]d Heaven at the [...]adix of the Business, as by Prob▪ 26. of the second Book you were directed to find the Right Ascer [...]on of the [...]; and [...] add 87 degrees for eve­ry Y [...]a [...] since the Radix: Then substract 360 so o [...] as you can from the whole and the R [...]m [...]s shall be the Right Ascension o [...] Mid H [...]aven for the A [...]al Revolu [...]on.

I [...] y [...]u [...] the number of degrees of the Equator contained between the R [...]ght A [...]cension of the Mid H [...]aven and the Right Ascension of the Sun, and convert that number of degrees [...] Time by allowing for every 15. degrees 1 Hour of Time it will shew, if the Suns place be on the Western side of the Meridian the number of Hours and minutes Afternoon the Revolution shall h [...]ppen on, but if on the East side the Meridian, the number of Hours and minutes Before-noon the Revolution shall happen on.

PROB. X.

How a Figure of Heaven may be erected by the Revoluti­on thus found.

SEek the degree of Right Ascension of Mid Heaven, and bring it to the Meridian, so shall the four Cardinal points of the Globe be the same with the four Cardinal points in Heaven at the time of the Revolution. The other H [...]ses are [...] by the Circle of Position: as in the first Pro­bleme of this Book▪

The End of the Fourth Book.

The Fifth BOOK, Shewing the Practical Use of the GLOBES: Applying them t [...] the Solution of Gnomonical Problems

PRAEFACE

DYals are of two sorts, Pendent, and Fixed. Pende [...] are such as are hung by the hand, and turned to­wards the Sun; that by its Beams darting throug [...] smal Pin-holes made for that purpose, the hour of the Da [...] may be found. These are of two sorts, Vniversal, and P [...] ­ticular.

Vniversal Dyals are those commonly called Equi [...]oc [...] or Ring-Dyals: They are used by Sea-men and Tr [...] ­vellers, that often shift Latitudes.

Particular are such as are made and only serve for Par­ticular Latitudes. Of these sorts are the several Dya [...] discribed on Quadrants, Cilinders, &c.

Fixed Dya [...]s shall be the matter of this discourse; and they are such as are made upon fixed Planes, and shew the Hour of the Day by a Stile or Gnomon made Parallel to the Axi [...] of the World.

Of the several Kinds of Dyal Plains: and how you may know them.

A Plain in Dyalling is that flat whereon a Dyal is discribed.

There is some disagreement among Older and Later Authors in the naming of Plains: for some name them according to the Great Circle in Heaven they ly in: and others according to the scituation of the Poles of the Plains. Thus they which name them according to the Great Circle in Heaven their Plains ly in, call that an Horizontal Plain, which others call a Vertical Plain; those Vertical, which others will call Horizontal; and those Po­lar, which others call Equinoctial.

However they be called it matters not, so you can but distin­guish their kinds, which with a little consideration you may ea­sily learn to do: For remembring but upon what grounds either the Order or Later Authors gave the Plains their Names, upon the same grounds you may also learn to know them. I confess both waies admit of some just exception against for in the Older Rule a Plain about the Pole, is called an Equinoctial Plain; when as to a sudden apprehension it would sound more significant to call it a Polar Plain, as Later Authors do: Again, Later Authors call an Horizontall Plain a Vertical Plain; when as it sounds more significant to call it an Horizontal Plain, as Older Authors do be­cause it lie flat upon the Horizon: But I shall give you the names according to both Rules, and leave you to your liberty to accept of which you please.

First therefore, you have an Equinoctial Plain otherwise called a Polar Plain. This Plain hath two Faces, upper, and under: These two Faces ly in the Plain of the Equinoctial: the upper Face beholding the Elevated Pole, the under Face the depressed Pole.

2. An Horizontal Plain, otherwise called a Vertical Plain: it lies in the Plain of the Horizon, directly beholding the Zenith.

Erect Plains, otherwise called Horizontal Plains are the sides of Walls, and these are of seven sorts, viz 1. Erect Direct Ver­tical, North or South, 2. Erect Direct, East or West. 3. Erect Vertical Declining. 4. Erect Inclining Direct. 5. Erect Inclining Declining. 6. Erect Reclining Direct. 7. Erect Reclining Decli­ning.

3. Erect Vertical, North or South Direct, otherwise called [Page 138] Direct North or South Horizontals, behold the North or South Directly, and ly in the East or West Azimuth.

4. Erect Direct East or West, otherwise called Direct East or West Equinoctials, behold the East or West Directly, and lies in the Plain of the Meridian, having its Poles in the Equinoctial.

5. Erect Vertical Declining Plains, otherwise called Decli­ning Horizontals, do not behold the North or South Directly, but swerves from them so much as the Azimuth Parallel to their Plains swerves or Declines from them.

6. Erect Inclining Direct Plains, have the upper side of their Plains Inclining or coming towards you, and their Plains do ex­actly behold either the East, West, North, or South.

7. Erect Reclining Direct Plains, have the upper side of their Plains Reclining or falling from you, and their Plains exactly be­holding either the East, West, North, or South.

8. E [...]ct Reclining Declining, or Erect Inclining Declining Plains are those Plains which are either Inclining or Reclining, but [...] behold the East, West, North or South, Directly but [...] or Decline more or less from them.

9. Polar Plains are Parallel to the Axis of the World, and to the M [...]ridians that cuts the East and West, or North and South, points of the Horizon.

All these kinds of Plains have two Faces; the one beholding the North Pole with the same respect that the other beholds the South Pole; except the Equinoctial Plain, which, because neither Pole is Elevated, hath but one Face: yet that one contains as many Hour lines as two other Faces.

These two Faces or Plains will receive just 24. hour lines, fo [...] the 24 Hour-lines of Day and Night: for so much as the one side or Face wanteth or exceedeth 12. the other side shall either ex­ceed or want of 12.

Every Dyal Plain is Parallel to the Horizon of some Country or other in the World: therefore a Dyal made for any Horizon in the World may be set to such a Position that it will shew you the Hour of the Day in your own Habitation: At least for so long as the Sun continues upon that Plan [...].

All Plains may be aptly demonstrated by the Globe, by set­ting it correspondent to all the Circles in Heaven, as by Prob. 2. of the second B ok: for if you imagine the Globe in that Posi­tion were prest flat into the Plain of any Circle, that Flat shall [Page 139] represent a Dyal plain, which shall be called after the name of that Circle it is prest into.

Thus if the Quadrant of Altitude be applyed to any degree of Azimuth, and you imagine the Globe were prest flat to the edge of the Quadrant of Altitude, so much as that Azimuth Declines from the East, West, North, or South, in the Horizon, so much shall that flat on the Globe be said to Decline either from the East, West, North, or South. Or if you imagine the Globe were prest flat down even with the Plain of the Horizon, that flat shall represent an Horizontal Plain; because as was said before, the Plain lies in that Circle cal'd the Horizon.

The Style or Gnomon is that straight wyre that casts the sha­dow upon the Hour of the Day: it is alwaies placed Parallel to the Axis of the World.

There are several waies to find the scituation of all Plains; but the readiest and speediest is by a Clinatory. The Clinatory is made of a square board, as A B C D, of a good thickness, and the larger the better; between two of the sides is discribed on the Center A a Quadrant as E F divided into 90 equal parts or de­grees, which are figured with 10, 20, 30, to 90; and then back again with the Complements of the same numbers to 90: be­tween the Limb and the two Semidiameters is made a Round Box, into which a Magnetical Needle is fitted; and a Card of the Sea Compass, divided into 4 Nineties, beginning their num­bers at the East, West, North, and South points of the Compass, from which points the opposite sides of the Clinatory receives their Names of East, West, North, or South. Upon the Center A whereon the Quadrant was discribed is fastned a Plumb-line, having a Plumbet of Lead or Brass fastned to the end of it, which Plumb-line is of such length that the Plumbet may fall just into the Grove G H below the Quadrant, which is for that purpose made of such a depth that the Plumbet may ride freely within it, without stopping at the sides of it. See the Figure an­nexed.

With this Clinatory you may examine the scituation of Plains▪ As if your Plain be Horizontal; it is Direct: and then for the true scituating your Dyal you have only the true North and South line to find: which is done only with setting the Clinatory flat down upon the Plain, and turning it towards the right or left hand, till you can bring the North point of the Needle to hang [Page 140]

[figure]

just over the Flower-de-luce: for then if you draw a line by either of the sides Parallel to the Needle, that line shall be a North and South line. Put herein respect must be had to the Variation of the Compass in the Place you make your Dyal: for if the North point of the Needle swerves from the North point of the World, then have you not a true North and South line. But if in your Place there be no Variation of the North point of the Needle from the North point of the World (as now it happens here at London) then the line drawn by the side of the Clinatory (as a­foresaid) shall be a true North and South line.

But admit there be Variation, Having by Prob. 19. of the third Book found the number of degrees of this Variation to­wards the East, or West, count the same number of degrees from [Page 141] the North point in the Card either to the Eastwards or West­wards, and note the degree in the Card terminating at that num­ber, for that degree shall be the North point; and its opposite degree the South point: 90. degrees from it either way shall be the East and West points.

Therefore, whereas before you were directed to turn the Clinatory till the North point of the Needle point to the Flower-de-luce on the [...]aid you m [...]st now turn (or move) the Clina­tory till the North point of the Needle [...]arg just over the degree of Variation thus sound; and then a line drawn as aforesaid, by the side of the Clinatory Paral [...]el to the Needle shall be a North and South line or (to speak more properly▪ a Meridional line.

You may fi [...]d a M [...]ridian li [...]e several other waies; as first; If the Sun shine just at Noon, hold up a Plumb-line so as the shadow of it may fall upon your Plain; and that shadow shall be a Meridian li [...]e.

Secondly, on the backside the Clinatory discribe a Circle, and draw a line through the Center to both sides the Circumference; cross this line with an other line at R [...]ght Angles in the Center, so shall the Circle be divided into four equal parts. These four parts you must ma [...]k with East, West, North, South and divide each of them into 90. degrees. In the Center of this Plain erect a straight wyer prependicularly: when you would find a Meridian line examine by the tenth Prob. of the second Book the Ampli­tude of the Suns Rising or Setting from the East or West points, and waiting the just Rising or Setting that Day, turn the Instru­ment about till the shadow of the wyer falls upon the same de­gree from the East or West the Amplitude is of, for then the North and South line in the Instrument will be the same with the North and South line in Heaven.

Thirdly by the Suns Azimuth: Find the Azimuth of the Sun by Prob. 22. of the second Book: and at the same instant turn the Instrument till the shadow of the wyer fall upon the de­gree on the Instrument opposite to the degree of the Suns Azi­muth▪ so shall the Meridional line of the Instrument agree with the Meridional line in Heaven.

You may the same way work by the Azimuth of any Star. Only, whereas the shadow of the wyer should fall upon the op­posite degree aforesaid: Now you must place a Sight or Per­pendicular upon that opposite degree, and turn the Instrument a­bout [Page 142] till the wyer at the Center, the Sight in the opposite degree of the Stars Azimuth, and the Star in Heaven, come into one straight line, so shall the Meridian line of the Instrument agree with the Meridional line in Heaven.

Fourthly It may be found by any Star observed in the Meridi­an, if two Perpendiculars be erected in the Meridian line of your Instrument; for then by turning the Instrument till the two Per­pendiculars and the Star come into a straight line, the Meridian line of your Instrument will be the same with the Meridian line in Heaven. See more waies in Mr. Palmer on the Planisphear Book 4. Chap. 9:

If your Plain either Recline or Incline, apply one of the sides of your Clinatory Parallel to one of the Semi-diameters of the Quadrant to the Plain, in such sort that the Plumb-line hanging at liberty may fall upon the Circumference of the Quadrant, for then the number of degrees of the Quadrant comprehended be­tween the side of the Quadrant Parallel to the Plain, and the Plumb-line shall be the number of degrees of Reclination, if th [...] Center of the Quadrant points upwards, or Inclination if th [...] Center points downwards.

If your Reclining or Inclining Plain Decline, draw upon it a line Parallel to the Horizon, which you may do by applying the back-side of the Clinatory, and raising or depressing the Center of the Quadrant till the Plumb-line hang just upon one of the Se­mi-diameters, for then you may by the upper side of the Clinato­ry draw an Horizontal line if the Plain Incline, or by the under side if it Recline. If it neither Incline or Recline, you may draw [...] an Horizontal line both by the upper and under sides of the Cli­natory. Having drawn the Horizontal line, apply the North [...] [...] of the Clinatory to it, and if the North end of the Needle [...] directly towards the Plain, it is then a South Plain. If the [...] point of the Needle points directly from the Plain, it is a Nor [...] plain: but if it points towards the East, it is an East Plain: if to­wards the West a West Plain. If it do not point directly [...] East, West, North, or South, then so many degrees as the [...] declines from any of these four points to any of the other of [...] four points, so many degrees is the Declination of the Plain, [...] respect (as aforesaid) had to the Variation of the Compass.

Or if you find the Azimuth of the Sun by its Altitude ob­served just when its beams are coming on or going off you [...] [Page 143] Plain, that Azimuth shall be the Azimuth of your Plain.

Or you may erect a wyer Perpendicularly on your Plain, and wait till the shadow of that wyer comes to be Perpendicular with the Horizon, which you may examine by applying a Plumb-line to it, for then the shadow of the Plumb-line and the shadow of the Perpendicular will be in one: then taking the Al­titude of the Sun you may by Prob. 22. of the second Book find its Azimuth, and thereby know in what Azimuth the Plain of your Dyal lies: for the Azimuth your Plain lies in is distant from the Azimuth of the Sun just 90. degrees.

PROB. I.

How by one position of the Globe to find the distances of the Hour-lines on all manner of Plains.

YOu may have Meridian lines drawn from Pole to Pole through every 15. degrees of the Equinoctial, to represent the Horary motion of the Sun both Day and Night; and when the Pole of the Globe is Elevated to the height of the Pole in any Place and one of these Meridian lines be brought to the Brazen Meridian, all the rest of the Meridian lines shall cut any Circle which you intend shall represent the Plain of a Dyal in the number of degrees on the same Circle that each respective Hour-line is distant from the Noon-line point in the same Circle.

Thus if you should enquire the distance of the Hour-lines up­on an Horizontal Plain in Londons Latitude; The Pole of the Globe as aforesaid) must be Elevated 51½ degrees, and one of the Meridian lines (you may chuse the Vernal Colure) be brought to the Brazen Meridian, which being done, you are only to exa­mine in the Horizon (Because it is an Horizontal Plain) at what distance from the Meridian (which in Horizontals is the Noon-line) the several Meridians drawn on the Globe intersect the Horizon, for that distance in degrees shall be the distance on a Circle divided into 360. degrees that each respective Hour-line must have from the Meridian or a Noon line chosen in the same Circle; and lines drawn from the Center of that Circle through those degrees shall be the Hour lines of an Horizontal Plain.

If it be an Erect Direct South Dyal you enquire after; Keep­ing [Page 144]

[figure]

the Globe in its former position, apply the Quadrant of Al [...] ­tude to the Z [...]h, and its lower end to the East point o [...] th [...] Horizon▪ for then as was shewed in the Preface) by imagining th [...] Globe to be pre [...]t to the graduated edge of the Quadra [...] Altitude, that [...] [...] be a South Plain and the number of [...] grees the M [...]ridi [...]s cuts in the Quadrant of Altitude numbe [...] from the Z [...]ai [...]h downwards shall be the number of degree that each [...] line shall be distant from the Meridian or [...] line in a Circle of 360. degrees, and lines drawn from the Co [...] ­ter of that [...] through those degrees shall be the Hour [...] of half the D [...]y: the Hour lines for the other half of the Day [...] of the same [...] from the Noon-line, with these; only they must be p [...]ced on the other side the Noon line.

If your Plain be not Direct but declines East or West▪ [...] must number the Declination Eastwards or Westwards re [...] ­pectively in the degrees of the Horizon and (the Quadrant [...] [Page 145] Altitude screwed to the Zenith, (as aforesaid) bring the lower end of the Quadrant of Altitude to the said degrees of Declina­tion, and the number of degrees cut by the Meridians in the Quadrant of Altitude numbred downwards, is the number of degrees that the Hour-lines are distant from the Noon line in a Circle of 360, degrees: And lines drawn from the Center of that Circle through those degrees be the Hour lines of half the Day. And if you turn about the Quadrant of Altitude upon the Zenith point till the lower end of it come to the degree of the Horizon opposite to the degree of Declination found before, the Meridian lines on the Globe (as before) shall cut the Qua­drant of Altitude in the number of degrees (counted downward) that each Hour-line is distant from the other side the Noon-line: And lines drawn from the Center of that Circle through those degrees shall be the Hour-lines of the other half of the Day,

If your Plane Decline, and also Recline or Incline, you must use the Gnomonical Semi-Circle, discribed in Prob. 12▪ which must be Elevated on the Quadrant of Altitude when it is set to the De­clination (as by the former Rule) according to the complement of Reclination, or Inclination: But if your Plane be Direct, and Re­cline, or Incline, it must be set to the Meridian, and the Meridians on the Globe shall cut that Semi Circle in the number of degrees counted from the Quadrant of Altitude if the Plane Declines, or from the Brasen Meridian, if it be Direct, that the several Hour lines are distant from a line Perpendicular to an Horizontal line, in a Circle divided into 360 degrees; And lines drawn from the Center through those degrees shall be the Hour-lines of such Reclining or Inclining Planes.

If your Plane be an East or West, either Direct or Declining; or an Equinoctial Plane (for they are upon the matter all one) you may better conceive how they are to be made, then make them by the Globe. And for the help of your fancy herein, take M r Blagraves conceit, who in his Book 6. Chap. 8. very properly demonstrates the Rules for projecting the Hour-lines on these Planes. He proposes to take 12. wyers bowed into exact Cir­cles, all of equal Diameter, and set together at equal distance one from another in two opposite points, as in two Poles, and to have a straight line to pass from one Pole to another, as an Axis. These 12 Wyers shall represent 24 Meridional Semi-Circles, Or indeed they may represent the Globe it self, containing 24 Me­ridional [Page 146]

[figure]

Semi-Circles to be discribed on the Globe, as aforesaid; And if you place the Horizon of the Globe Horizontal, and the North and South points of the Globe towards the North and South points in Hea­ven, and bring one of these Wyer Meridians directly under the Brasen Meridian, and the Axis of this Wyer-Globe in the Plain of the Horizon, and fasten a Thred in the middle of the Axis, that thred drawn from the middle of the Axis by every one of these wyers shall, if prolonged till it touch an East and West line drawn directly under or over the points Zenith or Nadir, point out on that East and West line the di­stances of each Hour-line from the 12 a clock line; And lines drawn at Right Angles through that East and West line▪ shall be the Hour lines of an East or West Plane, or of an Equinoctial Plane.

The moving this thred from wyer to wyer represents the mo­tion of the Sun, which as it passes over all the Meridians causes the shadow of that Meridional Semi Circle which it is directly over▪ and the Axis, and the Meridional Semi-Circle directly op­posite to the upper Meridional Semi-Circle to fall all into one straight line: And upon what point in the East and West line (mentioned before) that shadow-line shall fall is marked [...]ut by the application of the thred as aforesaid: and is an Hour-line on any of the foresaid Planes.

If you understand this Probleme rightly, you do already know how to draw the Hour lines upon all manner of Planes, and need no further Instructions; yet partly fearing a raw Student should [Page 147] not clearly understand these Rules, and partly doubting) because other Authors have been more Copious upon this Subject) that I should be censured to be too sparing of my pains, if I should light­ly touch so eminent a Doctrine as Dyalling is: Therefore I shall more distinctly handle Dyalling by the Globe, according to the way or Method that other Authors have used, and that after so plain a manner as possibly my Genius can devise.

PROB. II.

To make an Equinoctial Dyal.

DIscribe a Circle, on a square board or Plane as B C E D, and through A the Center thereof draw a straight line Parallel to one of the sides, as B E; Cross that straight line with another straight line as C D at Right Angles, so shall the Circle be divided into 4 equal parts: Divide each of these four equal parts into 90. degrees; as in the Figure. This Circle shall represent the Horizon.

Erect a wyer exactly perpendicular to the Center of the Plane; and that wyer shall be the Gnomon or Style of the Dyal.

Then Elevate one of the Poles of your Globe into the Zenith, and bring the Equinoctial Colure to the Meridian. And because in every hours Time 15 degrees of the Equator passes through the Meridian in Heaven, therefore turn the Globe till 15 degrees of the Equator pass through the Meridian of your Globe; so shall the Colure pass by 15 degrees of the Horizon also. Therefore from the Center of your Plane draw straight lines through 15▪ degrees from one of the Semidiameters both waies: and those straight lines shall be two Hour-lines: Then turn the Globe till 15 degrees more of the Equator pass through the Me­ridian, and you will find as before, the Colure pass by 15 degrees more of the Horizon: therefore on your Plane number 15. de­grees further beyond both the former lines, and from the Center draw straight lines through both those 15. degrees, and they shall be two Hour lines more. Fór all the other Hour lines turn the Globe till 15. degrees of the Equator at a time pass through the Meridian, as before, and you will find that for every 15. de­grees of the Equator that passes through the Meridian, the Colure will pass through 15. degrees of the Horizon: therefore those [Page 148] Hour lines must be drawn from the Center according to the succession of every 15 degrees on your Plane, Having drawn the Hour lines, you may set figures to them, beginning to num­ber your Hour lines from one of the Diameters, marking it with XII, and the next Hour line to the left hand with I, and the next II, the next III, &c. to XII. and begin again with I, II, III, &c. till you come to the other XII, where you began: and then your Dyal is finished. See the Figure.

[figure]

This is an Universal Dyal, and serves in all Latitudes: therefore when you place it you must set one of the XII s downwards, and the Axis Parallel to the Axis of the World.

But note, Both faces of this Dyal ought to be divided, and the Gnomon must appear on both sides like the stick in a Whir­ligig, which childeren use; or else you must turn it upside down, so oft as the Sun passes the Equinoctial.

PROB. III.

To make an Horizontal Dyal.

DIscribe a Circle on your Plane, as C B D E, and through the Center A of that Circle draw a Meridian line, as B E; cross that line at Right angles with another line, as C D; so shall your Circle be divided into four e­qual parts: Divide each of these four parts into 90. degrees; so shall the whole be divided into 360. These 360 degrees re­present the 360 degrees of the Horizon, which a Meridian line drawn through the place of the Sun runs through in every 24. Hours: The motion of which Meridian line through the de­grees of the Horizon is Regular in a Parallel Sphear; for in e­qual Time it moves an equal Space throughout the whole Cir­cle, viz. it will pass through 15. degrees of the Horizon in one Hours Time, (or which is all one) whiles 15. degrees of the E­quator passes through the Meridian; as was shewed in the last Probleme: But in an Oblique Sphear its motion through the Horizon is Irregular, and that more or less according to the more or less Obliquity of the Sphear: For far Northwards or Southwards you may see this Meridian line pass through 40, 50, yea 60. degrees of the Horizon in one Hours time, viz, whiles 15. degrees of the Equator passes through the Meridian: but in an other Hours time you will scarce have 4 or 5 degrees pass through the Horizon whiles 15 degrees of the Equator passes through the Meridian.

But that you may know the motion of the Sun (represented by this Meridian line) through the Horizon in all Latitudes; E­levate the Pole to the Elevation of your Place, and chuse instead of a Meridian line drawn through the Place of the Sun the Ver­nal Colure to be your Meridian line; both because it is most visible; and because from thence the degrees of the Equator are begun to be numbred, so that what so ever decimal degree of the Equator you light on at the Meridian, or else where, you will find its number from that Colure already set down to your hand, without either adding to, or substracting from it. Bring this Colure therefore to the Meridian, and the Index of the Hour Circle to 12. in the Hour Circle. Then turn the Globe [Page 150] Westwards, and so oft as 15 degrees of the Equator passes through the Meridian, so oft you must examine what degrees of the Horizon the Vernal Colure cuts; and those degrees and mi­nutes so cut by the Vernal Colure must be found in the Circle C B D E, beginning your account or reckoning at B towards D, and markt with Pricks: through which Pricks you must draw lines from the Center A, and those lines shall be the Hour lines after noon. Then bring the Colure to the Meridian again to find the Fore-noon Hour-lines, and turn the Globe Eastwards, and so oft as 15 degrees of the Equator passes through the Me­ridian, so oft you must examine what degrees of the Horizon the Vernal Colure cuts; and those degrees and minutes so cut by the Vernal Colure must be found in the Circle C B D E, be­gining your reckoning from B towards C, and markt with Pricks: through which Pricks you must draw lines from the Center A, and those lines shall be the Fore-noon Hour-lines.

These Hour-lines must be markt from the Meridian line, viz. the line A B, which is the 12 a clock line towards D, with I, II, III &c. till you have numbred to the Hour of Sun set (found by Prob. 7. of the second Book) the longest Day, and from the Meridian line towards C with XI, X. IX, &c. till you have numbred to Sun Rising the longest Day.

The Stile must be placed in the Center and Elevated so many degrees above the Plane, as the Pole is elevated above the Hori­zon of the Place,

Example of the whole.

I would make an Horizontal Dyal for Londons Latitude: Therefore I E evate the North Pole 51½ degrees above the Hori­zon, and bring the Vernal Colure to the Meridian, and the Index of the Hour Circle to 12 on the Hour Circle;

And turning the Globe Westwards till the In­dex points to 1 a clock or till 15 deg of the Equa­tor pass through the Meridian; I find the Colure cut the Hori in 11. 4 from the Meridian.
2 24. 15
3 38. 4
4 53. [...]6
5 71. 6
6 90.

These are the distances of the Hour lines from Noon till 6 at Night: and to these distances on the Plane (counting from B to­wards [Page 151] D,) I make pricks; and from the Center I draw lines through these Pricks; and these lines are the Hour lines from 12 to 6 Afternoon. But the Sun in the longest Day shines till past 8 at Night, as you may find by Prob. 48. of the second Book, therefore here wants the two Evening Hour lines; which though they may be found after the same way I found the former, (viz. by continuing the turning of the Globe Westwards) yet that I may the sooner reduce my work to the Plane I Count the num­ber of degrees between the 6 a clock line and the 5 a clock line in the Circle on the Plane; for the same number of degrees counted from D towards E is the distance of the 7 a clock Hour line from the 6 a clock Hour line; and the number of degrees contained be­tween the 6 a clock Hour line and the 4 a clock Hour line is the distance of the 8 a clock Hour line from the 6 a clock Hour-line.

[figure]

Or I need not draw the 7 and 8 a clock Hour lines, till I have drawn the forenoon Hour lines: for then by laying the edge of a [Page 152] Ruler (that will reach through the opposite side of the Plane) to the Morning 7 and 8 a clock Hour lines, I may by the side of that Ruler draw lines from the Center through the opposite side of the Plane, and those lines shall be the 7 and 8 a clock Hour lines Afternoon.

Having thus all the Afternoon Hour lines, I bring the Vernal Colure to the Meridian again; so shall the Index again point to 12. Therefore, as before I turned the Globe Westwards, so now

turning it Eastwards, till the In­dex points to 11 a clock, or till 15 deg. of the Equa­tor pass through the Meridian, I find the Colure cut the Hori. in 11. 40 from the Meridian.
10 24. 15
9 38. 4
8 53. 36
7 71. 6
6 90.

These are the distances of the Hour lines from Noon to 6. a clock in the Morning: and these distances I seek in the Circle of the Plain (counting from the Noon line B towards C) and mark them with Pricks; through which pricks (as before) I draw lines from the Center to the outside the Plane: and those lines shall be the Hour lines.

Or having the distance of all the Afternoon Hour-lines, I have also the distance of all the forenoon Hour lines from the Meridi­an; as you may see by comparing the two former Tables. For the 1 a clock Hour line Afternoon is equidistant from the Meri­dian or Noon line with the 11 a clock Hour line before Noon, viz. they are both 11 degrees 40 minutes distant from the Noon line, and the 2 a clock Hour line Afternoon is from the Noon line equidistant with the 10 a clock Hour line Beforenoon; for they are both 24. degrees 15. minutes distant from the Meridi­an or Noon line: and so all the other Morning Hour lines are di­stant from the Noon line by the same space that the same num­ber of Afternoon Hour lines (told from the Meridian on the con­trary side the Noon line) are distant from the Meridian.

Whence it follows, that since (as aforesaid) the same number of Hour lines after 6 at Night, and before 6 in the Morning have the same distance from the 6 a clock line that the same number of Hour lines before 6 at Night and after 6 in the Morning have from the 6 a clock line; and since the same number of Hour [Page 153] lines before Noon are equidistant from the Meridian or Noon line by the same space of degrees that the same number of Hour lines Afternoon are; It follows (I say) that having found the distance of the six Hour lines either before or after Noon, you have also given the distance of all the other Hour lines.

If you will have the half Hour lines placed on your Dyal you must turn the Globe till the Index points to every half Hour in the Hour Circle, as well as to the whole, and examine the degrees of the Horizon cut by the Vernal Colure, as you did for the whole Hours; and in like manner transfer them to your Plane.

Having thus drawn all the Hour lines I count from the Noon line 51½ degrees, the Elevation of the Pole here at London; and from the Center A I draw a straight line, as A F through these 51½ degrees, for the Gnomon or Style, and prolong it to the far­thest extent of the Plane: From this Gnomon or Style I let fall a Perpendicular upon the Noon line, as F G: (this Perpendicular is called the Substile, and this Perpendicular and its Base (which is the Noon line) and Hypothenusa (which is the Gnomon) shall make a Triangle, which being erected upon the Base, so as the Substile may stand Perpendicular to the Plane, the Hypothenu­sa A F shall be the Gnomon, and be Parallel to the Axis of the World; and cast a shadow upon the Hour of the Day.

PROB. IIII.

To make an Erect Direct South Dyal.

DRaw on your Plane an Horizontal line as C A D, as was shewed in the Preface: in the middle of this line (as at A) discribe as on a Center the Semi-Circle C B D: from the Cen­ter A let fall a Perpendicular, which shall divide the Semi-Circle into two Quadrants each of which Quadrants you must divide into 90 degrees, Then Rectifie the Globe, Quadrant of Alti­tude, Colure and Hour Index▪ thus, Elevate the Pole of the Globe to the Latitude of your Place, and screw the Quadrant of Altitude to the Zenith, Then bring the Vernal Colure to the Meridian, and the Index of the Hour Circle to the Hour of 12. in the Hour Circle; so shall your Globe, Quadrant of Altitude, Co­lure and Hour Index be Rectified. A [...]d [...]us you must alwaies Rectifie them for the making of most sorts of Dyals by the [Page 154] Globe. Then to make an Erect Direct South Dyal, Bring the lower end of the Quadrant of Altitude to the West point of the Horizon; And turn the Globe Westwards till the Index points to all the Hours Afternoon; and examine in what numbers of degrees from the Zenith the Colare cuts the Quadrant of Alti­tude when the Index points to each Hour: for a line drawn from the Center A through the same number of degrees reckoned from the Perpendicular A B (which is the 12 a clock line) to­wards D on the Plane, shall be the same Hour lines the Index points at.

Thus in our Latitude, viz. 51½ degrees, the Vernal Coloure be­ing brought to the Meridian and the Index to 12;

If you turn the Globe West­wards, till the Index points to 1 a clock, or till 15 deg. of the Equator pass through the Meridi­an, the Colure will cut the Quadrant of Altitude in 9. 18 counted from the Zenith.
2 19. 15
3 32. 5
4 48. 0
5 67. 4
6 90.

And these are the distances of the Afternoon Hour lines; which you must transfer to the East side of your Plane, viz, from B to­wards D; and draw lines from the Center A through these di­stances; and these lines shall be your Afternoon Hour lines.

Note (once for all) when the Colure goes off that Circle you examine the Hour distances in, the Sun will shine no longer upon that Plane; As in this example the Colure goes off the Qua­drant of Altitude at 6 a clock, therefore the Sun will not shine longer then till 6 a clock upon this Plane.

The Hour lines before Noon have the same distance from the Meridian that the Afternoon Hour lines have, as was shewed in the last Probleme: Only they must be drawn on the West side the Noon line, and counted from B towards C.

Otherwise.

You may reduce all Verticals into Horizontals; if you Elevate the Pole of the Globe to the Complement of the Latitude of your Place, and bring the Vernal Colure to the Meridian under the Horizon, and the Index of the Hour Circle to 12; and turn [Page 155] the Globe Westwards; for as the Index passes through every Hour on the Hour Circle, the Colure shews in the Horizon the distance of the several Afternoon Hour lines from the Meridian, or 12 a clock line, in the Circle on your Plane, numbred from B to D: and lines drawn from the Center through these distances on your Plane shall be the Afternoon Hour lines of your Dyal.

Example.

Londons Latitude is 51½ degrees, Its Complement to 90. is 38½. Therefore I Elevate the Pole 38½ degrees above the Hori­zon, and bring the Vernal Colure to the Meridian under the Horizon, and the Index of the Hour Circle to 12 on the Hour Circle. Then

Turning the Globe West­wards, till the Index of the Hour Circle points to 1 a clock, or till 15 deg. of the Equa­tor pass through the Meridian, I find the Colure cut the Horizon in 9 18 from the Intersecti­on of the Meridian and the Horizon: as in the former Ta­ble.
2 19 15
3 32 5
4 48 0
5 67 0
6 90

And these are the distances of the 6 Hour lines from the Merid.

[figure]

By this Example you may see that it is easie to reduce Verticals into Horizon [...]als: and Horizontals into Verticals: for this Erect Direct South Dyal is an Horizontal Dyal to those People that Inhabite 90 degrees from us, viz. in the South Latitude of 38½ degrees.

Then make a Triangle, whereof the Noon line shall be [Page 156] Base: from it count the Complement of the Poles Elevation, viz. 38½ degrees, and through them draw the line A F, from the Cen­ter A which shall be Hypotenusa; Then [...]et fall a Perpendicular upon the Noon line A B, so is your Triangle made. If this Triangle be erected Perpendicularly upon the Base or Noon line, The Hypotenusa A F shall stand Parallel to the Axis of the World, and cast a shadow upon the Hour of the Day.

PROB. V.

To make an Erect Direct North Dyal.

IF the Erect Direct South Dyal were turned towards the North; and the line C A D were turned downwards, and the line marked with 7 be now marked with 5, and the line 8 with 4, the line 5 with 7, and the line 4 with 8, then have you of it a North Erect Direct Dyal.

All the other Hour lines in this Dyal are useless, because the Sun in our Latitude shines on a North Face the longest Day only before 6 in the Morning, and after 6 at Night.

PROB. VI.

To make an Erect Direct East Dyal.

THese sorts of Dyals may better be demonstrated then made by the Globe; unless the Axis of your Globe were accessible, as in the Wyer-Globe, specified in Prob. 1. Therefore when you would make an East, or West Dyal, or a Polar Dyal.

Provide a square Board, as A B C D, draw the straight line e f upon it Parallel to the sides A C, and B D. and just in the middle between them: Cross this straight line at Right Angles with another straight line, as g h, quite through the Board.

Upon this Board with a little Pitch or Wax fasten the Semi-Circle of Position, so as both the Poles thereof may ly in the line g h, and the middle of the Semi-Circle marked co may ly upon the line e f, so shall i be the Center of the Semi-circle of Position: [Page 157] In this Center make a smal hole through the Board fit to receive a Wyer or a Nail. So may you with this Circle of Position thus fitted, and the side C D applyed to a line of Contingence ele­vated to the Height of the Equinoctial, draw line, from the Cen­ter through every 15 degrees of the Circle of Position, and by continuing them intersect the line of Conti [...]gence in the points from whence the Hour lines of an East or West Dyal is to be drawn:

Example.

I would make an Erect Direct East Dyal for Londons Lati­tude. Therefore I fasten a Plumb-line a little above the place

[figure]

on the Wall where I intend to make my Dyal, and wait till it hangs quietly before the Wall: then if the line be rub'd with Chalk (like a Carpenters line) I may by holding the Plumber end close to the Wall, and straining it pretty stif, strike with it a [Page 158] straight line as Carpenters do. This line shall be a Perpendicu­lar as E F: I chuse a convenient point in this Perpendicular, as at G, for a Center; whereon I discribe an occult Arch as H I: this Arch must contain the number of degrees of the Elevation of the Equinoctial counted between H and I, (which in our La­titude is 38½,) Therefore in a Quadrant of the same Radius with the occult Arch I measure 38½ degrees, and set them off in the Plane from H in the Perpendicular to I: Then from I to the Center G in the Perpendicular, I draw the prickt line I G, and this line shall represent the Axis of the World: I cross this Axis at Right Angles with the line G K and draw it from G. to K, so long as I possibly can: this line shall be the Contingent-line. I find a convenient place in this Contingent line as, at VI, to which I apply the side of the Board C [...] D, so as that the point [...] may ly just upon VI in the Contingent line; And having a thred fastned in the Center of the Semi-Circle of Position, I draw that thred straight over the first 15. degrees of the Circle of Position, numbred from 0 towards h, and where the thred cuts the Contin­gent line I make a mark, for that mark shall be the mark for the 7 a clock line. From thence I remove the thred to 30. degrees of the Semi-Circle, and draw it through the Contingent line, and where it cuts the Contingent line, there shall be the mark for the 8 a clock line, From thence I remove the thred to 45. degrees of the Semi-Circle and draw it through the Contingent line, and where it cuts the Contingent line there shall be the mark for the 9 a clock line. From thence in like manner I remove the thred to 60. and 75. and where the thred cuts the Contingent line shall be the mark for 10 and 11 a clock lines: The 12 a clock line cannot be drawn on this Plane, as you may see, if you apply the thred to 90 degrees, for though you should draw it out never so far yet would it never touch the Contingent line: because it is Parallel to the line g h, and lines Parallel never meet.

But because in our Latitude the Sun Rises before 4. in the Morning, therefore two Hour-lines are yet wanting, viz. 5, and 4, which I may find either by applying the thred first to 15, and next to 30 degrees from 0 towards g in the Semi-Circle, and so marking where it cuts the Contingent line, as before: Or else by transfering the distance of the same number of Hour lines from the 6 a clock line already drawn on the side e [...] to the side e g, as in Prob. 2. of this Book is more fully shewed.

[Page 159] Having thus marked out on the Contingent line the distances of each Hour; I draw a line Parallel to the Contingent line, and draw lines from every Hour markt on the Contingent to cross the Contingent line at Right Angles and continue each line to the line Parallel to the Contingent; and these lines shall be the Hour lines of an East Plane. To these Hour-lines I set Figures as in the Scheam may be seen.

The Style D K of this Dyal (as well as of others) must stand Parallel to the Axis of the World: it must be also Parallel to all the Hour lines, and stand directly over the 6 a clock line, and that so high as is the distance between the Center of the Semi-Circle of Position and the point where the 6 a clock line cuts the Contingent line: Or (which is all one) at such a height as when it is laid flat down upon the Plane it may just reach the 3 a clock line,

PROB. VII.

To make an Erect Direct West Dyal.

AN Erect Direct West Dyal is the same in all respects with an Erect Direct East Dyal; Only as the East shews the Fore-noon Hours, the West shews the Af­ter-noon Hours.

Thus if you should draw the East Dyal on any transparent Plane, as on Glass, Horn, or an Oyled Paper, on the one side will appear an East Dyal, and on the other a West. Only the Fi­gures as was said before (must be changed); for that which in the East Dyal is 11, in the West must be 1: that which in the East Dyal is 10, in the West must be 2: that which in the East Dyal is 9 in the West must be 3. &c.

PROB. VIII.

To make a Polar Dyal.

POlar Dyals are Horizontal Dyals under the Equinoctial: They are of the same kind with East and West Dyals; On­ly whereas East and West Dyals have but the Hour lines of half the longest Day discribed on them, these have all the Hour lines [Page 160] of the whole Day; and are marked on both sides the Noon line: as in the following Figure.

The Style of this Dyal must stand over the Noon line, Parallel to the Plane; for then it will also be Parallel to the Axis

[figure]

of the World: and its height above the Plane must be the di­stance between the Center i of the Semi-Circle and the point in the Contingent line cut by the Noon-line. But I have inserted the Figure, which alone is sufficient Instructions.

PROB. IX.

To make Erect South Dyals, Declining Eastwards, or Westwards.

DRaw on your Plane an Horizontal line, and on it discribe a Semi-Circle, as you were taught in Prob 4.

Then Rectifie the Globe, Quadrant of Altitude Colure and Hour Index▪ as by the same Probleme: and bring the lower end of the Quadrant of Altitude to the degree of Declination from the East or West point, according is your Declination is Eastwards or Westwards; for then the Quadrant of Altitude shall represent a Plane declining from the South E [...]stwards, or Westwards accordingly. Then tu [...]n the Globe Eastwards, till the Index of the Hour-Circle points to all the Hours before Noon, and examine in what number of degrees from the Zenith the Colure cuts the Q [...]drant of Altitude, when the Index points to each Hour, For a line drawn from the Center A through the [Page 161] same number of degrees reckoned from the Perpendicular A B, which is the 12 a clock line towards Con the Plane, shall be the same Hour-lines the Index points at.

Example.

I would make an Erect Dyal declining from the South to­wards the East 27. degrees: The Globe, Quadrant of Altitude, Vernal Colure, and Hour Index Rectified, as before, I bring the lower end of the Quadrant of Altitude to 27. degrees counted from the East point of the Horizon towards the North: Then

I turn the Globe East-wards till the Index points to 11 a clock, or till 15. deg. of the Equa­tor pass through the Meridian, and find the Colure cut the Quadrant of Altitude in 9.43 counted from the Zenith.
10 19.0
9 25.57
8 35.10
7 45.56
6 60.15
5 79.45

And these are the distances of the Fore-noon Hour-lines, which I seek in the West side of the Plane, viz. from B to­wards C; and through these distances I draw lines from the Cen­ter, and these lines shall be the Fore-noon Hour-lines.

Now herein is a difference between Declining Dyals, and Di­rect Dyals: For having found the distances of the Hour lines for one half of the Day, be it either for Before Noon or After Noon in a Direct Dyal, you have also found the distances for the other half Day; because, as was said Prob. 3. Equal number of Hours have equal distance from the Noon line: But in Declining Dy­als it is not so: Because the Sun remaining longer upon that side of the Plane which it declines to, then it doth upon the contrary side, there will be a greater number of Hour lines upon it, and by consequence the distance of the Hour lines less then on the con­trary side of the Plane.

Therefore for finding the After Noon Hour lines, I turn about the Quadrant of Altitude upon the Zenith point till the lower end of it come to the degree of the Horizon opposite to that de­gree of Declination that the Quadrant of Altitude was placed at when I sought the Fore Noon Hour lines, viz, to 27. degrees [Page 162] counted [...]om the West towards the South, and bring the Ver­ [...]al Colure again to the Meridian, and the Index (as before) to 12. Then,

turning the Globe Westwards till the Index poin [...]s to 1 a clock, or till 15 degr. of the Equator pass through the Me­ridian, I find the Colure cut the Quadrant of Altitude in 11.20 counted from the Zenith.
2 26.47
3 49.20
4 75.52

And these are the distances of the After Noon Hour lines; which dista [...] I seek in the East side of the Plane, viz. from B towards D (as before) and so drawing lines from the Center A through these distances, I have all the Afternoon Hour lines also drawn on my Plane.

You may note, that this Plane is capable to receive no more Hour lines After Noon then 4. for when the Colure goes off the Quadrant of Altitude, the Sun goes off these kind of Planes.

To these Hour lines I set their numbers, as you may see i [...] the Figure.

Then to find both the distances of the Substilar line from the 12 a clock line, and the Elevation of the Style above the Plane, Bring the Colure to the number of degrees of the Planes Decli­nation, counted in the Horizon from the South point towards the East point, and the Quadrant of Altitude to the degrees of the Planes Declination, counted in the Horizon from the East point to­wards the North so shall the Quadrant of Altitude and the Co­lure cut each other at Right Angles; and the number of degrees comprehended between the Colure and the Zenith in the Qua­drant of Altitude, shall be the number of degrees between the Sub­styler line and the 12. a clock line, which in this Example is 19. degrees 45. minutes: And the number of degrees comprehended between the Quadrant of Altitude and the Pole, counted in the Colure, shall be the number of degrees that the Style is to be Ele­vated above the Plane; which in this Example is 33. degrees 40. minutes. Wherefore for the distance of the Substyler line from the 12 a clock line, I count in the Circle from the 12 a clock line in the contrary side of the Plane, viz. in the West side, because the Plane declines towards the East 19. degrees 45▪ minutes, as at D, and through that number of degrees and minutes from the Center A, I draw the line A G, which shall be the Substyl [...]r line: And from the Substylar line (either way) I number 33. de­grees 40. minutes, the Elevation of the Style above the Plane, and [Page 163] through those degrees and minutes I draw from the Center A, the line A F, for the Style or Gnomon; Then I let fall the Per­pendicular F G upon the Substyle A G: So is there a Triangle

[figure]

made, which if it be erected Perpendicularly upon the Substyle A G, the Style A F shall be Parallel to the Axis of the World, and cast a shadow upon the Hour of the Day.

Here you may see that in Declining Dyals the Style doth not stand at the same Elevation above the Plane, that it doth in Erect Direct Dyals; neither doth it stand over the 12 a clock line; but swerves from it towards the Quarter of Declination.

PROB. X.

To make a North Erect Dyal declining Eastwards, or Westwards.

AS in Prob. 5. an Erect Direct North Dyal hath the same Delineation that an Erect Direct South Dyal hath, and differs only in the placing the Figures of the Hour lines: So a North Erect Dyal that declines Eastwards, or Westwards, differs from a South Erect Dyal that Declines Eastwards, or Westwards, the same number of degrees, only in placing the Hour lines at the same distance on the contrary side of the Plane, and by transposing the Figures of 11 for 1: 10 for 2: 9 for 3. &c.

Thus, if you draw upon Glass, Horn, or an Oyled Paper, the South Dyal Declining Eastwards, as in the foregoing Probleme, [Page 164] and place it to its due scituation, the back side of it shall be a North Dyal declining towards the West so many degrees as the foreside Declines towards the East; and the only difference in it will be the Figures of the Hour lines; as was said before.

PROB. XI.

To make Direct Reclining, or Inclining Dyals.

DIrect Reclining or Inclining Dyals are the same with Erect Direct Dyals that are made for the Latitude of some other Places: The Latitude of which Places are either more then the Latitude of your own Place, if the Plane Recline, or less if the Plane Incline; and that in such a proportion as the arch of Re­clination or Inclination of your Plane is.

Thus a Direct South Dyal Reclining 10. degrees in Londons Latitude, viz. 51½ degrees, is an Erect Direct Dyal made for the Latitude of 61½ degrees: And a Direct South Dyal Incli­ning 10. degrees in the Latitude 51½ degrees is an Erect Direct Dyal in the Latitude of 41½ degrees: and is to be made accord­ing to the Directions in Prob. 4.

PROB. XII

To make Declining Reclining, or Declining Inclining Dyals.

THe distances of the Hour lines either for a Declining Reclining Plane, or a Declining Inclining Plane may most easily be found upon the Plane of the Horizon, That is (as some Authors call it) by the Horizontal Dyal, by changing the Circles of the Globe one into another: So as the Plane of the Horizon may serve to represent the Dyal Plane; Yet this way not being natural, because you must admit one Cir­cle to be another, and that in Young Learners might sometimes breed a little difficulty, Gemma Frisius, Metius, and Blaew hath prescribed a thin Brass plate to be made equal to a Semi-Circle of the Equinoctial, and divided from the middle point of it either way into 90 degrees, which may not unproperly be called a Gno­monical Semi-Circle. This Semi-Circle must be bowed close [Page 165] to the Body of the Globe into a Semi-Circular form, and so set to any Reclination, or Inclination, and then it will represent a Re­clining or Inclining Plane: And by the motion of the Colure through the several degrees of this Semi-Circle the distances of the Hour lines may be found: Thus,

The Globe, Quadrant of Altitude, Colure, and Hour Index, Rectified; as by Prob. 4. Bring the lower end of the Quadrant of Altitude to the degree in the Horizon of the Planes Declinati­on, if your Plane be a South Declining Recliner, and count on the Quadrant of Altitude from the Zenith downwards the number of degrees of Reclination, or Inclination, and to that number of degrees bring the middle of the Gnomonical Semi-Circle, and let the ends of [...]t cut the Horizon on either side in the degrees of the Planes Azimuth, so shall the Gnomonical Semi-Circle represent a Reclining Plane. And so oft as 15. degrees of the Equator passes through the Meridian, so oft shall you enquire what de­grees of the Gnomonical Semi-Circle the Colure cuts; for so ma­ny degrees asunder must the several respective Hour lines of a Reclining Declining Plane be in a Semi-Circle divided into 180. degrees.

But if your Plane be a South Declining Recliner, or a North Declining Incliner; Bring the Quadrant of Altitude to the degree of the Horizon opposite to the degree of the Planes Declination, (because the upper side of the Plane lies beyond the Zenith) counted from the South point in the South Recliners, and from the North point in North Incliners.

Then find the height of the Style, and place of the Substyle: thus, Keep your Gnomonical Semi-Circle in its position: But turn the Quadrant of Altitude about on the Zenith point till the lower end of it comes to the degree of the Horizon opposite to the degree it was placed at before, and turn about the Globe till the Colure cut the Quadrant of Altitude above the Horizon in the number of degrees the Plane Reclines from the Zenith; so shall the Colure cut the Gnomonical Semi-Circle at Right Ang­les; Then count the degrees contained between the middle of the Gnomonical Semi-Circle and the Colure, for that number of de­grees is the distance of the Substyle from a Perpendicular line in the middle of your Plane, and must be placed Westwards of the said Perpendicular, if your Plane decline from the South East-wards; or Eastwards, if your Plane decline from the South West­wards. [Page 166] Then observe how many degrees are contained between the Semi-Circle and the Pole; for that number of degrees is the number of degrees that the Style is to be Elevated above the Substyle.

Example.

Here at London I would make a Dyal upon a Plane Declining from the South Eastwards 30. degrees, and Reclining from the Zenith 20. degrees; Londons Latitude is 51½ degrees: There­fore, Having on the Plane discribed a Semi Circle, &c. as was directed Prob. 4. I Rectifie the Globe, Quadrant of Altitude, Colure, and Hour Index, as by the same Probleme▪ and bring the lower end of the Quadrant of Altitude to 30. degrees from the North point of the Horizon towards the West, because that is the degree opposite to the degree of the Planes Declination, viz▪ to 30 degrees from the South Eastwards, And I bring the middle of the Gnomonical Semi Circle to 20. degrees of the Quadrant of Altitude counted from the Zenith downwards towards the Ho­rizon, and the ends of the Gnomonical Semi Circle to the degrees of Azimuth the Plane lies in in the Horizon, viz. to 30. degrees from the East point Northwards, and to 30. degrees from the West point Southwards, so shall 11. degrees 10. minutes of the Gnomonical Semi Circle be comprehended between the Qua­drant of Altitude and the Brasen Meridian: These 11. degrees 10. minutes shews that the 12 a clock line is distant from the Perpendicular A B 11. degrees 10. minutes: and because the Plane Declines to the Eastwards, therefore the 12 a clock line must stand on the West side the Plane 11. degrees 10, minutes. Then to find all the Fore Noon Hour lines,

I turn the Globe East-wards till the Index points to 11 a clock, or till 15, degr. of the Equa­tor pass through the Meridian, and find the Colure cut the Gnomonical Semi-Circle in 15. 8 counted from the middle of the Gnomonical Semi Circle.
10 18. 56
9 22. 37
8 26. 52
7 32. 37
6 42. 5
5 62. 43

And these are the distances of the Fore Noon Hour lines; to [Page 167] which distances you may set Pricks on the West side the Semi Circle of the Plane, viz. from B to C.

The After Noon Hour lines are found by bringing the Colure again to the Meridian, and the Index of the Hour Circle to 12. for then

turning the Globe West­wa [...]s till the Index points to 1 a clock, or till 15 degr. of the Equator pass throug the Me­ridian, I find the Colure cut the Gnomon, Semi-Circle in 5. 45 counted from the middle of the Gnomon. Semi-Circle.
— —
2 2. 54
3 20. 52
4 64. 36

And these are the distances of the After-noon Hour-lines; and must all but the 1 a clock Hour-line be prickt down at their re­spective distances on the East side the Plane, viz. from B to D: But because the Colure comes not to the middle of the Gnomoni­cal Semi-Circle before the first 15. degrees of the Equator pass thr [...]ugh the Meridian after 12. therefore the 1 a clock must stand 5▪ [...] [...]5. [...] on the West side of the Plane: And for this cause I [...] [...]tinction with a line between the 1 a clock

[figure]

and the 2 a clock, in the foregoing Table. Then I draw lines from the Center A through every one of these pricks in the Semi-Circle, and they shall be the Hour lines of this Declining Reclining Plane.

Having drawn the Hour-lines, I remove the Quadrant of Al­titude to the degree of the Horizon opposite to the degree it was at before, viz. to 30. degrees from the South Westwards, which is so much as the Plane declines Eastwards; But I let the Gno­monical Semi Circle stand as it did: And turning about the [Page 168] Globe till the Colure cut the Quadrant of Altitude in 20. de­grees counted from the Horizon upwards, viz. the degrees of Re­clination, I find 18. degrees 40. minutes contained between the middle of the Gnomonical Semi Circle and the Brasen Meridian, which is the distance of the Substyle from the Perpendicular; And I find the Gnomonical Semi Circle cut the Colure in 13. degrees 49. minutes from the Pole, which is the Height that the Style must be raised over the Substyle; Therefore I prick off in the Semi Circle on the Plane, the distance of the Substyle 18. de­grees 40. minutes from the Perpendicular Westwards; because this Plane declines Eastwards: And from the Center A, I draw through that prick the line A E, which shall be the Substyle, and from this Substyle (either way) I count in the Semi Circle on the Plane 13▪ degrees 49. minutes, and there make a Prick: Then from the Center A, I draw through that Prick the line A F, to represent the Style or Gnomon: Then I let fall the Per­pendiculer F G upon the Substyle A G; So is a Triangle made; which if it be erected Perpendicularly upon the Substyle A G, the Style A F shall be Parallel to the Axis of the World, and cast a shadow upon the Hour of the Day.

Having made this Dyal, you have made four several Dyals, whereof this is one: And his opposite, viz. North Declining Westwards 30. degrees Inclining to the Horizon 70. degrees is another. The South Declining Westwards 30. degrees Recli­ning from the Zenith 20. degrees is another: And his opposite, viz. North Declining Eastwards 30. degrees Inclining to the Horizon 70. degrees is the other.

PROB. XIII.

To make a Dyal upon a Declining Inclining Plane.

THe Precepts for making these Dyals are delivered in the foregoing Probleme: Therefore we shall at first come to an Example.

I would make a Dyal upon a Plane in Londons La­titude Declining from the South Westwards 25. degrees and In­clining towards the Horizon by the space of an Arch containing 14. degrees. Having first discribed on the Plane a Semi Cir­cle, as was directed Prob. 4. I rectifie the Globe, Quadrant of [Page 169] Altitude, Colure, and Hour Index, as by the same Probleme, and bring the lower end of the Quadrant of Altitude to the degree of the Planes Declination, viz. to 25. degrees counted from the South Westwards, and the ends of the Gnomonical Se­mi Circle to the degree of Azimuth the Plane lies in, viz. to 25. degrees from the West Northwards, and the middle of the Gnomonical Semi Circle to the degree of the Planes Inclination, viz. 14. degrees counted from the Zenith downwards on the Quadrant of Altitude, Then counting the degrees of the Gno­monical Semi Circle contained between the middle of the same and the Brasen Meridian, I find 5. degrees 30. minutes: These 5. degrees 30. minutes shews the distance of the 12 a clock line from the Perpendicular; Therefore I number in the Semi Circle discribed on the Plane, from the Perpendicular Westwards, (Be­cause the middle of the Gnomonical Semi Circle lies Westwards on the Globe) from the Meridian▪ And for finding all the Fore-Noon Hour-distances

I turn the Globe East-wards till the Index points to 11 a clock, or till 15 degr. of the Equa. pass throug the Meri­dian, and find the Colure cut the Gnomon, Semi-Circle in 20. 5 counted from the middle of the Gnomon. Semi-Circle.
10 36. 57
9 56. 24
8 76. 31

And these are the distances of all the Fore Noon Hour lines; to which several distances I make pricks on the West side the Semi Circle on the Plane, viz. from B to C.

The After Noon Hour lines are found by bringing the Colure again to the Meridian, and the Index of the Hour Circle to 12. For then

turning the Globe West­wards till the Index points to 1 a clock, or till 15. degrees of the Equa­tor pass through the Meridian, I find the Colure cut the Gno­monical Semi-Circle in 6. 20 counted from the middle of the Gnomoni­cal Semi Cir­cle.
2 18. 2
3 28. 45
4 39. 56
5 52. 30
6 67. 19
7 84. 13

And these are the distances of the After Noon Hour lines, which I also prick down at their respective distances from the Perpen­dicular Eastwards, viz. from B towards D on the Plane; and by drawing lines from the Center A through all the Pricks, I have all the Hour lines that this Plane will admit of.

[Page 170] Having drawn the Hour lines, I remove the lower end of the Quadrant of Altitude to the degree of the Horizon opposite to the degree it was at before, viz. to 25. degrees from the North Eastwards, which is so much as the Declination is Westwards; but I let the Gnomonical Semi Circle stand as it did, and turn about the Globe till the Colure cut the Quadrant of Altitude in 14. degrees counted from the Horizon upwards, which is the Inclination of the Plane: Then I find 24. degrees 3. minutes comprehended between the middle of the Gnomonical Semi Circle and the Brasen Meridian, which is the distance of the Substyle from the Perpendicular: and this distance I count West­wards on the Plane▪ because the middle of the Semi Circle lies Westwards on the Globe and draw the line A G through it for the Substyle: And I find the Gnomonical Semi Circle cut the Colure in 48. degrees 5. minutes▪ for the Heigth that the Style must be Elevated over the S [...]bstyle: Therefore I make a prick on the Plane 48. degrees 5 minutes distant from the Substyle, and through that prick I draw the line A F to represent the Style or Gnomon; Then I let fall the Perpendicula [...] F G upon the Sub­style A G, so is there a Triangle made; which if it be erected

[figure]

Perpendicularly upon the Substyle A G, the Style A F shall be Parallel to the Axis of the World, and cast a shadow upon the Hour of the Day.

Having made this Dyal you have also four Dyals made; as well as in the former Probleme: For this is one▪ and its opposite viz. North declining Eastwards 25. degrees Reclining 76. de­grees is another; The South declining Eastwards 25. degrees [Page 171] inclining 14▪ degrees is another; and its opposite, viz. North de­clining Westwards 25. degrees Reclining 76. degrees is another;

PROB. XIV.

To find in what Place of the Earth any manner of Plane that in your Habitation is not Horizontal, shall be Horizontal.

IT was said in the Preface that all manner of Planes however scituate are Parallel to some Country or other on the Earth: Therefore all manner of Planes are indeed Hori­zontal Planes; and the distances of the Hour lines to be [...]scribed on them may be found as the distances of the Hour lines of the Horizontal Dyal in Prob. 3. It rests now to learn in what place of the Earth any Plane that is not Horizontal in your Habitation shall become Horizontal: And for help of your understanding herein, Take these following Rules.

1. If your Plane be Erect Direct North, or South, it shall be an Horizontal in the same Longitude at 90. degrees distance on the Meridian, (counted from the Zenith of your Place,) through the Equinoctial. See an Example of this in Prob. 3. where I have reduced an Erect Dyrect Dyal▪ to an Horizontal. Thus an Erect Plane under the Pole is an Horizontal under the Equa­tor; and an Erect Direct in 80. degrees North Latitude is in the same Longitude an Horizontal at 10. degrees South Latitude: An Erect Direct in 70. degrees North Latitude, is in the same Longi­tude, an Horizontal at 20. degrees South Latitude: and so to any other degrees of Latitude (as aforesaid) till you come to 45. degrees Latitude▪ where an Erect is an Horizontal, and an Hori­zontal an Erect▪ Only as the Hour lines of the Horizontal (being [...] downwards) are numbred from the right hand towards the left, in the Erect Direct Dyal they are numbred from the left hand towards the Right.

2. If your Pla [...] be Erect Declining, it shall be an Horizontal Plane at that point on the Globe which is against the degree of Declination, found in the Horizon.

But note, If your Plane declines Westwards, the Sun comes sooner to the Meridian of it, then to the Meridian of the Place [Page 172] where it becomes an Horizontal Plane; and that by so many Hours or minutes as the degrees of the difference of Longitude between the two Places converted into Time amounts to. If it declines Eastwards, the Sun comes so much later to the Meridian of it: And for this Cause (though the making this Dyal be the same with an Horizontal Dyal for another Place, yet in Respect of Time) there will be a difference between them.

Example.

I would make the South Dyal Declining East 27. degrees, as in Prob. 9. by the Plane of the Horizon: First I seek in what Place of the Earth it shall become an Horizontal Plane: Thus, I Elevate the Pole of the Globe 51½ degrees above the Horizon, and bring the Vernal Colure to the Meridian, then I count from the South point in the Horizon Eastwards 27. degrees, and on the point on the Globe directly against those 27. degrees I make a prick for the Place where a Plane that declines 27. degrees from the South Eastwards at London shall be Horizontal; or which is all one, this Declining Plane at London shall ly in the Horizon of that Prick: This Prick for distinction sake we shall hereafter call the Horizontal Place: Then by Prob. 1. of the Se­cond Book, I examine the Latitude and Longitude of this Hori­zontal Place, and find Latitude 33. 40. South; and Longitude from the Colure 33. degrees, which is the difference of Longi­tude between London and the Horizontal Place: which being converted into Time by allowing for every 15. degrees 1. hour of Time, gives 2 hours 12. minutes that the Sun comes sooner to the Meridian of the Horizontal Place, then to the Meridian of the Plane at London: so that when it is 12 a clock there, it will be but 9. a clock 48. minutes here; when 12 a clock here, it will be 2 a clock 12. minutes There, &c.

Having thus found in what Longitude from London and Lati­tude this Plane is Parallel to the Horizon, I seek the distances of the Hour-lines upon the Planes of the Horizon Thus, I Elevate the Pole of the Globe to the Height of the Pole in the Horizontal Place, viz. 33. degrees 40, minutes, and bring the Horizontal Place on the Globe to the Meridian, and the Index of the Hour Circle to 12. Then I examine the degree of the Horizon the Co­lare cuts, and find it 19¾ from the South Westwards. This 19¾ [Page 173] degrees respresents the Meridian line of the Horizontal Place: And also the Substylar line here at London; Therefore this 19¾ degrees I count from the Perpendicular A B of the Plane, and from the Center A draw the line A G through them; Because from this line on the Plane all the Hour lines must be numbred, and not (as all along hitherto) from the Perpendicular of the Plane, Then

turning the Globe East-wards till the Index of the Hour Circle points to 11 a clock, or till 15. degr. of the Equa­tor pass through the Meridian, I find the Colure cut the Horizon in 10. 2 from the Meri­dian.
10 0. 45
9 6. 12
8 15. 25
7 26. 11
6 40. 30
5 60. 0

And these are the distances of the Forenoon Hour lines: which distances I transfer by pricks to the Plane. But as in Prob. 9. I sought the distances from the Perpendicular on the Plane, so now in this Case (as was said before) I seek them from the Substyle, and through these pricks I draw lines from the Center, as in other Dyals, and these lines shall be the Fore Noon Hour lines.

To find the Afternoon Hour distances, I bring the Horizontal Place on the Globe again to the Meridian, and the Index of the Hour Circle to 12. and

turning the Globe Westwards till the Index points to 1 a clock, or till 15 degr. of the Equator pass through the Me­ridian, I find the Colure cut the Horizon i [...] 31. 5 counted from the Meridian.
2 46. 32
3 68. 5
4 95. 37

And these are the distances of all the Afternoon Hour lines; which I also transfer to the Plane, counting them from the Sub­style, and draw lines from the Center A through these distances; and these lines shall be all the Afternoon Hour lines.

Then from the Substyle I count the degrees and minutes of the Latitude of the Horizontal Place, viz. 33. degrees 40. mi­nutes, and through these degrees and minutes I draw the line A F from the Center A, for the Style: Then from the Style I let fall the Perpendicular F G upon the Substyle, so is there a Triangle made; which if it be erected Perpendicularly upon the Substyle A G, the Style A F shall be Parallel to the Axis of the World, and cast a shadow upon the Hour of the Day.

[Page 174] 3. If your Plane be a Direct Recliner, Seek in the Longitude of your Place the Complement to 90. of your Planes Reclination▪ For there a Direct Recliner becomes an Horizontal Plane.

4. If your Plane be a Declining Recliner: The Globe and Quadrant of Altitude Rectified, Bring your Habitation on the Terrestrial Globe to the Meridian, and the Quadrant of Altitude to the Declination, as by the second Rule in this Probleme; and count upwards on the Quadrant of Altitude the Reclination, and there make a prick on the Globe by the side of the Quadrant of Altitude, for at that prick on the Globe the Declining Recliner shall become an Horizontal Plane. Then examine the Latitude of that prick as by Prob. 1. of the second Book, and the difference of Longitude, as by Prob. 9. of the third Book: And convert the difference of Longitude into Time, by allowing for every 15. degrees 1. hour: Time, for every degree 4, minutes Time, and so proportionably, so shall you know what Hours and Minutes the Sun comes sooner or later to the Meridian of your Habitation then to the Meridian of that Place where it becomes an Hori­zontal Plane: Sooner, if the Globe were turned Eastwards; but Later if it were turned Westwards.

Having thus found out where this Plane becomes Horizontal, make your Dyal to this Plane, as by the second Rule in this Probleme: Find also the Style as is there directed.

5. If your Plane be a Declining Incliner, The Globe and Quadrant of Altitude Rectified, Bring the Colure to the Meridi­an, and the Quadrant of Altitude to the degree of the Horizon opposite to the degree of the Planes Declination, and count up­wards on the Quadrant of Altitude the degrees of Inclination, and make a [...] there; For in the [...] of that prick (found as by [...] [...], of the Second Book) that Declining In­ [...] shall become an Horizontal Plane. Then find the Lati­tude and difference of Longitude of this [...] ▪ by the [...] [...] and make a [...]yal to that [...] by the second [...] in this Probleme. Find also the Style as therein is directed.

PROB. XV.

To make a Dyal on the Ceeling of a Room, where the Di­rect Beams of the Sun never come.

FInd some convenient place in the Transum of a Window to place a smal round peece of Looking-Glass, about the bigness of a Groat, or less; so as it may ly exactly Hori­zontal: The point in the middle of this Glass we will marke A, and for distinctions sake (with Mr Palmer) call it Nodus: Through this Nodus you must draw a Meridian line on the Floor, Thus: Hang a Plumb line in the Window exactly over Nodus, and the shadow that that Plumb line casts on the Floor just at Noon will be a Meridian line; Or you may find a Meridian line otherwise, as by the Preface. Having drawn the Meri­dian line on the Floor: find a Meridian line on the Ceeling, thus: Ho [...]d a Plumb line to the Ceeling, over that end of the Meridian line next the Window; If the Plumbet hang not exactly on the Meridian line on the Floor, remove your hand on the Ceeling one way or other, as you see cause till it do hang quietly just o­ver it: and at the point where the Plumb line touches the Ceel­ing make a mark, as at B; that mark B shall be directly over the Meridian line on the Floor: then remove your Plumb line to the other end of the Meridian line on the Floor, and find a point on the Ceeling directly over it, as you, did the former point, as at C, and through those two points B and C on the Ceeling strain and strike a line blackt with Smal Cole or any other Culler (as Car­penters do,) and that line B C on the Ceeling shall be a Meridian line, as well as that on the Floor: Then examine the Altitude of the Equinoctial, as by Prob. 6. of the Second Book you did the Meridian Altitude of the Sun; and fasten a string just on the No­dus, and remove that string in the Meridian line on the Ceeling till it have the same Elevation in a Quadrant, that the Equinoctial hath in your Habitation; and through the point where the string touches the Meridian line in the Ceeling shall a line be drawn at right Angles with the Meridian, to represent the Equinoctial line. Thus in our Latitude the Elevation of the Equator being 38½ de­grees; I remove the string fastned to the Nodus forwards or back­wards in the Meridian line of the Ceeling, till the Plumb line of a [Page 176] Quadrant, when one of the sides are applyed to the string, falls up­on 38½ degrees: and then I find it touch the Meridian line at D in the Ceeling: therefore at D I make a mark and through this mark strike the line D E (as before I did the Meridian line) to cut the Meridian line at Right Angles: This line shall be the Equinoctial line.

Then I place the Center of the Semi-Circle of Position upon Nodus, and under-prop it so that the flat side of it may ly Parallel to the string when it is strained between the Nodus and the E­quinoctial, and also so as the string may ly on the division of the Semi-Circle marked o, when it is help up to the Meridian line in the Ceeling: Then removing the string the space of 15. degrees in the Circle of Position to the Eastwards, and extending it to the Equator on the Ceeling, where the string touches the Equator there shall be a point through which the 1 a clock Hour-line shall be drawn: and Removing the string yet 15. degrees further to the Eastwards in the Semi-Circle of Position, and extending it also to the Equator, where it touches the Equator there shall be a point through which the 2 a clock Hour-line shall be drawn: Removing the string yet 15. degrees further to the Eastwards in the Semi-Circle of Position, and extending it to the Equator, there shall be a point through which the 3 a clock Hour-line shall be drawn: The like for all the other After-Noon Hour lines; so oft as the string is removed through 15. degrees on the Semi-Circle of Position, so oft shall it point out the After-Noon distances in the Meridian line on the Ceeling.

The scituation of the Semi-Circle of Position cannot conveni­ently be shewn in this Figure, unless it be drawn by the Rules of Perspective; Neither if it were would it suit with the other de­monstrations, expect they were drawn by the same Rules also; which to do would be hard for young Learners to understand: Therefore I have left out the Semi-Circle of Position in this Fi­gure and refer you for a demonstration thereof to the sixth Pro­bleme; For even as the lines drawn through every 15, degrees of the Semi-Circle there, denote in a Contingent line the di­stance of any Hour line from the Meridian line, even so a line drawn through every 15. degrees of the Semi-Circle of Position posited (as aforesaid) point out in the Equinoctial line on the Ceeling the distance of each respective Hour line from the Meri­dian line,

[Page 177] Having thus found out the points in the Equator through which the After-Noon Hour-lines are to be drawn, I may find the Fore-Noon Hour distances also the same way, viz. by bring­ing the string to the several 15. degrees on the West side the Se­mi-Circle of Position; or else I need only measure the distances of each Hour distance found in the Equator from the Meridian line on the Ceeling; for the same number of Hours from 12 have the same distance in the Equinoctial line on the other side the Meri­dian both Before and Afternoon: The 11 a clock Hour distance is the same from the Meridian line with the 1 a clock distance on the other side the Meridian, the 10 a clock distance the same with the 2 a clock distance, the 9 with the 3, &c. And thus the distances of all the Hour lines are found out on the Equator.

Now if the Center of this Dyal lay within doores, you might draw lines from the Center through these pricks in the Equator, and those lines should be the Hour lines, as in other Dyals: But the Center of this Dyal lies without doores in the Air, and there­fore not convenient for this purpose: So that for drawing the

[figure]

[Page 178] Hour lines you must consider what angle every Hour line in an Horizontal Dyal makes with the Meridian; that is, at what di­stance in degrees and minutes the Hour lines of an Horizontal Dyal cut the Meridian; which you may examine as by Prob. 3. for an Angle equal to the Complement of the same Angle must each respective Hour-line make with the Equator on the Ceeling.

Thus upon the point markt for each Hour distance in the E­quinoctial line on the Ceeling, I discribe the Arches I, II, III, IIII, as in the Figure, and finding the distance from the Meridi­an of the Hour-lines of an Horizontal Dyal to be according to the third Probleme. Thus

The 1 a clock Hour-line 11.40 whose Com­plement 90. is 78.20
2 24.15 65.45
3 38.4 51.56
4 53.36 36.24

I measure in a Quadrant of the same Radius with those arches already drawn from the Equinoctial line

for the 1 a clock Hour 78.20
2 65.45
3 51.56
4 36.24

and transfer these distances to the Arches drawn on the Ceeling: For then straight lines drawn through the mark in the Arch, and through the mark in the Equator, and prolonged both waies to a convenient length, shall be the several Hour-lines (a foresaid;) And when the Sun shines upon the Glass at Nodus, its Beams shall re­flect upon the Hour of the Day.

PROB. XVI.

To make a Dyal upon a solid Ball, or Globe, that shall shew the Hour of the Day without a Gnomon.

THe Equinoctial of this Globe, or (which is all one) the middle line must be divided into 24 equal parts, and mark­ed with 1, 2, 3, 4 &c to 12. and then beginning again with 1, 2, 3, &c. to 12. Then if you Elevate one of the Poles so many degrees above an Horizontal line as the Pole of the World is Elevated above the Horizon in your Habitation, and place one of the 12 s directly to behold the North, and the other to behold the South: [Page 179] when the Sun shines on it the Globe will be divided into two halfs, the one enlightened with the Sun-shine, and the o­ther shadowed: and where the enlight­ned half is parted from the shadowed half, there you shall find in the Equi­noctial the Hour of the Day; and that on two places on the Ball; because the E­quinoctial is cut in two opposite points by the light of the Sun.

A Dyal of this fort was made by M r John L [...]k, and set up on a Compo­site Columne at Lea­den Hall Corner in London, in the Ma­joralty of S r John Dethick Knight. The Figure whereof I have inserted, be­cause it is a pretty peece of Ingenuity, and may perhaps stand some Lover of Ar [...] in stead, either for Imitation, or help of Invention.

[figure]

PROB. XVII.

To make a Dyal upon a Glass Globe, whose Axis shall cast a shadow upon the Hour of the Day.

FIrst divide the Equinoctial of your Globe into 24 equal parts; and having a Semi-Circle cut out of some Brass plate, or thin Wood to the same Diameter your Globe is of, or a very little wider: Apply this Semi-Circle to the Globe, so as the up­per edge of each end of the Semi Circle may touch the Poles of the Globe, and the middle of the Semi Circle may at the same edge cut through some division made in the Equinoctial: for then a line drawn by the edge of the Semi Circle thus posited shall be a Meridian line; The same way you must draw Meridian lines through every division of the Equinoctial, and set figures to them, beginning with 1, 2, 3, 4, &c. to 12, and then beginning again with 1, 2, 3, 4, &c. to 12, again. This Globe being made of Glass, and having an Axis of Wyer passing through [...]t from Pole to Pole, will be an Horizontal Dyal all the World over; if its Axis be set Parallel to the Axis of the World in the same Place; and one of the Meridians marked 12 be set so as it may directly be­hold the North point in Heaven, and the other the South point in Heaven; for then the Axis of the Globe shall cast a shadow upon the Hour of the Day.

And if you divide the upper half of the Glass Globe from the under half, when the Axis stands Parallel to the Axis of the World, by a Circle drawn round about the Globe, that Circle shall re­present the Horizon; and the Meridian lines drawn on the Globe shall be the Hour lines, and have in the Horizontal Circle the same distance from the 12 a clock line that the same respective Hour line was found to have, as by Prob. 3. of this Book.

But because the shadow of this Axis will not be discerned through the Glass Body; therefore you may with Water and white Lead ground together, lay a Ground on the Inside of the under half of the Glass to the Horizontal Circle (as Looking-glass makers do their Looking Glasses with Tinfoil) for then the shadow will appear.

Such a Glass Globe Dyal hath the Lord Robert Titchborn standing in his Garden supported by Atlas.

The End of the Fifth Book.
[Page 181]
[figure]

The Sixth BOOK. Shewing the Practical Use of the GLOBES: Applying them to the Solution of Spherical Triangles.

PRAEFACE.

THe Solution of Spherical Triangles is to know the length of its Sides, and the width of its Angles. These have already by many learned Men been taught, to be performed by a Canon of Sines and Tan­gents; and also by many Instruments some serving as Ta­bles of Sines and Tangents, such as are the Sectors, Scales, the Spiral line, &c. and others serving to represent the Globe; such as be the Mathematical Jewel, Astrolabi­um Catholicum, and several other Projections of the Sphear. But none hath as yet taught the Solution of Sphe­rical Triangles by the Globe it self; though it be the most natural, and most demonstrative way of all, and indeed ought first to be learnt before the Learner enters upon any o­ther way.

[Page 183] To this Authors of Trigonometry agree, for the most of them in their Books give Caution that the Learner be alrea­dy sufficiently grounded in the Principles of the Globe: For those Lines or Circles which either in Tables or other In­stuments your force your Imagination to conceive represents your Line or Circle in question, those Lines and Circles I say, you have Actually and Naturally discribed on the Globe, and therefore may at a single Operation, or perhaps only by a sudden inspection, have an Answer annexed, ac­cording as the nature of your Question shall require: and that more Copiously then by Tables of Sines and Tangents: For therein you find but one Question at once resolved: but by the Globe you have alwaies two resolved together.

Of the Parts and Kindes of Spherical Triangles. THEOREMS.

1. ALL Spherical Triangles are made of six parts; Three Sides, and three Angles. The Sides are joyned toge­ther at the Angles, and measured by degrees of a Great Circle, from one end to the other. The An­gles are the distance of the two joyned sides: and they are also measured by an Arch of a Circle, discribed on the Angular point. If any three of these parts be known, the rest may be found.

2. All Spherical Triangles are either Right Angled, or Ob­lique Angled. A Right Angle contains 90. degrees: An Ob­lique Angle either more, or less.

3. If a Spherical Triangle have one or more Right Angles; it is called a Right Angled Spherical Triangle. But if it have no Right Angle; it is called an Oblique Angled Spherical Triangle.

4. If an Oblique Spherical Triangle have one Angle greater then a Right Angle: it is called an Obtuse Angled Spherical Tri­angle: But if it have no Angle greater, it is called an Accute Angled Spherical Triangle.

5. In Right Angled Triangles the sides including the Right Angle are called Legs: And the side opposite to the Right An­gle [Page 184] is called Hypothenusa. Thus the sides A B and A C in the following Triangle are called Legs; and the side B C is called Hy­pothenusa.

[figure]

6. In a Right Angled Spherical Triangle one of the Legs are called Base; the other Perpendicular: Thus the Leg B A is Base; and the Leg C A Perpendicular. But the Terms may be varied: for the Base may be made Perpendicular, and the Perpendicular Base. Also One of the adjacent Angles is called the Angle at the Base; the other the Angle at the Perpendicular: Thus the Angle B is cal­led the Angle at the Base: the Angle C the Angle at the Per­pendicular.

PROB. I.

The Legs of a Right Angled Spherical Triangle given; to find the Hypothenusa, and the two other Angles.

THe Base of a Right Angled Spherical Triangle shall in this following Treatise be alwayes placed on a Me­ridian, the Perpendicular on the Equator, the Hy­pothenusa on the Quadrant of Altitude, and the An­gle at the Base shall be measured in an Arch of the Horizon.

Elevate the Equinoctial into the Zenith, so shall the Poles of the Globe ly in the North and South points of the Horizon.

Then count from the Equinoctial on the first Meridian, if you use the Terrestrial Globe; or on the Vernal Colure, if you use the Celestial, because they are divided from the Equinoctial either way into 90. degrees; and because from thence the de­grees of the Equinoctial are begun to be numbred: Count (I say) from the Equinoctial the number of degrees the Base con­tains, and there make a prick: Then count in the Equinoctial from the first Meridian the number of degrees the Perpendicular contains, and make there a second Prick: Bring that second Prick to the Brasen Meridian, so shall the first Meridian be sepa­rated from the Brasen Meridian by the quantity of an Arch e­qual to the measure of the Perpendicular: Then having the Quadrant of Altitude screwed in the Zenith, turn it about till the side of it cut the Prick made in the first Meridian; so shall the [Page 185] Triangle be represented on the Globe. The Base shall ly on the first Meridian between the Equinoctial and the Quadrant of Altitude, the Perpendicular in the Equinoctial between the first Meridian and the Brasen Meridian; and the Hypothenusa on the Quadrant of Altitude between the Zenith and the first Meridian: and the number of degrees between each of these respective Ar­ches shall be the measure of each respective Side. For the An­gles; The Right angle is known to be 90. degrees, by the se­cond Theorem in the Preface. The measure of the Angle at the Perpendicular is numbred between the East point in the Hori­zon and the graduated edge of the Quadrant of Altitude: But to find the Angle at the Base you must turn the Triangle, make­ing the Perpendicular Base, and the Base Perpendicular.

Example.

Having the two Legs given A B 79. degreee 15. minutes, and C A 23. degrees 8 minutes, I would find the measure of the Hypothenusa C B, and the Angles B C.

The Equinoctial Elevated, as before, I make A B Base, and C A Perpendicular, counting in the first Meridian from the Equi­noctial 79. degrees 15. minutes, and there I make a prick: Then I number in the Equinoctial from the first Meridian 23. degrees 8. minutes, the length of the Perpendicular, and there I make a second Prick: This prick I bring to the Brasen Meridian, so is the first Meri­dian separated from the Bra­sen Meridian so many de­grees and mi­nutes as is the length of the Perpendicular C A; Then I screw the Quadrant of Altitude to the Zenith, viz. directly over the Equinoctial, and move it about till the edge of it touch the Prick made in the first Meridian: So is the Triangle made on the Globe: And the num­ber of degrees and minutes of the Quadrant of Altitude compre­hended between the first Meridian and the Zenith is the measure of the Hypothenusa C B; which in this Example is 80. degrees 8. minutes: The number of degrees in the Horizon compre­hended

[figure]

[Page 186] between the Equinoctial and the Quadrant of Altitude is the measure of the Angle C, 85. degrees 44. minutes: the Angle A is a Right Angle, 90. degrees: And to find the Angle B, turn the Triangle, (all but the Letters;) Thus: As before A C was Base, so now I make B A Base; and as before A B was Perpendicular, so now C A shall be Perpendicular: so is your Triangle turned.

[figure]

Now, as before I counted 79. de­grees 15. minutes from the Equinoctial on the first Meridian, which was the length of that Base, so now I count 23. degrees 8. minutes on the first Meridian, which is the length of this Base, and there (as before) I make a Prick: and as be­fore I counted 23. degrees 8. minutes on the Equinoctial from the first Meridian, which was the length of that Perpendi­cular; so now I count 79. degrees 15. minutes on the Equinoctial, which is the length of this Perpendicular; and there I make a prick on the Equinoctial: Then I bring this Prick (as before) to the Brasen Meridian, so shall the first Meridian be distant (as before) from the Brasen Meri­dian so many degrees and minutes as is the length of this Perpen­dicular, viz. 79. degrees 15. minutes: Then Having the Quadrant of Altitude screwed to the Zenith, I turn it about till the edge of it touch the Prick made in the first Meridian at 23. degrees 8. minutes distant from the Equinoctial; so is the Triangle Turned: And so shall the Arch of the Horizon comprehended between the Equinoctial and the Quadrant of Altitude be the measure of the Angle C in the former Triangle, (but now made B) 23. de­grees 30. minutes: you also see again the measure of the Hypothe­nusa B C 80. degrees 8. minutes on the Quadrant of Altitude, counted between the Zenith and the first Meridian.

[figure]

PROB. II.

A Leg and the Hypothenusa given, to find the Rest.

EXample. The Leg given shall be C A in the former Triangle 23. degrees 8. minutes, The Hypothenusa C B 80. degrees 8. minutes. The Equinoctial and Qua­drant of Altitude Rectified, as by the last Probleme; Number the Leg C A 23. degrees 8. minutes on the Equinoctial from the first Meridian, and there make a prick; Bring this Prick to the Brasen Meridian; Then number on the Quadrant of Altitude the Hypothenusa B C 80. degrees 8. minutes from the Zenith towards the Horizon, and make there on the edge of the Quadrant of Altitude another prick: Then turn the Qua­drant of Altitude about till the prick made on the edge of it touch the first Meridian; so shall the Triangle be made: The arch of the Equinoctial comprehended between the first Meridi­an and the Brasen Meridian, shall represent A C the Perpendicu­lar; the arch of the Quadrant of Altitude comprehended be­tween the Zenith and the First Meridian, shall represent B C the Hypothenusa; and the arch of the first Meridian comprehended between the Equinoctial and the Quadrant of Altitude shall re­present B A the Base; which was one Leg sought, and is (as you will find) 79. degrees 15. minutes: The Angle C you will find in the Horizon 85. degrees 44. minutes: The angle A is the Right Angle 90. degrees: And to find the Angle B you must turn the Triangle, as you were directed in the former Probleme.

PROB. III.

The Hypothenusa and an Angle given, to find the Rest.

THe Hypothenusa given shall be B C of the Triangle in Prob. 1. 80. degrees 8. minutes, The Angle given shall be C 85. degrees 44 minutes: The Globe and Quadrant of Altitude Rectified, as by Prob. 1. Count the given Angle 85. degrees 44. minutes on the Horizon from the Equinoctial, and there place the Quadrant of Altitude: Then turn about the Globe till the first Meridian touch 80. degrees 8. [Page 188] minutes of the Quadrant of Altitude counted from the Zenith downwards, so shall the Triangle be made on the Globe: The Arch of the Equator comprehended between the first Meridian and the Brasen Meridian shall shew the length of the Perpendi­cular C A 23. degrees 8. minutes; the Arch of the first Meridian comprehended between the Equinoctial and the Quadrant of Al­titude shall shew the length of the Base A B 79. degrees 15 mi­nutes; the Right Angle made at the Interfection of the Brasen Meridian with the Equinoctial is 90. degrees: and to find the measure of the Angle B you must turn the Triangle, as you were directed Prob. 1.

PROB. IIII.

A Leg and Angle adjoyning given, to find the Rest.

IN the Triangle of Prob. 1. The Leg given shall be C A 23. degrees 8. minutes, the Angle adjoyning shall be C 85. de­grees 44 minutes: The Globe and Quadrant of Altitude Rectified, as by Prob. 1. I turn about the Globe till the first Meridian be distant from the Brasen Meridian 23. degrees 8. minutes, the length of the Leg C A: Then I count in the Hori­zon from the Equinoctial 85. degrees 44. minutes, the measure of the Angle C; so is the Triangle made on the Globe. The Arch of the first Meridian comprehended between the Quadrant of Altitude and the Equinoctial shall shew the length of the Base A B 79. degrees 15. minutes; The Arch of the Quadrant of Altitude comprehended between the Zenith and the first Meridi­an shall shew the length of the Hypothenusa C B 80. degrees 8. minutes; The Right Angle made at the Intersection of the E­quinoctial and the Brasen Meridian is 90. degrees: And to find the measure of the Angle B, you must turn the Triangle, as you were directed Prob. 1.

PROB. V.

A Leg and the Angle opposite given, to find the Rest.

IN the Triangle of Prob. 1. the Leg given shall be A B 79. degrees 15. minutes, the Angle opposite shall be C 85. degrees [Page 189] 44. minutes, The Globe and Quadrant of Altitude Recti­fied, as by Prob. 1. I bring the Quadrant of Altitude to 85. de­grees 15. minutes of the Horizon, the measure of the Angle C: Then I turn the Globe till 79. degrees 15. minutes of the first Meridian (which is the measure of the Leg A B) touch the Qua­drant of Altitude, so is the Triangle made on the Globe. The Arch of the Equinoctial comprehended between the first Meridian and the Brasen Meridian shews the length of the Leg C A 23. de­grees 8. minutes; the Arch of the Quadrant of Altitude com­prehended between the Zenith and the first Meridian, shall shew the length of the Hypothenusa C B 80. degrees 8. minutes: The Right Angle made at the Intersection of the Equinoctial and the Brasen Meridian is 90. degrees: And to find the measure of the Angle B, you must turn the Triangle, as you were directed in Prob. 1:

PROB. VI.

The Angle given, to find the Sides.

IN this Case you must turn the Angles into Sides, making an Oblique Triangle on the Globe, whose Sides shall be equal to the given Angles: so shall the Angles of this Triangle found, be the measure of the Sides required.

Example.

In the Triangle of Prob. 1. The Angle A is 90. degrees, the Angle B 23. degrees 30. minutes, the Angle C. 85. degrees 44. minutes: The Globe and Quadrant of Altitude Rectified, as by Prob. 1. I set the Right Angle A 90. degrees on the Brasen Me­ridian, between the Pole and the Equinoctial; For the Angle B I number downwards on the Quadrant of Altitude 23. degrees 30. minutes, which shall be the side representing that Angle: for the Angle C I number on the first Meridian from the Pole to­wards the Equinoctial 85. degrees 44. minutes, which shall be the side representing that Angle: Then I turn the Globe and Quadrant of Altitude till I can joyn the 23. degrees 30. minutes counted before on the Quadrant of Altitude and this 85. degrees 44. minutes counted in the first Meridian together; So is a Tri­angle [Page 190] made on the Globe; whose sides being equal to the Angles given, shall have its Angles equal to the sides required: Thus the Arch of the Equinoctial comprehended between the first Me­ridian and the Brasen Meridian shall be found 23. degrees 8. mi­nutes, the measure of the side A C: The Arch of the Horizon contained between the nearest Pole and the Quadrant of Altitude shall be found 79. degrees 15. minutes, the measure of the side B A: And to find the Hypotenusa B C, you have now Data's e­nough, either to find it as by some of the former Problemes; or else you may find it by turning the Triangle as by Prob. 1.

These Cases of Right Angled Spherical Triangles may be wrought otherwaies by the Globe, If you alter its Position; making the North or South points of the Horizon, Zenith; or else the Poles of the World, or the Poles of the Ecliptick; and use the Circle of Position insteed of the first Meridian or Circles of Longitude: But these Instructions together with a little Pra­ctise, are (I judge) sufficient; Therefore I shall refer Varieties to the Studies of the Industrious Studient.

Of Oblique Triangles. PROB. VII.

The three Sides given, to find the Angles.

ELevate the Pole of the Globe above the Horizon to the Complement of one of the given Sides and screw the Qua­drant of Altitude in the Zenith, so shall that given Side be com­prehended between the Pole and the Quadrant of Altitude; Then count from the Pole upon the first Meridian the measure of the Second Side, and there make a prick; Count also from the Ze­nith upon the Quadrant of Altitude downwards the measure of the third Side, and make there on the edge of the Quadrant of Altitude another prick; Then turn the Globe and Quadrant of Altitude till you can joyn these two pricks together; so shall your Triangle be made on the Globe: And then the number of de­grees of the Equinoctial comprehended between the first Meridi­an [Page 191] and the Brasen Meridian shall be the measure of the Angle at the Pole: The Arch of the Horizon comprehended between the Quadrant of Altitude and the intersection of the Brasen Meri­dian with the Horizon on that side the Pole is elevated, shall be the measure of the second Angle: And for finding the third An­gle, you must turn the Triangle, as by Prob. 1.

Example.

In the Triangle A B C annexed, The Side A B contains 38. degrees 30. minutes, the side B C 25. degrees, and the side A C 60. degrees; I would measure these Angles; I place one of these sides upon the Meridian, viz. A B 38. degrees 30 mi­nutes, the Complement of 38. degrees 30. minutes is 51 de­grees 30. minutes; Therefore I Elevate the Pole 51. degrees 30. minutes above the Horizon, so shall the Zenith be distant from the Pole 38. degrees 30. mi­nutes; here I screw the Quadrant of Altitude and count down­wards on it the measure of the side B C 25. degrees, and there I make a prick: Then from the Pole I count on the first Meridi­an 60. degrees, the measure of the side A C, and there I make a­nother prick: Then I turn the Globe and Quadrant of Alti­tude backwards or forwards till these two pricks are joyned to­gether; so shall the Triangle A B C be made on the Globe: The arch of the Brasen Meridian comprehended between the Pole and Zenith shall represent the side A B; the Arch of the Quadrant of Altitude comprehended between the first Meridian and the Brasen Meridian shall represent the side B C; and the Arch of the first Meridian comprehended between the Pole and the Quadrant of Altitude shall represent the side A C; The Pole shall represent the Angle A, the Zenith the Angle B; and the intersection of the first Meridian with the Quadrant of Altitude shall represent the Angle C. The Angle at the Pole is measured in the Equator; for the degrees comprehended between the first Meridian and the Brasen Meridian being 17. degrees 15. minutes shews 17. degrees 15. minutes to be the measure of the Angle A. The Angle at the Zenith is measured in the Horizon; for [Page 192] the degrees comprehended between the Intersection of the Brasen Meridian with the Horizon on that side the Pole is Elevated be­ing 142. degrees 42. minutes, shews that 142. degrees 42. mi­nutes is the measure of the Angle B, Thus two angles are found; the third is wanting: which I find thus,

[figure]

I turn the Triangle, placing either A or C in the Zenith. Ex­ample: I place A at the Zenith, which before was at the Pole; so shall C be at the Pole, and B at the Intersection of the first Meridian and the Quadrant of Altitude, and the side A C shall be comprehended between the Pole and Zenith: The side A C contains 60. degrees; its Complement to 90 is 30. degrees; therefore I Elevate the Pole of the Globe 30. degrees above the Horizon; so shall 60. degrees be in the Zenith; therefore to 60. degrees I screw the Quadrant of Altitude and count on it down­wards the measure of the other side next the Zenith, viz. 38. degrees 30. minutes; and there I make a prick: Then from the Pole on the first Meridian I count the measure of the last side, viz. 25. degrees, and there I make another prick: Then I turn the Globe and Quadrant of Altitude (as before) till these two pricks joyn; so is the Triangle altered on the Globe: For the Arch of the Brasen Meridian comprehended between the Pole and Zenith which before was 38. degrees 30. minutes, is now 60. de­grees; the Arch of the Quadrant of Altitude Comprehended be­tween the first Meridian and the Brasen Meridian, which before was 25 degrees, is now 38. degrees 30. minutes; and the Arch of the first Meridian comprehended between the Quadrant of Altitude and the Pole, which before was 60. degrees is now 25. degrees. Thus the Angle C being now at the Pole, its measure is found in the Equinoctial, viz. that Arch comprehended be­tween the first Meridian and the Brasen Meridian, which is 25. degrees 24. minutes; and the measure of the Angle A, which is now in the Zenith, having its sides, the one an Arch of the Bra­sen Meridian, the other an Azimuth, (or which is all one) an Arch of the Quadrant of Altitude, is measured in the Horizon, as all Azimuths are, and found 17. degrees 15. minutes, as before.

PROB. VIII.

Two Sides and the Angle contained between them given, to find the Rest.

EXample. In the former Triangle I have given the sides A B, 38. degrees 30. minutes, A C, 60. degrees, and the Angle A 17. degrees 15. minutes.

The Method I have hitherto used is to place the given side up­on the Meridian between the Pole and Zenith; but because the Angle at the Pole in this Example falls out so large that the Quadrant of Altitude will not reach the first Meridian; therefore I shall use another way to work this Probleme as well.

I Elevate the Pole of the Globe to the Com-plement of one of the given sides; suppose the side A B, which being 38. degrees 30. minutes, its Complement to 90. degrees is 51. degrees 30. minutes, so shall the Zenith be distant from the Pole 38. degrees 30. minutes, the measure of the side A B: The other side is 60. degrees, this 60. degrees I count from the Pole in the first Meridian, and there I make a prick: The Angle given is 17. degrees 15. minutes; this I count in the Equinoctial from the first Meridian, and this degree and minute in the Equinoctial I bring to the Brasen Meridian, so shall the first Meridian be se­parated from the Brasen Meridian 17. degrees 15. minutes: Then I screw the Quadrant of Altitude to the Zenith, and bring the side of it to the prick made in the first Meridian: so shall the Tri­angle be made on the Globe. Then to find the unknown side B C, I count the number of degrees on the Quadrant of Altitude comprehended between the Zenith and the first Meridian, and find 25. degrees, which is the measure of the side B C: To find the measure of the Angle B, I count the number of degrees con­tained between the Intersection of the Meridian with the Horizon on that side the Pole is Elevated and the Quadrant of Altitude, and find 142. degrees 42. minutes, which is the measure of the Angle B: And to find the Angle C I turn the Triangle, as in Prob. 7.

PROB. IX.

Two Sides and an Angle opposite to one of them given, to find the Rest.

EXample. In the Triangle in Prob. 7. the Sides given are A B 38. degrees 30. minutes, and A C 60. degrees: The Angle given opposite to A C is B 142. degrees 42. minutes: I Ele­vate the Pole to the Complement of one of the given sides; sup­pose A B, which being 38. degrees 30. minutes, its Complement to 90. degrees is 51. degrees 30. minutes; so is the Zenith di­stant from the Pole 38. degrees 30. minutes: To this 38. de­grees 30. minutes I screw the Quadrant of Altitude, and count in the Horizon from the Intersection of the Meridian with the Ho­rizon on that side the Pole is Elevated the measure of the given Angle B, viz. 142 degrees 42. minutes, and to this number of degrees and minutes of the Horizon I bring the edge of the Qua­drant of Altitude, then I count in the first Meridian from the Pole the measure of the side A C 60. degrees; and there I make a prick, and turn about the Globe till that prick come to the edge of the Quadrant of Altitude, so is the Triangle made on the Globe. The degrees of the Quadrant of Altitude comprehen­ded between the first Meridian and the Zenith being 25. degrees, is the measure of the side B C: The degrees of the Equinoctial comprehended between the first Meridian and the Brasen Meridi­an being 17. degrees 15. minutes, is the measure of the An­gle A; and for finding the measure of the Angle C, I turn the Tri­angle, as in Prob. 7.

PROB. X.

Two Angles and the Side comprehended between them gi­ven, to find the Rest.

EXample. In the Triangle of Prob. 7. the Angles given are A 17 degrees 15. minutes, and B 142. degrees 42. minutes, the side comprehended between them is A B 38 degrees 30. minutes, I Elevate the Pole to the Complement of the side A B which being 38. degrees 30. minutes, its Complement to 90 de­grees [Page 195] is 51. degrees 30. minutes, so is the Zenith distant from the Pole 38. degrees 30. minutes; to this 38. degrees 30. minutes I screw the Quadrant of Altitude, and count in the Horizon from the Intersection of the Meridian with the Horizon on that side the Pole is Elevated the measure of the given Angle B, viz. 142. degrees 42. minutes, and to this number of degrees and minutes of the Horizon I bring the edge of the Quadrant of Altitude; then I turn about the Globe till the first Meridian is distant from the Brasen Meridian 17. degrees 15. minutes of the Equinoctial, which is the measure of the other given Angle; So shall the Tri­angle be made on the Globe: and the Arch of the Quadrant of Altitude comprehended between the first Meridian and the Ze­nith shall be the measure of the side B C 25. degrees, and the Arch of the first Meridian comprehended between the Pole and its Intersection with the Quadrant of Altitude shall be the mea­sure of the side A C 60. degrees: The measure of the Angle C is found by turning the Triangle, as in Prob. 7.

PROB. XI.

Two Angles and a Side opposite to one of them given, to find the Rest.

EXample. In the Triangle of Prob. 7. the Angles given are A 17. degrees 15 minutes, and B 142. degrees 42. minutes, the side given is B C 25. degrees, being the side opposite to the Angle A; the Angle A is made at the Pole of the Globe, and mea­sured in the Equator: Therefore I separate the first Meridian from the Brasen Meridian 17. degrees 15. minutes, so doth the Pole represent the Angle A; the Angle B is made at the Zenith, and measured in the Horizon; therefore I count in the Horizon 142. degrees 42. minutes, and there I make a prick, to this prick I bring the edge of the lower end of the Quadrant of Altitude, (not minding to what degrees of the Meridian the upper end of it is placed) Then I count from the upper end of the Quadrant of Altitude 25. degrees downwards the measure of th e side B C and there I make a prick, and keeping the lower end of the Quadrant of Altitude to the prick made in the Horizon, I slide the upper end of it forwards or backwards till the prick on the Quadrant of Altitude come to the first Meridian, so shall the Triangle be made [Page 196] on the Globe: Then the Arch of the Brasen Meridian compre­hended between the Pole and the upper end of the Quadrant of Altitude shall be the measure of the side A B 38. degrees 30. mi­nutes; and the Arch of the first Meridian comprehended between the prick on the Quadrant of Altitude and the Pole shall be the measure of the side A C 60. degrees; But the Angle C you must find by turning the Triangle; as in Prob. 7.

In the working this Probleme I would have placed the given fide B C 25. degrees upon the Brasen Meridian between the Pole and Zenith; but then the Angle B (being so Obtuse) would have had that side which would be intersected by the Quadrant of Altitude (viz. the first Meridian under the Horizon, which the Quadrant of Altitude cannot reach.

PROB. XII.

Three Angles given, to find the Sides.

THis Triangle is taught to be resolved by M r Palmer on the Planisphear; Book 3. Chap. 19.

It is to be known (saith he) That if you go to the Poles of the three great Circles whereof your Triangle is made, these Poles shall be the Angular points of a second Triangle; and the two lesser sides of this second Triangle shall be equal to the two lesser Angles of your first Triangle: the greatest side of the second Triangle shall be the supplement of the greatest Angle of the first Triangle (that is, shall have as many degrees and minutes as the greatest Angle of the first Triangle wanted of 180. degrees (see Pitiscus Trigonometry Lib. 1. Prop 61.

This second Triangle therefore (all whose sides are known from the Angles of the first) you shall resolve by Prob. 7. And ha­ving by that Probleme found the Angles of this second Trian­gle, know that the two lesser Angles of the second Triangle shall be several and respectively equal to the two lesser sides of the first Triangle, (and the least Angle to the least side, the middle Angle to the middle side) and the greatest Angle of this second Triangle being subtracted out of 180. degrees, shall leave you the greatest side of your first Triangle.

Example. If the Angles be given 142. degrees 42. minutes, 17. degrees 15. minutes, and 25. degrees 24. minutes; and the [Page 197] sides be enquired. Draw by aim a rude Scheam of this first Tri­angle, writing in the Angle A 17 degrees 15. minutes, in B 142. degrees 42. minutes, in C 25. degrees 24. minutes; supposing the sides yet unknown: then draw under this by aim also, a Scheam of the second Triangle, setting his Base Parallel with the Base of the first and making the Base of the second shorter then the Base of the first. Set also B at the Vertical Angle, and A C at the Base; as in the first Triangle. Then say,

Because A in the first Triangle is 17, degrees 15. minutes, there­fore in the second Triangle B C (which subtendeth A) shall be 17. degrees 15. minutes: and because C in the first Triangle is 25. degrees 24. minutes, therefore in the second Triangle the side A B which subtendeth C) shall be 25. degrees 24. minutes; and because B the greatest Angle in the first Triangle, is 142. de­grees 42. minutes, therefore in the second Triangle the side A C (which subtendeth B) shall be the complement thereof to 180. degrees, viz. 37. degrees 18. minutes: Write now upon the sides of this second Triangle the quantities of the sides, so is your second Triangle ready to be resolved, as by Prob. 7. Whereby you shall find the Angles of the second Triangle, as I have ex­pressed them in the Scheam. A 25. degrees, C 38. degrees 30. mi­nutes, B 120. degrees.

N [...]w lastly, I say these Angles of the second Triangle thus found, give me the sides of the first Triangle, which I seek, in this manner.

In the second Triangle.   In the first Triangle.
A is 25. degrees Therefore B C is 25. degrees
C is 38. 30. A B 38. 30.
B is 120. 00. A C 60. 00.

Complement of 120. degrees to 180. And thus by all the Angles given, we have found out all the sides, which was required.

[figure]

Having then the Angles of your first Triangle given, and his sides now found; you shall find his scituation on the Globe thus Place him as in Prob. 7. A B 38. de­grees 30. minutes between [Page 198] the Pole and Zenith, A C 60. degrees in the first Meridian separated from the Brasen Meridian 17. degrees 15. minutes of the Equinoctial, B C 25. degrees on the Quadrant of Al­titude, counted from the Zenith when its lower end is applyed to the 142. degrees 42. minutes of the Horizon: you shall say, Because the East point of the Horizon is the Pole of the Arch A B, therefore at the East point of the Horizon shall stand the An­gle C, which A B subtendeth: Next follow the 142. degrees 42. minutes of Azimuth which maketh B C of your Tri­angle to the Horizon, and from thence number in the Horizon to­wards the East point 37, degrees 18. minutes, the Complement of the Angle A to 180. degrees, and number yet further 52. degrees 42. minutes beyond the East point to make up 90, and there is the Pole of the Arch B C: Therefore there shall stand the Angle A, which B C subtendeth. Then count in the Equator from the first Meridian 90. degrees, which will end under the Horizon, and there make a prick; for there is the Pole of the Arch or side A C. Therefore at that prick shall stand the Angle B, which A C subtendeth.

Here you see your second Triangle made by the Poles of the first adjoyning to the East point of the Globe: only the side A B is wanting: To get that, make a prick upon the Globe against the 52. degres 42. minutes from the East point of the Horizon found before, to represent the Angle A: Then turn about the Globe and Qudrant of Altitude till that prick and the prick made before for the Angle B are both at once cut by the side of the Qua­drant of Altitude, and you will find 25. degrees 24. minutes of the Quadrant of Altitude comprehended between the two pricks, for the measure of the side A B

PROB. XIII.

How to let fall a Perpendicular that shall divide any Ob­lique Spherical Triangle into two Right Angled Spherical Triangles.

THis Probleme is much used when an Oblique Triangle having two sides and an Angle given is to be solved by the Cannon of Sines and Tangents: but by the Globe it may be solved without it, as was shewed Prob, 8, 9. [Page 199] Yet because letting fall a Perperdicular is so frequent in all Au­thors that treat of Trigonometry, I have inserted this Pro­bleme also.

[figure]

In the Oblique Triangle of the fromer Problemes there is given the sides A B 38½ degrees, and B C 25. degrees, and the Angle C 25. degrees 24. minutes; It is required to let fall a Perpendicular as B a from the Angle B. upon the Base A C; and to know both the measure of this Per­pendicular, and the parts it divides the Base into.

Therefore Elevate the Pole of the Globe above the Horizon so much as is the measure of the Angle C, which in this Example is 25. degrees 24. minutes, and bring the intersection of the first Meridian with the Equinoctial to the East point of the Horizon; so shall the Angle at the East point of the Horizon comprehended between the Horizon and the first Meridian be equal to the An­gle C: then count in the first Meridian from the East point of the Horizon the measure of the side B C 25. degrees, and having the Quadrant of Altitude screwed to the Zenith bring the gra­duated edge of it to these 25. degrees, so shall the Arch of the Ho­rizon comprehended between the East point and the lower end of the Quadrant of Altitude be the number of degrees that the Per­pendicular falls upon the Base, counted from the Angle C to a, which in this Example is 21¾ degrees, and the Arch of the Qua­drant of Altitude comprehended between the Horizon and the first Meridian is the measure of the Perpendicular B a 11. degrees.

And thus by letting fall this Perpendicular you have two Right angled Spherical Triangles made, the one B a C, wherein is found C a, 21¾ degrees, B C 25. degrees B a 11. degrees C 25. degrees 24. minutes, and a the Right Angle: There remains only the angle B unknown; which you must find by turning the Triangle, as was taught Prob. 1. The other Right angled Spherical Trian­gle made, is B a A, wherein is found A a (Complement of 21 2/4 degrees to 60 degrees (the whole Base before given) 38¼ de­grees, A B 38. degrees 30. minutes, B a 11. degrees, and a the Right Angle; which is more then enough to find the Angl [...]. A and B; as was shewed in the Preface. Theorem 1.

The End of the Sixth Book

Here follows the Ancient STORIES of the several STARS, and CONSTELLATIONS. Shewing the Poetical Reasons why such Various Fi­gures are placed in HEAVEN.

Collected from Dr HOOD. And First, Of the Northern Constellations.

1. URSA MINOR. This Constellation hath the preheminence, because it is neerest of all the rest unto the North Pole; And is called of the Greeks [...] whereupon the Pole is called the Pole Arctick, for that it is neer unto that Constellation. It is also called Helice minor, because of the smal revolution which it maketh round about the Pole: or rather of Elice, a Town in Arcadia, wherein Calysto the great Bear, and mother to the less, was bred. It is called Cynosura, because this Constellati­on, though it carry the name of a Bear, yet it hath the taile of a Dog: Last of all, it is termed Phoenice, because that Thales, who first gave the name to this Constellation, was, a Phoenician: And therefore the Phoenicians being taught how to use it in their Navigations, did call it by the name of the Country where­in Thales was born. It consisteth of 7. stars, which the Latines call Septemtriones; because by their continual motion, those seven stars do as it were wear the Heavens. The Spaniards call them all Bosina, that is, an Horn; because they may be very well brought into that form; whereof that which is in the end of the tail, is called the Pole-star, by reason of the neareness thereof unto the Pole of the world▪ for it is distant (according to the opinion of most) from the true Pole, but 23. deg. 30. min. The Arabians [Page 201] call it Alrukaba: And of the Scythians it is said to be an Iron nail, and is worshipped by them as a God. The two stars that are in the sholders of the Bear, are called Guards, of the Spa­nish word Guardare, which is to behold; because they are di­ligently to be looked unto, in regard of the singular use which they have in Navigation.

The reason why this Constellation was brought into the Hea­vens, is diversly set down, and first in this manner: Saturn having received of the Oracle that one of his Sons should banish him out of his kingdom, determined with himselfe to kill all the men children that he should beget: whereupon he gave command to Ops his wife, being then great, that she should shew him the child so soon as ever it was born: But she bringing forth Jupiter, and being greatly delighted with his hair, gave the child unto two Nymphs of Crete, dwelling in the mount Dicte; whereof this was one, and was called Cynosura; the other was Helice.

Jupter, after that (according to the Oracle) he had bereft his Father of the kingdom, in recompence of their paines and cour­tesie, translated them both into the Heavens, and made of them two Constellations; the Lesser Bear, and the Greater Bear.

Othersome say that it was Arcas, the son of Calysto; and they tell the tale on this manner. Calysto a Nimph of singular beauty, daughter to Lycaon King of Arcadia, induced by the great desire she had of hunting, became a follower of the Goddess Diana. After this, Jupiter being enamored with her beauty and out of hope, by reason of her profession, to win her love in his own person, counterfeited the shape of Diana, lay with Calysto, and got her with child; of whom was born a son, which was called Arcas. Diana, or rather Juno, being very much offen­ded here-with, turned Calisto into a Bear. Arcas her son at the Age of fifteen, hunting in the woods by chance lighted upon his mother in the shape of a Bear: who knowing her son Arcas, stood stil, that he might come near unto her, and not be afraid: but he fearing the shape of so cruel a Beast, bent his bow of pur­pose to have slain her: Whereupon Jupiter to prevent the mis­chief, translated them both into Heaven, and of them made two se­veral Constellations: unto the lesser Bear, there belongs but one star unformed.

2. URSA MAIOR, the Greater Bear, called also of the Greeks Arctos, and Helice, consisteth of 27. stars: Among the [Page 202] which, those seven that are in the hinder part and tail of the Bear, are most observed; the Latines call them Pla [...]strum; and of our men they are called Charles Wayn; because the stars do stand in such sort, that the three which are in the tail resemble the Horses, and the other four which are in the flank of the Bear, stand (after a manner) like the Wheels of a Waggon, or Chariot; and they are suposed by some to be greater then the Sun. The reason of the Translation of this Constellation into the Heaven, is at large set down in the other Constellation, and therefore needs not here to be repeated. This Constellation was first invented by Nau­plius, the Father of Palamedes the Greek: and in great use among the Grecians; and this is to be noted both in this and the former Constellation, that they never set under the Horizon, in any part of Europe: which though it fall out by reason of their scituation in the Heavens; yet the Poets say, that it came to pass through the displeasure and hatred of Juno; who for that she was by Ca­listo made a Cuckquean, and they notwithstanding (as she took it) in dispight of her, were translated into Heaven, requested her brother Neptune, that he should never suffer those Stars to set within his Kingdom: To which request Neptune condiscended; so that in all Europe they never come neer unto the Sea, or touch the Horizon. If any one marvel, that (seeing she hath the form of a Bear) she should have a tail so long; Imagine that Jupiter fearing to come too nigh unto her teeth, laid hold on her tail, and thereby drew her up into heaven; so that she of her selfe being very weighty, and the distance from the Earth to the Heaven very great, there was great likelyhood that her tail must stretch. The unformed stars belonging to this Constellation are eight.

3 DRACO, the Dragon, of some named the Serpent; of others the Snake, by the Arabians, Aben; and by Junctinus Flo­rentinus, Vrago; because he windeth his tail round about the Ecliptick Pole; it containeth 31. stars. This was the Dragon that kept the Golden Apples in the Orchard of the Hesperides, (now thought to be the Islands of Cape de Virde) and for his di­ligence and watchfulness, was afterwards translated into heaven: Yet others say that he came into Heaven by this occasion; when Minerva withstood the Gyants fighting against the Gods; they to terrifie her, threw at her a mighty Dragon; but she catching him in her hands, threw him presently up into Heaven, and pla­ced him there, as a memorial of that her resistance. Others [Page 203] would have it to be the Serpent Python, whom Apollo slew, after the Deluge.

4. CEPHUS, containeth in him 11. stars, and hath two unformed. This was a King of the Aethiopians, and Husband unto Cassiopeia, and father of Andromeda, whom Perseus mar­ried. He was taken up into Heaven, with his wife and daughter, for the good deeds of Perseus his son in law; that he and his whole stock might be had in remembrance for ever. The Star which is in his right shoulder, is called by the Arabians Aldera­hiemin; i. e. his right Arm.

5 BOOTES, the driver of the Oxen (for so I suppose the name to signifie, rather then an Herdsman; for he hath not his name because he hath the care of any Cattle, but only because he is supposed to drive Charles his Wain, which is drawn by 3. Ox­en) he is also called Arctophilax, the keeper of the Bear, as though the care of her were committed to him. This Constellation con­sisteth of 22 Stars. Some will have Bootes to be Areas, the Son of her who before was turned into the Great Bear; and they tell the Tale thus: Ly [...]aon the Father of Calisto, receiving Jupi­ter into his house as a guest, took Arcas his daughters son, and cut him in pieces; and among other Services, set him before Ju­piter to be eaten: for by this means he thought to prove if his guest were a God, as he pretended to be. Jupiter perceiving this heinous fact, overthrew the table, fired the house with light­ning, and turned Lycaon into a wolf: but gathering, and setting together again the limbs of the child, he commited him to a Nymph of Aetolia to be kept: Arcas afterwards coming to mans estate, and hunting in the woods, lighted at un-awares upon his mother, transformed by Juno into the shape of a bear, whom he persued into the Temple of Jupiter Lycaeus, whereunto by the law of the Arcadians, it was death for any man to come. For as much therefore as they must of likelyhood be both slain. Calysto by her son, and he by the Law; Jupiter to avoid this mis­cheif, of meer pitty took them both up into heaven. Unto this Constellation belongeth but one star unformed, and it is between the legs of Bootes, and by the Grecians it is called Arcturus, be­cause of all the stars neer the great Bear named Arctos, this star is first seen neer her tail in the evening. The Poetical invention is thus.

Icarus the father of Erigone, having received of the God [Page 204] Bacchus a Flagon of wine, to declare how good it was for mortal men, travelled therewith into the Territories of Athens, and there began to carouse with certain shepheards: they being greatly delighted with the pleasantness of the wine, being a new kind of liquor, began to draw so hard at it, that ere they left off, they were past one and thirty; and in the end, were fain to lay their heads to rest. But coming unto themselves again, and finding their brains scarce in good temper, they killed Icarus, thinking indeed that he had either poysoned them, or at the least-wise made their brains introxicate. Erigone was ready to die for grief, and so was Mera, her little dog. But Jupiter to allay their grief, pla­ced her father in Heaven, between the legs of Arctophilax.

6. CORONA BOREA, the Northern garland, con­sisteth of eight stars; yet Ovid saith, that it hath nine. This was the Garland that Venus gave unto Ariadne, when she was mar­ried unto Bacchus, in the Isle Naxus, after that Theseus had for­saken her: which Garland, Bacchus placed in the Heaven, as a token of his love. Novidius will have it to be the Crown of the Virgin Mary.

7. ENGONASIS: This Constellation hath the name, because it is expressed under the shape of a man kneeling upon the one knee, and is therefore by the Latines called Ingeniculum. It containeth 29. stars, and wanteth a proper name, because of the great diversity of opinions concerning the same. For some will have it to be Hercules, that mighty Conquerer, who for his 12. labours was thought worthy to be placed in the heaven. and nigh unto the Dragon whom he overcame. Others tell the tale thus: That when the Tyta [...]s fought against the Gods, they for fear of the Gyants, ran all unto the one side of the heaven: whereupon the Heaven was ready to have fallen, had not Hercu­les together with Atlas set his neck unto it, and stayed the fall: and for this desert, he was placed in the Heaven.

8 LYRA, the Harp, it containeth 10. stars; whereof thus goeth the Fable. The River Nilus swelling above his banks, overflowed the Country of Aegypt; after the fall whereof there were left in the fields divers kinds of living things, and amongst the rest a Tortois [...]; Mercury, after the flesh thereof was consumed, the sinews still remaining, found the same, and striking it, he made it yeild a certain sound; whereupon he made an Harp like unto it, having 3. strings and gave it unto Orpheus the son of Cassiopea. [Page 205] This Harp was of such excellent sound, that Trees, Stons Fowls, and wild Beasts are said to follow the sound thereof. After such time therefore that Orpheus was slain by the women of Thrace, the Muses by the good leave of Jupiter, and at the request of Apollo, placed this Harp in Heaven. Novidius will have it to be the Harp of David, whereby he pacified the evil spirit of Saul. This Constellation was afterwards called Vultur Cad [...]ens, the fall­ing Grype: and Falco, the Falcon; or Timpanum, he Timbrel.

9 OLOR, or Cygnus, the Swan, called of the Caldaeans Adigege: it hath 17. stars: of this Constellation the Poets Fable in this manner. Jupiter being overtaken with the love of Laeda, the wife of Tyndarus King of Oebalia, and knowing no honester way to accomplish his desire, procured Venus to turn her selfe into an Eagle, and himself he turned into the shape of a Swan: Flying therefore from the Eagle, as from his natural enemy, that earnestly pursued him, he lighted of purpose in the lap of Leda, and, as it were, for his more safety, crept into her bosome. The woman not knowing who it was under that shape, but holding (as she thought) the Swan fast in her armes, fell a sleep: In the mean while Jupiter enjoyed his pleasure; and having obtained that he came for, betook him again unto his wings; and in me­morial of his purpose (attained under that form) he placed the Swan among the stars.

Ovid calleth this Constellation Milvius, the Kite, and telleth the tale thus. The Earth being greatly offended with Jupiter, because he had driven Saturn his father out of his Kingdom, brought forth a monstrous Bull, which in his hinder parts was like a Serpent; and was afterwards called the Fatal-Bull; because the Destinies had thus decreed, that whosoever could slay him, and offer up his entrails upon an Altar, should overcome the eter­nal Gods. Briarens that mighty Gyant, and ancient enemy of the Gods overcame the Bull, and was ready to have offered up his entrails according to the decree of the Destinies: But Jupiter fearing the event, commanded the Fowls of the Air to snatch them away: which although to their power, they endavoured, yet there was none of them found so forward and apt to that action as the Kite, and for that cause he was accordingly rewar­ded with a place in Heaven. Some call this Constellation [...] that is, the Bird: others call it Vultur [...] volans, the Flying Grype: It is also called Gallina, the Hen. Unto this Constella­tion do belong two unformed stars.

[Page 206] 10. CASSIOPEIA, She consisteth of 13. Stars. This was the Wife of Cepheus, and mother of Andromeda, whom Perseus married, and for his sake was translated into Heaven, as some write. Others say that her beauty being singular, she wax­ed so proud, that she preferred her self before the Nereides, which were the Nymphs of the Sea: for which cause, unto her disgrace, and the example of all others that in pride of their hearts would advance themselves above their betters, she was placed in the Heaven with her head as it were downwards, so that in the revolution of the Heavens, she seemeth to be carried head-long.

11. PERSEUS, he hath 26. Stars. This was the Son of Jupiter, whom he in the likeness of a Golden shower begat upon Danae, the daughter of Acrisius. This Perseus coming unto mans estate, and being furnished with the Sword, Hat, and Wings of his brother Mercury, and the Shield of his sister Minerva, was sent by his foster-father Polidectes, to kill the Monster Medusa, whom he slew; and cuting off her head, carried it away with him: But as he was hastning homeward, flying in the Air, he espied Andromeda the daughter of Cepheus and Cassiopeia, for the pride of her mother, bound with a Chain unto a Rock, by the Sea side there to be devoured by a Whale: Perseus taking notice and pitty of the case, undertook to fight with the Monster, upon condition that Andromeda might be his Wife; to be short, he delivered Andromeda, married her, and returning homeward un­to the Isle Seriphus▪ he found there his Grand-father Acrisius, whom by mischance, and unadvisedly, he slew with a quoit: (or as Ovid reporteth, with the terrible sight of the horrible head of Medusa, not knowing that it was his Grand-father: but afterwards understanding whom he had slain, he pined away through extream sorrow: whereupon Jupiter his Father pitty­ing his grief, took him up into Heaven and there placed him in that form wherein he overcame Medusa, with the sword in one hand, and the head of Medusa in the other, and the Wings of Mercury at his Heels. This Constellation, because of the un­luckiness thereof, is called by Astrologers Cacodemon, (i. e.) Un­lucky, and Unfortunate. For (as they say) they have observed it, that whatsoever is born under this Constellation, having an evil Aspect, shall be stricken with sword, or loose his Head. Novidius saith that it is David with Goliah his head in the one hand, and his sword in the other. The unformed Stars belonging unto this Constellation, are three.

[Page 207] 12. AURIGA, the Waggoner, or Carter: he consisteth of 14. Stars; the Arabians call him Alaiot; the Greeks Heniochus, i. e. a man holding a bridle in his hand, and so is he pictured. E­ratostenes affirmeth him to be Ericthonious King of Athens, the son of Vulcane: who having most deformed feet, devised first the use of the Wagon or Chariot, and joyned horses together to draw the same, to the end that he sitting therein, might the bet­ter conceal his deformities. For which invention, Jupiter transla­ted him into the Heavens.

In this Constellation there are two other particular Constella­tions to be noted; whereof the one consisteth but of one Star a­lone, which is in the left shoulder of Auriga, and is called Hir­cus, or Capra the Goat; the Arabians call it Alhaioth: The o­ther consisteth of two little Stars a little beneath the other, stand­ing as it were in the hand of Auriga; this Constellation is [...]cal­led Haedi, the Kids. The tale is thus; Saturn (as you heard be­fore) had received of the Oracle, that one of his sons should put him out of his Kingdom, whereupon he determined to devoure them all: Ops by stealth conveyed away Jupiter, and sent him to Melissus King of Crete, to be nourished: Melissus having two daughters, Amalthaea and Melissa, committed Jupiter unto their Nursery; Amalthaea had a Goat that gave suck unto two Kids, so that by the milk of this Goat, she nourished Jupiter very well. To requite this her care and courtesie, Jupiter (after he had put his Father out his Kingdom) translated her Goat and her two Kids, into Heaven; and in remembrance of the Nurse, the Goat is called Capra Amalthaea. Novidius saith, that when Christ was born, and his birth made manifest by the Angels unto the Shep­herds, one of them brought with him for a Present, a Goat and two young Kids; which in token of his good will, were placed in Heaven.

13. OPHIUCHUS, or SERPENTARIUS, That is, the Serpent-bearer. This Constellation hath no proper name, but is thus entituled, because he holdeth a Serpent in his hands. It containeth 24. Stars. Some say that it is Hercules, and report the tale on this manner Juno being a great enemy to Hercules, sent two snakes to kill him as he lay sleeping in his Cradle: but Her­cules being a lusty Child (for Jupiter had spent two daies in be­getting him) without much ado strangled them both: In me­morial of so strange an event, Jupiter placed him in the Heavens, with a Serpent in his hands,

[Page 208] 14. SERPENS, the Serpent of Ophiuchus, which consisteth of 18. Stars. Some say that it is one of the Serpents that should have slain Hercules in his Cradle. Novidius saith, it is the Viper that bit Paul by the hand. Others deliver the tale in these words; Glaucus the son of Minos King of Crete, was by misfortune drowned in a Barrel of Honey: Minos his father craved the help of Aesculaptus the Physitian: and that he might be driven per▪ force to help the child, he shut him up in a secret place, together with the dead carcass: whiles Aesculapius stood in a great maze with himself what were best to be done, upon a sudden there came a Serpent creeping towards him; the which Serpent he slew with the staff which he had in his hand. After this there came another Serpent in, bringing in his mouth a certain herb, which he laid upon the head of the dead Serpent, whereby he restored him unto life again. Aesculapius using the same her [...], wrought the same effect upon Glaucus. Whereupon (after that) Aescu­lapius (whom some affirm to be Ophiuchus) was placed in the Heaven, and the Serpent with him.

15. SAGITTA, or Telum; the Arrow or Dart. This was that Arrow wherewith Hercules slew the Eagle or Grype that fed upon the Liver of Promotheus, being tyed with chains to the top of the mount Caucasus; and in memorial of that deed, was translated into Heaven. Others will have it to be one of those Arrows which Hercules at his death gave unto Phyloctetes, up­on which the Destiny of Troy did depend. The whole Constel­lation containeth five Stars.

16. AquILA, the Eagle, which is called Vultur Volans, the flying Grype: It hath in it 9. Stars. The Poetical reason of this Constellation, is this; Jupiter transforming himself into the form of an Eagle, took Ganimides the Trojan Boy, whom he great­ly loved, up into Heaven, and therefore in signe thereof (because by that means he performed his purpose) he placed the figure of the Eagle in the Heaven. There belong unto this Constellation 6. Stars (before time) unformed, but now brought into the Con­stellation of Antinous. But whereupon that name should come, I know not, except it were that some man devised it there to cur­ry favour with the Emperour Adrian, who loved one Antinous Bithynicus so well, that he builded a Temple in his honour at Mantinea.

17. DELPHINUS, the Dolphin: It containeth 10. Stars; [Page] yet Ovid in his second Book de Fastis, saith that it hath but nine. Neither did the ancient Astronomers attribute unto it any more, according to the number of the Muses; because of all other Fishes, the Dolphin is said to be delighted with Musick. The tale goeth thus concerning this Constellation. When Neptune the God of the Sea greatly desired to match with Amphitrite, she being very modest and shame-faced, hid her self: whereupon he sent many messengers to seek her out, among whom, the Dolphin by his good hap, did first find her; and perswaded her also to match with Neptune: For which his good and trusty service, Neptune placed him in the Heaven.

Others say, that when Bacchus had transformed the Mariners that would have betrayed him, into Dolphins, he placed one of them in Heaven, that it might be a lesson for others to take heed how they carried any one out of his way, contrary both to his desire, and their own promise. Novidius referreth this Constel­lation unto the Fish which saved Jonas from drowning.

18. EQUICULUS, is the little Horse, and it consisteth of 4. Stars. This Costellation is named almost of no Writer, saving Ptolomeus, and Alphonsus, who followeth Ptolomy, and there­fore no certain tale or History is delivered thereof, by what means it came into Heaven.

19. EquuS ALATHS, the Winged Horse, or Pegasus, it containeth 20. Stars. This Horse was bred of the blood of Me­dusa, after that Perseus had cut off her head, and was afterwards taken and tamed by Bellerophon, whiles he drank of the River Piren [...] by Corinth, and was used by him in the conquest of Chi­mera: After which exploit, Bellerophon, being weary of the earthly affaires, endevoured to fly up into Heaven: But being amazed in his flight, by looking down to the earth, he fell from his horse; Pegasus notwithstanding continuing his course, (as they feigne) entred into Heaven, and there obtained a place among the other Constellations.

20. ANDROMEDA, She consisteth of 23. Stars; but one of them is common both unto her, and Pegasus, This was the daughter of Cepheus and Cassiopeia, and the Wife of Perseus: the reason why Minerva, or Jupiter placed her in the Heavens, is before expressed. Novidius referreth this Constellation unto Alexandria the Virgin, whom S. George through the good help of his horse, delivered from the Dragon.

[Page 210] 21. TRIANGULUM, the Triangle, called also Delt [...]ton, because it is like the fourth letter of the Greeks Alphabet Δ, which they call Delta; it consisteth of four stars. They say it was placed in Heaven by Mercury, that thereby the head of the Ram might be the better known. Others say, that it was placed there in honour of the Geometricians, among whom, the Triangle is of no small importance. Others affirme, that Ceres in times past requested Jupiter that there might be placed in Heaven some Fi­gure representing the form of Sicilie, an Island greatly beloved of Ceres, for the fruitfulnesse thereof: now this Island being tri­angular, (at her request) was represented in the Heaven under that form.

Thus much concerning the Constellations of the Northern Hemisphear. Now follow the Poeical Stories of the Constellati­ons of the Southern Hemisphear.

Secondly, Of the Southern Constellations.

1. CETUS, the Wha [...], it is also called the Lion, or Bear of the Sea. This is that monstrous fish that should have devoured Andromeda, but being overcome by Perseus, was afterwards translated into Heaven by Jupiter, as well for a token of Perseus his manhood, as for the hugeness of the fish it self. This constellation consisteth of 22. Stars.

2. ORION, this hath 38. Stars. The Poetical reason of his translation into the Heaven, shall be shewn in the Scorpion, amongst the Zodietical Constellations. The Ancient Romans called this Constellation Jugala; because it is most pestiferous unto Cattel, and as it were the very cut-throat of them. There are bright Stars in his girdle, which we commonly call our La­dies yard, or wa [...]d. Novidius, applying this sword of Orion unto Scripture, will have it to be the sword of Saul, afterwards called Paul, wherewith he persecuted the Members of Christ: which after his conversion was placed in Heaven. In his left shoulder there is a very bright Star, which in Latine is called Bel­latrix, the Warriour, in the foeminine gender. I cannot find the reason except it be this; that Women born under this Constellati­on [Page 211] shall have mighty tongues. The reason of the Ox-hide which he hath in his hand, may be gathered out of the next story.

3. FLUVIUS, the River; it comprehendeth 34. Stars. It is called by some Eridanus, or Padus; and they say that it was placed in Heaven in remembrance of Phaeton, who having set the whole World on fire by reason of misguiding of his father Phoebus his charriot, was slain by Jupiter with a thunder-bolt, and tumbling down from Heaven, fell into the River Eridanus, or Padus, which the Italians call Po. Others say that it is Ny­lus, and that that Figure was placed in the Heaven because of the excellency of that River, which by the Divines is called Gihon; and is one of the Rivers of Paradice. Others call it Flumen Ori­onis, the flood of Orion; and say, that it was placed there, to be­token the Off-spring from whence Orion came: for the tale is thus reported of him.

Jupiter, Neptune, and Mercury, travelling upon the earth in the likeness of Men, were requested by Hyreus to take a poor lodging at his House for a Night: they being overtaken with the evening, yeilded unto his request; Hyreus made them good cheer, killing an Ox for their better entertainment: The Gods seeing the good heart of the old man, willed him to demand what he would in recompence of his so friendly cheer. Hyreus and his Wife being old, requested the Gods to gratify them with a Son. They to fulfil his desire, called for the hide of the Ox that was slain, and having received it, they put it into the Earth, and made water into it all three together, and covering it, willed Hyreus within ten moneths after to dig it out of the Earth again; which he did, and found therein a Man-child; whom he called Ouri­on, ab Urina, of piss; although afterwards by leaving out the se­cond letter, he was named Orion. At such time therefore as he was placed in Heaven, this flood was joyned hard to his heels, and the Ox hide wherein the Gods did piss, was set in his left hand, in memorial of his Off-spring.

4. LEPUS, the Hare, which consisteth of 12. stars. This Constellation was placed in Heaven between the legs of Orion, to signifie the great delight in hunting which he had in his life time. But others think it was a frivolous thing, to say that so notable a fellow as Orion would trouble himself with so smal and timerous a beast as the Hare: and therefore they tell the tale thus.

[Page 212] In times past there was not a Hare left in the Isle D [...]r [...]s: a cer­tain youth therefore of that Island, being very desirous of that kind of beast, brought with him from another Country therea­bout, an Hare great with young; which when she had brought forth, they in time became so acceptable unto the other Countri­men, that every one almost desired to have and keep a Hare. By reason whereof, the number of them grew to be so great, within a short space after, that the whole Island became full of Hares, so that their Masters were not able to find them meat: whereup­on the Hares breaking forth into the fields, devoured their Corn. Wherefore the inhabitants being bitten with hunger, joyned to­gether with one consent, and (though with much ado) destroy­ed the Hares. Jupiter therefore placed this Constellation in the Heavens as well to express the exceeding fearfulness of the beast, as also to teach men this lesson; that there is nothing so much to be desired in this life, but that at one time or an other it bring­eth with it more grief then pleasure. Some say, that it was placed in Heaven at the request of Ganimedes, who was greatly delight­ed with hunting the Hare.

5. CANIS MAIOR, the Great Dog, it consisteth of 18. Stars. It is called Sirins Canis, because he causeth a mighty drought by reason of his heat. This is the Constellation that gi­veth the name unto the Canicular or Dog-days; whose beginning and end is not alike in all places, but hath a difference according to the Country and Time: as in the Time of Hypocrates the Phisitian, who lived before the time of Christ 400, years, the Canicular days began the 13. or 14. of July. In the time of A­vicenna, the Spaniard, who lived in the year of our Lord 1100. the Canicular days began the 15, 16, or 17. of July. In our Country, they begin about S. James-tide, but we use to account them from the 6. of July, to the 17. of August; which is the time when the Sun beginneth to come near unto, and to depart from this Costellation.

Novidius will have it to be referred to Tobias Dog; which may very well be, because he hath a tail; Tobias Dog had one; as a certain fellow once concluded, because it is written that Tobias his Dog fawned upon his Master, therefore it is to be noted (said he) that he had a tail. The Poets say, that this is the Dog whom Jupiter set to keep Europa, after that he had stolen her away, and conv [...]ied her into Crete, and for his good service [Page 213] was placed in Heaven. Others say, that it was one of Orion his Dogs. There belong unto this Constellation 11. Stars unformed.

6. CANIS MINOR; the Lesser Dog; this of the Greeks is called Procyon, of the Latines Ante Canis; it containeth but two Stars. Some say, that this also was one of Orions Dogs, O­thers rather affirm it to be Mera, the Dog of Origone, or rather of Icarius her father, of whom mention is made in the Constella­tion of Bootes, and Virgo. This Dog of meer love to his Master, being slain, as is aforesaid, threw him self into the River Anygrus, but was afterward translated into Heaven with Origone. Among the Poets there is great dissention which of the two should be the Dog of Origone; some saying one, and some the other, and therefore they do many times take the one for the other.

7. ARGO NAVIS, the Ship Argo, which compre­hendeth 41. Stars; this is the Ship wherein Jason did fetch the Golden Fleece from Colchis, which was afterward placed in Hea­ven as a memorial, not only because of the great Voyage, but al­so, because (as some will have it) it was the first Ship wherein a­ny man sayled. Their reason why this Ship is not made whole is, that thereby men might be put in mind not to despair, albeit that their Ship miscarry in some part now and then. Some avouch it to be the Ark of Noe. Novidius saith it is the Ship wherein the Apostles were, when Christ appeared unto them walking on the Sea. In one of the Oars of this Ship, there is a great Star, called Canopus, or Canobus, which the Arabians called Shuel, as it were a bone-fire, because of the greatness thereof. It is not seen in Italy, nor in any Country on this side of Italy. Some say that Canobus the Master of Menelaus his Ship, was transformed into this Star.

8. HYDRA, the Hydre; that hath 25. Stars, and two unfor­med.

9. CRATER, the Cup, or standing piece; that hath se­ven Stars. Some say that this was the cup wherein Tagathon, that is, the chief God, mingled the stuff whereof he made the souls of Men.

10. CORVUS, the Crow; this hath seven Stars. These 3. Constellations are to be joyned together, because they depend up­on one History, which is this. Upon a time Apollo made a solemne feast to Jupiter, and wanting water to serve his turn, he delivered a cup to the Crow (the bird wherein he chiefly delighted) and [Page 214] sent him to fetch water therein: The Crow flying towards the Ri­ver, espyed a Fig-tree, fell in hand with the Figs, and abode there till they were ripe: In the end, when he had fed his fill of them, and had satisfied his longing, he bethought himself of his errand, and by reason of his long delay, fearing a check, he caught up a snake in his bill, brought it to Apollo, and told him that the snake would not let him fill the Cup with water. Apollo seeing the im­pudency of the bird gave him this gift, that as long as the Figs were not ripe upon the Tree, so long he should never drink: and for a memorial of the silly excuse that he made, he placed both the Crow, Cup, and Snake▪ in Heaven.

11. CENTAURUS, the Centaure, which comprehendeth 37. Stars. Some say, that this is Typhon, others call him Chi­ron, the Schoolmaster of those three excellent men, Hercules Achiles, and Aesculapius; unto Hercules he read Astronomy, he trained up Achilles in Musick, and Aesculapius in Physick: and for his upright life he was turned into this Constellation. Yet Virgil calleth Sagit [...]arius by the name of Chiron. In the hinder feet of this Constellation, those stars are set which are called the Crosiers, appearing to the Mariners as they fail towards the South Sea, in the form of a crosse, whereupon they have their name. The four stars which are in the Garnish of the Centaures Spear, are accounted by Proclus as a peculiar Constellation, and are called by him Thyrsilochus, which was a Spear compassed about with vine leaves: but they are called by Copernicus and Clavius, and other Astronomers, the stars of his Target. It should seem that they were deceived by the old translation of Ptolome, wherein Scutum is put for Hasta, i. e. the Target, for the Spear, as it is well noted by our Countryman M. R. Record, in his Book intituled The Castle of knowledge.

12 LUPUS, the Wolf, or the beast which the Centaùre holdeth in his hand, containeth 19. stars; the Poetical reason is this, Chiron the Centaure being a just man, was greatly given the worship of the Gods: for which thing, that it might be noti­fied to all posterity, they placed him by this beast, which he seem­eth to stick and thrust through with his Spear, (as it were) ready to kill for sacrifice.

13. ARA, the Alter, it is also called Lar, or Thuribulum, i. e, a Chimney with the fire, or a Censor. It consisteth of se­ven stars, and is affirmed of some Poets, to be the Alter where­on [Page 215] the Centaure was wont to offer up his sacrifice. But others tell the tale thus, When as the great Gyants called the Tytans, la­boured as much as might be to pull Jupiter out of Heaven, the Gods thought it good to lay their heads together, to advise what was best to be done: Their conclusion was, that they should all with one consent joyn hands together to keep out such fellows: and that this their league might be confirmed, and throughly ra­tified; they caused the Cyclops, (which were work-men of Vul­can) to make them an Altar: about this Altar all the Gods as­sembled, and there sware, that with one consent they would withstand their enemies; afterwards, having gotten the victory, it pleased them to place this Altar in Heaven, as a memorial of their League, and a token of that good which unity doth breed.

14. CORONA AUSTRINA, the South Garland, it hath 13. Stars. Some say that it is some trifling Garland which Sagittarius was wont to wear, but he cast it away from him in jest, and therefore it was placed between his legs: others call it the Wheel of I xion, whereupon he was tormented for that great courtesy he would have offered unto Juno, thinking indeed to have gotten up her belly: but Jupiter seeing the impudency of the man, tumbled him out of Heaven (where by the licence of the Gods he was somtime admitted as a guest) into Hell, there to be continually tormented upon a Wheel. The Figure of which Wheel was afterwards placed in Heaven, to teach men to take heed how they be so saucie to make such courteous proffers unto other men wives. The Greeks call this Constellation by the name of Uraniscus, because of the Figure thereof: For it representeth the palate or roof of the mouth, which they call Uraniscus.

15. The last is PISCIS AUSTRINUS, or Notius, the South Fish, which comprehendeth 11. Stars besides that which is in the mouth thereof, belonging to the water, which runneth from Aquarius, and is called by the Arabians Fomahant. The reason why this Fish was placed in the Heaven, is uncertain: yet some affirm, that the daughter of Venus going into a water to wash her self, was suddenly transformed into a fish; the which fish was afterwards translated into Heaven. The unformed Stars belonging unto this Constellation are six.

Thus much concerning the Constellations of the Northern and Southern Hemisphears; now follow the Poetical Stories of the Zodiatical Constellations.

Thirdly, Of the Zodietical Constellations:

1. ARIES, the Ram, it is called by the Greeks [...], it containeth in it 13. Stars, which were brought un­to this Constellation by Thyestes, the son of Pelops, and brother of Atreus. This is the Ram upon which Phrixus, and Helle his sister, the children of Athamas did sit, when they fled from their step-mother Ino, over the Sea of Hellespont: which Ram was afterward for his good service, translated into Heaven by Jupiter. Others say, that it was that Ram which brought Bacchus unto the spring of water, when through drought he was likely to have perished in the desert of Lybia. Novidius will have this to be the R [...]m which Abraham offered up in stead of his son Isaac. The Star tha [...] is first in the head of the Ram, is that from whence our [...]ater Astronomers do account the Longitude of all the rest, and it is distant from the head of Aries, in the tenth Sphear, 27. degrees 53. minutes. The unformed Stars belonging unto this Constellation, are five.

2. TAURUS, the Bull, which consisteth of 23. stars. This was translated into Heaven in memorial of the rape commit­ted by Jupiter on Europa the daughter of Agenor, King of Si­don; whom Jupiter in the likeness of a white Bull stole away, and transported into Candia. Others say, That it was [...] the daughter of Inacus: whom Jupiter loved, and turned into the form of a Cow, to the intent that Juno comming at unawares, should not perceive what a part he had playd: Jupiter afterward in memorial of that craftie conveyance, placed that Figure in Heaven; The reason why the Poets name not certainely whether it be a Cow or a Bull, is because it wanteth the hinder parts; yet of the most of them it is called a Bull. In the Neck of the Bull there are certain stars standing together in a cluster, which are commonly called the seven Stars; although there can hardly he discerned any more then six. These are reported to be the seven daughters of Atlas, called Atlan [...]iades, whereof six had com­pany with the immortal Gods, but the seventh (whose name was Merope) being married unto Sysiphus a mortal man, did [Page 217] herefore withdraw and hide her self, as being ashamed that she was not so fortunate in matching her self as her sisters were. Some say, that that star which is wanting is Electra, the eldest daughter of Atlas, and that therefore it is so dim, because she could not abide to behold the destruction of Troy; but at that time and ever since, she hid her face. The reason why they were taken up into Heaven, was, their great pittie towards their father, whose mishap they bewayled with continual tears. O­thers say, that whereas they had vowed perpetual virginity, and were in danger to lose it, by reason of Orion, who greatly as­sayled them, being overtaken, with their love; they requested Ju­piter to stand their friend; who translated them into stars, and placed them in that part of Heaven. The Poets call them Ple­iades, because when they rise with the Sun, the Mariners may commit themselves to the Sea. Others will have them to be so termed a pluendo; because they procure rain. Others give them this name, of the Greek word [...], because they be ma­ny in number. They be also called Vergiliae, because they rise with the Sun in the Spring time: likewise Athoraiae, because they stand so thick together. Our men [...]call them by the name of the seven Stars, or Brood Hen. The Astronomers note this as a special thing concerning these stars, that when the Moon and these stars do meet together, the eyes are not to be medled withall, or cured if they be sore: their reason is, because they be of the na­ture of Mars and the Moon.

Moreover, there be five stars in the face of the Bull, represen­ting the form of the Roman letter V, whereof one (which is the greatest) is called the Bull's Ey. They be called Hyades, and were also the daughters of Atlas, who so long bewayled the death of Hyas their brother, slain by a Lion, that they died for sorrow, and were afterwards placed in Heaven for a memorial of that great love they bare to their brother. The ancient Ro­mans call the Bul's Ey, Parilicium, or Palelicium; of Pales their goddesse; whose feast they celebrated after the conjunction of this star and the Sun. The unformed stars belonging unto this Constellation, are eleven.

3. GEMINI, the Twins; it consisteth of 18. stars. The Poets say they are Castor and Pollux, the sons of Leda, brethren most loving, whom therefore Jupiter translated into Heaven. Some say that the one of them is Appollo, and the other Hercu­les: [Page 218] but the most affirm the former. The unformed stars of this Constellation are seven, whereof one is called Tropus, because it is placed next before the foot of Castor.

4. CANCER, the Crab, it hath 9. Stars. This is that Crab which bit Hercules by the heele as he fought with the Serpent Hydra i [...] the Fen Lerna, and for his forward service, was pla­ced in Heaven by Juno, the utter enemy of Hercules. In this Constellation, there are Stars much spoken of by the Poets; al­though they be but small; whereof one is called the Crib, other two are the two Asses, whereof one was the Asse of Bacchus, the other of Vulcan, whereon they rode to battel, when as the Gy­ants made war with the Gods; with whose braying and strange noise, the Gyants were so scared upon the sudden, that they for­sook the field, and fled. The Gods getting the victory, in try­umphing manner translated both the Asses, and their manger into Heaven. The unformed stars of this Constellation are four. It is called animal re [...]rogradum, for when the Sun cometh into his Signe, he maketh Retrogradation.

5. LEO, the Lyon; it hath 27. Stars, this is that Lyon which Hercules overcame in the wood of Nemaea and was placed in Heaven in remembrance of so notable a deed. Novidius saith, this was one of the Lyons which were in the den into which Da­niel was cast, and was therefore placed in Heaven, because of all other he was most friendly unto Daniel. In the breast of this Con­stellation is that notable great Star, the light whereof is such, as that therefore it is called by Astronomers [...] or Regulus i. e. the Victroy, or little King among the rest. The unformed Stars belonging to the Lyon are eight; whereof three make the Constellation which is now called Coma Berenices, that is, the hair of Berenice. This Constellation was first found out and invent­ed, by Canon the Mathematician, but described by Calimachus the Poet. The occasion of the Story was this, P [...]olomeus Ever­getes having married his sister Berenice, was shortly after enfor­ced to depart from her, by reason of the wars he had begun in Asia: whereupon Berenice made this vow, that if he returned home again in safety, she would offer up her hair in Venus Tem­ple. P [...]olome returned safe; and Berenice, according to her vow, cut off her hair and hung it up. After certain daies, the hair was not to be found; whereupon Ptolome the King was greatly dis­pleased: but Canon, to please the humor of the King, and to cur­ry [Page 219] favour with him, perswaded him that Venus had conveyed the hair into Heaven. Canon attributeth seven Stars unto it, but Ptolome allotteth it but three, because the other be insensible,

6. VIRGO, the Virgin, it hath 26. Stars. This is affirmed to be Justice, which among all the Gods somtime living upon the Earth, did last of all forsake the same, because of the wickedness that began to multiply therein, and chose this place for her seat in Heaven.

Others say, that it was Astraea, the daughter of Astraeus, one of the Gyants that were called Titans, who fighting against the Gods, Aftraea took their parts against her own Father, and was therefore after her death commended unto the Heavens, and made one of the 12. Signes.

Others say, that it was Erigone, the daughter of Icarius, who for that her father was slain by certain drunken men, for very grief thereof did hang her self: but Jupiter taking pitty of the Virgin for her natural affection, translated her into Heaven.

In her right wing there is one Star of special note, which by the Astronomers is called Vindemeator (i. e.) the gatherer of Graps. This was Ampelos the son of a Satyr and a Nymph, and greatly beloved of Bacchus, unto whom in token of his love, Bac­chus gave a singular fair Vine, planted at the foot of an Elme, (as the manner was in old time.) But Ampelos in Harvest gathering Graps, and taking little heed to his footing, fell down out of the Vine, and brake his neck. Bacchus in memorial of his former affection, translated him into Heaven, and made him one of the principal Stars in this Constellation. There is another great Star in the hand of the Virgin, called of the Latines Spica, of the Greeks Stachus, of the Arabians Azimech (i. e.) the Ear of Corn: whereby they signify, that when the Sun cometh to this Signe, the Corn waxeth ripe. Albumazar the Arabian, and Novidius, take this Constellation for the Virgin Mary. The unformed Stars in this Constellation, are six.

7. LIBRA, the Ballance, it containeth 8 Stars. Cicero calleth it Jugum the Yoak, and here it is to be noted, that the Ancient A­stronomers that first set down the number of the Constellations contained in the Zodiack, did account but eleven therein, so that the Signe which now is called Libra, was heretofore called [...], that is to say, the Claws of the Scorpion, which possesseth the space of two whole Signes. But the latter Astronomers, being de­sirous [Page 220] to have 12. Signes in the Zodiack, called those eight where­of the Claws of the Scorpion do consist, by the name of Libra; not that there was any Poetical Fiction to induce them thereto, but only moved by this reason, because the Sun joyning with this Constellation, the Day and the Night are of an equal length, and are (as it were) equally poyzed in a pair of Ballance. Yet (as I remember) some will have this to be the Ballance wherein Justice, called also Astraea, weighed the deeds of mortal men, and therein presented them unto Jupiter. It hath 9. unformed Stars appertaining unto it.

8. SCORPIO, the Scorpion; called of the Arabians, Ala­trab; of Cicero, Nepa. It consisteth of 21, Stars. The Fiction is thus. Orion the son of Hyreus greatly beloved of Diana, was wont to make his boast, that he was able to overcome what beast soe­ver was bred upon the Earth: The Earth being moved with this speech brought forth the Scorpion, whereby Orion was stung to death. Jupiter thereupon (at the request of the Earth,) translated both the Scorpion, and Orion into Heaven; to make it a lesson for ever for mortal men, not to trust too much unto their own strength▪ and to the end he might signify the great enmity between them, he placed them so in the Heaven, that whensoever the one ariseth, the other setteth; and they are never both of them seen together above the Horizon at once: Gulielmus Postellus will have it to be the Serpent which beguiled Eve in Paradise. The unformed Stars about this Scorpion are three.

9. SAGITTARIUS, the Archer. It hath thirty one Stars. Touching this Signe, there are among the Poets many and sundry opinions. Some say that it is Crocus, the son of Puphen [...], that was nurse unto the Muses. This Crocus was so forward in learning of the liberal sciences, and in the practise of feats of acti­vity, that the Muses entreated Jupiter that he might have a place in Heaven. To whose request Jupiter inclining, made him one of the 12. Signes: And to the end that he might express the excellent qualities of the Man, he made his hinder parts like unto a Horse, thereby to signify his singular knowledge in Horse-manship: and by his Bow and Arrow, he declared the sharpness of his Wit. Whereupon the Astrologers have this conceit, that he that is born under Sagittarius, shall attain to the knowledge of many Arts, and be of prompt wit, and great courage. Virgil affirmeth this to be Chiron the Centaur, who for his singular learning and Justice, [Page 221] was made the Master of Achilles. At which time Hercules com­ing to visit him (for he had heard both of the worthiness of the School-master, and of the great hopes of the Scholler) brought with him his quiver of Arrows dipped in the blood of the Serpent Hydra; but Chiron being desirous to see his shafts, and not taking heed of them, being in his hand, let one of them fall upon his foot, and being greatly tormented, not only by the anguish of the poyson working in the wound, but much more because he knew himself to be immortal, and his wound not to be recovered by medicine, he was enforced to make request unto the Gods, that he might be taken out of the World, who pittying his case, took him up into Heaven, and made him one of the 12. Signes.

10. CAPRICORNUS, the Goat, it consisteth of 28. Stars. The Poets say, that this was Pan, the God of the Shepherds, of whom they faign in this manner: The Gods having war with the Gyants, gathered themselves together into Aegypt, Typhon the Gyant pursued them thither, whereby the Gods were brought into a quandary, that well was he that by changing his shape might shift for himself, Jupiter turned himself into a Ram: Apollo became a Crow: Bacchus, a Goat: Diana lurked under the form of a Cat: Juno transformed her self into a Cow: Venus into a Fish: Pan leaping into the River Nilus, turned the upper part of his body into a Goat, and the lower part into a Fish. Jupiter won­dring at his strange device, would needs have that Image and Picture translated into Heaven, and made one of the 12. Signes. In that the hinder part of this Signe is like a Fish, it betokeneth that the latter part of the moneth wherein the Sun possesseth this Signe, inclineth unto Rain,

11. AQUARIUS, the Waterman. It hath 42. Stars, whereof some make the Figure of the Man: other some the Wa­terpot; and some, the stream of water that runneth out of the pot. This is feigned to be Ganimedes the Trojan, the son of Oros, and Callirhoe whom Jupiter did greatly love for his excellent favour and beauty, and by the service of his Eagle carried him up into Heaven, where he made him his Cup bearer, and called him Aquarius. Others notwithstanding thinke it to be Deucall­on the son of Prometheus whom the Gods translated into Hea­ven, in remembrance of that mighty deluge which happned in his time, whereby mankind was almost utterly taken away from the face of the earth. The unformed stars belonging unto this Signe are three.

[Page 222] 12. PISCES, the Fishes: these, together with the line that knitteth them together, contain 24. Stars. The Poets say that Venus and Cupid her son coming upon a certain time unto the River Euphrates, and sitting upon the bank thereof, upon a sud­den espied Typhon the Gyant, that mighty and fearfull enemy of the Gods coming towards them; Upon whose sight, they being stricken with exceeding fear, lept into the River, where they were received by two Fishes, and by them saved from drowning. Venus for this good turn, translated them into Heaven. Guliel­mus Postellus would have them to be the two Fishes wherewith Christ fed the 5000. men. The unformed stars of this Constel­lation, are four.

Thus have I breifly run over the Poetical reasons of the Con­stellations: It remains now that I speak of the Milky way.

VIA LACTEA, or Circulus Lacteus; by the Latines so called; and by the Greekes Galaxia; and by the English the Milkey way. It is a broad white Circle that is seen in the Hea­ven, in the North Hemisphere, it beginneth at Cancer, on each side the head thereof, and passeth by Auriga, by Perseus, and Cassiopeia, the Swan; and the head of Capricorn the tayl of Scor­pio, add the feet of Centaur, Argo the Ship, and so unto the head of Cancer. Some in a sporting manner do call it Wa [...]ling street; but why they call it so, I cannot tell; except it be in regard of the narrownesse that it seemeth to have; or else in respect of that great high way that lieth between Dover and S. Albons, which is called by our men, Watling street.

Ovid saith, that it is the great Causey, and the high way that leadeth unto the Pallace of Jupiter; but he alledgeth not the cause of the whiteness: belike he would have us imagine that it is made of white Marble.

Others therefore alledge these causes: Jupiter having begot­ten Mercury of Mai [...] the daughter of Atlas, brought the child when he was born, to the breast of Juno lying a sleepe: But Ju­no awaking threw the child out of her lap, and let the milke run out of her breast in such aboundance that (spreading it self about the Heaven) it made that Circle which we see. Others say, that it was not Mercury, but Hercules; and that Juno did not let the milke run out of her breast; but that Hercules suckt them so ear­nestly, that his mouth run over, and so this Circle was made.

Others say; that Saturn being desirous to devour his children, [Page 223] his wife Ops presented him with a stone wrapped in a clout, in­stead of his child: This stone stuck so fast in Saturn his throat as he would have swallowed it, that without doubt he had there-withall been choaked, had he not been relived by his wife, who by pressing the milke out of her breasts saved his life: the milke that missed his mouth (whereof you must suppose some sufficient quantity) fell on the Heavens, and running along made this Cir­cle.

Dr HOOD Commenting upon Constellations, saith; The Stars are brought into Constellations, for Instruction sake, things cannot be taught without names: to give a name to every Star had been troublesome to the Master and for the Scholler; for the Master to devise, and for the Scholler; to remember: and there­fore the Astronomers have reduced many Stars into one Constel­lation, that thereby they may tell the better where to seek them; and being sought, how to express them. Now the Astonomers did bring them into these Figures, and not into other, being mo­ved thereto by these three reasons: first these Figures express some properties of the Stars that are in them; as those of the Ram to to be hot and dry; Andromeda chained betokeneth imprisonment, the head of Medusa cut off signifieth the loss of that part: Orion with his terrible and threatning gesture, importeth tempest and terrible effects: The Serpent, the Scorpion, and the Dragon, sig­nify poyson: The Bull insinuateth a melancholy passion: The Bear inferreth cruelty, &c. Secondly, the Stars, (if not precisely, yet after a sort) do represent such a Figure, and therefore that Figure was assigned them: as for example, the Crown, both North and South: the Scorpion, and the Triangle, represent the Figures which they have. The third cause was the continuance of the memory of some notable men, who either in regard of their singular pains taken in Astronomy, or in regard of some other notable deed, had well deserved of Man-kind.

The first author of every particular Constellation is uncertain; yet are they of great antiquity; we receive them from Ptolomie, and he followed the Platonick [...]; so that their antiquity is gre [...]a▪ Moreover we may perce [...]ve them to be ancient by the Scriptures, and by the Poets. In the 38. Chapter of Job there is mention made of the Pleiades, Orion, and Aucturus, and Mazzaroth, which some interpret the 12. Signes: Job lived in the time of Abraham, as Syderocrates maketh mention in his Book de Commensurandis locorum distantiis.

[Page 224] Now besides all this, touching the reason of the invention o [...] these Constellations, the Poets in setting forth those Stories, [...] this purpose, to make men fall in love with Astronomy: When Demosthenes could not get the people of Athens to hear him in a matter of great moment, and profitable for the Common-wealth, he began to tell them a tale of a fellow that sold an Ass; by the which tale he so brought on the Athenians, that they were both willing to hear his whole Oration, and to put in practice that whereunto he exhorted them. The like intent had the Poets in these Stories: They saw that Astronomy being for commodity singular in the life of man, was almost of all men utterly negle­cted: Hereupon they began to set forth that Art under these Fi­ctions; that thereby such as could not be perswaded by commo­dity, might by the Pleasure be induced to take a view of these matters, and thereby at length fall in love them. For commonly note this, that he that is ready to read the Stories, cannot content himselfe therewith, but desireth also to know the Constellation, or at leastwise some principal Star therein.

FINIS.

A Discourse OF THE Antiquity, Progress, AND Augmentation OF ASTRONOMIE.

FIRST it seems not to be doubted, but Articl. I. that there was some kind of observa­tion of Bodies Coelestial, as soon as Observation Celestial, from the beginning of the world▪ though rude and in-artifici­al. there were Men: considering that the spectacle which the Heavens con­stantly present, is both so glorious, and so usefull, that men could not have eyes to see, and not fix them attentively and considerately there­upon. For, among other Apparen­ces, when they saw the Sun dayly to change the places of its rising and setting; at certain times of the Year: to approach neerer to the Earth in its Diurnal arch, and at others again to mount up to a height much more sublime and remote from it: and that his coming neerer to the Earth made Winter, and his remove higher made Summer: we say, when they beheld these things; doubt­less, [Page 2] they could not but seriously remark and consider this vicissi­tude, according to which they might expect the Season would be more hard, or mild, to them in this lower Region of the World. Again, so admirably various did the Moon appear, in her seve­ral shapes and dresses of light, that she could not but invite mens eyes, and engage them to frequent Speculations: specially when she assumed those various faces or apparences, at set and certain Times; in respect whereof it came to pass, that every Nation measured their times and Seasons, by those her constant and perio­dical circuits; and this, because those periods succeded much more frequently, than the Erections and Depressions of the Sun. To these, we may add that beautifull shew of the Nightly Stars, undergoing likewise their Variations, according the varie­ty of Seasons; and more particularly that bright star of Lucifer, rising sometimes later, sometimes earlier, and sometimes not at all before the Sun, and the like. But, what we shall principally note, is only this; that though Mankind was long, before they came to make inquiries into the Causes of these Coelestial chan­ges and variations, restrained to set periods: yet they observed them from the very first Age, and not only admired, but also ac­commodated what they observed, to the uses of their Lives and their Successors. Here it might not be fruitless, to remember, that PROMETHEUS, who was imagined to have framed the first Man, was also imagined to have given him an erected Figure, and sublime Countenance; to the end he might the more advan­tageously advance his eyes to the Heavens, and contemplate the glory and motions of the Coelestial Lights. But, because this is too General, and rude a way of observation; and it is our bu­siness to look back into those times wherein men first made such Observations of Sydereral bodies, as gave hem the hint and occa­sion of reducing them to Method, and founding the principles of the Art, or science of Astronomy, thereupon: we must have re­course to the monuments in Sacred Writ, for the understanding of that obscure matter.

And indeed, the light we expect from Sacred Leaves, would Articl. II. Sacred records examined, and Moses found to b the First A­stronomer there spoken of. soon be clear enough to discuss all the darkness, wherein the Ori­ginal of Astronomy seems involved; could we but from them deduce the least evidence for that which the learned Antiquarie among the Jewes, Josephus affirms of the Sons of Seth; viz. that they invented the science of the Heavens, before the Flood, [Page 3] and engraved the same on two Pillars, the one of Brick, the other lib. 1. Ant. c. 3. of Stone, that so it might be preserved in the one, in case the fury of the Deiuge to come, should demolish and deface the other: or if there remained to us any the most slender testimony of the Reason he there gives, of the so great Longevity of men in those cap. 4. dayes; namely, that the duration of their lives was sufficiently long, to perfect the knowledge of Astronomy, which requires full 600 Years, at the least, to the observation of all the Varieties of Coelestial motions: Whereupon He notes, that the Great Year (as they call it) doth consist of six hundred common Years; the vulgar opinion being, that the Celestial Motions do continual­ly vary,

Donec consumpto, Magnus qui dicitur, Anno,
Epigram. de etat, Anim.
Rursus in [...] antiquum redeant vaga sidera cursum,
Qualia praeteriti steterant ab origine mundi.

Again, the business might be deduced from not long after the Flood, if in Scripture we could find but the least word from whence might be argued the truth of what the same Author writes; namely that the Egyptians were taught Astronomy, by A­braham. Probable enough it is, we confess, that Berosus and others, quoted aswell by Josephus, as Eusebius, had read some such thing in some Books of the old Rabbins: but that the same should be fetched from Holy Writ, is most improbable, therein being no mention at all of any such thing. Besides, there are pious and learned Doctors, and among them Salianus, who will not allow it to be so much as probable, that Abraham should instruct the Egyptians in Astronomy: because of the very smal time of his stay among them in Egypt. It is written indeed, that Abraham came from Ur of the Chaldeans: but not that he re­ceived Gen. 11. Astronomy from the Chaldeans, or that he delivered it from them to the Egyptians. And therefore they conclude, that what Josephus said of Abrahams reading Astronomy in Egypt, may with more probability be imputed to his Great-grand child, Joseph. Concerning Him, therefore, we read (in truth) that he was singularly favourable to the Priests in Egypt, at such time, as all the rest of the people mortgaged their lands to the King, for bread, during that wofull and long Famine. For, He excep­ted [Page 4] the Lands belonging to the Priesthood, and (as the Text saith) assigned them certain portions out of the publick Grana­ries; Gen. 47. so that from hence may be proved (what Aristotel tells us, from other Authority) that amongst the Egyptians, the most ancient Nation, the Priests were exempted from labour, and left to 1. Polit. cap. and 1 Metaph. cap. 1. the easy imploiment of their minds: and that this gave them occa­sion to invent and constitute the Mathematiques: and yet for all this, it is not written, either that Joseph taught those Egyptian Priests the Mathematiques, or that they taught them to him. And, perhaps that Favour He shewed the Priests, was an argument not only of the Respect and Veneration, born them by the King and all his people; but also of his particular Gratitude toward them; in that He, who had been bred up only to Sheppardry and Coun­try imployments, and was wholy ignorant of all Arts and Sciences, at his first comming among them being afterwards ad­vanced to the height of a Courtier, and lustre of a Favorite, had bin instructed by them in something more noble and sublime. And truely, the Divine Moses, not long after admitted into the same Court, is not delivered so much to have erudited any others, as to have been himself learned in all the Wisdom of the Egyptians. Nevertheless, considering that this Wisedom of the Egyptians, Act. [...]7 doubtless contained the Mathematiques; and that Astronomy was ever esteemed the best and noblest part of them: this Eru­d [...]tion of Moses seems to be the most Ancient monument of the Science of the Stars, that can be found in Holy Writ.

Astronomy, you see, is of great Antiquity, even upon the Records of Divinity; and might be proved of much greater, could we but evince (what some alleage) that the History of Job was penn'd by Moses, as living a good while after him. Because Job there mentions Arcturus, Orion, and the Hyades, or watery Constellation: and therefore it must be, that before Cap. 9. that time the Stars had been ranged and dispossed into certain Asterisms according to some certain method or artificial Theory then in use. But, be the time of his life never so uncertain, yet we may certainly observe from the History thereof; that it seems Job, being an Alien to the Hebrews, derived his knowledge of God from that which in Scripture is called, Coelorum Exercitus, the Host of Heaven. Forasmuch, as the Invisible things of God are not so well learned from any visible things of Nature, or the effects of his Wisedom and Power, as from the Coelestial [Page 5] Orders and therefore Synesius justly calling Astronomy [ [...]] a truly-venerable Science; he saith, that it advanceth de done ad Poeon. the mind to somthing of greater both Antiquity and Nobility, viz. ineffable Theology. That we may be breef, and only touch upon that sentence in the Book of Wisedom that God gave to Solomon, among other of Natural Science, to understand the cap. 7. Course of the Year and the Dispositions of the Stars: if any thing in Sacred Writ doth expressly prove the Antiquity of Observations Astronomical, and the founding or erecting any setled Art there­upon; it must be that, of which the Holy Prophets complaind Esa. 47. in their dayes; viz. that there were Chaldaeans, who at Baby­lon, did contemplate the Stars, and compute the Months, that from them they might foretell things to come. For, from hence we understand, that the observation of the Motions of Heavenly bodies was a certain profest Art; and of great Antiquity, among the Chaldeans.

In the Second place, we are to revolve the Records of Eth­nick Articl, 3. Ethnick monu­ments likewise revolved; and first those of Fabulous times: accor­ding to which Coelus is found the most anci­ent Astrono­mer: lib. 3. Authors, to see if among them we can find the time of the Nativity of Astronomy.

Look we therefore back, first, into the remains of that part of Time, which is called Obscure, or Fabulous; because possibly enough something of truth, concerning our enquiry, may be found wrapt up in the darksome shrouds of Fables. And be­gin we at the most ancient of Heathen Gods, Coelus, in Greek [...] who, as Diodorus Siculus delivers, was so named, because of his high devotion to, and delight in the observation of the Stars. This eminent person being the Father of many Sons as Ailas, Saturnus, the Titanes, and among those especi­ally Hyperion and Japetus; it is lawfull for us to conjecture, that led by his example, his whole family were addicted to the same Study, For seeing, that Coelus lived in Mauritania, not and after him his Senns. 1. Atlas, who taught Astro­my to his Son. far from the Ocean; and thence extended his Kingdom not only over all Africa, but also into a considerable part of Europe: it is well known that his Son Atlas, who succeded him in the same Dominions, is allowed to have given his name to the highest Mountain of that Country; only because he had made his observations of the motions of the Heavens and Stars, from the top thereof. For, the Ancients in those dayes, as the vul­gar now in ours, imagined the arch of the Heavens to be so little distant from the tops of great Mountains; as that by how [Page 6] much the higher any man ascended on those hills, by so much the more clearly and distinctly might he behold Coelestial ob­jects. To this, Diodorus, Plinie, and others add; that Atlas lib. 3. lib. 2. cap. 8. was feigned to support Heaven on his Shoulders, only because He had framed a Sphear, wherein the whole Heavenly machine was strongly represented: and Clemens Alexandrinus observes, Astrom. 1. that Hercules, being both Vates and Physicus, a Prophet and Philosopher, was reported to come and relieve Atlas (his great Uncle) by taking the vast Burden of Heaven upon his own Shoulders; because He succeded him in that difficult task the Study, or science of Coelestial bodies. Of Hesperus, the Sonne Hisperus. of Atlas, it is recorded, that while he was busy in speculating the Stars, on the top of the same mountain, he was snatched away by the violence of some disease, and could never be found: and that thereupon, the common people, in respect of his piety and justice, gave his name to the most beautifull and resplendent Star, which is also called Vesperugo, being Venus, while she is in the West. As for his Sisters, called both Atlantiades, and And Daughters, the Atlantides and Pleiades, from one of whom came Mercury. 1. Astron. Pleiades; these likewise gave their name to that glomeration of Stars, which are visible in the back of Taurus: and of one of them, named Maia, was born the Famous Mercurius, said to have brought the Science of the Stars first into Egypt. Whence Marcilius, writing of the Astronomy of the Egyptians, Saies of Mercury

Tu Princeps, Author (que), sacri, Cyllenie, tanti. &c.

Though we well know, that the Ethiopians, allowing the Egyp­tians to be no other, but one of their Colonies, sent abroad to find room to subsist in, contend; that they recieved Astrono­my from them: as first Diodorus, and after Lucian have observed. lib. 3. lib. de Astrol. 5. Tusculan. Here it is well worthy our commemoration, what Cicero saith, as of Atlas and Promotheus, so also Cepheus, a King of the Ethiopians: viz. ‘Neither had Atlas been beleived to have sustain'd Heaven, nor Prometheus to have been chain'd on Caucasus: nor Cepheus with his Wife, Son-in Law, and Daugh­ter, to have been Stellified: had not their Divine cognition of Coelestial bodies first occasioned the perpetuation of their Names in the disguise of Fables.’

[Page 7] To return to Saturn, another Sonne of Coelus; He, leaving 2. Saturn, who delivered the same to his Son. Africa, and reigning only in Italy, Sicily and Crete; may be thought to have prosecuted his Fathers studies, no less than the former: and we have this argument for it, that the Slowest of all the Planets bears his name, to this very Day; probably, bacause he was the first, who understood the motion and course of that Planet, which was by the Greeks called [...] from [...] Time, forasmuch as of all the Coelestial Circuits none was found so diuturn. And of his Sons, since Pluto addicted him­self intierly to Husbandry, Neptune to Navigation; we may conceive, that Jupiter, applying his mind to nobler cares, succeded his Father in the Study of the Heavens: as also that he chose Jupiter. Olympus, accounted the highest mountain, to make his ob­servations upon: so that in process of time, he came therefore to be called Olympius; and the name of that mountain to be trans­ferred upon Heaven it self; whose orders and laws He well un­derstanding, was thereupon said to have the Dominion of Hea­ven. Certain it is, that the Grecians ascribed the Original of this noblest Science, partly to the Gods themselves, and partly to ancient Hero's: which Achilles Tatius seasonably alluding Isagog. ad Phoen. unto, introduceth old Aeschylus attributing to God, that He shewed the risings and settings of the Stars, and distinguish't Winter, Summer, and the other Seasons; and Ovid Fathers the same wholly upon Jupiter.

Per (que) Hiemes, Aestus (que), & in aequales Autumnos,
1. Metamorph.
Et breve Ver, spatijs exegit quatuor Annum.

Besides, it is in the Fiction, that Jupiter took his Father, Sa­turn, bound him, and precipitated him into Hell. Now this seems to intimate, that Jupiter having imposed his own name upon one of the most eminent and illustrious of the Planets, gave that of his Father to another of them, that was more remote, situate in the deepest part of the Aetherial spaces, and of the slo­west progress: though all this while we are not ignorant, that those names were fixed upon those Planets a long time after: since more anciently the Planet Jupiter was called Phaeton, and that of Saturn, Phoenon. For, we may collect very neer as much from Lucian, who by Tartarus understands the immense Alti­tude, [Page 8] or Profunditie of the Aetherial Region: & so denies that Sa­turn was either exil'd by Jupiter into Hell, or cast into bonds; as common heads were perswaded to beleeve.

As for Hyperion; Diodorus hath a tradition, that he being 3. Hyperion. of the progeny of old Coelus, demonstrated the courses of the Sun and Moon: and therefore called the Sun, Helios, after the name of his Sonne; and the Moon, Selene, after that of his Daughter.

Last of all comes Japetus, who also was the Sonne of Coelus, 4. Japetus: from whom came Prome­theus, who followed the same study. in Eccles. 7. but performed nothing worthy commendation in the advance of his Fathers Speculations: but Promotheus, whom he begat, was therefore imagined to have been chained on the hill Cauea­sus, and to have his heart perpetually torn by a hungry Eagle or Vultur; Because (as Servius expounds the riddle) with rest­less care, and solicitude of mind, he constantly excruciated him­self with observing the Stars, and studying their Ascensions and Declinations. We shall not insist upon what follows in the same Author, namely that this Prometheus was the first, who introduced Astrology to the Assyrians (not far from Cau­casus:) it being more usefull for us now to observe, that He was imagined to have stolen Fire from Heaven, for the inanimation of Man, for no other reason, but because he infused this Heaven­fetch't Knowledge into the breasts of men, and inflamed their souls with the desire and love thereof. For, as to the remain­der; for as much as Belus was the same with Jupiter, among the Assyrians, as Diodorus testifies: it is He rather, who was ac­counted both the most sacred of their Dieties, and the Inventor lib. 2. lib. 37, o. 10. of this Sideral Science; as Pliny affirms.

It is not needfull for us here to examine many other of the an­cient Traditions, accounted likewise among the Fabulous; as, in so did Phae­ton, particular, the Fable of Phaeton, which hath this Mythology, that in his life time he had made a considerable progress toward the discovery of the Suns Annual course; but dying immaturely, he left the Theory thereof imperfect. That other of Bellerophon, whom Interpreters maintain to have been carried up to Heaven, not by a flying horse, but a studious and contemplative mind, eager in the the quest of Syderal mysteries. That of Doedalas, who indeed, by Doedalus, Icarus, th [...] same towring speculations, as by the artifice of wings moun­ted up to the Northern part of Heaven; while his less ingenious Sonne, Icarus, falling short in his attempt of imitating his Fa­thers [Page 9] sublime flight (as not so well understanding the demon­strations of the reasons of his Theory) flaggd very low in his Studies: and fell from the true and apodicticall cognition of Coe­lestial motions and vicissitudes: with many other the like, re­counted by Lucian; as that of Endymion, the favourite of the Moon; of Tiresias, the Prophet, &c. Yet one thing there is, de Astrol. in Isagog. mentioned as well by Lucian, as Tatius; which we cannot well pass by; which falling under the account of Heroicall times, seems to come somwhat neer to that which is called Historicall. And that is the notable Centention that arose betwixt Atreus Atreus and Thyestes. and Thyestes about supreme dominion. For when by the pub­like Consent and Vote of the Argives, the Kingdom was to be his of the two, who should give the most eminent testimony of Sci­ence: it came to Atreus share to be King: because, though Thyestes showed them the signe Aries, in Heaven (for which he was honourd with a golden Ram) yet had Aireus declared a thing more excellent: while discoursing about the variety of the Suns rising, he made it appear, that the Sun and the World (i. e. the Starry Orb) were not carryed the same, but quite contrary wayes; and consequently, that that part of the Heavens which was the West or Occident of the Starry Orb, was the very rising, or Orient of the Solary. Hence that verse of Euripides,

[...]
Qui Astrorum enim contrariam ostendi viam.

To the same times likewise are we to refer the Institution of Hercules and Iphitus. the Olympick Games, by Hercules; which after a long inter­ruption were renewed by Iphitus. For, inasmuch as those sports cap. 18. were instituted for no other end (as may be assured from Cen­sorius) but that their celebration might put men in mind of that Intercalation of a month and half, that was to be made con­stantly every fourth Year, in respect of those four times eleven, or 44. Dayes, by which the mo [...]ion of the Moon anticipated that of the Sun; and the four times six hours, or one whole Day, by which the circuit of the Sun exceded 365 Dayes: ma­nifest it is, that Hercules could not understand this, without ha­ving first exactly observed the Motions of Sun and Moon. Hi­ther also belongs that which is reported of Orpheus, who must Orpheus. needs have attentively observed the seven Planets, if it be true, as [Page 10] Lucian averrs, that he represented their Harmony by his Seven­stringed de Ast [...]ol Harp: which the Grecians thereupon designed in Heaven, by some Stars, that to this Day retain the name of Lyra. So likewise doth what Sophocles saith of Palamedes, Palamedes. who pointed out the several Asterisms, and particularly

[...]
Vrsum volutam, gel [...]dum & occasum Canis.

And lastly, what Homer recounts, that in those times were well known (besides Bootes and the Bear, or Wain) Homer.

[...].
Odyss. E.
Pleiades, at (que) Hyades, robur (que) ipsum Orionis.

We have now struggled through the Darkness of Fabulous Times, and are advanced as far as to discerne the twilight of Articl. 4. Historicall. An here, the first thing we clearly perceive, is that Secondly, those Historical times; accor­ding to which the antiquity of Astron. Obser­vations belongs either to the Egyptians, or Babylonians. the whole controversy about the Antiquity of Astronomical Ob­servations, lies betwixt the Egyptians and the Assirians, or Baby­lonians. For, as to the Grecians, though some have thought they might put in also for a claim to the honour of being the An­thors of this admirable Science; yet by the Verdict even of Plato himself, they are to lay by the presence of Competition, ‘For, sayth He, the first who made Syderal inspections, was a Barbarian; a more ancient Nation than ours bred those men, in Epinom. who first devoted their minds to that Study, in respect of the Summer-like serenity and perspicuity of the Air, such as Egypt enjoyes, and Syria, where all the Stars are, clearly visible and no Clouds or Mists to obscure the beautifull face of Heaven.’ And certainly, if we except what we newly mentioned, the Insti­tution of the Olympick Games by Hercules, and the restauration of them after some Intermission, by Iphytus, which hapned about 800. Years before Christ; and some places in the writings of Homer, and more especially of Hesiod, who lived neer upon the same time, or not long before; we shall find that the Grecians can produce no Monuments of their Observations of the Hea­vens, more ancient than those of Thales, who flourisht, full 600. Years before Christ; and who yet borrowed his knowledge of [Page 11] Aetherial Matters from Egypt. It being manifest therefore, that the Aegyptians, or their Priests, are the only men, that ought to be admitted to a Dispute with the Assirians or Babylonians, or their Philosophers, concerning the Antiquity of Observations; and that their several Pleas seem equally reasonable. Truly, it is no easy matter to determine the difference, so as to place the Lawrell on their heads to whom it doth of right belong. For, albeit Josephus assignes the Honour to the Chaldaeans, and 1. Antiq. 8. others again stand firmely for the Egyptians: yet Plato, Diodo­rus, in Epinom. 2. lib. de A­strolog. Isagog. Lucian, Achilles Tatius, and others alleadge such quotati­ons for each party, as seem to have no other, but the authority of the parties themselves. Nor ought that to seem strange; since both sides equally alleadge the convenience of their vast Companies, and the serenity of the sky; since they both boast themselves the Original Nation and allow their Competitors to be only Colonies; since both glory in fabulous beginnings, which we cannot trace or discusse; and both recur to egregious falshoods about the time when their Ancestors first made Coele­stiall Scrutenies. For, the Chaldaeans (as we find on the Register of Diodorus) affirm, that their Nation applied themselves to loc. citat. these Studies, from times of incredible Antiquity viz. of four hundred and three thousand Years: And the Egyptians (as Ci­cero de Divi [...]at. observes) talk of Observations of four hundred thousand and seventy Years standing. Unless you shall please to consigne the Victory to the Egyptians, because they put a value only them­selves by Auction. As if it were not enough for them to boast those four hundred nine thousand Years (mentioned by Laertius) in which from the time of V [...]lcan, the Sonne of Nilus, to that of Alexander of Macedon, there hapned of Eclipses of the Sun in praefat. three hundred seventy three, and of the Moon eight hundred thirty two. These considerations premised, we cannot indeed deny, but the Egyptians had some Observations, some ages before Thales and other Grecians travelled among them: but, when we would enquire more precisely into the time, when those Ob­servations first begun; we find our selves at a loss, and brought back again into the cimmerian obsurity of Fabulous Times.

Now forasmusch as, though Pliny writes, that Epigenes found lib. 9. c. 56. no Observations among the Babylonians of above seven hundred and twenty Years antiquity, and those engraven on artificial Tyles or Slates; and the most ancient Eclipses deduced from them, were [Page 12] transmitted to Ptolomy, about the same Number of Years before in Almagest. lib. 4. cap 6. Christ: and that by the great Hipparchus. And to the same Time belongs what Berosus and Critodemus say, that in their Dayes, there were extant no Observations of more than four hundred and thirty Years as may be found also in Pliny: foras­much, we say, as we have brought some considerable Monuments of Observations much elder than that time; yet shall not concede beyond what the Chaldeans themselves profest, when they testifi­ed to Callisthenes (who went to them upon no other errand, by the perswasion of Aristotel, as Simplicius relates) that they had in lib. 2. de Coe lo, and com­ment. 46. nothing of that kind among them beyond a thousand nine hun­dred and Three Years past: which Years seem to commense at Ninus, the Sonne of Belus, and first King of the Assyrians. It is clear, that the Antiquity of Observations ariseth to (but not a­bove) one thousand and ninety Years before Alexander the Great.

But, alas! after all this great adoe, What did the Observa­tions Articl. 5. Yet neither of of them obser­ved any thing considerable; at to the desig­nation of Times: but corrupted what they had obser­ved, to the in­troduction of Astrology Ju­dicial. themselves amount to? Why truely, for ought we can ga­ther from all that is extant concerning them, those of the Ae­gyptians amounted to nothing at all: and those of the Chaldeans to very little. For the Egyptians, we confess, are said to have observed the rising of the Dog-Star, and some other, no very difficult apparences: but we have no remains delivered down to us, of that or any other particular they observed, with the ex­act designation of the Time, as they ought. And from the Chal­daeans we have as little, besides those Eclipses mentioned in Pto­lomy. But, when I speak of the Egyptians, I except Ptolomy himself and some others, who lived and studied at Alexandria, about there hundred Years before the Nativity of our Saviour; or after Alexander: as Timocharis, Eratosthenes, Hipparchus: for all these were either Grecians, or to be accounted among Grecians, in respect of the language they used and wrote in, ra­ther than among the ancient Egyptians, by whose Inventions even Ptolomy himself (one of their own Country men, without dispute) was very little, or nothing at all assisted in his Study of Astronomy. But, what concerns aswell the Egyptians, as Chalde­ans; their Observations are to be distinguisht (according to the division vulgarly received into (1.) Astronomical, and (2) Astro­logical: the former relating to the Motions, Magnitudes, Di­stances, and proportion of the Stars; the Latter to the Effects of them, which they conjectured were dependent on the Vertues [Page 13] and Influences of Heavenly Bodies, aswell in the affections of the Air, as in the actions and affairs of Mankind. For, both Na­tions being wonderfully prone to Supersttition, and surprised with excess of Admiration at the Eclipses of the Sun and Moon, when they first beheld them; and observing ever now and then some Stars that moved in Courses contrary to the West, they began presently to think, that those apparences hapned not without natural Causes; and that it remained only on Mans part, to Study how those events might come to be fore-known, which those apparences did portend. Hereupon, having attributed the most powerfull Vertue to the five wandering Stars (as Diodo­rus loc. citat. testifieth particularly of the Chaldaeans) as understanding them to be the Proclaimers of the will and purposes of the Gods; because they sometimes arose, and sometimes set in various places of the Heavens; because they varied their magnitude and colour: therefore they conceived, that they ought to adress their Studies and Disquisitions principally to these varieties. And, because they imagined, that the higher the place was, from whence they should observe these Wandering Stars, the more clearly and distinctly might they be discerned; they builded Structures of vast altitude; and particularly that immense Tower at Babylon, described by Herodotus, from the highest area whereof (where lib. 1. stood also the Temple of Belus) they might exactly behold and observe the rising and setting of the Stars, and other Syderal occurrences They took notice likewise, that those five Planets did keep almost the same Course, as the Sun and Moon; and thereupon they pointed out the Zodiack, imagining that there must be some eminent vertue in that part of the Heavens, because all the Planets kept constantly to it. And this Zodiack they di­vided into 12. parts, or Signes; because the Moon run it over 12. times, and the Sun only once, in one Year: and according to the number of the Dayes, during which the Sun was in passing through one Signe, they distinguished each Signe again into 30. parts, which we call Degrees. I shall not recount to you, how they would have Twelve Principal Dieties belong­ing to these 12. Signes, whereof each had his particular regi­ment over his proper Signe and Moneth dependent thereupon: nor how they substituted thirty of the fixt Stars, to assist the Planets, and called them Concelling Gods: nor how they placed 12. Stars always visible in the North, for government of [Page 14] the Living; and as many more in the South, alwaies visible, for the government of the Dead, there gathered together; with many other the like dreams and ridiculous absurdities. But the thing I think most worthy your notice, is, by what rude kind of artifice they distinguished the Zodiack into 12. Signes; as we find it described, concerning the Chaldaeans, by Sextus Empiricus, ad Astrolog. 1. in Somn. 21. and concerning the Egyptians, by Macrobius.

The manner this. They took a vessell with a small hole in the bottom, and filling it with Water, suffered the same to distill Drop by Drop into another Vessell, placed beneath to receive it; and this from the moment of the rising of some one Star or other, observed in one Night, untill the Moment of its rising again the next Night following. The Water fallen down into the Receiver, they divided into [...]2. equal parts, and having two other smaller vessells in readiness each of them fit to contain one twelfth part of the Water, they again poured all the Water into the upper Vessel, and strictly marking the rising of some one Star in the Zodiack, they at the same Moment gave the Water leave to distill into one of the smaller Vessells, and so soon as that was filled, observing likewise another rising Star, they put under another small Vessell; and so alternately shifting the small vessels, they noted, if not in one Night, yet in many, the twelve Stars, by which they might discriminate the whole Zodiack into twelve equal parts. Now with what Art and exactness these Ancients measured out the Heavens, may be conjectured from this one example. I might adferr another foppery of the Chaldaeans, from the same Empiricus, who relates; that taking it for grant­ed, that the future fortunes of Men did depend on their particu­lar Horoscope, or Signe rising at their Birth, when they had a mind to divine in this Kind; Two of their wise men agreed toge­ther in the calculation of the Nativity of the Person proposed: the one stood by the Mother in Travell, the other on some high place neer at hand; and as he that was below gave the Signe, that the Infant was then newly come into the World, the other above took care to observe the Signe, that was just then newly risen. ibid. cap. 20. But, it will be of more use for us to hear what Macrobius tells of the Egyptians. They, when they would know the Diameter of the Sun, had in readiness a Vessell of Stone, hollowed to the form of an Hemisphere, exactly made, with a style or Gnomen erected in the middle, and twelve Horary Lines drawn within. [Page 15] And on the very Day of the Equinox, observing the Moment, when the upper Limbus of the Sun first shewed it self above the Horizon; they marked that place on the brim of the Vessel, on which the Gnomen cast its shadow. Then again marking that place on which the shadow ended, when the lower Lim­bus of the Suns body appeared just above the edge of the Hori­zon; they measured the space or distance betwixt the two marks of the Shadowes, and found it to be the ninth part of an hour, or the hundred and eight part of the Hemisphere, and con­sequently the two hundred and sixteenth part of the whole Cir­cuit: and from thence they deduced, that the Diameter of the Sun was the two hundredth and sixteenth part of its whole Orb; (which, in truth, is the 700th neer upon) or did contain one Degree and an hundred Minutes; which yet is no more than halfe a degree, or 31. Minutes, at most. To this we might su­per-ad, that it was the practice of elder times, to commensurate the Diameter of the Sun by an Hydrologie, or Vessel of Water; collecting the same from part of the Water flowing down the whole Day, which had dropped until the Sun was wholly ri­sen; as is insinuated by Plutarch, and deduced from Capella: but Cleomedes hath at large declared, that this way of measu­ring by Water falling slowly and equally from Vessel to Vessel, was an Invention of the Egyptians. Now the reason, why we touch upon these particulars, was only to satisfy, that (as we said afore) no great matter in Astronomy was ever observed either by the Egyptians, or by the Babylonians.

And, if you desire any further Argument thereof; Pray take this. They were very far from suspecting that the Fixt Stars had any motion proper to themselves; or that they had any Eccen­tricity (excepting only that the Egyptians thought Venus and Mercury to move round about the Sun, as their center; as is affirmed by Macrobius, and some others) or that the Sun had any Apogaeum at all, with many other Particulars fully as consi­derable. Which doubtless must be the reason, why they invent­ed no Hypotheses, by which they might regulate themselves, in making their Caluclations of the various motions of the heavenly bodies. And Peter Ramus not long since complaind, that we have not our Astronomy free from the trouble of Hypotheses; such as the Interpreters of Aristotel themselves, and Proclus on Timaeus have recorded the Egyptians and Babylonians to have [Page 16] had amongst them: while, incroth, he complaind, that we had not our Astronomy as rude wild and imperfect, as theirs was. For, however some Hypotheses are more simple (and so more easy) than other-some: yet it is absolutely impossible, that Astronomy should consist without some or other. Hereupon, they could observe, indeed, that the Planets were one while Direct in their Progress, another while Retrogarde, and then again Stationa­ry; that they in their wanderings sometimes inclined towards the North, and sometimes deflected again toward the South: but all that while, they could neither comprehended the rea­sons of those various apparences, nor calculate them by numbers. The most they could doe, was darkly to represent those motions, by certain Hieroglyphicks, as in particular by the windings and flexures of Serpents; and the motion of the Sun, by only a Beetle rowling his pill of dung backward: as we may read in Clemens Alexandrinus: and then came Eudoxus, who having learned that variety of motions among them, was the first who invented Hypotheses of various Orbs, for the Solution of the Phenomena.

Again, they were very far from attaining the determinate places of the Fixt Stars, according to Longitude and Latitude; or according to their Right Ascension, and Declination: so that neither could they define the true places of the Planets, by Com­paration to the Fixt Stars, nor (consequently) designe any Ob­servations with due exactness. And truely, this was the Cause why Hipparchus met with no Observations, either of the E­gyptians or Babylonians, by which he could receive the least help or advantage, toward his composing either Hypotheses, or Tables, to represent the motions of the Five errant Stars: and Ptolomy was the first, who partly by the benefit of Observations left him by Hipparchus, and partly by those he made himself, became able to attempt such a Work; as stands recorded in his Almagest. There were only the Eclypses, which both these Nations had set down: as observed in their Commentaries: and those only so, as that from Past, they might be able to conjecture somthing of what were to Come. Not from the motions of Sun and Mon, exactly calculated by the help of Tables; but having learnd from common experience, that every ninetneenth Year, Eclypses did return again upon the same Day, for the most part: thereupon they endeavoured to praedict what Eclipses would hap­pen, and the time when; and this after they had perceived not any [Page 17] Anomaly in the Sun, but some certain Inequality in the Moon, which reducing to a medium, they concluded that the Moon did every Day run throug [...] thirteen Degrees, and a little more than one sixth part of a degree; as Geminus delivers of the Chaldae­ans. But in their predictions of Lunar Eclipses, they were som­what more confident; aswell because these Eclipses usually uturn, for the three Ages next succeding, within the compass of the same Dayes; as because it is very rare, in respect of the great­ness of the Earths shadow, but the Moon, either in the whole, or some part of her, more or less, falls into it: but, because (as to Solary Eclypses) the Moon is both so small, and hath so large a Parrallax, as that she doth not for the most part intercept the light of the Sun from the Earth; therefore was it (as Diodorus witnesseth specially of the Babylonians) that they durst not de­termine Eclypses of the Sun to come, to any certaine time; but if they predicted any, with limitation of time, they alwayes (to save their credit, in case of failing) annexed this Condition, If the Gods be not prevailed upon, by Sacrifices and Praiers, to avert them.

Truth is, these Astronomers were also Priests, and it was their interest to cast in this Proviso. For, being ambitious to be reputed interpreters of the Will of the Gods to the People, and so both knowing in things to come, and skillfull in such Ceremo­nies, wherewith their respective Deities were most attoned and delighted: unwilling to be thought able to predict nothing, and as unwilling again to be found erring in their chief predictions, they wrapt up all in Misteries, and amused the vulgar with su­perstitious opinions and rites. The Egyptians, in a great part of their sacred Worship, had recourse to the Astrological Books of their Mercurius (one of the Order of the Fixt Stars; a se­cond, of the Conjunction of Sun and Moon; a third and fourth, of their rising.) which with what ceremonious Pomp they used to carry about with them, in a kind of solemne Procession, you may find amply described by Clem. Alexandrinus. Nor is it lib. 6. stromat. strange that those Priests accounted so sacred and knowing, should also be estemed for Prophets. Further, you meet with no mention of the Five Errant Stars, all this while; and the reason seems to be, because they attributed an energie of them only as they were referrable to the Inerrant or Fixt, and particu­larly, as they possest this or that part of some Signe in the Zo­diack, [Page 18] and together with it had their rising, or setting. For, so much did they ascribe to the Zodiack, as that the Babylonians, and (in imitation of them, the Persians and Indians) thought, that each decimal of degrees, or thirds of the Signes, (and the Egyptians came as low as to each single degree) could not be varied in the rising, but some eminent variation most happen, especially in him, who should be borne at that time. And here­upon was it, that the Egptians made that great Circle of Gold (described in Diodorus) of a cubit in thickness, and three hun­dred sixty five cubits in circumference (plundred at last by Cambyses) that upon each cubits space might be inscribed each Day of the Year, 365. Dayes in the whole round, and also what Stars did rise, what set upon each Day, nay the very hour of their respective rising and setting, and what they did signifie: and whereas others used to assigne the form of some Animal or other, to each ten degrees; they assigned one to each single de­gree, and so made their harsolations or conjectural predictions accordingly. For Example; to the first degree of Aries they assigned the figure of a Man, holding a Sicle or hook in his right hand, and a Sling in his left; to the second, a Man with a Dogs­head, his right hand stretcht forth, and a staff in his left; and so of the rest; then annexing the signification to each, they deter­mined, that he, who should have the first degree of Aries for his Horoscope, should be some part of his life a Husbandman, and the rest of it a Soldier; that he, who should be born under the second, should be contentious, quarrelsom, and envious; and so of the rest, all which Scaliger hath fully deduced from Aben Ezra. In a Word; what ever knowledge either the Egyptians or Chal­deans had of the Stars; certain it is, they referred it wholly to Astronomantie, or Divination by Stars: and therefore among them there flourisht, no true and genuine Astronomy, but a spuri­ous and false, one i. e. Astrology Divinatory, or the fraudulent Art of Fortune-telling by the Heavens.

Berosus (whom we formerly mentioned) coming into Grece, a little after the death of Alexander, is discovered to have brought with him nothing sollid touching Astronomy, but only Judicial A­strology [...]; lib. 9. cap. 7. lib. 9. cap. 37. for which, as a thing new, and strange to the people, he was highly esteemed, as Vitruvius and Pliny remark. And Eudox­us, who had returned out of Egypt before that, well knew what sort of Astrology this was (the principal Contrivers and Founders [Page 19] of which are said to have been Petosires, Necepsus, Esculapius) 2. de divinat. but he highly contenmed it as Cicero remembers, and brought home no other fruit of his tedious Travells, beside a list of some Eclipses, and the varieties of the motions of the wandering Stars, by which he first essaied to compose accommodate Hypotheses, as we have formerly hinted. Nay, Plato himself, who was Com­panion to Eudoxus, for thirteen Years together, in Egypt: pro­fest: in Epinom. that he could attain nothing sollid and satisfactory touching those Stars, and therefore placed all his hope only in the sagacity and industry of the Grecians, such as he knew Eudoxus to be. For, having first recounted what ever he knew concerning them; he saith, ‘It is to beleeved that the Grecians make more perfect whatsoever they receive from Barbarians; and therefore is it fit, we allow the same, touching the argument of which we have discoursed. Truth is, it is difficult to find out the way, how all these Apparences, so involved in ob­scurity may be explicated: nevertheless there is great hope that things of that sort will be better and more advantageous­ly handled, than they were delivered to us by Barbarians.’

From the Egyptians and Chaldeans, therefore (as Astronomy Articl. 6. And after them to the Grecians among whom the most anci­ent mention of Astron. is in Hesiod. her self, while young and rude) we come to the Graecians: and the most antique record of Syderal Observations to be found among them, seems to be that of Hesiod; who in his Book of Weeks and Dayes teacheth Husbandmen the most opportune times of reaping, sowing, and other labours of Agriculture, from the rising and setting of the Pleiades, and Hyades, and Arcturus, the Dog-star, and Orion:

[...].
Donec Pleiades, quae & Atlantiades, exoviuntur, &c.

And I cannot tell, whether it were that book, or some other, that Pliny meant, when speaking of Hesiod, he sayes, Hujus quo (que), nomine extat Astrologia, there is extant an Astrology of his. However, we are here to remark two things, in order to our more exact disquisition; the First is, that the Ancient Greeks principally attended to these risings and settings, aswell that they might distinguish the several Seasons of the Year, as that they might fore-know Rain, Winds and other dispositions of the Air, usually attending those Seasons. And hereupon, Thales, Anaximander, Democritus, Euctemon, Meton, Eudoxus, and Ex Gem Ptol. & aliis. [Page 20] many others, composed certain Parapegmata, Tables, (as E­phemerides, or Diaries) in which they inscribed each Day of the Year, with the particular Stars rising or setting on each Day, and what mutations of the Air each one did portend. Such a Darapegme as these, was composed likewise by Julius Caesar himself, for the Horizon of Kome; in allusion where to he might justly own, what Lucan said for him, lib. 10.

Nec meus Eudoxi fastis superabitur Annus.

And, him doubtless, did Ovid translate into his Fasti; pro­mising lib. 1. in the beginning, that he would sing of the Stars and Signes, that rose and again descended under the Earth. But, to keep close to the Grecians; among them, he was held a great Astrologer, who had discovered and observed only these risings and settings here spoken of; and so of whom that might be spoken, which Catullus said of Conon,

Omnia qui magni dispexit lumina Mundi,
Stellorum (que) ortus comperit, at (que) obitus.

For, before the Advent of Berosus, this was the only [ [...]] Praesignification or Divination by the Stars, the Gre­cians had among them: unless what Hesiod hints, in his in [...]ebns.

[...],
Primùm prima dies, & quarta & septima sacra, &c.

where he points out, what Dayes of the Moon were accounted Lucky, and what Unlucky.

The Second observable is; that among the Grecians, and in­deed among divers other Nations, beyond all Memorials of either Traditions or books, the Stars were reduced to certain Images, or Constellations, and denominated accordingly (as their names yet shews) as it pleased the fancies of Husbandmen, Shepheards, Matiners and the like, who used to be vigillant and gizing upon the Heavens in clear Nights. Though there have been some Constellations added of latter times, as that of the lesser Wain, by Thales, which Lacrtius and Tatius recite out of Eb. 1. de vit. [...] de Com. [...] Callimachus, who also took the same elswhere, and that of Be­renices [Page 21] Hair, removed into Heaven by Conon, as Catullus relates. Cleostratus likewise (as we have it from Hyginus) found lib. 2. A [...]. lib. 2. cap 8. out the Kidds: though, (which Pliny moreover attributes to him,) his invention of the Signes in the Zodiack, is so to be un­derstood, as that he taught men through what Signes the Sun and other Planets passed. But (that we may couch also upon this) at first, the Grecians had only Eleven Signes in their Zodiack; and it was long after ere they came to add the twelfth, in imitation of the Egyptians, who (as may be collected from Servins, in 1. Geog. l. 8. Marcianus, and others) instead of the Clawes of the Scorpion, placed Libra, the place destined to Augustus, by Virgil,

—Ipse tibi jam brachia contrahit ardens Scorpius.—
1. Georg.

They added the Twelfth, we say, to the end, that as the whole Compass of the Zodiack was divided into Dodecatemoria (as they call them) twelve equal parts, so it might consist also of twelve Signes. Albeit, being (as it were) necessitated to make use of such Signes, as had been brought up, rather by chance, than Art; those 12. Signes were not exactly proportionate to the 12. Divisions of the Zodiack, but took up more space some, than others as in particular, Leo possest more room than Can­cer; Taurus than Gemini. I say, than Gemini, which though composed of Castor and Pollux; in so little space as is allowed them, it is impossible the one should rise, when the other Sets, and both in the East: but this Empiricus interprets of the two 1. adven. Physic. Hemisphears. I omit to insist upon this, that all Nations had not the same Constellations: as among the Egyptians was no Bear, no Cepheus, no Dragon; but other formes or representati­ons, as Tatius reports; and shall add only, that Eudoxus seems to have been the first, who partly out of the Egyptian Fi­gures, partly out of the Grecian, furnished the whole Zodiack with Images resembling the Asterismes, (as men had fancied, at least) and caused them to be drawn on a Globe, or solid Sphear. For, Aratus (upon whose Poem, intitul'd [...], Apparen­ces, there have been so many Commentaries set forth, as that no fewer than forty have been extant in Greek; besides those of Cicero, Germanicus, Avienus, and other Latin Interpreters.) did no more, but only express in verse, what Eudoxus had said before in prose, of this argument; as Hipparchus Bythinus de­monstrates. [Page 22] I know not, whether it would be seasonable for me, lib. 1. in Arat. [...]han [...]. here to advertise, that it is no wonder Aratus erred so grosly in many particulars; considering that (as is written in his life) he Living with Antigonus Gonata, in the quality of his Physician, and Nicander in the quality of his Astrologer; and both were good at Poetry: Antigonus commanded the Physician to give him a tryall of his Poesie, upon an Argument in Astrology; and the Astrologer to give another of his, upon somthing in Phy­sick: delivering to the one, the Book of Eudoxus; and to the other, all that was extant of Treacles, Antidotes, or Counterpoisons. So each wrote of what he did not well understand. One thing I shall not, forget; and that is, that the Phenomena of Euclid, who lived neer about the same time, and taught at Alexandria (as in the Memorials of Pappus) were quite of another kind; lib. 7. being indeed no other, but certain Principles of Astronomy, con­cerning the figure of the World, and the Circles of the Sphear, and chiefly, that of the Zodiack.

But, to return back to the more primitive Greeks; I remember and next of Thales Mile­sius. I said, that Thales Melesius was accounted the First, who after old Hesiod and Homers Dayes, enquired into the Order of the Stars. And, certainly He was the Man, who among the Grecians may challenge the Palme; as to Antiquity; for, Apuleius calls him, ut antiquissimus, sic peritissimus Astrorum Contemplator, and Eudemus in Laertius attesteth, that this was lib. 1. the Opinion of most, adding moreover, that Xenophanes and Herodotus highly admired him, for that he had first predicted the Eclypses and Conversions of the Sun; and that Heraclitus and Democritus witnesseth as much. And whereas Apuleius further subjoyns, that he found out the motions and oblique tracts of the Syderal Lights: Pliny ascribes that to Auaximan­der, a Disciple of Thales Milesius, (whence he was said Rerum fores aperuisse, to have opened the Doors of Celestial matters) and Diodorus to one Oenopides Chius: which Thales could not yet be ignorant of the Obliquity of the Zodiack, when he had written of the Solstices, and Equinoxes, and had conversed a long time with the Egyptians in their own Country, as Laertius re­members. Further, it is delivered to us, that among others, he predicted that notable Eclipse of the Sun, which hapned in the time of the warre betwixt the Meads and Lydians; which he could not doe by any other reason, but only because, coming [Page 23] newly out of Egypt, he had learned, that Eclipses generally re­turn upon the same Day after the space of nineteen Years; and having taken notice of one, that fell out 19. Years before, he concluded that there would be one at such a time. Nor is there reason why any should think, that otherwise his whole life might be sufficient to observe all the motions of the Sun and Moon, as from thence to be able to invent all things necessary for the calculation of the times of their Several Eclipses. Moreover, it in vit. Dionys. doth not appear, how by any other way, but that Helicon Cy­zicenus came afterward to fore-tell that Eclipse of the Sun (mentioned in Plutarch) for which he was so much admired by Dyonisius, and rewarded with a Talent of Gold. Nor likewise, how Sulpitius Gallus could fore-tell that other of the Moon. which as most opportunely predicted to the Roman Army, then ready to joyne battell with the Persian, is so higly celebrated, not only by Plutarch and Pliny, but also by Valerius, Quintilian, and other Historians: for other Rule for the calculation of fu­ture Eclipses, there was none before Hipparchus, who inven­ted Hypotheses and Tables fit for that purpose. Besides, what La­ertius imputed to Anaximander, Plinius as confidently imputes to one Anaximenes, an Auditor of his: (namely that he should be the Inventor of that Gnomon, by which the Conversions of the Sun, or the Solstices and Equinoxes, were indicated, and that he set up such a one at Lacedemon.) Neer upon the same then of Pytha­goras, and his Disciples. time was it, that Pythagoras is said to have first discoursed (though Phavorinus, in Laertius, confers that honour upon Parmenides,) that Lucifer and Vesper was one and the same Star of Venus, Now, whether may we conceive, that he borrowed this of the Egyptians, from whom being taught, that not only Venus, but Mercury also, were carried round about the Sun, as their Center, so that one and the same might be both Morning and E­vening Star: possibly, from thence he might take the hint of his Conjecture, that the Sun was the Center of not only those two, but of the other Planets also, and consequently of the whole World: and moreover that the Earth it self, as one of the Planets, moved about the Sun? For truely, this was an eminent and con­stant Tenent in his School; as may be understood not only from Aristotle in the general, but also from Laertius in particular of 2. de coelo. 13. de Arenar, num. Philolaus, and from Archimed of Aristarchus, both Pythagorus his Disciples: that we may not rehearse all those many passages [Page 24] in Plutarch, concerning this memorable particular; nor name those, who held, that the Earth was not so much moved about the Philolaus, Aristarehus, Timaeus. Sun as dayly turned rouud upon an Axis of its own; as Timaeus, a Pythagorian also, who is therefore by Synesius esteemed, after de don. ad paeon. in Timaeun. Plato, the most excellent Astronomer.

Furthermore, in the next Age after Thales, or neere upon, comes Cleostratus (the same who was beleeved to have depre­hended. After these suc­ceeded Cleo­stratus. the Signes of the Zodiack) and he, seriously remarking that the Intercalation, which as we said, was wont to be made every fourth Year, celebrated with the Olympick Games, did indeed restore the motion of the Sun to the same Day again; but did not restore the motion of the Moon till the eight Year, or two Olympiades, in which the intercalatory Dayes amounted to ninety Dayes, or three months: He, we say, thereupon interduced, in­stead of the Tetacteris, or space of four Years, the Octaeteris, or space of eight Years, which compleatly past, the New-Moons, and Full-Moons would returne again on the same Dayes. But, when in short time men had perceived, that this Institution failed them, in exactness of computation; and that sundry wayes had bin at­tempted to cure this uncertainty: at length riseth up Meton, som­what more ancient than Eudoxus; and he demonstrateth from Meron. &c. the New-Moons, and Full-Moons Eclyptical, that they did not return upon the same Dayes, till after full nineteen Years: and thereupon he became the Author of the Enneadecaeteris, or Period, or Cycle of 19. Years. In respect of which discovery, together with the Heliotrope, or Sun Diall he made at Athens, and some other the like Inventions, he was in eminent esteem among the Athenians. But as concerning that Period; Callip­pos, familarly acquainted with Aristotle, discovering it to be too long, by the fourth part of a Day; inferred, that from four Pe­riods one whole Day ought to be detracted: and so erected a new Period, or Cycle of Sixty six Years, or four times nine, at the end of which one Day was to be cut off; and this was cal­led the Callippik Period, and remained in use for a long time to­gether. After him succeeded Hipparchus, who detecting this Period, to be yet too long; demonstrateth that after four Cal­lippik Periods, or three hundred and four Years, there would re­main one whole Day too much. And in truth, the experience of many succeding Ages declared, that to this detraction of Hippar­chus, nine or ten Years over and above were to be expected. [Page 25] However, it is worthy our notice, that the Period of Meton, to­gether with the Conection of it, applied by Callippus, was of long use in the Church under the name of the Golden-Number: though wanting the Application of Hipparchus his Correction: also, a mistake of about four Dayes, relating to the New and Full Moons, crept into the account, even from the time of the Nicene Councel; which was one of the two main causes of the Reforma­tion of the Kalender in the eighty second Year of the last Age.

And now we have an opportunity to speak more expresly of Articl. 7. Eudoxus, who first discovered the necessitie of manifold Spheares. Eudoxus, so frequently mentioned. This man, well understand­ing, after his return out of Egypt, that not only the Sun and Moon, but also the five Errant Stars, did keep their courses round in the Zodiack; and so, as that aswell the Sun and Moon, as those wandering Stars did sometimes vary their latitude, or deviate from the Ecliptick Line in the midle of the Zodiack; (for, he thought that the Sun was also extravagant, as well as the rest; and again, that the other Planets did not only go forward, but were also some times upon their retreat backward; and somtimes made a hault or stood still: we say, pondering all these various motions in his mind, and casting about what might be the reasons thereof in nature; he at last imagined to himself, that besides the Aplanes or Sphear of Fixt Stars, which being supreme, carried all the rest toward the West, there ought also to be allowed three other Sphears, as well to the Sun, as to the Moon, and four to each one of the other Errant Stars; of which one, and that the highest, should follow the Impression of the Fixt Stars, or rather of the Primum Mobile; the next to that should move counter to the First, or toward the East; the third make the deviation from the Eclip­tick, or midle of the Zodiack; and the fourth, or lowest, cause in the Stars their Direction, Station and Retrogradation, and that by a certain Vibration, or Waving to and agen. So that he supposed in all, twenty seven Sphears, and all those Concentri­call, that the Superior might carry on the Inferior, and these might be turned round within those. Afterwards, Callippus adjoyned two Sphears to the Sun, two to the Moon, and one a peece to Mars, Venus, and Mercury: and so made thirty three. And Aristotle, to all the Sphears, which did not follow the motion of the Aplanes, or Primum Mobile (excepting only the Lunar Sphears) added as many more, which he called the Revolvent ones, to the end he might conform them to the mo­tion [Page 26] of the Inerrant Sphear, or Primum Mobile: and so in the whole he constituted Fifty six Sphears; for as much, at least, as we can collect from his own context. Now all these, and even Plato himself likewise, thought that the Moon was the lowest of all the Planets; next to her, the Sun; and above the Sun the five wandering Stars: Nor indeed doth it appear, that Archi­medes himself Living a whole Age or two after them, represented the Planets in any other, than this very order, in that so famous Sphear of his In which though Claudian tells us, that no more was represented, but only the motions of the Sun and Moon;

Percurrit proprium mentitus Signifer annum,
in Epigram.
Et simulata novo Cynthia mense redit:

Yet Cicero adds other motions, when speaking of Archimedes, he saith; ‘when he collected together the motions of the 2. de divinat. Moon, Sun, and five wandering Stars; he did the same as that God, who in Platoes Timaeus framed the World, that one and the same Conversion might regulate sundry motions, most dif­ferent each from other in slowness and swiftness’. But, Hippar­chus afterwards finding, that aswell the Sun, as the Moon and the other five Stars did come somtimes neerer to the Earth, and sometimes again mounted up farther from it; and plainly percei­ving that that particular apparence could not possibly be explica­ted by those Sphears, that were all Concentrical to the Earth: therefore, wholly rejecting them, he resolved, that the motions of the Planets were to be accounted Eccentrick; and though he could not himself determine each particular, he yet demonstra­ted the way, in which Ptolomy afterwards insisting, accomplisht the Invention. But, before wee advance further, we are to com­memorate two or three Persons of note, by whose Observations both Hipparchus and Ptolomy profited very much. One was Timocharis, who, about three hundred Years before Christ, among other things relating to the Fixt Stars, observed that that Star which is called Spica Virginis, doth antecede the point of the Atumnal Equinox, by eight degrees. And with him are we to joyn Arist [...]ll [...]s, whose Observations of something about the Fixt Star; Ptolomy made great use of, in order to his demonstrating that the Fixt Stars never change their latitude. Afterwards (scarce [Page 27] in Age) succeded Eratosthenes, who being Library-keeper to Pto­lomy Evergeta the fomer, perswaded him to set up the Armillae in the Porticus of Alexandria; which Hipparchus and Ptolomy Prolom. lib. 1. cap. 11. afterwards made use of; and himself, among other things obser­ved, that the Obliquity of the Zodiack was of twenty three de­grees, and fifty one minutes; which account Hipparchus and Ptolo­my constantly adhered to.

Now that we may at length remember the great Hipparchus, Articl. 8. Hipparchus, who first obser­ved the places of the Fixt Stars, accord­ing to Long. and Latitude. who florish't neer upon an hundred and forty Years before Christ: truely, we find it no easy task to recount, how highly Astronomy was beholding to him. For, in the first place, exa­mining that foresaid Observation of Timocharis, with some o­thers; albeit he could not conceive them to be in all points exact, yet because himself had found that Spica Virginis did not ante­cede the Equinoctial point by more than six degrees, and the other Stars in the like Proportion: he thence understood, that the Fixt Stars also were moved Eastward according to the Zo­diack; and thereupon wrote a Book of the Transgression of the Solstices & Equinoxes. And, being that in his time, as not long agoe in Tycho Brahes, there appeared a certain New Star, he therefore came to doubt (to speak the language of Pliny lib. 2. cap. 26. concerning him) ‘whether the like happened often, or not; and whether those Stars, that were thought to be fixt, had also some certain motion peculiar to themselves. Wherefore (as the same Pliny goes on) he attempted a task of difficulty sufficient even for the Gods themselves, namely to number the Stars for Poste­rity, and reduce the heavenly Lights to a rule, so that by the help of Instruments invented, the particular place of each one, together with its magnitude, might be exactly designed: and where­by men might discern, not only whether they disappeared, or newly appeared, but also whether they removed their Stations; as likewise, whether their magnitude encreased, or diminished; Leaving Heaven for and Inheritance for the Witts of succeding Ages, if any were found acute and industrious enough to com­prehended the mysterious orders thereof.’ And this was the first time when the places of the Fixt Stars were observed and markt out according to Longitude and Latitude: and that Ca­talogue of the Fixt Stars, which he composed, is the very same, which Ptolomy afterward inserted into his Almagest. In the lib. 7. cap. next place, he denoted was positions sundry Stars had in respect [Page 28] each of other; whether they were posited in a right Line; or in a triangular form; or in quadrate or square, &c. as is mani­fest even from Ptolomy himself. Further, though the motions of ibid cap. 1. Sun and Moon were already in some measure known; he yet made that knowledge much more exact. For, He did not only much correct the Callippick Period, formerly spoken of, but also, He also corre­cted the Cal­lippick Period, and predicted future Eclip­ses, for 600. Years together. having collected a long Series of Eclipses (namely, from the time of those Babylonish ones, in the Dayes of Mardocem­pades, down to those observed by himself, for full six hundred Years together.) and remarking, that neither the like Eclipses did return on the same Dayes, after the space of every nineteen Years, nor that after some recurses of ten Novennales, or ten times nine Years, any such Eclipses happened at the times supposed; and that the cause thereof consisted both in the various Latitude of the Moon, and the anticipation of her Nodi, or Knotts, and her Eccentricicy, by reason whereof her motions to her A­pogeium were found to be sometimes slower, and those to her Perigeium more speedy: therefore, we say, He comprehended and gave Reasons for all these difficulties, and composed certain Hypotheses, and according to them, certain Tables, by which he could safely and exactly calculate and predict what Eclipses were to follow, how great they were, and when. And this was it, which Pliny remembred, when having spoken of Thales, and Sulpitius Gallus, he comes to mention Hipparchus. ‘After these (saith He) Hipparchus foretold the courses of both Lu­minaries, for six hundred Years to come; comprehending the months, Dayes and hours of Nations, and the Scituations of Places, and turns of People: his age testifying, that he did all these great things, only as he was partaker of Natures Councels.’ For, it must be, that Hipparchus, besides the precise times, when such or such Eclipses were to be visible to the Horizon of Rhodes, or A­lexandri [...], pointed forth also some Countries, and principal Citties, together with the Designation of the Months in use among them; as also the very Days and hours when each Eclipse would happen; and other praedictions succeding to Rome, in the Dayes of Pliny.

Again, it is well worthy our recital, that Hipparchus labour­ing with long desire both to constitute Hypotheses, and reduce into Tables the motions of the other Planets, or five wandering Stars; and yet not being able to furnish himself either from the Egyptians, or from his Country men the Grecians, with any [Page 29] competent Observations respective to those Planets, (for while the places of the Fixt Stars remained unknown, it was impossi­ble any such could be made) and again those he had himself made, were of a much shorter time, than was requisite for the establishing any thing certain and permanent in that sort: He therefore only digested such Observations as he had recorded by him, into the best order and method he could devise; and so left them for their use and improvement, who should come after him, in case any were found capable of understanding and ad­vancing them. And at length, by good fortune, it so fell out, that those his Observations came into the hands of Ptolomy; who comparing them with his own, and finding them judicious and exact, thereupon first began to erect both Hypotheses, and Tables of Motions fit for those Planets: yet not without much timerousness and diffidence; because his Observations being but few, nor of sufficient time, he durst not promise himself any cer­tainty of his Tables for any considerable space, or number of Years. But, for more assurance let us hear his own ingenious Confession in that point. ‘The Time (saith He) from whence Almagest. lib. 9 cap 2. we have the Observations of the Planets set down, is so vastly short, in comparison of the greatness of Coelestial vicissitudes, as that it renders all predictions, that are for any great number of Years to come, infirm and uncertain. And therefore I judge that Hipparchus (that zealous lover of truth) considering this difficulty, and withall receiving not so many true Obser­tions from the Ancients, as he bequeath'd to us, undertook indeed the business of the Sun and Moon, and demonstrated that it might be performed, by equal and circular motions: yet, as for that of the Planets, those Commentaries of his, which have come into our hands, clearly shews, that he attempted it not: but collecting all his own Observations concerning them together, into one order and method, for their more commodi­ous use, resigned them to the industry of after times; having first demonstrated, that they were not congruous to those Hypothe­ses, which the Mathematicians of those Dayes made use of. And, for Others; sure I am, that either they demonstrated nothing at all, or else only attempted the business, and left it un­finisht. But, Hipparchus being eminently knowing in all kinds of learning, conceived, that he ought not (as others had done before him) to attempt, what he should not be able to [Page 30] accomplish.’ So that we see, Ptolomy was the first, who from true Observations, reduced the Motions of the Planets into Hy­potheses and Tables correspondent.

But before we speak more particularly of him, who lived Articl. 9. about an hundred and thirty Years after Christ; forasmuch as in the space of time betwixt Hipparchus and Ptolomy, these studies Betwixt Hip­parchus and Ptolemy, came Sosigenes, of Alexandria, by whose help Jul. Caesar endea­vored the re­formation of the Calendar. so florisht at Alexandria, as that Julius Caesar returning thence, brought along with him that Sosigenes, by whose assistance he endeavoured the restitution of the Calendar, and so may be thought to have propagated the Study of Astronomy among the Romans: let us reflect a little upon that time, and see what care they then had of Celestial matters. In the first place, we are to lay aside the Commemoration of Sulpitius Gallus (of whom more then once afore, as one that falls not under this account, concern­ing whom we may not yet forget, what Cato is induced by Cice­ro, saying. While we saw that Gallus dye, that familiar friend of thy Father, O Scipio, who was restless in measuring Heaven and Earth; I say, while we saw him dying even in that Study. How often did Day oppress him, when he had set himself to observe and describe somthing in the Night? and how often did Night op­press him, when he had begun his Speculations in the Morn? How was he delighted, when he had a long time before predi­cted to us Eclipses of the Sun and Moon? &c. For he was a man clearly singular, and in an Age when so great ignorance and neglect of good Arts tyrannized over mens minds, being himself studious and inquisitive, could not but have borrowed his skill either from Egypt or Greece, where having obtained a Series of Eclipses, and the way of deducing them through the circuit of of nineteen Years (as we said afore) he became able to calcu­late them, so as Cicero relates For, as to the rest; how great doe you think was the ignorance and neglect, nay even con­tempt of studies of this nature among the Romans? Why, truely so great, as that Virgil could not dissemble it, in the Poesy attri­buted to Anchisa, according to which the Romans should in­deed come to rule the World; but yet should yeeld to others, in learning to know the Stars, and describe the Heavens.

—Caeli (que) meatus
Describent radio, & surgentia sidera dicent.
6. A [...]nl.

And Cato himself is cited by Agellius to have left in writing [Page 31] that it was not lawfull to write what is in a Table kept by the High Preist, how often scarcity of Provision would happen, how lib. 2. c 28. often the light of the Sun, or Moon should be darkned: so far, saith Gellius, did Cato contemne the Science of Astronomy, and thought it useless either to know, or fore-tell the Eclipses of Sun and Moon. Furthermore, though from times as high as Numa, the Romans made several Intercalations; yet they took all their art of that Sort, from the Greeks: and Pliny remarks, that in France, Spain and Africa, there was no one man, who could so much as tell the Rising of the Stars. Nevertheless we are not to 1. Meteor 7. Pythias Massi­liensis, a Gaul. and contempo­rary to Alex. of Maced. forget, that among the Gauls was one Pythias, the Philosopher (as Cleomedes calls him) of Masilia, who about the time of Alexander of Macedon, found the proportion of the Gnomon to the Solsticial shadow, to be the same at Massilta, as Strabo tells us Hipparchus had observed it at Byzantium; who first attempted the Northern Ocean, and discovered the utmost Thule, in which Cleomedes cohaerently proves the Summer Tropick to be the same with the Polar, or greatest of allwayes apparent ones: and who (as from his Book, de Oceano, may be inferred) was ex­cedingly curious to find out what was the Position of Heaven, re­spective to the variety of Countries and Climates. But, not so lib. 7. cap. 60. soon to digress from the Romans; Pliny delivers, that in those first times of Romes being a Common-wealth, the Invention of Dialls was very raw and imperfect: for that they had only the risings and settings named, out of twelve Tables. That after some Years, they added the Meridian, and by the indication of a certaine columne, the last hour: nor that neither, but only in clear weather, even as long as till the first Punick warre. After­ward they advanced so far, as to make one, or two Sun Dialls; but not with lines exactly correspondent to the hours, untill about an Age after, when Q. Marcus Philippus ordered the busi Quintus Mar­cius Philippus, &c. ness more diligently and succesfully. And, because the hours of the Day remained yet uncertain in dark and cloudy weather, Nasica Scipio began to divide the Hours of Day and Night equally Nasica Scipio, Romans. by Water distilling from Vessel to Vessel, and called it The Diall within Doores, in the Year Urbis conditae DXCV. And till then, saith Pliny, Populi Romani indiscreta lux fuit. And thus much of Hipparchus, and some Astronomers betwixt him and the Prince of them all, Ptolomy.

And of him, so great is his name, all we need to say, is only, Articl. 10. [Page 32] that He was the very Founder of the Art, or Science of Astrono­my. Prolemy, the true Founder of Astronomy in one intire structure. For, though Hipparchus had indeed, as it were hewn out the Stones and Beams fit for so noble a Structure, and prepa­red good part of the Materials; yet was it Ptolomy alone who put them into Order and Form, and by adding many admirable In­ventions of his own, by infinite labour and cost, erected that so fa­mous Building, worthily called [...], the great Co-or­dination, Construction, or Composition; which consisting of no less than thirteen Books, contains all the Doctrine, that could then be advanced, concerning the Sun, Moon, and aswell the Fixt, as wandering Stars. And, albeit one Day teacheth another, and that (as Himself had truely foretold) there came others after him, who saw good cause for the Castigation and Correction of many things delivered in that Work: yet, in the general, the Art he had instituted, remained firm and constant, and was after­wards imbraced, not only by the Alexandrians, but also by all the Arabians, Latins and others, who devoted themselves to the service of Urania, ever since. For, that the Study of her Celestial mysteries continued in great esteem and Veneration, at Alexan­dria, for some Ages after his desease, may be undeniably attested, not only from hence, that (among others) both Theon, and Who next resig­ned it to Theon and Pappus, both Alexandrians. Pappus, named Alexandrians, were eminent therein; of which the one put forth eminent Commentaries upon Ptolomies Works, and the other, among sundry excellent peeces, of which his sixth Book of Mathematicall Collections is one, observed, that about four hundred Years from Christ, the Obliquity of the Ecliptick was not so great, as Erathosthenes, Hipparchus and Ptolomy had conceived: but neer upon the same we discover it to be in our Dayes: we say, that this is not the only Monument that is ex­tant of the flourishing of Astronomy at Alexandria, long after Prolomy had given it so great a Reputation there; but there re­mains another as fresh and lively, which is the memorialls of those Patriarchs of the Alexandrine Church, to whose judge­ment the determination of that great dispute about the true time of Easter, was thought fit to be wholly referred, aswell by the Ni­cene Councel, as by divers learned Bishops afterward, and by Holy Leo himself, then Pope. Now, among these Patriarchs were Theophilus, Cyrillus and Proterius, whose advice and directions were thought necessary, in regard that the Controversies raised about the Celebration of Easter, about the time of the Veneral [Page 33] Equinox, about the Full-Moon next following, and about consti­tuting certain constant Rules respective to them; could not be better composed, than by the definitive sentence of these Pre­lates, who Living at Alexandria, where Astronomy was in such Height, had the advantage of others, in point of knowing those things which were requisite to the finding out of the truth. But, of the Arabians, who in the Study of Astronomy succeded the Alexandrians, and translated into their own language, the Great Composition of Ptolomy, which they called Almagestum; the First, and most worthy to be remembred, was Albategnius other­wise and long after. to Albategnius, then to called Mahometes Aractensis, born of a Family of the Dynastae of Syria; He about 800, Years after Christ, made divers Celestial Observations, partly at Aracta, and partly at Antioch: and found, both that the Apogeium of the Sun, since the Dayes of Ptolomy, was advanced to the following Signes; and that the Stars did regress toward the East, one degree, not in the space of a hundred Years, as Ptolomy also had designed; but of somwhat less than seventy; as also, that the Obliquity of the Ecliptick, according to Pappus his Theory, was less (viz. above 23. degr. 35. minutes) with many other particulars con­cerning aswell the Fixt Stars, as the Planets: whereupon he both corrected Ptolomy in many things, and composed new Tables, and wrote a Book intituled, De Scientia Stellarum. After him, within 2 or 3 Ages following, succeeded Alphraganus, Arzachel, Alphraganus and other Ara­bians. Almeon, and other Arbians; among whom, (as being already tainted with that superstition which had corrupted the simplici­ty of Astronomy, with Astrological Fooleries) some certain Jewes, as ambitiously affecting the glory of Divination as the others, in­termixed themselves.

After them, for a long time, the Worship of Urania lay neg­lected, Articl. 11. Alphonsus, K. of Castile; who made and named the Alphonsine Tables. nor did Astronomy receive any the least (considerable) advantage by Observators; till neer about four hundred Years since, Alphonsus King of Castile and Lion, being himself also toucht with the curiosity of Astrological predictions, and disco­vering that the Tables aswell of Ptolomy, as Albategnius were not exactly agreeable with the Celestial motions; set himself to the composing of new ones; and to that purpose convocated as many Arabians and Jewes, as were eminent in those Dayes for A­stronomy; imploying them about Observations necessary to so great a Work, and comparing with them those of their Predecessors, [Page 34] that so they might be the more exact in the performance of their task proposed. And very memorable it is, that (as hath been credibly reported) He spent four hundred thousand peeces of Gold on that undertaking: a munificence truely worthy the He­roick mind of so great a Prince, and which well deserves to be had in perpetual commemoration by all lovers of Learning: but somwhat unhappily imployed, in respect the Persons set a Work were not so strict in studiously and constantly observing, as scru­pulosly computing, directing their calculations not so much to what themselves and others had really observed, as to certain tra­ditional, mysteries, or Caballistical dreams: that we may pass by their heedlesness, which Regiomontanus detecting, perceived, that they had mistaken the true places of the Fixt Stars, by very neer two whole degrees; as accounting the numbers of Ptolomy, as if they had bin constituted by him from the beginning of the Years of Christ. Which considered, we have the less reason to wonder, if the Tables composed by them, called from the Kings name, the Alphonsine, and sometimes from the place, where they were made the Toletane Tables (whence also He, who was Pre­sident of that assembly of Astronomers, is said to have been one Isaac Chanter of the Toletun Synagogue) have been found, ever since the time of K. Alphonsus, to disagree with the Heavens, and to require the review and castigation of some new and more faithfull hands. Thence forward Astronomy lay neglected, and after whom, the Science lay neglected. till, Georg. Peur­baechius and Ioh. Regio­montanus arose, and again cal­tivated the same. almost buried in oblivion, (only Thebitius an Arabian, and Prophalius a Jew, observed in the mean time some small matters, about the motion of the Fixt Stars, and the obliquity of the Eclip­tick,) untill about two hundred Years since, Georgius Peur­hacchius, and Joh. Regiomontanus, his disciple, seemed to revive it. For, these worthy men delivered it cut of the double cloud of ignorance and vanity, which the Arabians and Jewes had raised, to the Observation of its lustre; and kindled the Light thereof afresh in Germany: reducing Ptolomy, providing Instruments, and making not a few faithfull Observations: though they were not so happy, as to bring their designe to that perfe­ction they hoped and had proposed to themselves; both of them dying in the middle and flower of their Age.

Animated by their example, Nicholaus Copernicus (a Borussian born, and Canon of the Cathedral Church of Warmes, scituate neer Articl. 12. Then followed the m [...]st accute Nich. Coper. Fruemburgh, in the same Country) about the beginning of the last [Page 35] Age, seriously addressed himself to the Illustration of Astronomy; nicus, who re­vived the do­ctrine of Py­thagoras, con­cerning the Earths motion. and reviving the long neglected Systeme of the World excogi­tated by Pythagoras, he made many good Observations, in or­der to the composing of new Tables But, forasmuch as he could not determine any thing concerning the Fixt Stars, besides their Promotion Eastward, which they appeared to have made since Ptolomy's time; he therefore composed some Canons of their motions, and those as exact as possibly he could: yet both those, and the Prutenick Tables that were built upon them, were in­correspondent to the motions of the Heavens, though less incor­respondent than the Alphonsine. Nevertheless, the man is to be highly commended, both for his sublime perspicuity, and mode­sty, in that foreseeing his Canons would need correction, he was wont frequently to exhort and encourage that ingenious young man, Georgius Joachimus Rheticus, deeply enamoured of the beauties of Astronomy, to apply himself principally to the Restitu­tion of the Fixt Stars, and cheifly of those, which were in the Zodiack, or neer it, and with which the Planets might be most conveniently compared: because, without their restitution, it was impossible either to attain to the true places of the Planets, or to atcheive any thing of Moment or certainty, toward the advance of Astronomy.

And then at last enters that Noble Dane, Tycho Brahe, upon Articl. 13. And last of All, the noble Ty­cho Brahe, who out-did all the rest in discoveries and inventions. the Theatre of Astronomy. Who, as by in the impulse of his Genius, being addicted to beholding and noting the Stars, even almost as soon as he saw the light of them; was so much the more spurred on by that advice of Copernicus, published in the Works of George Joachim newly mention'd, by how much the more clearly he discerned the impossibility of determining the true and proper place of that famous New Star, (appearing in the Constellation of Cassiopeia, from the beginning of November, in the Year M. D. LXXII. for above sixteen months together) without the restitution of the Fixt Stars to theirs. For, He plain­ly perceived, that most, if not all the Errors, which had bin found in Astronomy even from its first foundation or original, took their rise chiefly from hence, that the Fixt Stars really were not in those places, in which they were supposed to be, by Observa­tors; But some of them were much neerer, and others again as much farther off; and this, whether because Hipparchus in the beginning had not with due exactness consigned all the Fixt Stars [Page 36] to peculiar places, which indeed he had designed by the Sextant's of degrees (and truely it is very difficult at once to invent any thing of Moment, and perfect the invention) or whether because the Transcribers of Ptolomy, out of carelesness, or ignorance, had corrupted the Original Text in many places; or whether the ad­ditions afterward made, in respect of the Stars progress to the following Signes, had occasioned any mistake and imperfection in that Theory; or whether by any other unhappy cause what­ever. Now, in Order to this great Work, of rectifying those fundamental Errors, it pleased Fate, that about the very same time, that truely generous and never enough commendable Prince William Landgrave of Hassia, had zealously devoted his mind and industry to the same care, of restoring the Fixt Stars to their true mansions: but yet the honour he aimed at, was de­creed only for the incomparable Tycho; who in an Heriocal bravery of Soul, had now resolved with himself to enterpise no less than the Instauration of the whole Science of Astronomy from its very fundamentals; and so to spare neither labour, nor cost (especially while he was so happy, as to have good part of his expences defraied by the liberal contributions of that eminent Mecenas, Frederick the II. King of Denmark, who thereby re­corded his name in immortal Characters on the leaves of Fame) that should be necessary to the making all Sorts of Observations requisite. As soon therefore as he had furnished himself with that Astronomical Colledge, or Tower for Observations, built by him in the Island of Huenna, to that purpose assigned him by the King, and furnished that Heavenly Cittadel by him called Uraniburg, with store of exquisite and magnificent Instru­ments Mathematical, he begun (having provided himself of sundry learned and competent Coadjutors) exactly to observe the Altitude of the Pole, in that place, by the Circum-polary Stars. By which understanding likewise the Altitude of the Equator, he pointed out the Equinoctial points, by the passing of the Sun through them: and attending besides to the middle parts of Taurus and Leo, he found out the Apogeium of the Sun, and the Eccentricity of it, and deduced its Course from the point of the Vernal Equinox. Moreover, from Venus, in the Day time compared with the Sun, and in the Night with the Fixt Stars; he endeavoured to search out the right Ascensions, and Declinations of the Fixt Stars: which the Ancients had per­formed, [Page 37] but fallaciously, by using the Moon, not Venus, to that purpose. And his success was as exquisite as his care in this, that he constituted that bright Star which is in the top of Aries, and ranged the chief of those in order along the Zodiack: and then advancing to enquire or rather find out the distances of the rest aswell from them, as each from other, he defined both the right Ascensions and Declinations of all; prescribed their several Longitudes and Latitudes, and added to the Catalogue of the Ancients about 200. other Stars, wholly by them omitted. Be­cause the Ancients, Living in an Horizon much more Southern, had observed and set down neer upon 200. Stars, that are invi­sible in the Danish Horizon, which is highly Northern: and Ty­cho again collected about 200. more than they could discern; and as being somwhat small, he intermixed them among others of greater magnitude. Further, having in the mean space, al­waies observed the passings of all the Planets through the Meri­dian, and their several distances from the cheif Fixt Stars neerest to them: he laid such sollid foundations, as by them might be exactly known not only the true places of each, but also their se­veral Motions. So that he came very neer the heighth of his noble hopes of building the whole Theory of Astronomy a new from the very ground, and of erecting compleat and everlasting Tables for Calculation thereupon: but, alas! prevented by an immature death, He could not accomplish his designe. It was very much, however, that He went so far, as [...]o have recorded and bequeathed to Posterity such excellent Observations, by which Kepler was soon after enabled to compose an intire Theory, and make the Tables called the Rudolphine; and by which, and others afterward contriveable, whatever can be desi­red in these Tables, may be fully supplied and perfected. And this among the rest deserves singular commendations, that He left us the Fixt Stars re-installed in their true mansions: wherein He alone, in few Years practice, performed and finished that prodigiously great Work, which no man, from the Dayes of Hipparchus, had either attempted, or in any measure advanced.

I pass by many other admirable discoveries of his; as that he was the first, who demonstrated all Comets to be carried freely through the Etherial Spaces; that Refractions ought to be care­fully considered and allowed for, and how; that he perceived that the Latitude of the Moon ought to be augmented by more [Page 38] than a Quadrant, or fourth part, than had been conceived; that He almost demonstrately convinced the Latitudes of the Fixt Stars to be varied; that he excogitated an Hypothesis, which all those, who cannot allow of the Ptolomaicall, or fear to allow the Copernican, may well adhere to and defend; with many other things, as difficult in their Invention, as excellent in their use. And observe only how vastly he transcended all that went before him, in point of exactness and certainty. As for Instru­ments Mathematicall, it is well known, He made such, as for the condition of their matter, for the Vastness of their magnitude, for the variety of forms, for the care of their elaboration, for the preciseness of their divisions, and for the facility in using; as the World had never the like before. Again, so prodigious was his and his Coadjutors subtility, diligence, industry; that whereas the Observations of Hipparchus, Ptolomy, and all others before him, had bin marked out only by the Sixth or at most by the twelfth parth of degrees; he designed all his by the sixtieth parts of degrees, called Minutes, or Scruples, and very often also by subdivisions of Minutes. So that we may well demand what comparison can be made betwixt that gross way found out by Erastothenes, and approved and followed afterward by Hippar­chus and Ptolomy, for the Observation of the Obliquity of the Zodiack; and that most fine and exact one invented by Tycho? His being, by a division of the Meridian into 83, parts, and the Interval of the Tropicks deprehended to take up 11. of them, it appeared that the distance of one Tropick from the Equator, a­mounted to 5. of thoseparts and an half, or, by a reduction of them again to degrees, of 23. degr. 51. Min. and ⅓: and theirs, being by an hollowed Hemispear of Stone, with a Gnomon erected in the middle, as we have formerly described it; and to what de­gree of subtility and exactness this way of commensuration could arrive, the meanest Novice in Astronomy may soon judge. That Quadram likewise of Ptolomy, so much admired by ancient Au­thors; Pray, How vastly short did it come of the perfection of the least that Tycho used? And the same may be said of his Rules; for, that those Armillae, set up by Pt [...]lo [...]y in the entrance of A­lexandria had any thing in them comparable to those erected by Tycho, in his Uraniburg, cannot in the lest measure be argued from the other Instruments then in use. It is not necessary, we should here again review those machinaments, or engines, which [Page 39] the old Egyptians and Babylonians made use of, either in discern­ing the Signes of the Zodiack, or taking the Diameter of the Sun: or those, which Aristarchus and Archimedes used, for commensurating the same Diamater. Only we cannot but won­der, by the by, how Aristarchus, having aimed so neer the white of truth, in the matter of the Suns Diameter, and determining it to be the 720th. part of the Circle, or half a degree; as is deli­vered de Acenar. num. by Archimed: should yet err so widely in his Book of Magnitudes and Distances, as to make the Diameter of the Moon (which in truth; is very neer as great as that of the Sun) to be the 180th. part of the Circle, or 2. degr. when he called it the Fifteenth part of a Signe; which mistake of his was long since taken notice of by Pappus. Nor is there any necessity, why we should survey those Instruments, that Albateginus, Peurbacchius, Regiomontanus, Copernicus, and other more moderne Astronomers used: considering, that besides the Rules made by Regiomonta­nus (which Bernardus Waltherus, his disciple, preserved, and had recourse to, in his Observations of the Suns Altitude) they came so short of the least of Tychoes, in point of exact reasoning, and am­plitude, that they deserve rather to be perpetually forgotten, than remembred to competition. However it is seriously to be wished, that the Observations made by those incomparable Instruments of His, may ly no longer concealed from the World (for by singu­lar Providence, they have been hitherto preserved, as Gassendus attesteth, ïn the Life of Tycho) but soon be brought to Light. And this aswell for sundry weighty Considerations there alleadged by Gassendus; as for this, that not all the Stars, of which Tyeho hath given a copious Catalogue, in his Progymnasmata, may be found reduced to congruous Calculation (in as much as they doe not exactly correspond with the Heavens) and that various Cata­logues have been pretended from the same, which are very much different each from other: for all the difficulties hereupon depend­ing may soon be removed, and all mistakes rectified, by having re­course to the Fountain, or Original observations, which! will clearly declare, what hath bin already corruptly deduced, and what may be at length carefully and demonstratively deduced from them.

And, in the mean while, if Hipparchus his memory be so highly and (indeed) justly precious among learned men, for his great merrits in excogitating and framing Instruments, whereby to take the dimensions, distances, motions &c. of Heavenly bo­dies: [Page 40] certainly, that of our Tycho ought to be as highly esteem­ed by us and all Posterity; since he alone, for so many Ages to­gether was found, that durst not only imitate him in those sub­lime inventions; but so imitate, as very much to exceed him. For my part, truely; since Hipparchus may rightfully be called At­las the Second: I shall doe but justice to name Tycho, Hercules the Second, who releived his Predecessor, long languishing and ready to faint under so prodigious a burden; which doubtless was the Reason, why Kepler called him, the Modern Hipparchus.

And thus have we in a short Relation, rehearsed to you, what we could gather together, concerning the Original, Progress, and Advance of Astronomy, from the highest of times, of which there remain any Authentick memorials, down to the decease of Tycho Brahe, the Noble and the Great. As for what Additions this excellent Science hath received, by the industry of Astronomers in this present Age, by the help of the Telescope, whose Invention may seem to have been unhappily deferred too long, as being de­ferred till some Years after Tychoes death: they may be easily summed up. For, all that our Dayes can justly challenge the ho­nour of discovering, is (1.) the spotts in the Sun: (2.) the inequality of the superficies of the Moon: (3.) Venus shifting her apparences, as doth the Moon: (4.) Mercury and Jupiter, in some Proportion, doing the like: (5.) Jupiter with a kind of bound about him, and guarded with four lesser Stars, as Attendants: (6.) Saturn triple-bodied: (7.) the Gallaxy fully beset with small Stars: and (8.) divers pale assemblies of very small Stars, seeming to be only little white clouds in the Welkin; with some other particu­lars lately remarked. Now, if you please to add this to the for­mer summary: you have the whole (though brief) Story of Astro­nomy, from its very infancy to that augmented state it now hath attained to: I wish I might have said, to its Full growth and Perfection. But, alas! that is reserved for Posterity.

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