The desire of know­ledge. THE TIME SEMETH longe (bee it neuer so shorte in deed) to hym that desirously looketh for any thing: for as the obtainīg of it bringeth great pleasure, namelye the thinge it selfe being profitable, so the wante therof causeth displea­sure and cōtinuall grief tyll the desire be eyther fully satisfied, other partly (at the least) accomplished.

And sometimes we see, that when the desire is partly perfourmed, and the pleasantnes of the same ones ta­sted of, the desire therby nothinge asswageth, but contrarye ways greatly increaseth: and the more it getteth, the more it desireth. so that in this point may knowledge well be cō­pared to couetousnes: for as the couetous mynd with get­tyng is neuer satisfied, so knowledge by knowing doth co­uet styll more: And as it increaseth, so doth it still learne the vilenes of Ignorance, and profite of Sciences, and therfore can not rest from searching more knowledge, as long as it spyeth any spot of ignorance.

This oftentymes as I haue considered, maketh me to muse what mynd is in them, which care for no know­ledge, nor esteeme any science.The grose­nes of i­gnorance.

This is the greatest pointe of all ignorance, not [Page 2] to know the grossenes of ignorance, and not to vnderstand the benefite of knowledge, and with this faulte are a greate numbre spotted. The nexte is their faulte, whiche perceaue sufficientlye what vilenes is in ignorance, and what profite in knowledge, and yet of a certaine negligence partelye, and partlye for other pleasures, they omytte to trauayle a­nye whitte for knowledge, and contente them selues wyth wilfull ignoraunce: but as these men do trouble the good state of the worlde, so the talke of them wyll hynder the talke of the worldes knowledge, whiche is the thinge that you so muche longe after: and therefore beste it is, that wee let them lye still tomblinge in the dyche of ignoraunce, and that wee trauaile forward towarde the Castle of knowledge. But first let me heare what is your chief desire.

The occa­sion of this booke.Syth my laste talke with you aboute the knowledge of the worlde and the partes of it, I haue readd dyuers bookes that intreate of that matter, as namelye Proclus sphere, Ioannes de Sacro bosco, Orontius cos­mographye, and diuers other, whose woordes in manye thinges I remembre, but of the matter I haue sondry doub­tes, and therefore desire muche your healpe therein. For althoughe I haue consulted with diuers men therein, yet me thynketh they tell me but the same woordes in lyke sorte as I readde theym before, or lyttle other wayes altered, but lyghte of vnderstandynge, I haue gotten lyttle yet.

Then proue againe, peraduenture your chaunce may be better: that whiche at the fyrste semeth harde, maye at lengthe become easy: for Vse maketh masterye, all men confesse. And, The best thynges are not moste ea­siest to attayne. begynne in that ordre as youre Au­thors doo.

The diuer­sitye of writers.Theyr ordres bee as dyuers as theyr names be, so that I knowe not whose ordre is best. For Proclus in treatinge of the Sphere, defineth firste the Axe tree of [Page 3] the worlde, before hee had shewed other what the worlde is, or what hee calleth a Sphere, or what neede the worlde hathe of anie Axe tree. Therfore I tourned to Ioannes de Sacro bosco our contry man, whiche beginneth firste with the definition of a sphere, but nothinge lyke to that sphere, whiche I before had bought, as an apt instrument to learne by. Then see I Orontius disagree from them bothe: and generallie, eueryeone from other, so that I know not wher to beginne.

As touchynge those writers, I will saye no more nowe, but although eueryeone of them haue some thinges that exactlie scanned may be misliked, yet he that hath doone worste, is woorthie of thankes, for his studi­ous paines in furtheringe of knowledge. And seyng you doubte of their ordre, lette the thinge it selfe minister or­dre. What is it that you desire to knowe?

I see in the heauen meruailous motions, and in the reste of the worlde straunge transmutations, and therfore desire muche to know what the worlde is,The argu­ment of this booke. and what are the principall partes of it, and also how all these straung sightes doo come.

Then is the worlde the thinge that you woulde knowe first, syth all these other thinges are incident to it. What doo your authors call the Worlde?

what the worlde is.Orontius defineth the worlde to be the per­fect and entiere composition of all thinges: a diuine worke, infinite and wonderfull, adorned with all kindes and for­mes of bodies, that nature coulde make.

This definition doth muche agree with those that bee writen by aunciente authors, and namely Aristotle whiche defineth it thus.

The worlde is an apte frame of heauen and earthe, and all other naturall thinges contained in them. The like wordes hath Cleomedes and others. So that the worlde is that en­tiere body, whiche containeth all thinges that euer God made, and man can see, nothinge excepted but God himself only, whiche is not comprehensible by any worldly meanes. This worke is so pure and wonderfull in beauty, that it bea­reth the name of cleannes,wherof the worlde is named. bothe in Greke and Latine, that is [...]in Greeke, and Mundus in Latine. and thereto allu­deth Sibyll in her verses, speakinge of the dissolution of the worlde, saying: ‘ [...].’ ‘Erit mundus immundus, pereuntibus hominibus.’ The worlde (saith she) shalbe vnclean, or leese his beuty, whē all mē shal perish.

And so dooth that sentence leese his beautye by the translation, for there canne bee no suche allusion of woordes in the englyshe of that sentence, as there is in the other tongues.

You say truthe, except a man wold rather allude at the woordes, then expresse the sentence, for so might it be translated thus: It shall bee an vnworldlye worlde, when all men shall perishe: But here the sense is loste: for this name Worlde,Diuers si­gnificatiōs of that worde worlde. hath not the like deriuation of cleannes in englysh, as the Latine and Greeke names haue in their tongues: no­ther can I well tell wherof this englyshe name is deriued, al­though I remembre som other significations of this worde, as firste it is vsed in Scripture for a name of long continu­ance of tyme, when we say: Worlde without ende. and, tho­rough worlde of worldes: whiche signifieth for euer. Also this name dooth signifye sometymes a greate wonder, as when wee saye: It is a worlde to see the crafte that some menne vse vnder colour of simplicitye. Nowe if anye man wyll contende, that this worde Worlde dooth principal­lye betoken a wonder, and that the worlde for the won­derfull shape of it, tooke that name, as the chieffe won­der [Page 5] of all wonders, I will not greatelye repine, but then muste I needes wonder, to see the chieffe worldely men to wonder so lyttle at this wonderfull wonder, and to bend all theyr studye to the centre of the worlde, I meane the Earthe, whiche in comparison to the whole worlde is not onlye a parte without all notable quantitye, but also leaste adourned with meruailous woorkes, and moste subiecte to all frayle transmutation and chaunge, styll repleni­shed with continuall corruption. And yet on it only doth the greatest numbre set all their studye. For it they su­staine greate trauaile and toyle: for yt they chide, quarrell and fyghte: to gette it they venter lyfe and lymme, and when they thynke moste assuredlye that they haue got­ten the Earthe, then in deede the earthe hathe gotten them, and moste commonlye then doothe the earthe consume them, when they thinke theym selues fulle maisters of yt.

By these mennes trauaile (I thynke) it came to passe, that the earthe doothe vsurpe the name of the Worlde, as thoughe it were all, and that besides it were nothinge.

Thereof commeth that common Prouerbe of a couetous manne: All the worlde is to lyttle for him. where he in deede seeketh nothynge but the earthe,The smale­nes of the earthe to the whole worlde. whiche earthe in comparison to the whole worlde beareth no grea­ter vewe, then a mustarde corne on Malborne hylles, or a droppe of water in the Occean sea. for of all the par­tes of the worlde, the earthe is the leaste, and that with­oute comparison, as hereafter I shall not onlye tell you, but also prooue it by inuincible reason. And there­fore to proceede in oure matter, I thynke it beste not onlye to make discourse lyghtlye of the principall par­tes of the worlde, but to dooe it in suche a brief sorte, as the mynde maye conceaue it soonest,The best ordre in teachinge. and the memo­rye also retaine it longest: and therefore will I omytte [Page 6] all proofes, tyll we haue ones generally drawen the ymage of the whole worlde, so shall not your memory be troubled with sundrye thinges at ones, as in learnyng a science whi­che seemeth sumthing straunge, and in conceauyng the rea­sons of it, whiche in declaring, seeme much more straunge.

In deed I haue felt the discommoditie of suche hasty desires: for where I haue sought reason, before I vn­derstoode, whereto that reason tended, I haue troubled my mynde, and hyndred my knowledge. wherefore it may please you in your ordre to procede.

I haue all ready sayd, that of all the partes of the worlde the Earthe is the leaste:The ordre of the ele­mentes. wherby you may conceaue, that within it is nothyng: for so should that (what so euer it were) be lesser then the earthe. but without the earthe, dooth the Waterlye, whiche couereth a greate parte of the same: about them bothe, dooth the Ayer run, and occupi­eth (as we maye easilye consider) muche more roome, then bothe the sea and the londe: aboue the ayer, and rounde a­bout it, (after the agreement of moste wise men) dooth the Fyer occupye his place. And these foure, that is, earth, water ayer and fyer, are named the foure elementes, that is to say, the fyrste, symple and originall matters, whereof all myxt and compounde bodies be made,All thinges compounde ar made of the foure elementes. and into whiche all shall tourne againe.

Oftentimes haue I heard it, that bothe man and beastes are made of earthe, and into earthe shall retourne againe: but I thought not that they had been made of wa­ter, and muche lesse of ayer or fyer.

Of earthe only, nothinge is made but earthe: for an herbe or tree can not growe (as all men confesse) ex­cepte it be helped and nourished with ayer conuenient, and due wateringe, and also haue the heat of the Son, and gene­rally, syth all thynge is maintained by his lyke, and is de­stroyed by his contrarye, than if man can not be maintai­ned without fyer, ayer and water, it must needes appeare, [Page 7] that he is made of them, as well as of earthe, and so like­waies all other thinges that be compounde.

This talke delyteth me meruailously, so that I can not bee wearye of it, as longe as it shall please you to continue it.

This talke is not for this place, partly for that it is more physicall then astronomicall: and partly bicause I determined in this firste parte, to omitt the causes and rea­sons of all thinges, and brieflie to declare the partes of the worlde, whereof these foure elementes, beinge vncom­pounde of them selfe, that is simple and vnmixt, are accōp­ted as one parte of the worlde,The elemē­tes are simple. The elemē­tes do alter dailye in their parts The skye. The ordre of the spheres. The seuen Planetes. whiche therfore is called the Elementarie parte, and bicause those elementes do dailye in crease and decrease in some partes of them (though not in all partes at ones) and are subiecte to continuall corruptiō, thei are distinct from the rest of the worlde, which hath no suche alteration nor corruption, whiche parte is aboue all the foure elementes, and compasseth them about, and is cal­led the Skie, or Welkin, & also the Heauens: this part hath in it diuers lesser or special parts, named cōmonly Spheres: as the sphere of the Moone which is lowest, and nexte vnto the elementes: then aboue it, the sphere of Mercury: and nexte to it the sphere of Venus: then foloweth the Sonne, with his sphere: and then Mars in his ordre: aboue him, is Iupiter: and aboue him, is Saturne. These seuen, are named the seuen Planetes, euery one hauinge his sphere by himselfe seuerallie, and his motion also seuerall, and vnlike in time to anie other. But aboue these seuen planetes, is there an other heauen or skie, whiche commonly is named the Firma­ment, and hath in it an infinite numbre of starres, wherof it is called the Starrye skie. and bicause it is the eighte in or­dre of y^e heauēs or sphers, it is named also the Eight sphere. This heauen is manifest inough to all mennes eies, so that no man needeth to doubte of it, for it is that skie, wherein are all those starres that we see, except the fiue lesser planets, [Page 8] whiche I dyd name before, that is Saturnus, Iupiter, Mars, Venus and Mercurye.

The Sonne and Moone also must bee excepte oute of that numbre, for they haue their spheres by them selues, as well as the other Planetes.

Truthe it is. but bicause no man dooth ac­compte them as starres, therefore they neede none ex­ception, where mention is made of starres onlye, where as the other fiue smaller Planets (which I named before) ar so like to other starres, that no manne, but suche as are of good experience in Astronomy, can discerne them from the other starres,Howe the Planets are knowen from other starres. although manye men doo make a diffe­rence of them by twinkelinge, affirming that the Fixed star­res doo twinkle, and not the Planetes, with other differēces difficult to obserue, and scarse certeine in distinction. But this is their moste certaine difference, that all those starres, whiche be in the firmament, do stande and continue in one forme of distaunce eche from other, and chaunge not their places in their spere, and therefore be they called Fixed star­res: for althoughe thei go rounde aboute the worlde in 24. houres, that is euerye day ones, yet they keepe their places in their sphere, and tourne onlye with their sphere: or (as Aratus sayth) thei be drawen with their heauen, wher as the seuen Planetes are not only carried round about the earthe with the like motiō of heauen euery day, but they do moue of them selues, and doo chaunge their places in their owne spheres, and for that cause are they called Planetes, that is to say, Wanderynge starres.

Oftentimes haue I hearde this, but yet can I not tell howe to perceaue it.

That shall be referred to the fourth treatise, wher I wyll shewe you the proofe of all that you shall thinke doubtfull.

Yet I beseche you lette me knowe this, Whye are those heauens called Spheres? for (in my phantasye) [Page 9] they are nothinge like that instrument of sundrye cirkles, whiche is commonly called the Sphere, syth neither can I se in them suche cyrkles as are in that materiall sphere: nother is there in the materiall sphere anye suche representation of suche dyuers heauens, nother of suche varietie of starres.

This doubte was moued before nowe, by Ioa­chim Ringelbergh, in a treatise that he wrote of the Sphere, but it shall be answered easily by your selfe, after a lyttle de­claration of the celestiall spheres. And for that cause, I wyll omitte it tyll anone, and will firste declare certaine other ac­cidentes of the heauens, and of the other partes of the worlde.

Hitherto you haue hearde onlye the names of the partes of the worlde, and of their situation, howe they be placed in ordre. Nowe for the forme and shape of them, you shall vnderstande, that the whole worlde is rounde exact­lye as anye ball or globe,The forme of the world and his partes. and so are all the principall par­tes of it, euerye sphere seuerallye and ioyntlye, as well of the Planetes, as of the Fixed starres, and so are all the foure Elementes.

And they are aptely placed togither, not as a numbre of rounde balles in a nette, but euery sphere inclu­deth other, as they be in ordre of great­nes, beginning at y^e eightesphere or fir­mamente, and so de­scending to the laste and lowest sphere, is the Sphere of the Mone: vnder which the foure elementes succede: first the fier, then the ayer: nexte foloweth the water: which with the earth [Page 10] ioyntlie annexed, maketh as it were, one sphere only.

This I do well vnderstande in wordes, and the easier by this picture, whiche I finde in euerie booke of the Sphere, but that I see there more spheres, then you speake of: for in some bookes mention is made of nyne spheres: and in other are ten spheres named, where you sette foorthe but eighte.

The cause of this diuersitie will I in the fourthe treatise declare: in the meane season, I thinke it best to tell you of no mo spheres, then are perceptible by sighte, for so manye are we certaine of. And therefore vnderstande you thus, that as the eihhte sphere is the greatest, and hath none other without him that maye be seene, so the earthe is the leaste,The earthe is the cētre of the worlde. and hathe none other within hym, but it standeth in the middle and in the centre of the whole worlde, and of euery one of these spheres, and therfore it is called the Cen­tre of the worlde: so that although the earthe in it selfe haue a greate and notable quantity,The earthe hath no quantity in respecte to the world. yet in comparison to the fir­mament, it is to bee esteemed but as a centre or little pricke, yea in deed muche lesse than any notable starre that you see, & if I shall speak boldly that which I intend herafter to proue certainly, the earthe is lesser then the leaste starre in the fir­mament whiche is commonly seen, but yet is it greater thē Venus or Mercury, yea greater then the Moone.

This affirmation seemeth to me impossible, or at the least contrary to sence: for the Mone seemeth bygger muche then any starre, yea somwhat bigger then the Sonne.

Content your selfe to credite me, tyll tyme serue for the proof of my woordes, and in the meane season, to procede as I began. You must thinke, that the earth and the water annexed togither in one globe, are of no notable quantitye, in comparison to the firmament, and that it stan deth as the centre of the worlde,The earthe hath no motion. and hath no motion out of his place, nother yet circular mouyng about his owne cen­tre, but resteth (as we may say) quiete without all such mo­uyng, [Page 11] Lyke wayes must you thinke of the other elementes, whiche of their owne nature haue none other motion then a stone or a lyghte fether, so that they may be accompted all four to be without naturall motion.

Yet in the water and in the ayer we see euerye day notable mouynge. and sometime I haue hearde of mo­uynge of the earthe, by earthquakes: and as for the fyer that we see, it alwaies moueth and fly ckereth in burninge.

And so you haue seene a stone moue swiftelye, when it fell from anye hyghe place. but these motions haue an ende quicklye, excepte they be continued with violence, as hereafter I will sufficientlye declare. But as the stone al­though it wyll moue in fallinge, yet in his place lyeth quiete without motion: so the earthe of it selfe, and the other ele­mentes muste be accompted quyete by nature, and without motion.

The moti­ons of the heauens.¶ The heauens contrarye wayes haue suche a naturall mo­tion that neuer resteth nyghte nor daye, nother can be staied by any violence. This motion wee se in the heauens daylye by their mouinge from the easte to the weste, and from the weste to the easte againe, aboute the earthe, ones euerye 24. howers, and therfore is thys motion named the Daily mo­tion, for it is the measure of a Naturall day,A Daye. commonly ac­compted. and this motion is lykewayes called of aunciente writers the motion of the First firmament, accordynge to whiche motion you see the Sonne in the daye tyme, and the starres in the nyghte tyme, and the Moone both in the day and the nyghte, to passe from the easte into the southe, and so into the weste, and at the ende of 24. houres to come a­gaine into the easte: wherby you may easily vnderstand, that this motion is common to all the spheres of heauen.

This maye all men see, that can see any thing. yet haue I heard of some so grossely witted, that they doubted which way the Son and the Moone dyd come into the cast agayne, as though they did not thinke that the skye dydde [Page 12] moue about the earthe.

Suche grosse ignorance happened somrymes to famous men, for lacke of due consideration of that, whiche all men maye see, as I will in place conueniente more large­lye note.

Yet one doubte I haue, of whiche I wolde glad­ly be rydde, and that is of the Moone: for as you saye, and by syghte wee perceaue, all the starres with the Sonne and Moone go round about the earth in 24. houres,A diuers motion in the Mone. saue that the Moone is slacker then all the rest, for she is euerye daye later in rysynge by an hower, then she was the daye before: but howe that cometh to passe, I doo not vnderstande.

This doubt is well moued, and in good tyme, for by it will I take occasion to instruct you not only in the true knowledge of it, but also of other sondrye motions in all the heauens: for in euery one of them dooth there appeare a lyke motion, contrarye to the dailye mouinge of the Fir­mament, whiche in the Moone is moste swiftest, and there­fore may be perceaued daylye of all men: but in the Sonne it is not so swifte, and therfore not so easilye perceaued: yet all men see a greate alteration in the mouynge of the Sonne in one yeare:A scuerall mouing in the Sonne. for somtimes he is hygher and nearer ouer our headdes, and sometime farther from our headdes, and lower in the southe: yea sometime he shineth with vs almoste 18. howers, (as in the middle of the Sommer) and in the middle of Winter hee shineth but 6. houres or lyttle more: this euerye childe dooth see, althoughe they knowe not the rea­son thereof.

Yet the reason of that is easy inough to be con­ceaued, for when the daye is at the longest, the Sonne muste needes shine the more tyme, and so must it needes shine the lesser tyme, when the day is at the shortest: this reason I haue hearde many men declare.

That may well be called a crabbed reason, for it goeth backward lyke a crabbe. The day maketh not the son [Page 13] to shyne, but the Sonne shynynge maketh the daye. And so the lengthe of the daye maketh not the Sonne to shine longe, nother the shortenes of the day causeth not the Son to shyne the lesser tyme, but contrarye waies the longe shy­ninge of the Sonne maketh the longe daye, and the shorte shyning of the sonne maketh the lesser daye: els answere me, what maketh the dayes longe or shorte?

I haue heard wise men say, that Sommer maketh the longe dayes, and Wynter maketh the longe nyghtes.

They myghte haue sayde more wiselyc, that long dayes make sommer, and shorte dayes make winter.

Why all that seemeth one thing to me.

Is it all one to say. God made the earth. and the carthe made God▪ Couetousnes ouer cometh all men. and all men ouercome couetousnes.

No not so, for heere the effecte is tourned to bee the cause, and the agente is made the paciente.

So is it to saye, Sommer maketh longe dayes, where you shoulde saye: Longe dayes make sommer.

I perceaue it nowe, but I was so blynded with the volgare erroure, that if you hadde demaunded of me farther what dydde make the Sommer, I hadde beene lyke to haue aunswered, that greene leaues doo make Sommer: and the sooner by remembraunce of an olde sayinge: that a yeare shoulde come, in whiche the Sommer shoulde not bee knowen, but by the greene leaues.

Yet this sayinge dooth not importe that greene leaues do make sommer, but they betoken sommer: so are they the signe and not the cause of sommer.

So I perceaue nowe that the longe shinynge of the Sonne doth make the dayes longe. But nowe can I not tell what causeth the Sonne to shine longer one tyme of the yeare, then an other.

That is it that draue wise menne to searche, and [Page 14] marke the motions of the Sonne, whereby at lengthe they founde, that the Sonne hathe an other course, contrarye to the daylye motion of the skye. And as the Moone doth accomply she her propre course (whiche is from the west into the easte, contrarye to the daylye motion) euerye mo­neth in the yeare,A yeare. so the Sonne dothe ende his course, in his propre motion, but ones in the yeare. And to expresse it aptlye, I muste saye, that the true terme of a yeare is no­thynge els, but the verye tyme of the course of the Sonne from a certaine pointe in heauen, tyll his retourne to the same pointe againe.A moneth. And a Moneth is the iuste time of the propre course of the Moone, from chaunge to chaunge: and euerye quarter of the Moone maketh a Weeke.A weeke. of whiche I will speake more in the nexte treatise, with the declaration of the diuersitye for the begynninge of Mo­nethes and Yeares. But nowe to contynewe oure princi­pall matter the more ordrelye, I woulde haue you repeate the chieffe articles of our talke hitherto.

This is the summe of all your doctrine hy­therto.The fyrste repetition.

1. That the worlde is that entiere body, which containeth in it all the heauens and the elements, with all that in them is.

2. The partes of the world ar two especial, the heauens whi­che are eighte in numbre, and the elemenents whiche are .iiij. in kinde.

3. The ordre and situation of all these partes, as well ele­mentes as heauenly spheres, beginning at the highest, and proceding to the lowest, is this. the Firmanent, Saturne, Iupiter, Mars, the Sonne, Venus, Mercury, and the Moone.

THE FOVRE ELEMENTES. Fyer, Ayer, Water, and Earthe. and euer the hygher incloseth all that is vnder it.

4 The worlde and all his principall partes are rounde in fourme and shape, as a globe or ball.

5. The earthe is in the middle of the worlde, as the centre of it: & beareth no vewe of quātitye in cōparison to the worlde.

6. The earthe hathe no motion of it selfe, no more then a stone, but resteth quietly: and so the other elementes do, ex­cept they be forceably moued.

7. The heauens do moue continually from the easte to the west, and that motiō is called, The dayly motion: and is the measure of the Common day.

8. The Mone hath a seuerall motion from the west toward the easte, contrarye to that mouyng of the dailye course, and that motion is y^e iust measure of a moneth, and euery quar­ter dooth make a weeke.

9. The Son also hath a peculier motion from the west to­ward the easte, whiche he accomplisheth in a yeare, and of that course the yeare taketh his measure and quantitye.

Now then it may please you to procede to farther expli­cation of the apparaunces which are noted in the heauens, and to shew the manner of their motions.

To the intent that you may vnderstand all thin­ges the more easilye,A materi­all sphere. I thinke it good to describe vnto you a Materiall sphere, whiche shall containe in it suche nota­ble cyrcles only, as haue speciall vse in the declaration of the heauenly motions, and suche as reason shall driue a man to appointe, as certaine boundes of the motions in the hea­uens: yea suche I saye, as your selfe shall by interrogatories be constrayned to confesse needfull to that knowledg which you desire.

If nothinge bee placed in that sphere but that which must needes be had, then can I not accompt any part of it superfluous. And againe, if it serue sufficiently to in­structe me in that I desyre to knowe, I canne not iustlye blame it in anye pointe as insufficiente, so muste it nee­des be a perfect instrument, voyde of defaulte, and without superfluitye.

So shall it be, for so muche as this parte of know­ledge [Page 16] requireth. Now then to begin. ye doo beleue that the worlde is rounde.

Yea for soothe.

The makig of a Globe.Then must that instrument also be round, which shall aptelye expresse the forme of the worlde.

Truth it is.

Can there be any thinge more round then a circle?

No trulye.

And dooth not twoo halfe cyrcles make a whole circle?

It can not be denayed.

Then take halfe a circle, and fasten it on an axtre or on any diameter, and then tourne it rounde about, fyrste lettyng the halfe cyrcle hang downward vnder the diameter

as heere you se it

figured, in y^e halfe cirkle A B, C. thē tourne y^e half cyr­cle right vp ouer the diameter, as here also is represented in the halfe cyrcle A, D, C. do not these two positi­ons make a whole cyrcle?

Yes surely.

Then set the halfe circle so, that the diameter may stande styll firmelye fixed, and the halfe cyrcle maye tourne rounde about. Do not you imagin nowe that euery dyuers position of this halfe cyrcle with the contrary place against it, dooth make a whole cyrcle.

Yes verelye.

And bycause there is no place round aboute that diameter, within the reache of that halfe circle, but that half circle hathe passed it, there can no voyde place be assigned but it is occupied and fylled with halfe a cyrcle, and euerye halfe cyrcle with his contrarye dooth make a whole cyrcle, so doth this whole reuolution of the halfe circle make a iust cyrcular bodye.

So it appeareth trulye.

A Sphere is defined.This circular body is na­med a sphere, as it may appeare by the description that Euclide maketh of a sphere: whiche is this in greeke, as him selfe wrote it, in his eleuenth booke of Geometrye.

Whiche into Latine may well be translated thus.

And thus it soundeth in englishe.

A Sphere is a sound figure, made by the tournynge of half a circle, tyll it ende where it began to be moued, the diameter of that halfe circle continuyng steddye all the meane whyle. This description dooeh Ioannes de Sacro bosco expounde thus: that a sphere is a rounde and sound body made by the tournynge of halfe a circle.

So that a sphere is nothinge els but a rounde and massye bodye closed with one plat forme, whiche you in your Pathwaye doo call a Globe.

The centre of a Globe or Sphere.You take it ryghte. But nowe must you marke, that as a circle is made about his centre, so a globe also hath his centre, as you may easilye vnderstande, from which cen­ter all the lynes that may be drawen to the plat forme, or vt­ter parte of the globe, are all equall togither, accordyng to Theodosius definition, whiche saythe thus: A sphere is a massye bodye, inclosed with one plat forme, and in the mid­dle of it there is a pricke, from which all lynes drawen to the sayde plat forme, are equall eche to other, and that pricke is the centre of the globe and so sayth Euclide also.

The centre of a globe is the same centre that a semicircle hath, by whiche the globe was made.

It muste needes bee so: and lykewaies the dia­meter of them bothe muste needes be all one, as I thynke.

You saye not muche amysse. Yet must you put a difference in a globe,A Diame­ter and an Axe tree differ. betwene a Diameter and an Axe tre. For euery right lyne that passeth frō side to syde in a globe, and toucheth the centre, is aptely called a diameter. so that as ther may be many diameters in a cyrkle, so may ther be as many also in a Globe: But of all that multitude, one only is called the Axe tree, and that is it on whiche the globe tour­neth. This difference did Ioannes de Sacro bosco ouerpasse not ignorantly, but negligently, or els wittingly: but so dyd not Euclide, whiche defineth them bothe thus.

The Axe tree (saith he) is that righte lyne whiche moueth not, but the halfe cirkle moueth aboute it. These wordes haue respect not only to the makynge of a Globe or Sphere, but also to the vse of it. But now the diameter is de­fined by him thus:

The diameter of a Sphere, is anye ryghte lyne that is drawen by the centre, and ended in the plat forme of the sphere.

This difference muste needes seeme reasonable, syth there maye be so ma­ny diameters drawen as a man lysteth, but Axe trees there can be but one in one globe.

When a globe tourneth rounde, are there anye mo poyntes then twoo in that globe, on whiche it doothe tourne?

By proof it appeareth, that all partes of the globe moue, excepte the two endes of that Axe tree, wher­on it mooueth, and they mooue not out of their place.

Poles of a Sphere.Those twoo pointes are named the poles in a sphere, wherby also you may vnderstande, that there can be but two poles in one sphere: marke this well, for it will serue your turne in place conueniente. Nowe applye all these to the worlde, whiche in his whole substaunce is rounde, and therefore aptelye maye bee called a sphere: yow see it tourne aboute rounde, and therefore must it haue twoo poles, on whiche it tourneth so. Also bicause it is rounde, it muste haue a centre (whiche I dyd affirme before to bee the earthe) and by this centre, we may imagine a right line to run from the one pole to the other, whiche righte lyne muste be cal­led the Axe tre of the worlde.

For the centre of the worlde, it muste needes be somthinge: for I perceaue a globe can not be, but it must necessarily haue a middle pricke or centre, no more then a lyne maye be made whiche hath no myddell, or a circle that hathe no centre: whiche bothe appeare vnpossible. Also for the pooles, they appeare needefull, or rather of necessity to folowe the mouinges of heauen. For in all rounde thinges that mooue roundly, there be suche two pointes that seeme not to moue: but why there shoulde be any axe tree requy­red in the worlde, I see no reason: for if the myghtye power of God dyd not staye the worlde, there coulde bee no Axe tree able to beare it.

Your imagination in this pointe is to grosse. I sayde not that the Axe tre was made to stay the worlde, but that it passeth as a lyne only from the one pole to the other: and is not without greate and profitable vse, bothe in do­ctrine, and also in practise, for placynge of instruments, as [Page 20] you shall know better hereafter. But nowe heare howe Pro­clus dooth applye these to the worlde.

Whiche wordes our worthye contrye man D. Linaker, translateth thus.

The Axe tree of the worlde, is named the Diameter of it, aboute whiche it tourneth.The north and southe Poles. and the endes of that Axe tree, are called the Poles of the world. of whiche poles one is na­med the Northe pole, and the other the South pole. The North pole is alwaies seene of vs where as we dwell, and the Southe pole is neuer seene in this oure contrye, but is euer more vnder our Horizonte, and that as lowe, as the Northe pole is highe aboue our Horizonte.

I haue beene taughte to knowe the Northe pole, and I haue marked it oftentimes, wherby I perceaued a great numbre of starres to moue aboute it, and were sometymes higher then it, and sometymes lower then it: nowe on the easte syde of it, and nowe on the west syde: but that pole starre seemed not to sturre oute of his place at anye tyme: whereby I gather, that he is neuer oute of sighte to vs, when the starres appeare, and that is all the nyghte. but what be­commeth of him in the daye tyme, I can not tell.

I wyll cleere you of all suche doubtes before I leaue you:The Hori­zonte. but in the meane tyme I meruaile you founde no doubte at the name of the Horizonte.

That name I learned to signifye that cyrcle, whiche goeth along by the edge of the ground, and parteth that parte of the worlde whiche we see, from that part which we se not: & when the Son riseth, then is he in our horizonte, & so is he, when he is goyng downe as lowe as we can see him.

This is not greatlye amisse. the lyke expressynge [Page 21]

of it dooth Hyginius vse in his fyrste booke, and in the .iiij. also of his astro­nomye: but Proclus in his Sphere, dooth define it thus.

The Horizonte is a cyrcle whiche parteth that parte of the worlde that wee see, from that whiche wee see not: and it de­uideth the whole

sphere of y^e world into twoo equall partes, in suche sorte, that half of that sphere is e­uer abooue the grounde, & halfe alwaies vnder the earthe. This cyr­cle you perceaue to be necessary in the materiall sphere, seynge it hath so greate vse in the hea­uenly motions, that by it we iudge the risynges and settings of the Sonne and the Moone and all other starres. what say you then for the noone steede of the day, from whiche you recken all your houres, as it appeareth both by the clockes and dyals? for as the clocke striketh one nexte after noone,The meri­dian circle [Page 22] and so in creaseth forward in the numbre of houres, so like­waies are your howers marked in the dialles.

I thinke it very meete to haue the south pointe well knowen, as well for this, as for standynge dialles, and for knowledge of the tyme of the nyght by the moone, and by other starres.

Then muste there be a circle appointed for that vse, whiche is called therfore the Meridiane circle, and may be named well the Noone steede cyrcle.The None­steed circle This circle is thus defined by Proclus.

The Meridian is a cyrcle drawē by the poles of the world, & the point right ouer our heads. in which circle whē the Son is, he maketh the myddle of y^e day, & the middle of y^e nyghte.

Nowe farther to procede to other partes needfull in the sphere. you do se, that twise

in the year the daies & nights ar equall, & the Son riseth in the iust east, & goeth doune in y^e full west, wher as in y^e sōmer y^e Son riseth northeast, and setteth northweste: & at nonetide is very high ouer our heds: but in y^e winter, cō­trary ways y^e son riseth south east, & setteth southwest: & at nonetide is very low. thynk you not that these thre boū­des of the course of the Son would be well noted, and haue their peculiar circles, for distinction of those tymes?

I thynke nothinge more needefull then that.

These thre circles (with two other that I will next speake of) are named the fiue Paralelles: and the middle cir­cle of those, is named the Equinoctiall, bicause that when the Sonne is vnder it, the dayes and nyghtes are equall in all the worlde, except only twoo places. This circle is thus defined by Proclus.

The equinoctiall circle is the greatest of the fiue Parallele circles, and is deuided so equallye into two partes, by the Horizonte, that the one halfe of it is aboue grounde, and the other is vnder the horizonte: and when the Sonne is in this circle, he maketh the daies equall with the nightes, ones in the Springe tyme, and againe in the Haruest. This equi­noctiall circle and the other seuen that folowe, to be decla­red, doo moue all as the skye moueth. but the Horizonte and the Meridian doo not moue with the heauen, but stand stedye, and keepe their places.

That seemeth reasonable, els coulde not men knowe the risyng, setting, and noonesteed of the Sonne. but howe shall I knowe this equinoctiall circle in heauen, seynge I can not see any suche circle there?

Howe to knowe the place of the circle equinoctialMarke the course of the Sonne aboute the ele­uenth daye of Marche, or els about the fourtenth daye of Septembre, and so may you best vnderstande the place of this circle, for at those two tymes the Sonne runneth dire­ctly vnder the equinoctiall circle, and dothe (as it were) de­scribe it by his motion, in four and twenty-howers. And if [Page 24] you lyste do marke the rysinge of the sonne that daye, you maye know the precise pointe of the easte, and at nyghte he setteth in the iuste poynt of the weste.

I woulde I knewe as good markes of the other cyrcles.

So wyll I geue you in their conuenient places and times good orders to know them al: and first I must tel you, that these other two cyrcles, which I named before (with the equinoctiall) are called the twoo Tropike cyrcles after the greeke deriuation,The knowledg of the ij. tropikes and maye be called in englyshe the Sonne boundes, bycause the Sonne doth neuer passe them, nother towardes the northe, nor yet toward the southe: but when he toucheth any one of them, he doth tourn his course toward the other. as for example: All the tyme from the myddle of December vntill the eleuenth daye of Iune, you maye per­ceaue the Sonne to ryse hi­gher

• A, C. the Horizonte.
• * * The poles of the worlde.
• G, H. The Equinoctiall circle.
• B, F, one tropike, and
• E, D. the other tropike.
• A,
  The Sōmer tropike.
  I, the artike circle,
• C, K. the antartike circle.

and hygher, and that daye hee is at the hyghest that hee canne go towardes our heads, and then dooth hee by his course describe that Sommer tropike, after whiche daye hee draweth agayne lower and lower e­uerye daye, tyll the twelfte daye of December, for then he is at the lowest, and that daye he doth describe the Winter tropike. Nowe marke howe Proclus defi­neth them.

The Sommer tropike is the moste northerlye circle of all thē that the Sonne describeth: in the which when the Sonne is, he maketh his Sommer turne, at which time is the lōgest day of al the year, and the shortest night: for after this Som­mer turne, you se the Sonne go no more toward the north, but turneth to the contrary coaste of the worlde, and therof is that circle named (in greeke) a Tropike: that is to saye, a Returninge circle, or a circle of Returne.

The Sonne aftter he beginneth to turne, maye be perceaued euery day, or at the least euery weeke, and chiefly at nonetide to waxe lower & lower, vntill he come to the Winter tropike, and there he turneth againe, as by the definition of that tropike you may vnderstande.

The winter tropike, sayth Proclus, is the moste southerlye [Page 26] circle of all them that the Sonne doth describe, by the reuo­lution of the worlde, in whiche when the Sonne is, hee ma­keth his Winterly tourne, and then is the longest nyghte in all the year, and the shortest day, for after this Winter turn, the Sonne is not seene to go any farther towarde the south, but tournith to the contrarye coastes of the worlde, and thereof is this cyrcle also named a Tropike or cyrcle of Retourne. And thus haue we the three circles that are prin­cipallye noted for the course of the Sonne.The southe and northe circles. Nowe are there other twoo whiche be Paralleles with these thre, whereof the one is more southerlye (to vs) then is the Winter tropike, and the other is more northerly, thē is the Sommer tropik, whiche whether they be needfull or not, their vse maye de­clare. I remembre, that you sayd, you had oftentymes be­holden the Northe pole, where you myghte see manye star­res about it, that neuer go vnder our Horizont. do you not thinke it good that all those starres were inclosed in a circle to be discerued from al other, which rise somtime aboue the Horizont, and somtime againe do set vnder the same?

Yes verilye, it were pleasaunt to know.

And profitable also, as you shal hereafter perceaue. Now contrary waies,The vse of the Arctik and Antar­ctik circles there are other starres, that are neuer seene of vs in this cuntrye, and yet muche mention is made of them in writers, were it not good that their bounde were marked, that all other maye be knowen from them?

Els myghte men often looke for suche starres as they reade of, and shulde loose their labour, for they shall not see them.

And yet are there goodlye bryghte and notable starres, whiche are not seene here, but in southe Spaine, in Barbary, in Guinea and Calecut, and many other cuntries, they appeare fayre and pleasaunt to beholde.

I pray you, what call you those cyrcles that in­closeth those starres?

They are named after the coaste of the worlde [Page 27] where they bee. So that the circle whiche incloseth all those starres that be about the Northe pole, is named the Arctyke circle or Northe circle: and the contrary circle in the south, is called the Antartike circle by the greeke composition, as you woulde say, Contrary or against the Arctike circle: and it may well be called the South circle. But nowe heare howe Proclus defineth them.

The Arctike cirle is the greattest of all those circles whiche do alwaies appear, and toucheth the Horizonte in one only pointe, and is all togither aboue the earthe, and all the star­res that bee within this circle nother rise nother sette, but are seene to runne rounde about the Pole all the nyghte.

Thus haue you the fourth parallele, Nowe resteth the fyfte whiche is described thus of Proclus.

The Antartike circle is equall and equidistant to the Ar­ctike circle, and toucheth the Horizonte in one only point, and is all vnder grounde, and all the starres that be in it, are euer more out of our sighte.

These are al the Paralleles which are wont to be set forthe in the materiall sphere, and that agreeably of all men, saue that [Page 28] touchinge the two laste circles there is a difference, of which I will instruct you at large in the next part of our talke, and omitting it for this time, will go forward to other thre cir­cles whiche yet remaine,The zodi­ake. and are needfull to oure sphere. By­cause oure chieffe consideration consisteth aboute marking of the motions of the Sonne, the Moone and the other planetes, howe they chaunge their places in the skye, and therfore make diuers apparaunces to vs that beholde them, and mark their courses, and yet all they haue (as it were) one common path or waye, from whiche they swarue not, but kepe them selues still within the limites of it: how think you is not that path of theirs well to be marked, and worthy to haue a notable name?

Mary that is the principall pointe (as I take it) of all the reste: for without knowledge of that, nothing els can be knowen.

That common path of the Planets, wherin all thei haue their course, is called of Astronomers the Zo­diake: whiche is,The .xij. signes. as you maye englishe it, the Circle of the Signes: whiche signes are the greatest and notablest partes of that circle, and were inuented for the more exacte di­stinction of the motion of the Planetes monethlye. For as there bee but twelue monethes in the yeare, so there are twelue partes of the Zodiake distincte by seuerall names, and correspondent to euery moneth, althoughe they varye something now from their first application, wherof hereaf­ter I will instructe you sufficiently. and now will touch them briefly as this place doth require. Their order in the zodiak and their names ar these that folow, in greek and latin, which maye bee englished as I haue vnder written, and are often tymes mentioned of our english Poetes.

And bicause that their names alwaies can not bee placed in small instrumentes, there ar certain figures deuised for their names, whiche I haue also sette vnder their names, that you maye the better knowe them.The de­grees of the signes. These Signes are all of one lengthe, eche beynge the iuste twelfte parte of the Zo­diake. And for exacter knowledg of the motion of the pla­nettes euerye daye, eche Signe is deuyded into thyrtye equall partes, which are called Degrees, so that in the whole circuite of the zodiake there must bee 360 degrees, whiche agree almost with the dayes of the yeare.

And therby I gather, that as the Son doth moue throughout all the zodiake in a yeare, so euerye moneth he moueth, he runneth one signe, & euery daye nere one degree.

You gether well, but this muste you marke also, that by this same nombre of degrees all the cyrcles in the sphere are deuided, so that of euery circle greate or lesse,what a degree is in measure. a degree is the 360 parte and not anye measure certaine, as a foote, a yarde, a myle, or suche lyke.

I vnderstande you thus: as a quarter is no mea­sure certaine, but sometyme is referred to one thinge, and sometime to an other, and yet still it betokeneth the fourth parte of that whervnto it is referred, for when we say: a year and a quarter: an houre and a quarter: a yard and a quarter: a quarter of a foote: in all these sayings, the quarters differ. so when wee saye: a quarter of corne: a quarter of clothe: a quarter of pepper: a quarter of allame: by the accustumed measures all men vnderstande our meanynge, and yet these quarters differ, and be in common meaning, a quarter of a weye, or eight bushels, a quarter of a yarde, a quarter of a pounde, a quarter of a hundreth.

So is a degree the thirteth parte of a signe, and a [Page 30] signe the twelfte parte of any circle. howe be it, commonlye & chiefly the name of Signes, is attributed to the Zodiak. (whiche many doo call the Thwarte circle) This Zodiake is thus described of Proclus.

The thwarte cyrcle (or zodiake) is the cyrcle of the twelue signes, and is made of thre circles, wherof two are the boun­des of his bredthe, and the thyrd is called the Middle signe circle, (bicause it goeth by the middle of the signes in the zodiake) and it toucheth two equal

circles of the parallels: that is to say, the Sommer tropike in the firste point of the Crabbe called Cancer, and also the Wynter tropike in the firste degre of the Goate, called Ca­pricorne. The breadth of the zodi­ake, containeth twelue degrees. This zodiak is called a Thwart circle, by­cause it crosseth the parallele circles, goynge ouerthwarte them. By these wordes of Proclus you may vnder­stande, that the zodiake dooth not [Page 31] go directly betwene the two poles of the worlde, as all the fiue paralleles doo, but is drawen crosse the sphere, so that his middle (in breadthe) doth touche the two tropikes, and that middle line is called of latin writers the Ecliptike lyne,The Ecli­ptike line. bicause there can be no eclipse of Sonne or Moone, onles the Moone be vnder that lyne: as hereafter I wyll declare in place conuenient. But touching this zodiake (of which wee spake laste) I sayde it was diuided into twelue signes, accor­ding to the twelue monethes of the year. And bicause euery quarter of the yeare maye bee the more exactlye knowen a sonder, this zodiake is parted into foure partes principall, euery part (as it must needes folow) containing thre signes.

This is a very apte agreement of arte vnto na­ture: for as the whole zodiake agreeth with the whole year, so for the foure quarters of the one, there is foure quarters in the other: and for the twelue monthes of the yeare, twelue signes in the zodiake: and for the thirtye dayes of the mo­neth, thirtye degrees in euerye signe. But I praye you syr, dooth the beginninge of these signes answere to the begin­ning of our yeare?

The yeare when it be ginneth.The beginning of the yeare is diuers in dyuers nations, as I will shewe you an other tyme, with the reason why we begin our yeare in Ianuary: but for this tyme it shal be sufficient, to declare the agreement of our yeare with the Astronomers yeare. The Astronomers beginne the twelue signes of the zodiake at Aries, and lykewaise do they begin the yeare that daye and hower, that the Sonne entreth into that signe of Aries, whiche is nowe at the eleuenth daye of Marche:The spring of the year and from thence they recken the Springe of the yeare thre monethes, whyle the Sonne is in the fyrste three signes. Then at the eleuenth day of Iune; they accompte the ende of the springe, and the beginning of Sommer, bicause then the Sonne entreth into Cancer,The Sōmer whiche is the fourthe signe. and while the Sonne passeth other thre signes, (which maketh the seconde quarter of the zodiake) they accompte [Page 32] the second quarter of the yeare, which we call Sōmer, & that endureth till the 14 day of September, at which time y^e Son entreth into Libra, wher the third quarter of y^e zodiak doth begin, & so with it begīneth Haruest, which is the third quarter of the year,Haruest. and cōtinueth till the twelft day of Decēber, and then doth the Son entre into Capricorn.winter. & Winter be­ginneth, being the 4 and last quarter, which continueth tyll the eleuenth daye of Marche, where the olde yeare endeth, and a newe yeare beginneth.

These 4. signes, Aries, Cancer, Libra & Capricorn, seeme to haue a certain prerogatiue, y^t they begin y^e 4. quar­ters of y^e year, therfore thei wold be well noted in y^e zodiake.

You say well, and yet thei haue other notable qualities, for in the beginning of Aries and Libra, y^e son maketh the daies equall with the nights. & these 2. points ar named y^e equinoctial points. In the first part of Cancer, the day is at y^e longest, and beginneth to shorten by the descending of the son frō our heds, & when the son doth enter into Capricorn, the day is at the shortest, & then the son beginneth to returne to vs again, & the day doth thē begin to increase. and these 2. points ar called the ij. Tropike points:The Colu­res. Wherfore as these 4. points are notable, so are ther ij. circles appointed for their lymites, the one going by the beginning of Aries & Libra, and the other by the beginning of Cancer and Capricorn. these ij. circles ar called Colures,Tropike Colure. wherof the one only which passeth by Cancer and Capricorn, is described of y^e grekes, the reason thereof I will shewe you in the fourthe treatise. But this fyrste colure, whiche is called the Tropike colure, is thus described by Proclus.

The circles that go by the poles are those, whiche some men call Colures: thei haue the poles of the worlde in their circumference. And ar named Colures in greek, that is trunked circles, by­cause some partes of them come not into oure sighte. for the other circles by the turning of the world are all seene, but some parts of the Colures are not seene, that is, those partes whiche are in the Antartike circle, and remaine vnder our Horizonte.The Equi­noctiall co­lure. These cyrcles are deawen by the two tropike pointes of the eclipte circle, and so deuide it into two equall partes. The Equino­ctiall colure goeth by the poles of the sphere, and by the .ij. equinoctiall pointes of the Zodiake, in Aries and Libra. Thus haue you nowe all the cyrcles needfull for a materiall sphere. let me heare howe you doo remembre their names.

If I shoulde not remembre theim, I dydde but leese my laboure,A good lesson. and occasion you to spend your tyme in vaine: for I know that in this science and in all other, he that coueteth to runne styll forwarde, and remembreth not that, that is gone before, shall neuer attaine that whiche remai­neth behynde, but while he deliteth to muche to see the end, he deceaueth him selfe of the frutefull ende of knowledge. muche lyke a man that is delited in hearing a cunning song [Page 34] of musyke, but when it is done, doth remembre nothing of it, so is his profite and pleasure bothe ended, when the song is ended. Therfore (if it please you) I will repeate the chieffe pointes that I haue learned sythe my former repetition.

Doo so then.

This it is as I remmembre,

• The second repetition.
  1 Fyrst you taught me what a sphere is, and howe it is made, also what is his Centre, his Axetree, his Diameter, and his Poles, and what the Poles are named.
• 2 Nexte you declared two circles, that is the Horizonte, and the Meri­diane circle, whiche (I perceaue) stand styll, and tourne not with the worlde, but keepe their places.
• 3 Then did you describe fiue parallele circles, the Equinoctiall, the twoo Tropikes: the Sommer tropike, and the winter tropike, and then the other two Paralleles, that is, the Northe circle, and the Southe.
• 4 After that, you shewed me what the Zodiake was, and the twelue Si­gnes that be in him, and of their diuision.
• 5 And laste of all, you described the twoo Colures, whiche diuide the Zodiake into foure equall and principall partes, accordynge to the four tymes of the yeare.

This good remembraunce declared your good will to knowledge, whiche I shall with as good a will healpe to further. Now you looke (I think) to be instructed in the vse of all these thinges, and to vnderstand therby the cele­stiall motions, and the diuers appearances that therby doo ensue: how be it, bycause that a materiall instrumēt is a great helpe for them that begin to trauaile in this arte, and dothe as an image represent to the eies those thinges, which by only hearing, were very hard to conceaue, besides many other commodities, whiche shall be vttered in their place, I think it moste conuenient order, fyrst to teache you the manner howe to make suche a materiall sphere, as may serue both to learne by, and also to worke by, in practising the obseruati­ons needefull to this arte.

ALTHOVGHE THERE BE MANY and wonderfull instrumentes wittely deui­sed for practise in Astronomy, as the A­strolabe, the Plaine sphere, the Saphey,Instrumēts of Astrro­nomye. the Quadrante of diuerse sortes, the Chylyn­der, Ptolome his rules, Hipparchus rules, Tunsteedes rules, The Albion, the Tor­quete, the Astronomers staffe, the Astronomers ringe, the Astronomers shippe, and a greate numbre more, whiche hereafter in tyme you may knowe, yet all these are but parts, or (at the most) diuers representations of the Sphere. wher­fore as the Sphere is the grounde and beginner of all other instruments, so is it moste meete that we begin with it, and the rather bycause it dothe more aptlye represent the forme of heauen, then anye other instrument canne doo. What a Sphere is, you haue learned before: and howe a materiall Sphere or Globe maye bee made rounde, you maye conie­cture by the same description of Euclide. Therfore muste you haue an instrumente of steele made lyke a Semicircle, whiche in the inner circumference muste haue a sharpe edge apte to cutte and pare smothe,The tour­ning of a Globe. and (as I maye saye) by true woorkinge to iustifie your Globe, whiche fyrste maye bee made as rounde, as any Turner can doo it. and then shall your instrument not only duly examen the Turners work, but correct it exactlye if it be amysse.

This is the forme of that instrumente, and it is thus made iustlye. Firste drawe a righte lyne as longe as you wyll haue [Page 36]

the diameter of youre sphere, and an yche longer, or more. Then o­pen youre compas ac­cordynge to the halfe diameter of the sphere that you would make, and draw halfe a circle, so that the fixed foote of your compas be set in the myddle (as you may nearlye gesse) of the sayd line, and wyth the other moueable foote make the semicircle, but not fullye complete to the diameter, for there muste bee twoo holes made as bigge as a wheate strawe or bygger, accordynge to the bygnes of the Globe, for thoroughe these

holes muste the Turners spyn­dles pearse, that muste beare the Globe whyle it is in tournynge: but you muste take good heede, that those holes bee so made, that the foresayde lyne doo passe exactlye thoroughe the verye myddle of them, for so muche as you misse in makynge those holes, so muche will your sphere bee false in euerye quarter. Againe you muste take heede that youre instrumente doo not bowe inwarde withoute those holes towarde bothe the poyntes, excepte it bee in true compasse, but better it is to fyle it somewhat a slope outwardelye. What more is to be doone, I leaue it to the stu­diouse deuyse of your owne practise. for suche thynges are better taught by hande, then by mouthe.

I wolde I coulde as well vse it, as I could diuise to make it iuste rounde.

To find the Poles in a Globe.When you haue your globe so iustified in roundnes, marke well the twoo Poles of it, which you may easily do by the same instrument, whereby you did iustifye it, for the spindles that passed through the twoo holes of your in­strument, doo touche the twoo poles exactly.

That can I easilye doo.

Then muste you haue a payre of compasse aptelye made for to drawe the circles in youre Globe, and the poinctes of the shankes in that Compasse muste bowe somewhat inwarde (as here you see an example) and the poynctes of it muste bee verye fine and harde, that they maye graue deepely, and yet make a fine and small circle. for the fyner that your circles be, the exactlier will the diuisions be made, and the lesse erroure wyll bee in the ma­kynge

and vsyng of the same Globe.A compas for a Globe Then sette one foote of the com­passe in one of the Poles of the Globe, and open the other so wyde, as you thynke will suffise to reache to the myddle of the Globe, to­warde the other Pole, and with that foote make a lyghte marke in the Globe: and keepynge youre com­passe vnchaunged, putte one foote of it in the contrarye Pole, and tourne the other foote towarde the foresayde marke,To make equinoctial circle. in the myddle of the Globe, and if the foote touche it exactelye, then is that myddle duelye founde: but if the compasse reache to farre, or to shorte, make wyth yt an other lyghte marke, and the true myddle betweene [Page 38] those two marks is the iust middle of the Globe or Sphere, as by your compasse a little opened more or closid (as you see cause) you maye prooue.

That can I do well ynough, by experience lear­ned in often practisynge the conclusions of youre Path­waye.

The Path­waye.That Pathwaye wyll leade you rightlye to this woorke, if it bee well trauayled as it oughte to bee before you come to this woorke. But to procede with our Sphere: When you haue founde the iuste myddle of the Globe betwene bothe the Poles, then open youre compasse accor dynge to the distance of that middle marke, and one of the Poles, and set one foote of the compasse in the Pole (whiche you lyste) and with the other drawe a cyrcle rounde about the Globe. whiche whether it bee truelye doone or not, thus maye you prooue: Remoue the foote of your compas into the other Pole,Proof. and with the mouable foote trye the former circle, & if the compasse run iustly in it, then is that circle truly drawen betwene both the Poles, else haue you erred: and therfore graue not y^t circle to deepe, till you haue examined it.The diui­ding of the equinoctial And when you haue found it true, then without alteringe of the compas, set bothe feete of it in the sayd circle, & they will take the fourth part of the same circle, as by remouinge it four tymes, you maye knowe.

That haue I learned in the Pathwaye also, and if I haue myssed,Proof. it is by the grossenesse of the poyntes of my compasse, or else by myne owne grosse negligence, whyche bothe I canne quickly examine and amende, as the case requireth.

After that you haue marked oute those foure partes of that circle, dyuide eche of them into three euen partes, and so haue you that cyrcle dyuided into twelue equall partes: marke those partes with little crosse lynes, or else drawe an other circle wythin a corne breadthe of that other, on which side you list, but let it be somwhat lesse [Page 39] grauid then the fyrste, that the fyrste may bee knowen for the true circle, and this seconde cyrcle to serue but onlye for the markes of diuision in that other: and so drawe a lyne at euerye twelfte parte, from the one cyrcle to the other. Then dyuyde euerye one of those partes into three lesser partes, and eche of theym agayne into euen halues, and so haue you in all, 72. parts made of that cyrcle. After this, diuide one of those partes into fiue lesser porti­ons, equallye, and by the same example diuyde all the other 71. partes, and so haue you in the whole circle, 360. partes, whiche you shall marke with nombres of figures, from 10. to 10. beginninge where you lyste.

Those I maye call degrees, as I remembre by youre former lessons. and I muste marke them thus. 10.20.30.40. and so vnto 360.

So it is: And thys circle thus drawen in the middle betwene bothe the Poles, is the Equinoctiall cyrcle in that sphere. Now to make the two Tropiks,To drawe the twoo Tropikes. open your compas so▪ that they maye extend to 66. degrees and an halfe of the said Equinoctiall cyrcle. and then set one foot of the com­passe in which Pole you will, and with the other foot draw a circle on the Globe, which shal stand for one of the tropiks, and setting the foote of the same compasse vnaltered, in the other Pole, draw about it an other circle, for the other tro­pyke. Now appointe names for the Poles,The Poles. callyinge one the South pole or Antartike pole, and the other the North pole or Arctik pole: and then the tropikes of necessity will take their names: for that Tropike which is next the North Pole, must be the tropike of Cancer, that is,The Tro­pikes. the Sōmer tro­pike, and the other that is nexte to the Southe Pole, must needes bee the Tropyke of Capricorne, or the Wynter Tropyke. Then marke where you beganne the noum­brynge of the degrees in the Equinoctiall (whiche maye well be called the begynninge of the Equinoctiall) and set one foot of your compas in that beginning,The tropih Colures. openyng the [Page 40] other foote tyll it will reache vnto 90. degrees iustlye, and fyrste holde the one foote steddye in the begynninge of the Equinoctiall, and drawe a circle with the other foote, and if that circle touche bothe the Poles of the Globe, then is it trulye drawen.Proof. but it should go also by the ende of the 270 degree of the Equinoctiall, and if it misse anye whitte, examine it well, and amende the faulte, before you woorke anye farther.A generall rule. whiche rule you shall obserue styll, for els of one faulte neglected, many other may ensue.

The Equi­noctial Co­lure.This doone keepe youre compasse at the same wyde­nesse, and sette one foote in the Equinoctiall circle, at the ende of 90 degrees, and holdynge it steddye, with the other foote describe a circle,Proof. whiche shall passe by bothe the Po­les of the Globe, and by twoo pointes of the Equinoctiall, that is the beginninge of it, and the ende of 180 degrees. and if you haue missed, amende it by and by. This laste cir­cle is the Colure Equinoctiall, and the other last before dra­wen is the Colure Tropikall, or Solstitiall, or the Tropike Colure. These twoo circles shall you diuide into 360 parts eche of them,The diuisi­on of the Colures. beginninge your numbrynge at the Equino­ctiall, and rekeninge towarde the Pole, in euery quarter of them seuerallye, so shall you neuer recken aboue 90. But it is easilye knowen, that foure tymes nynetye doothe make. 360.

But in this ordre of numbrynge, the cōmon forme of accompte is not kepte, as it was in the Equinoctiall: for when I haue reckened in one quarter 90. degrees from the Equinoctiall to the Pole, then if I go forwarde in the same circle, the nexte numbre beyonde the Pole is nynetye againe, and so that seconde quarter decreaseth from 90 to 10, goynge backwarde, and then the thyrde quarter increaseth from 10 to 90, and the fourth quarter decreaseth againe from 90 to 10.

So must it be in these circles for moste aptenesse in accompte,Proof. as you shall perceaue hereafter. Nowe shall [Page 41] it be conuenient to mark in what degrees the two Tropikes do cut those Colures, for if you haue not erred, they touch the myddle of the four and twentith degre in euery quarter of the Colures. And if you haue doone well, then procede to the making of the Zodiake, whiche you shall draw thus. Open your compasse to the same wydenesse that you dydde for makyng the Colures, or the equinoctiall, & then recken from one of the poles (whiche you will) 23 degrees and an halfe, in any one of the Colures,Pole Cir­cles [...]. and it will lighte in 66 de­grees and an halfe, by cause the numbres from the poleward go backward. (as you confessed before) then with a lesser cō­passe (for it shall bee meete that you haue diuers sorts) draw a circle of that circuit abouteche Pole, setting the fixed foot of the compas in the Pole, and stretching the other soot vn­to 66 degrees & a half. After this looke whether these circles do cut lyke degrees in euery quarter of the Colures: and if it do, your woorke is righte, els it must be redressed. These circles maye well bee called Pole circles, or Polar cyrcles. Then take your greater compasse opened (as is before declared) to the wydenesse of a quarter of the Equinocti­all,The dra­wing of the zodiak and sette one foote of them in that poyncte where the Polare circle that is aboute the Northe pole, dooth crosse the tropyke Colure in that quarter, whyche goeth from that same Pole, to the. 270. degree of the Equinoctiall, and holdynge that foote steddye, with the other drawe a circle aboute the Globe.Proof. This circle will touche the twoo Tropikes in twoo of those places, where they crosse the Tropike Colures: and also it wyll crosse the Equino­ctiall in twoo pointes, that is, in hys very begynnynge, and in the ende of the 180. degree. Nowe to proue whether it be truely drawen or not, by an other meanes,An other proof. set one foote of that compasse (with whiche yow drew the Zodiake) in that pointe whiche is directly contrarye to the firste place, where you stayed hit: that is to faye, in the crossynge of the fouthe Polare circle, and that quarter of the tropike Co­lure, whiche goeth from the South pole to the 90. degree of [Page 42] the equinoctiall, and on that point proue whether the mo­uable foot of the compasse will exactly agree with the fore­sayd circle, whiche yf he doo, it is well drawen, els is there some erroure, which muste bee amended. This circle thus drawen, is the Ecliptike circle, whiche goeth by the myd­dle of the Sygnes and of the Zodiake. and these twoo poyntes wherein the fyxed foote of the compasse was stayed,The Poles of the zo­diake. are the Poles of the Zodiake. But considering that the Zodiake (as you hearde before) hath in it twelue degres of bredthe, that is, on eche syde of the Ecliptike lyne sixe, therefore open your compasse to 84. degrees only, that is sixe degrees lesse then a quarter of the Equinoctiall, and set one foote of it fixedly in the one Pole of the Zodiake, and with the other moueable foote drawe a circle, whiche wyll be a Parallele to the Ecliptike circle, distaunte from it in all partes by 6 degrees, and with the same compasse vnaltered, draw a lyke circle on the other Pole of the Zodiake, whiche shall bee a Parallele to the other twoo, and they three do make the full Zodiake in length and breadth.

I vnderstande all this verye well, but I muse what those Polare circles meane,The Polare circles, and their vse. of whiche I hearde no woord before in the firste treatise.

I dyd of purpose omytte them before, bicause they ar named of diuers men, as of Ioannes de Sacro Bosco and other later writers, for the circles Arctike and Antar­ctike, contrarye to Proclus, and all the greeke writers, and I pourposed (and so doo I still) to reserue the discussing of that repugnance, to the fourthe treatise, yet here was suche iuste occasion ministred to vse their helpe in fyndynge the poles of the Zodiake, by whiche poles they are described euery day, by the reuolution of the heauens, that I coulde not willyngly neglecte them: for although I myghte fynde the poles of the Zodiake without them, yet they bringe a proof of the woorke with them, as before I haue shewed, and also they enclose all suche starres as are within 23. de­grees [Page 43] and a halfe of the Pole, and are the lymites of the motion that the Poles of the Zodiake doo make about the poles of the worlde, as you shall better perceaue hereafter. And bycause their names shoulde not bee confounded with the circles, Arctike and Antarctike, I thinke it moste meete to cal them only Polare circles, or Pole circles, which name the other circles may not iustly chalenge, especially bycause they are not fixed (as the Pole circles are) but be chaungea­ble as the regions chaunge. which thing I will declare more largely hereafter, but nowe for the drawinge of the circles Arctike & Antarctike, that is (as I named them) the Northe circle, and the Southe circle,Circles ar­ctike and Antarctik. you muste learne the eleuation of the region for whiche the Globe is made, and according to it must you draw those circles, whiche thinge bicause as yet it is not easye for you to doo, I will in example of oure owne cuntrye shew their description, namely for the vniuer­sitye of Cambridge, whiche standeth in euen degrees of 52. Therfore recken from one of the Poles 52. degrees in anye Colure, and it will lyghte on 38. degrees (bicause the num­bres go backward) and there set one foote of your compas, extending the other foote to the next Pole, where you shall staye it, and with the other foote describe a circle fyrst about the one Pole, and then about the other: and those two cir­cles shall stand for our circles Arctike & Antarctike. And thus hath the Globe all those circles whiche were accomp­ted needfull vnto it, excepte the Horizonte and the Meri­diane circle, whiche are not so well placed in the Globe as without it, bicause they ought not to moue with the Globe.

Where shall they be made then?

That will I shewe you, as soone as I haue ended the Globe, whiche yet is not doone, for the Signes in the Zodiake are yet vndrawen. First therefore ye shall drawe by the Ecliptike line within a corne bredth of it,The diuisi­on of the zodiake. an other circle as you did by the Equinoctiall, it forceth not on whyche side, but let the Ecliptike line be more notable then it. Then [Page 44] consider that the Zodiake is all ready diuided into foure e­quall quarters by the two Colures, now it is meet to diuide euerye quarter into three equall partes, and so haue you twelue partes in the whole Zodiake, whiche stande for the twelue Signes, which shall be distinct by lynes drawen ouer thwarte all the breadth of the Zodiake.

Those are not easye to drawe, but errour may quickly be committed, in making them wyder in one place then in an other.

Therfore to auoyde that errour, thus shall you do. Open your compas equally with a quarter of the Zo­diake. then keepe one foote of it steddy in eche diuision, one after an other, and with the other drawe a portion of a cir­cle crosse ouerthwart all the breadth of the Zodiake, & thus shall you do it exactly,Proof. and in so doing, your compasse doth trye and examine the former diuision: for if at anye set­ting of your compasse it reache to shorte, or to far, and not iustly on the thyrde signe, then must you correct your fyrst diuisiō. When you haue drawen these twelue signes, thē must you diuide euery one of them fyrste into two parts equally, and eche of them againe into three euen partes, and lastlye, euery one of them into fiue iuste portions, and so haue you in euery Signe, thirtye partes or degrees.

This diuision is like the diuiding of the Equi­noctiall and the Colures, so that I maye conceaue the one by the other.

In deed they ar all thre lyke in their general diuisiō, but yet in placinge of their numbres, they differ eche from other, for the Equinoctiall had his numbres continuallye proceding from 1. to 360. The Colures, stay their numbres at euery quarter, neuer procedinge aboue 90. but the Zo­diake stayeth in a lesser numbre, for at euery signe, his num­bres chaunge: so that from the beginning of eche Signe to the ende of the same, you shall marke them from 10. to 10. thus: 10.20.30. and so lyke in all the Zodiake no numbre is [Page 45] greater then 30.

I perceaue that, sith you tolde me before, that euery Signe seuerally hath 30 degrees.

Those diuisions shall you marke with a little line drawen from the Ecliptike circle to that other which is dra­wen within a corne bredth of it: yet at euery tenne degrees it will do well to draw the line somwhat longer from the Ecli­ptike, that those degrees maye be the easier to see and to re­ken, and so maye you doo at euery fiue degrees, but some­what shorter then that other, and so shall you haue the de­grees more notablye distincte in sonder. Nowe resteth no more but to geue euery Signe his name, which you may do other by writinge it at lengthe, or els by settinge their Cha­racters and figures for their names, which I before haue set forthe vnto you in bothe formes.

That is easye inough to vnderstande, but how shall I knowe their places?

That is as easye also, if you marke the ordre of the circles. but for a full plainesse you maye beginne at the Tropike of Cancer, where the signe of Cancer doth begin, and in that quarter of the Zodiake, which is on your right hande, and descendeth toward the Equinoctiall, sette these three signes, Cancer, Leo, Virgo, and so procede forward as the signes succede in ordre: then will the seconde quarter haue Libra, Scorpius, and Sagittarius: and the third quar­ter, Capricornus, Aquarius and Pisces: and to make vp the fourth quarter, ther resteth Aries, Taurus and Gemini.

You name the seconde quarter of the Zodiake to be the fyrste, and so commeth it to passe, that you call the fyrste quaiter the fourthe, as I remembre youre former doctrine.

You maye perceaue, that I named them nowe not in their custumable ordre of quarters, but accordynge to the ordre of this woorke, els if you can discerne the place of Aries from the place of Libra, you may best begin with [Page 46]

Aries, & thē not only the signes, but y^e quarters wil keep their accustomed ordre, as here in a table it doth apear: wher I haue also annexed the quarters of the year for readines of remembrance, & for the better occasion to marke the motion of the son in eche of those quarters. And thus haue we ended the globe or sphere, with al y^e circles in it customably vsed, whose picture here you may se, as it will be drawen in flatte forme.

The makig of the Ho­rizonte.Now for the Horizōt & the Meridiā thus shal you do. Take 2. square bords of a quarter of an inch thick, & let y^e one be in bredth 3, inches, & the other one inch & a half more then y^e diameter of your globe, in y^e middle of the broder borde take a centre, & on y^t cētre make a circle, scarsly a corn bredth wider thē your globe is, which you shal thus find out. Open your cōpas as wide as ij. signs in y^e Zodiak, or 60. degres in y^e Equinoctial, [Page 47] any other of his greate circles, and that compasse wyll make a circle iust in bignesse with any great circle of your Globe, therfore make you the circle in the square borde, almoste a corne bredthe wyder then that circle of youre Globe. And without alterynge of the compasse, make the lyke circle on the myddle pointe of the narrower borde. Then haue you taken the iust measure for the inner part of your Horizont, and also of your Meridian.

I doubt not but I canne doo that with a lyttle labour by often triall where the myddle of the bord is. but is there no waye to fynde the place of the centre quickly?

Yes truly, and that maye you doo diuersly, but one redye way is this.To find the middle in any square.

Drawe with your ruler a right line from corner to corner, or if you lyst, make it onlye about the myddle of the bord, as you can ayme with your eye, but be sure that you drawe it longe ynough, then turne your ruler to the other two cor­ners, and make a lyne crosse that other, and where they doo crosse, there is the myddle of the borde, on whiche, as on a

cētre you may make your circles.The Path­way of Ge ometrye. This work might you easilye gather out of the 35 conclusion of the Pathway.

I see now cō­tinually more and more, that the Pathwaye ser­ueth to other vses, then I toke it.

It is a commō instrument to many arts, and infinite conclusions: and if you procede to farther knowledge of higher artes, without good exercise in it before, you do as a carpēter that goeth to woorke without his tooles. But nowe to proceede, [Page 48] When you haue drawen this circle on bothe those bordes, on the same centre make an other circle in eche bord, a corn bredth wider then that other: and after that an other some­what wider, as you may ayme two corne bredthes: and then the fourth wider then the thyrde by a quarter of an ynche: and yet againe one other a quarter of an ynche wyder then the fourth. and these fiue circles shall you make in bothe the bordes, and you shall diuide them bothe in one manner, af­ter this sorte.

Diuide the innermost circle saue one, into 4. quarters first, and after that, euerye quarter into three partes, and eche of those partes into 30. as you dyd before in dyuers cyrcles of the Globe. then set your ruler to the centre, and to euery di­uision,

and make a lyne from that second circle to the third: but at euery 10. degree you shall drawe the line longer, that [Page 49] is vnto the fifte circle, and at euery fift degree, you shall draw the lyne to the fowerth circle, so shall you both place your numbres best, and also recken them moste surely and most speedily in all vses of them.

All this I can do by the former examples, if I knewe how hyghe the numbres shall proceede. for in them I remembre ther was 3. varieties before, eche vnlike to other.

And in these shall be somwhat diuers from them all. for here shall be set double numbres, but yet the fyrsts placynge of the numbres shalbe lyke as it was in the Co­lures, I meane in eche quarter 90. and those numbres shalbe set in the space, betweene the thyrde circle and the fourthe. Then shall you set the lyke numbres betweene the fourthe circle and the fyft, but not in lyke ordre, for their ordre shal be contrary to the other, so that where 10. stoode in the fyrst ordre, & then 20, and so increasyng to 90. in this 2. ordre you shall set 90, and thē 80, & so decrease vnto 10. as here in example you may se, wher I haue drawen y^e Meridian lyne suffici­ently diuided, for y^e vse of y^e sphere: but thē y^e horizont must haue other things drawē in it, as in this figure folowing you may se. for in y^e inner part it is deuided like vnto y^e meridian, but then without those diuisions it hath a certain smal space all black, left for a partition, without which ther are drawē 3. other circles, eche one a lyttle wider then other, & the widest is vttermost, and y^t last circle is as large as the borde will permit, so that y^e whole bredth of y^e Horizont is an inch & a half, for bicause the whole bord was 3. inches wider thē the globe. And y^e Meridian shalbe but 3. quarters of an inche brode, seing his bord was but 1. inch & an half wider thē y^e globe. Now for the diuision of the vtter part of the Horizont, you shall dyuide the vttermoste of the three circles into eyghte partes only: The seconde circle shalbe diuided into 16. parts And the third or innermost of those 3. shall be parted into 32. partes, whiche do betoken the points of the Shypmans compas. or the 32. winds notable in sailyng, as some mē lyst [Page 50]

to call them. If your Horizonte bee large inoughe to re­ceaue their names, you shall write them at lengthe, els maye you write letters for theym, as youre owne phantasye ly­keth.

Their names are these folowinge, agreable to those places, and letters, whiche I haue drawen in the Horizont.

The foote of the Ho­rizonte.And thus nowe is the horizonte fully drawen. That Hori­zonte muste you set vpon a foote, that it may stande lyke a rounde table: and that foote muste be made of twoo halfe circles of woode, somewhat thycker then the Horizonte, but of the same compasse in the innermoste parte, and they must be ioyned so, that the one maye crosse the other, wyth ryghte corners, and them selues bee fastened on a stronge foote, that may beare all the whole frame, wyth the Globe. The ioyninge of them vnto the Horizont is diuersly to be ymagined, for if their headdes be flat, then muste you haue nailes or els pinnes, that must perse the Horizont and enter into their heddes, otherwaies there maye be left certaine te­nauntes on their heddes, and then must you make lyke morteyses agreable to them, in the Horizonte, to receaue those tenauntes. & so may there be ymagined diuers other formes, whiche I leaue to your owne deuise.

If I myght see their forme I shoulde be muche easyed in framynge it.

Here is the form, with their sockets, & one namely for the Meridiane, in that arme also that goeth from East to weste. Howe be it, it shall be best, to fasten those armes vnder the Horizonte in the Southe easte, Southe weste, Northe easte, and Northe weste, and so shall the Meri­diane synke beste into the Horizonte, with an easye socket in the meetinge of those armes, so that the iuste halfe of the Meridiane onlye maye appeare aboue the oouer edge of the Horizonte: in whyche thynge practise shall instructe you farther. As for the foote, make it as you thinke beste. But nowe muste you cutte out of bothe, the Meridiane and the Horizonte all that is within the inner­moste [Page 53] circle, and so muste you pare awaye all that is with­out the vttermoste circle, to make them bothe lyke iuste circles. Also you muste make in the Horizonte twoo soc­kets, one by the Southe lyne, and the other by the Northe lyne, so that the one syde of those sockets whiche is toward the easte, shall touche the Southe and Northe lynes, and the other side shall go westwarde from bothe those lynes, as muche as the thicknes of the Meridian is: and the length of eche of those sockettes shall bee agreable to the iuste breadthe of the Meridiane, so that the Meridiane maye entre iustlye into those socketts, and turne in them without stressynge.

This trobleth me somwhat, bi­cause the sockettes be not iustelye one agaynste the other, but bothe stande towarde the Weste halfe of the Hori­zonte.

It wolde trou­ble you worse to re­membre that the Globe muste be fastened to the Meridiane on the two poles, & both they placed within the Horizonte.

That is straunge in deade, for so shold the globe beare more toward the west, then toward the easte: and so all were misframed.

To auoide all that, you shall make twoo small [Page 34] clampes of thinne brasse plate,The hāging of the glob in the Me­ridiane. and bow them so in the mid­dle, that when they are tacked to the side of the Meridiane in twoo contrarye pointes, iuste ouer that line where 90. is set, thei may receaue in their bought the poles of the globe. I meane here by the poles two shorte pinnes, which shall go through those clampes of brasse, and be fastened or driuen into the twoo Poles of the Globe, excepte you will take the paine to pearse a hole through the globe, from one Pole to the other, for so maye you make an axetree to run tho­roughe bothe the clampes and the whole Globe, whiche is all to one effecte. And by this meanes shall the Globe not onlye hange in the iuste middle of the Horizonte, but also the one side of the Meridian (whiche hathe the diuisions in it) shall pointe exactly the southe and north partes of your Globe, whiche will be moste exactly seene, if you consyder the thicknes of your axetree, and frame youre clampes so, that the one halfe of the thicknes of the axetree, may be let into the syde of the Meridian.

I thynke I doo conceaue the true meanynge of your woordes, howe be it to bee oute of all doubte, I wyll be bolde to see your Globe, at some conuenient tyme.

So shall you doo well, for manye thynges in the makinge, and in the vse also of instrumentes, are better per­ceaued by a lyttle sighte, then by many woordes▪ and thus haue I ended the making of this Sphere.

Yet is this sphere vnlyke to that, whiche is cō­monly vsed, by the name of the Sphere, and is made all to­gither of hoopes.

You shall vnderstand that this is the true sphere, whiche I haue described, and that other (which you meane) ought rather to be called an Armylle or Ringe sphere, then absolutely a sphere,The Ar­mylle or Ringe sphere. for it is but a part of this other Sphere: I meane, that it doth contayne only the circles of the sphere and not the substaunce of it. And therfore do the many men cal that a Persed sphere, and is named in Latin Sphaera per­tusa, [Page 55] where as they call the other sphere, a Sound or Massye Sphere, that is in latine, Sphaera solida▪ but seynge that it is not only commonly receaued by the name of the Sphere, but the vse of it is very apte in teaching, and it is more easy to bee made in slyghte forme for yong learners then is the soonde sphere, and for other considerations, whiche nowe I omyt, I wyll also describe the composition of that Armylle sphere.The makīg of the Ring sphere. Fyrst you shall make of woode or of brasse (as you lyste to bestow the coste) four hoopes of one bignes in compas, the one of them beyng three times so broade as any of the other, as your eye may ayme. Then diuide eche of those circles into 360. partes, one of them accordynge as you did diuide the Equinoctiall in the former sphere,The equi­noctiall. ij. Colures. and the other two lyke vnto the two Colures, and the fourthe which must be the brodest of them, you shall diuide, as you learned to diuide the Zodiake in the other sphere. And when they are thus diuided,The zodi­ake. you shall call them by the names of those cir­cles whose diuision they folowe, wherefore if the Zodiake haue more breadth then twelue degrees are in lengthe, you shall abate the ouerplus, allowing it but 6. degrees in bredth on eche syde of the Ecliptike line, whiche as you remembre before, did run by the mydle of the Zodiake.

Then I perceaue I muste make in this Zodiake an Ecliptike line, and all the signes with their diuisions, as I learned in the other Zodiake.

You shall make them as like as you can deuise. Then shall you ioyne the two Colures so togither, that the one of them may crosse the other, (as thei do in the Globe) with righte and equall corners, obseruing well that the pla­ces of their crossyng be in the iuste pointes where 90. is set, in eche of them: and those places muste be called the Poles of the sphere. Then put on them bothe crossewaies (like a girdle) the Equinoctiall circle (so that it do crosse them ex­actly with his middle,The Poles. in those pointes where the numbre of eche quarter dooth beginne, and that the beginning of the [Page 56] Equinoctiall, in numbre be againste the iuste middle of one of them, that is, of it that standeth for the equinoctiall co­lure, and then shall the 180. degree of the same Equinoctiall stand iustly on the middle of the same Colure, in the contrarye pointe: and the other Colure whiche is the Tropike Colure, shalbe ioyned with the 90. degree, & the 270. of the equi­noctial,The .ij. tro­pikes. in ij. cōtrary points. Then shal the 2. tropike circles be set on y^e Colures equidistantly to the equinoctial, so that thei be fastened on the 23. degree & a half from y^e Equinoctial, wherby you may easilye conceaue, that they muste be some­what lesser then the equinoctiall, that they may ioyne close­ly to the foure Colures. Then muste you haue twoo other circles of one bygnesse, that may ioyne iustly with the Co­lures, 52. degrees from the Equinoctiall, on eche part equal­lye distaunte: and those muste be called the Arctike, and Antarctike circles,The Arctik and Antar­ctik circles or the South circle, & the Northe circle. Beside these you shall make two other lesser circles of equall bygnes, whiche shall be set on the Colures also equidistante frō the other paralleles: and they must be fastened with their middle on the 66. degre & a half frō the equinoctial on both sides, that is 23. degrees & a half from eche pole, and therfore I thinke meetest to call these circles peculiarly, Pole circles. This beinge doone,The Pole circles. you haue 2. Colures and 7. Paralleles fixed on them. Nowe muste you sette the Zodiake a slope waies crosse the Equinoctiall, so that his myddle lyne, na­med the Ecliptyke lyne, maye touche the myddle of eche Tropyke, and that maye you trye by the vtter edges of the breadthe of the Zodiake,The zodi­ake. for the one muste touche the 29. degree and an halfe, and the other the 17. degree and an halfe from the Equinoctiall. And thus is this sphere plaine­lye made, whose picture I haue here sette, as it will bee dra­wen in a flatte forme. Then if you make twoo small holes thoroughe bothe the Colures,The Axtre The Meri­diane and Horizonte. in the places of theyr crossynge, where the Poles of this Sphere are, and putte a small axe tree thoroughe theym, you maye thereby [Page 57] ioyne this Sphere to his Meridiane fyrste, and then place it in the Horizonte, as you didde place the Globe: for those twoo cir­cles, are like in both these Spheres.The Pro­portion of the circles in a sphere.

I vnderstand al thinges here in wel inough as I thinke, saue y ^t I doubte somwhat of the quantitye of the parallele circles. for although I know by triall I maye att lengthe make them meete, yet woulde I gladlye knowe their measure be­fore hande, if I myght, for so shall I be sure to woorke moste certenly.

Your desire is good. and all be it that the writers of the Sphere haue omitted it, as they haue doone manye thinges els, yet will I geue you a rate of proportion drawen out of the tables of Cordes and Arkes, called commonly in latine Tabulae Sinuum.

Fyrste you vnderstand, that the Equinoctiall, the Zo­diake and the two Colures must be of one compasse, that is of one bygnes, althoughe not of one bredthe, for the Zo­diake must be in bredthe twelue degrees, and the other cir­cles as small as they maye be, and beare any stresse, for the smaller they be, the better they are, and moste apte for the vse of the sphere. The other syxe paralleles wold be made as smalle as they maye beare conuenientlye, and in lengthe they muste haue three dyuers rates, whyche I wyll sette forthe, bothe in measure, and also in numbre, to the intent that you may alter the measure to what bignes that you list, by the helpe of the numbre.

And loe here is there formes.

1. The Equinoctiall with his diuision.

2. The Colures both of one forme.

3. The Zodiake with the 12. signes, and his bredth of 12. degrees.

4. The length of the twoo Tropikes.

5. The proportion of the Arctike and Antarctike circles.

6. The proportiō in length of the two Polare circles.

Here you see sixe seuerall formes.

The firste representeth the iuste lengthe of that plate or hoope, that shalbe the Equinoctial, and in it is the diuisions sett forth as they ought to succede in ordre, with their num­bres agreeablye.

The second is the forme, that serueth for the two Colures with their numbres and diuisions, as thei should be set.

The thirde is the draughte of the Zodiake with his iuste bredth of sixe degrees, and the twelue Signes sett forth with their degrees ordrely. And these three circles be all of one lengthe.

The fourth circle dothe represent the due lengthe of the two Tropikes, whiche must be shorter then the Equinocti­all by 30 degrees, for it is equall to 330 partes of the same: so that the lengthe of the Tropike dothe beare the same pro­portion to the Equinoctiall, as 11 doth to 12.

The fyfte plate, resembleth the measure of the circles Ar­ctike and Antarctike, and is in lengthe equall with 222. de­grees of the Equinoctiall, which proportion is as 37. to 60.

The sixte plate setteth forth the iuste measure of the twoo Pole circles, whiche is equall to 144. degrees of the Equi­noctiall, and so it beareth to him the same proportion that 2. dothe beare to 5. and eche of those circles Paralleles are diuided lyke vnto the Equinoctiall, into their 360. degrees.

This is so plainly sett forthe, and so certenlye, that I see no doubtfulnes nowe in the whole worke, for the makinge of it: for these plates are so made, as if they were of metalle, and shoulde haue bothe the endes soudred togi­ther. so that if any man wil make them of woodden hoopes, he must allow so muche more in the length of eche of them, as will suffise for to bynde them faste in compassed forme. But these hoopes of this lengthe will make but a very small Sphere, yet by the same forme of the numbres, and their proportion, I may make a sphere of what bignes that I will.

So may you do certenly. and if you will haue a [Page 60] Sphere twise so much in cōpas as these hoopes wold make, or thrise, or 4. tymes, and so forth, this measure also may serue you, taking for eche circle so often tymes the length of the lyke here in this patron, as you wil haue your Sphere greater then this in numbre of tymes.

And so I perceaue, if I woulde make an other three tymes and an halfe so bigge as this, I ought to take the measure of eche circle thre times and an halfe. and so for all other proportions.

Truthe it is, saue that you must augment the breadth of the Zodiake only in like numbre of times: But as for the other circles, they are brod inoughe if they be not to weake, for the smaller they be, the better is the Sphere, syth their breadth dothe serue only for strength, and for to receaue the diuisions as here you see.

And thus haue I described vnto you both sorts of Spheres, that is the Globe or Massye sphere, and the Persed sphere or Armille. One other forme of Sphere there is, whiche excel­leth both these formes, and is wonderful apt for the teaching and expressinge of the Theorikes of Planetes, therfore I wyll reserue it to that place.

Here needeth no repetition, bycause all standeth in woorkynge of the former lessons before re­peted, and therfore this seconde treatise shall ende here.

NOW YOV LOOKE TO HEARE SOMwhat of the vse of the Sphere, as you shall do anon: And for an induction thervnto, you must diligentlye knowe the plages of the world,The plages of the worlde. amongest whiche there are four principall, that is, the Easte, the Weste, the Northe and the Southe: and betwene these are there other diuers, which are sufficiently set forth in the Horizont of the Globe, as muche as shall at this time bee needefull.

You must knowe also,The Paral­leles in the earthe. that euery one of the Paralleles in the heauen hath a lyke circle in the earthe proportionably drawen, and answeringe to those that are in heauen, in iuste rate of distance. So is ther fyrst an equinoctiall in the earthe exactlye drawen vnder that Equinoctiall in heauen,The earth­ly equino­ctiall. and it diuideth the whole earthe into twoo equall partes, betwene the southe and the northe, so that it poynteth precisely the myddle of the earthe, in that respecte:The middle of the earth and all the partes of the earthe from that earthly Equinoctiall toward the north, is called the Northe parte of the earthe: and of the world lykewayes all that is beyond that cyrcle towardes the south,The northe part of the earthe. The southe parts of the earthe. is called the Southe partes of the earthe.

Yet wee doo call that parte only Northe, that is northe from vs: and that wee call Southe, that is southe from vs.

You muste consider that there is two formes of speakinge in suche talke, the one vulgare, and commonly vsed, as well of the vnlearned as of the learned, and that maketh not the comparison to the whole world, which few men [Page 62] doth know, but it regardeth principally their owne cuntry, which they do best know. The other talk is general in forme of speakinge, bycause it hathe respecte to the whole earthe, and yet is it not generall in knowledge, for fewe men canne aptlye skyll of it: so that bothe are true in their due vse, but the one is lesse knowen then the other.

So I perceaue then, that although in common talke we do call Spaine southe, and likewaies other cuntries, yet is not that true in comparison to the partes of the whole worlde, but in comparison to vs, for our common talke hath chiefe relation in suche thinges to our owne cun­trye. But I pray you then, where is the myddle of the earthe, from whiche we must make our accompt, and vnto whiche we muste haue regarde in all suche generall talke?

That wyll I tell you anone, but firste we muste ende that matter that we beganne withall, touchynge the Paralleles on the earthe, whereof I haue named yet onlye

the Equinoctial, but nowe must you ima­gin other 2. parallels next vnto it, the one toward the Southe, & the other towarde y^e north,The Tro­pikes on the earthe. which maye answer to the 2. Tropiks. And for a general knowledge fyrst, vnderstand this, y^t al nations ouer whose heds y^e son doth run directly, whē he is in y^e hyest point toward y^e north y^t is in y^e begīning of Cācer, wher he describeth y^e tropik of Cancer in the skie, al those people I [Page 63] saye dwell iust in the course of the like tropike in earth: And contrary waies, all those people ouer whose heddes the Son passeth directly, when he is in the Winter tropike, they dwell in the course of that south Tropike in earthe, and haue the sonne right ouer their heddes that daye that he entreth into the firste degree of Capricorne.

By these examples I can imagine the southe and north circles in y^e earth to be vnder the Antarctike and Ar­ctike circles in heauen,The other Parallele. and so two Polare circles in earthe vnder the two Pole circles in heauen. Then are there seuen Paralleles in earthe, answering to seuen other in the skye.

That is sufficient. howbeit for this time I will omit the circles Arctike & Antarctike, bicause in mine opinion, they make no Zone in earth, though all the Grekes in appe­rance do say the contrary, but I will bringe inuincible reasō for my purpose, when we come to the scanning of repugnāt sentences, especially whē I do disagree with the grekes, which are the fathers of witte. but in this pointe of the fiue Zones, I like much better our own cuntry man Iohn de Sacro bosco as I will now only affirme,Ioan. de S. Bosco zonarū restaurator & in the fourth treatise wil proue it substantially. Therefore to continew our matter as we be­gan: there are made by these v. paralleles, v. large roomes in the heauen, and other v. in the earthe,The fyue zones. agreable to them in heauen, whiche spaces are called Zones.

Example of the zones.By your fauour, ther are sixe Zones, if euery space betwene the Paralleles be accompted for one zone, and that doth not only the accompt of thē by memorye declare vnto me, but also the sighte of them in this figure, which is com­monly named the figure of the Zones.

Nother doth the accompte deceaue you, nother yet the sight of the figure, but wante of knowledge of their naturall qualities, whiche therefore I will tell you by and by, though these parallele circles do sufficiently distincte them, as their notable boundes,The quali­ties of the fiue zones. yet by the qualities bee they di­stincte also. for as reason doth leade you, all the space be­twene [Page 64] the 2. Tro­pikes,

must needes bee esteemed verye hotte, bycause the Sonne runneth al­waies betwene thē, so that in the myd­dle betwene the two Tropiks is y^e equi­noctial line, frō the which the Son is neuer fully 24. degres so must it seem to be as hotte there in the myddle of winter, as it is in Spaine in the myddle of Sommer, and for this cause all the olde Cosmographers dydde thynke that that countrye myghte not be inhabited for heate: and therefore called all that space betweene the twoo Tropykes, the Bur­nynge Zone,The Bur­ning zone. called in latine Zona torrida. And of eche syde of it, they noted twoo Zones, one vnder eche Pole, whiche they called the Frosen zones, (and are named in la­tine, Zonae Frigidae) where for extreme could,The Frosen zones. they thought that no man might dwell. and betweene those Frosen zones, & the Burning zone, they appointed two Temperat zones, (called Zonae temperatae of latine men) which were parta­kers of the heat on the one side,The Temperate zones and of the cold on the other side, so that of bothe, there was made a temperate mixture. Now se you that betwene the Equinoctiall and the one tro­pike, there is no other qualitie, then is betwene the same equinoctiall and the other tropike, wherfore all men (except on­ly Polybius) did accompt the space betwene the Tropikes but as one Zone: so that the Equinoctiall is the bounde of no Zone, but passeth by the middle of the Burning zone.

Nowe I see (as I haue had at other tymes often occasion) y^t we learn many things when we be childrē, which we vnderstande not all when we bee menne, for by this talke [Page 65] I remember that both in Ouide & Vergile I learned y^e distin­ction of those 5. Zones, but what was to be vnderstande by them, I neuer knowe till now. And nowe I see reason that be­twene the 2. Tropikes, all may well be accompted the Bur­ninge Zone, where no man can dwell, as bothe my authors affirme.

They had spoken more modestly, yf they had said that ther had been painful dwelling for heat. & likwaies of the cold Zones, y^t ther is hard dwelling for cold: but of this wil I more exactly reasō in an other place, and for this time (as y^e truth by experience is knowen) I suppose that all y^e 5. Zones haue their inhabitants, though not so plentifully as the two Temperat zones now haue, especially this tēperat zone that we dwell in. Who is it that hathe not hearde of the isles of Molucca, and of Samatra, where the Portingales gette the greate plentye of riche drugges and fine spices? and all that haue been there, confesse that those places ar right vnder the Equinoctiall line: and Calecut is but little from it, for it is

more thē 19. degres beyond the Tropike of Cācer toward y^e south so y^t it is within 5. de­grees of the very equinoctial line. Now therfore I thinke it moste apt place for my pur­pose to begin at these cūtries, ouer whose hed the equinoctiall dothe rightly passe, so y^t they muste nedes see both y^e Poles in their Hori­zonte.

That doth reasonably folow, bicause half [Page 66] the heauen iustly appeareth aboue the Horizont, and the o­ther halfe is vnder the Horizont. And also I perceaue that if I set the sphere so that the Equinoctiall stand full vprighte, then will bothe the Poles be in the very Horizonte. as this position of the Sphere doth shewe.

You consider it righte. And bicause the Equino­ctiall doth crosse the Horizont with right angles (for all 4. angles are equall) therfore is this placing of the sphere cal­led a Righte sphere:A ryghte Sphere. so that all other nations, whiche haue the one Pole aboue their Horizonte, must needes haue the other Pole vnder their Horizonte, and the Equinoctiall declinith from the point right ouer their heddes, that waye as the hidden Pole is, whether it be toward the South, or els toward the Northe.

The vse of the materiall sphere.All this seemeth easye to me, as longe as I be­holde this materiall sphere? but when I doo not conferre it wyth your woordes, then your saynges appeare the more doubtefull.

For that cause did I teache you the making of it, before I instructed you in the vse of it, knowing how greate a helpe the sighte of the eye doth minister to the righte and speedye vnderstandyng of that, whiche the eare doth heare. But againe to our matter: in all places where the equinoctial doth decline from the pointe ouer the heddes of any inha­bitauntes (whiche pointe is commonly called the Zenith) there the Equinoctiall maketh vnequall corners with the Horizont,The Zenith and therfore is that called a Bowyng sphere,A bowing Sphere. or a Leanynge sphere; bycause the Equinoctiall boweth or lea­neth toward one syde of the Horizont, more then towarde the other side.

I haue hearde it called a Crooked sphere also.

That name is vnapte for this arte, for there can bee no crooked corner betweene the Equinoctiall and the Horizonte, which myght make that name meet for the matter: and (as I haue sayde) the Sphere taketh those seuerall [Page 67] names of his diuers position,

and accordyng to the corners that the equinoctial doth make with the Horizonte.

And this may you cō­sider herein, that there is no Zone but one that canne haue a right Sphere: and to speake precisely, but one tracte in that zone, whiche is the very middle of the Burninge zone, righte vnder the Equinoctiall where as there be innu­merable places y^t haue Leaninge spheres, whi­che you may call Oblique spheres or Declininge spheres, if you delite more in latinelyke names then englishe.

So I perceaue that bothe we and all other nati­ons whiche dwell not righte vnder the Equinoctiall lyne, muste be named to haue a Leaning sphere. And this I con­sider resonably, that in some cuntries the sphere dothe leane and bowe more then it dothe in other, whiche difference I wolde gladly vnderstande.

The diuersitye in leaning of any sphere, is agre­able to the eleuation of the Pole in euerye cuntrye, so that where the Pole is hyghest aboue the Horizonte, there the sphere leaneth most: and where the Pole is lower and nearer to the grounde, there the sphere leaneth lesser.

The height of the PoleHowe shall I iudge truly the height of the Pole?

That true and exacte iudgement will I not treate of as now, to auoide interruption in teaching: it shall be suf­ficient for this place to shewe you a plaine and easye forme, [Page 68] with the vse of an instrument that may helpe you sumwhat in markinge the height of the Sonne and Moone and anye other starres that you lyste. and the manner of it is thus.

You shall take a Quadrāte

(whose composition I haue taught amōgst other instruments in the Gate of knowledge, but this which you se here, is the forme of the moste playnest sorte) and by the twoo syghtes of it, you shall marke the height of the Northe starre com­monly called the Pole, and when you se it through both y^e sights, thē mark what degree the lyne of the plōmet doth touch in the margent, and, that may you call Latitude of that region, or the heighte of the Pole, for this tyme and place where no precisenes is requi­red. for nowe it is sufficiente for you to vnderstande ge­nerallye, that there are suche diuersyties of eleuation of the Pole in diuers countries: and thereby maye you vn­derstande, that all Spheres bee not alyke in theyr posi­tion. As for example. In the southe partes of Englande aboute Sowthehampton,Southehampton. the Pole is not fullye 51. degrees hyghe, and in the isles of Orkenaye, beyonde Scotlande, the Pole is aboue 62. degrees highe: this maye easilye bee tryed by them that list to trauayle, but if you lyste to go no farther then Yorke,Yorke. you shall fynde the eleuation aboue 54. degrees, and so at Edynburghe shall you fynde the ele­uation aboute 57. degrees.Edynburgh And thus within your owne cuntrye maye you vnderstande a greate diuersitye, wherby you may coniecture the diuersities that bee in other partes of the worlde.

This is so appearaunte to them that will tra­uel any thing for knowledges sake, that they cānot pretend [Page 60] any ignoraunce, but wilfull ignorance: but herein I fynde one doubte, that maketh me to muse,The alteration of the Horizonte for in trauelyng thus from one place to an other, whereby the Pole is diuerslye chaunged in his eleuation, I can not thinke that the Pole it selfe dothe chaunge his place, but that rather the Horizont doth alter, from which we muste take the measure of height of the Pole.

You say well, for in deed there is no suche motion in heauen, that maye make the Pole so notably to chaunge his place: but as we doo chaunge our standinge, so dooth there appear a newe Horizonte, whiche causeth the Pole to seeme higher. if we go towarde the northe, for then wee see more of the skye (that waies) aboue our Horizont, then we did see before: but if we go toward the South, then will the Pole seeme lower and lower, still as we go Southward: not bycause the Pole chaungeth, but our Horizont chaungeth: for nowe wee see more of the skye towarde the Southe, and lesse towarde the Northe: but yet generally as much as wee leefe in the one parte, so muche wee wynne in the other coaste, so that euermore we may see halfe the skye.Whether the Hori­zonte doo moue or not.

Then this is my doubte, how I shal vnderstand your former woordes: for I remembre you sayd that the Horizont was a circle immouable, and did not turne as the circles in heauen do: & now you haue plainly declared that the Horizonte dothe chaunge, whiche can not be without mo­uinge of it.

You haue answered your owne question, if you marke it well: for the Horizonte moueth not as the circles in heauen do moue: that is to say, it goeth not round about the earth by a daily course, but it standeth steddye whyle the heauen moueth, so that if you neuer chaunge your place, your Horizont will neuer moue. And to speake more exa­ctly: the Horizont moueth not, thoughe you moue neuer so farre: but rather should we saye, that you are come into an other Horizonte, when you are come into an other [Page 70] cuntrye.

It muste needes appeare so, nowe that I do consider the matter more earnestly: for when I am at London, I see the same Horizonte that all other men there do see: then if I go to Yorke, I see the Horizont of Yorke, and not of London, so that the Horizont of London remaineth as it was, and so doth the Horizont of Yorke, whether I tarry or go. And thus I perceaue great alteration in the Horizonts betwene southe and northe, wherby the pole is diuersly alte­red in height aboue the Horizont. What if I go eastward or westward, shall I not fynde the lyke alteration?

It must needes appeare yes. for the same reason that causeth you to chaunge your Horizont betwene south and north, the same will cause it to chaunge betwene east and weste. And for declaration thereof, answere me to this que­stion: Do you think that there is any suche cuntry farre east from vs,Example of Calecut. as the Portingales reporte Calecut to be?

It were as muche folly to make a doubte of it, as it were to make a doubte of Babylon, or Hierusalem.

And do you thinke that the sonne doth rise to vs and to them at one tyme?

It can not be. for this muche I maye gether by that I haue learned already, that the rising of the sonne and of all other starres, is the apearing of them aboue the Horizonte, so that they rise to vs, when they beginne to appeare aboue our Horizont: and they rise to them in Calecut, whē they appeare aboue their Horizonte. And further I gether now by your briefe admonition of the chaunge of the Ho­rizontes, that as betwene southe & northe in our owne cun­try, we maye perceaue notable diuersitie, so maye wee consy­der y^e same much more in so greate a distaunce, as Calecut is noted to be from vs, which I haue heard to be named aboue 15000. myles, and that is farre greater (yea 20. tymes) then all the lengthe of Englande and Scotlande togither. where­fore I gather that the diuersities of the Horizontes must be [Page 71] twenty times so muche, as was betwene Southhampton and the northe parte of England.

The distaunce is not so muche, nor the difference so great, but by meanes that the Portingales do saile a mer­uailous compasse in goynge thether, they accompte the di­staunce by that compassed course, whiche is farre from oure talke now, for we must euer take right distaunce by a straight line, as often as we do speake of any suche matter. how be it for examples sake, suppose it to be. 6000. miles east from vs,The diuer­sities of the day in dy­uers Regi­ons. it seemeth to be more then a quarter of the whole compasse of all the earthe, (as I will proue it in the nexte treatise) and therfore must the Sonne at the leaste rise 6. houres to them soner then it dothe to vs. do you perceaue that?

The Son (as all men knoweth) doth compasse all the earthe in 24. houres, then muste it compas halfe the earthe in 12. houres, and a quarter of the earthe in 6. ho­wers. this is as plaine as can be: & thē it must needes folow, that if they bee a quarter of the earthe more to­ward the east then we, they must see the Son 6. houres sooner then wee.

And like­waies they that dwell farther easte then thei, as the inhabitantes of Molucca doo, must needes see the sonne before them: and [Page 72] those that dwell more westerly then they do, as at Hierusa­lem, or at Constantinople, must haue the daye springe later then they that be at Calecut. And thus you maye consider, that the Horizontes doo chaunge as well betweene east and weste, as it dothe betwene southe and northe: As this figure sheweth for London and Calecut.

That is plaine. for if all those places had one Horizonte, then should the sonne rise to them all at ones.

And as their morninges do differ, so must their noonetyde differ also.

No man that hathe reason can denye that.

Then muste their Meridian circles differ in lyke sorte, seeynge they be the limites of the nonetide.

So I perceaue that betweene easte and weste, the Meridianes do chaunge, as well as the Horizontes: and hereby I vnderstande, that when it is sonne risinge at Cale­cut, it is not day with vs, by 6. houres: and when it is noone with them, it is 6. of clocke in the mornynge with vs. and so of all other houres, whiche all appeareth by the for­mer figure.houres, whiche all appeareth by the for­mer figure.

This standeth for the declaration of diuersities of dayes in diuers regions: but yet you haue not heard what causeth the diuersities of dayes in one region.

Yes for soothe. I remembre that you reproued me for saying that the longe daies caused the Sonne to shine longe: and you tourned that sentence, affirminge, that the longe shinynge of the sonne dothe make the daies long, and the shorte shinynge of the sonne, doth make shorte dayes.

And are you satisfied with that reason?

I thinke it reason good ynoughe.

The reason is good, but not inough, syth farther reason is to be giuen. What maketh the son to shyne longe? can you tell?

By your helpe I truste to know it.

Set your Sphere before you, and first turn it so that [Page 73] bothe the Poles may

touch the Horizōt, which is the situation of the right Sphere. Then do you se y^t the horizōt doth cut not only the equinoctiall circle in 2. equall hal­ues, but lykewayes doth it cut bothe the tropikes, equally in­to 2. euen partes, so that there is as much of eche of them a­boue grounde, as there is beneth the Horizonte: and con­trarye waies. Wherfore it muste needes appeare, that the son when he runneth in anye of those three circles, is lyke tyme aboue the Horizont, as he is vnder it, so must the daies and the nyghts be equall, not only when the son is in the equinoctiall circle, but also when he is in any of the both tropykes: but this equalitye of dayes and nyghtes, when the sonne is in any tropike, is priuately appropried to the ryght sphere: for in all other varieties of the Bowinge spheres, then is the greateste difference in all the yeare, betweene the day and the nyghte, when the sonne is in any of the tropikes. as for example: Set the sphere to what eleuation that you lyst. that is to saye: Raise the Pole as many degrees aboue the Hori­zonte as you will.

I haue sette it nowe (as heere you see) to the eleuation of 52. degrees, whiche you saye is the eleuation at Cambridge.

And nowe maye you see that the Equinoctiall onlye is equallye dyuided by the Horizonte, and that the twoo Tropikes are verye vnequallye diuyded, so that the tropike of Cancer hath almost thre quarters aboue the Ho­rizonte, [Page 74] and litle more

then a quarter vnder the Horizont, wher cō­trarye wayes the Tro­pyke of Capricorne, hath almost thre quar­ters vnder the ground, and litle more then one quarter aboue the Ho­rizont: wherof it must nedes folow, that when the sonne is in the Sommer Tropyke, he is al­moste thre quarters of the Naturall daye aboue grounde, and lyttle more then one quarter of the same daye vnder grounde.

I knowe your mynde very well, and I doo ga­ther thereby, that when the daye is at the longest, it is al­most is. howers daye, and but lytte more then syx howers nyghte. And contrarye waies in the shortest of winter, the daye is lyttle more then sixe howers longe, and the nyghte almoste is. howers. And farther I heare you call the whole space of 24.A Naturall Daye. howers a Naturall daye: But I know not yet the reason of that name.

By that name of addition, the whole daye of 24. howers is distincte from the Artificiall daye, which is from sonne rysinge to sonne settinge:An Artifi­ciall Daye. and that Artificiall daye is moste commonlye vnderstande, when men speake of the daye. therfore for a difference it is good to vse suche an ad­dition. But nowe for the better practise, set your globe to some other eleuation.

I trow I haue set the pole highe ynoughe.

Let it stande. What is the numbre of the ele­uation?

I do see betwene the Pole and the Horizont in y^e [Page 75]

Meridian dyuers num­bres, but I take that numbre onli, which touchith the horizont, and I take that also of the twoo or­ders of numbres, which descendeth from y^e Pole, and that is here now 71.

That is the latitude or eleuation of the Pole at Wardhouse, where our newe vente­terers into Moscouia do touch in theyr viage: but now mark the varietie of the tropiks to the Horizont: The Tropike of Cancer is (as you see) more then foure de­grees aboue the Horizont cleare, so that the whole 2. signes of Gemini and Cancer, with 5. degrees of Taurus, and as muche of Leo, doth neuer sette vnder the Horizont.

Then while the sonne is goyng through those signes, from the 25. degree of Taurus, to the 6. degree of Leo, it is continuall daye, bicause the sonne doth not set vn­der their Horizont. but I pray you how long tyme is that?

It is from the 7. day of May vntill the 19. daye of Iuly;The lōgest Daye at Wardhous is 73. diaes continuall. so that it is continuall day with them by the space of 73 of our dayes, whiche is almost two monethes and an halfe.

This is meruailous straunge to me.

Yet shall you hear more strang matter then that: Sette your Sphere so, that the Equinoctiall maye be iustlye in the Horizont, and the north Pole righte vp in the place of the Zenith.

That haue I doone, as here you maye see.

Nowe marke how muche of the Zodiake dothe neuer go vnder that Horizont.

Howe shall I perceaue that?

Turne the Sphere rounde, as it shulde moue naturally on his owne poles, but sturre not the Hori­zonte.

Hereby I perceaue that 6. signes, Aries, Taurus, Gemi­ni, Cācer, Leo, Virgo, doo neuer sette vnder the Horizont, but continewe alwayes aboue it.

Then while the sonne is in those sixe signes, he can not bee out of theyr syghte, that dwell within that Horizonte.

It is truthe, yf any body doo dwell directly vn­der the Pole.

It is not now my purpose, to prooue what par­tes of the earthe be inhabited, (for that appertaineth to Ge­ographye) but to declare howe the sonne doth shewe in all partes of the worlde, as well on the sea, as on the londe: and as well in wyldrenes, as in populous countryes. Where­by it doothe appeare sufficientlye, that vnder the Po­les of the worlde, it is halfe a yeare continuall daye, and the other halfe yeare,The length of the daye vnder the Poles of the worlde. contynuall nyghte, bicause so longe againe the Sonne is not seene aboue that Horizonte.

This is as true as canne bee. the reason of it is so certayne and manifeste, that I coulde not better vnder­stande the state of that place, if I were there to see it, then I doo by thys beholdynge of the Sphere, and the motion of it. And thys (as I take it) is a meruaylous excellencye in knowledge,The excel­lencye of knowledge. to bee able so certaynly to iudge of thinges absente, as if they were present: to bee able to tell [Page 76] what houre of the daye it is in all the partes of the earthe, and when the Sonne ryseth and setteth in all nations vnder heauen.

Yow wolde accompt this knowledge more mer­uelous, if you vnderstoode other more wonderfull conclu­sions in it, whiche hereafter I will vtter as I shall haue occasi­on conuenient: but in the meane season, I will shewe you two or three conclusions, appertaining to our presente matter whiche we haue in hande.

As the houres of the daye are dyuers in dyuers regions, so the shadowes that the sonne causeth in their dialles, and all other shadows, doth disagree many waies, not only from our shadowes, but also one of them from an other. Againe the times of the yeare are not alyke through all the worlde, but when it is Sommer to vs, it is winter to som other: and when it is Springe time with vs, it is sommer in an other cuntrye: and when it is Haruest with vs, other people haue sommer: so when it is Winter with vs, som nations haue sommer: yea when the spring time beginneth with vs, it is haruest in some cuntries, and in other cuntries it is midsommer at the same time: but when it is midsōmer with vs, it it haruest no where in the worlde, but midde winter it is then in two diuers par­tes of the worlde.

This talke is meruailous, and in mine opinion the greatest meruaile is, y^t you can vnderstand the shadowes of their dials or any other thinges, in all partes of the world.

Peraduenture it wold seem more merueilous if I shoulde say, that by the knowledge of the shadow of a staffe, or any thing els that standeth vpright, (if I heare it trulye reported) I will tell you in what part of the worlde that sha­dowe was marked. And thinke you this no meruell, to tarry within Englande, and yet to measure all the compasse of the earthe, as certenly, as any man can do it, by going rounde about the earthe?

These thinges do exceede credit, saue that other [Page 78] thinges, whiche before I iudged impossible, and now I know them certenly, do perswade me to thinke many thinges pos­sible by learning, that seeme vnpossible to the ignoraunte, thoughe their wittes be neuer so good. I heare suche men say sometimes, that learned men and farre trauelers may be per mitted to talke at their pleasure, syth no man canne comp­troll them.

By those woordes they signifie, that they do not credite all that learned men do write or saye: wherfore I will constantly saye to them, that if they wolde vouchsafe to im­ploye somtyme in learninge, they shoulde be easilye perswa­ded, not onlye to beleue suche thinges as nowe they thynke impossible, but also to know them so certenly, as they know howe many fingers they haue. But to perswade you in the meane ceason,Thre con­clusions. I will presently shew you some of these thre conclusions before named, I meane for the generall know­ledge of the times of the year: for the declining of shadowes in diuers nations: and for the ordre to measure the whole earthe, and yet go not out of England.

If I maye vnderstande but the generall forme of those three, I will trust hereafter to attayne all the reste more certenly.

I will begin with the laste, whiche seemeth moste hardest, and I wyll alleage nothinge, but that whiche you shall graunt vnto.

The decla­ratiō of the fyrste con­clusion for measuringe of the whole earthe.Then shall your proofe bee as certaine as I can wishe.

Can you with a Quadrante marke the eleuation of the Pole aboue the Horizonte?

That is easye inoughe.

Then marke it fyrste at Southehampton, or in some other more easterlye place, on the south shore of En­gland. after that go to Newcastell beyond Yorke, and there take the eleuation with your Quadrante againe, and marke it well, and the difference of those two eleuations shall you [Page 79] set in your table, and by it you shall write the numbre of myles diligently and truly taken betwene those two places, where you toke those two eleuations.

This can I doo with diligence, although it bee as harde to marke the myles truly (the reportes of them be­ing so diuers) as it is to woorke truly with the Quadrante, but diligence will auoide errour in them bothe.

Then go forwarde to Edynburghe in Scotland, and marke the eleuation there: lykewayes go to the moste northerlye pointe of Catnesse, and take the eleuation there also, alwaies markinge the difference of euerye twoo places in myles of equall quantitie, and also the difference of the degrees of the Pole in eche of those places from other, and set them in your tables in ordre the one by the other, as here for examples sake only, I haue set them.

Here you see for Southehampton, where the fyrste eleua­tion was taken, no myles sette, bicause it is the beginning of your iourneye, but the eleuation of the Pole there is 51. de­grees: then at Newecastell the heighte of the Pole is 55. de­grees, and that is more then the other by foure degrees, so that foure degrees muste be set downe for their difference in degrees, and their distaunce in equall myles, is 240. Nowe to see howe many myles do the answere to a degree, I do di­uide 240. by 4. and the quotient will be 60. wherfore I saye, [Page 79] that 60. miles in earthe (by this triall) doth answere to one degree in heauen. Then at Edynburghe I finde the eleuatiō of the Pole to be 57, that is twoo degrees more then it was at Newcastell, and the distaunce betweene them in myles, is 120, whiche if I dyuide by 2, the quotient will be 60. as it was before: so that one of these workes doth confirme the other, bicause they agre so iustly.

I vnderstande all this, as by declaringe of the thirde woorke it shall appeare to you. At Catnesse pointe, the Pole is 62. degrees aboue the Horizont, whiche maketh 5. degrees more then it was at Edenburghe, and the space betwene those two places is 300. myles: now if I diuide 300. by fiue, there will amounte 60, whiche quotient doth agree with the other twoo before found: so it appeareth that in all Englande, 60. mile in earthe, answereth to a degree of lati­tude in the skye.

Prooue you also the whole difference in degrees with the whole distaunce in myles.

The whole difference in degrees betwene South­hampton (where the Pole is 51. degree highe) and Catnesse pointe, (where the latitude is 62.) dothe amount vnto 11. de­grees, and the distance in myles is 660: nowe diuidyng 660. by 11, the quotient appeareth 60. agreably as it was in all the other woorkes.

What if you dyd go farther northe, 19. degrees moare? I meane so farre Northe that the Pole were 81. degrees hyghe aboue the Horizonte, howe manye my­les thynke you woulde that place be from Southe hampton.

That can I quick­ly accompt by the Golden rule of proportion. [...]The difference betwene those 2. places in degres is 30. then seyng I found before, that 11. de­grees gaue 660. myles, I sette the numbres thus in their forme of woorke, [...] and then I [Page 80] multiply 660 by 30, whereof cometh 19800: whiche I must diuide by 11, and the quotient wyll be 1800.

Thynke you thys a true woorke?

This woorke is true and without any doubte, so that the measure of myles in Englande were true, whiche wee take for our grounde.

And if that measure bee not true, yet by that manner of woorkynge you maye attayne to a very true rate of myles betwene southe Hampton and Catnesse.

That is no greate matter, nother so harde to bee doone.

And it is no greater matter, in bothe those pla­ces to take the altitude of the Pole.

That is true also.

So that if this rate be not true, ther may be found a true rate by diligence.

Yea surelye.

And by that true rate you could fynde how ma­nye myles dothe answere to 30. degrees in the skye.

Easilye.

Well then: Take this for a true rate, tyll you can fynde an other more certaine. And nowe answere me: How manye myles are in compasse roude about the whole earth?

Nay that is impossible for me to discusse yett, tyll I haue farther knowledge.

Se how easye a thing seemeth impossible to you.

Howe manye degrees is there in the compasse of the whole skye?

That can I certenlye say to be 360: for as I lear­ned before, a degree is no standynge measure, but a rate of proportion, and dothe betoken the 360. parte of anye cyrcle.

You saye well. Now if the whole circumference of heauen be 360. degrees, I demaunde of you, howe manye myles doth answere to 360. degrees?

That maye I doo as in the former woorke, set­ting [Page 82] the numbres according to the rule of proportion [...]. Then multiplying 1800, The cōpas of the hole earthe. [...] by 360, there ryseth 648000, whyche I muste diuide by 30, and so the quotiente wyll bee 21600, whereby I knowe that 21600 myles, doothe answere vnto 360. degrees in the skye. And so it shoulde seeme that those are the iuste numbre of myles aboute the earthe.

You neede to make no doubte thereof, excepte you doubt whether there be any part of the earthe without the circuite of heauen: or els that you doubte, whether the earthe be in the middle of the worlde.

The fyrste doubte were to foolishe, and for the seconde (all bee it I doubte nothinge of it) yet I adsure my selfe by your promise; of the full proofe thereof in the next treatise.

And other doubte there canne be none, but this: Whether the earthe and the skye bee bothe rounde. whyche both I wyll so substantially proue vnto you, that no reaso­nable man will doubt of it.

Then am I certified in the possibilitie of the moste doubtefull conclusion of the three, whiche you proponed: It maye please you to proceede to the other two.

The decla­ration of the seconde conclusion, for declinīg of shadowsYou do consider that this conclusion being true, they that dwell 5400 myles from vs, doo dwell a quarter of the earthe from vs.

That muste needes be so: for four times 5400. doth make the whole circuite of 21600. miles.

And so they y^t dwel frō vs any māner of way, 10800 miles, thei dwel half the compas of the whole earthe frō vs.

It foloweth so by the former reason.

It is well knowen by the nauygations of the Portingales and Spaniardes, that there is almost south frō [Page 85] vs, certain places inhabited about 6300. myles, as namelye at the streight of Magellanus.Magellanus streighte. The cape of Good hope. Also at the great forelonde of Affrike, commonly called the cape of Good hope, are there diuers regions replenished with inhabitantes, and they be from vs southwarde aboue 5200. myles: then northward wee haue good knowledge of dyuers cuntries beyonde vs aboue 1200. myles, whiche bothe ioyned togither, do make from the greate forelonde of Affrike aforesaid in the south, vnto Wardehouse in the northe parte of Norwaye, aboute 6400. myles, whiche is more then a quarter of the compas of the earthe: but from Wardhouse to Magellanus streight, it is aboue 7500. myles, by which distaunce of myles, you maye easilye gether how many degrees of the heauen eche of those places is from vs, and from the Equinoctiall.

Therein I praye you, that I maye prooue my newe cunninge. [...] The cape of Good hope is from vs south­warde 5200. myles, that is in degrees of the skye 86 ⅔, accordinge to the former rate of 60 myles to eche degree. from whiche num­bre of 86 ⅔, if I abate so many degrees as we be northe of the Equinoctiall, which are 52 degrees, then doth there reste 34 ⅔ degrees. So that it appeareth hereby, that the sayd forelonde is 34 ⅔ degrees southe beyonde the Equinoctiall.

Now for Magellanus streight, prooue the lyke woorke.

It is 6300. myles southwarde from vs: then by the rule of proportion, [...] agreablye to the for­mer rate, it must yelde in degrees 105, oute of whiche abatyng our distaunce northe from the equinoctiall, (whiche is 52 degrees) and so re­maineth 53. degrees. thereby I vnderstand, that they are so far beyond the Equinoctiall south­warde. Now will I prooue for Wardehouse, how farre it is northe from the Equinoctiall. It is from vs towarde the [Page 84] northe 1200. myles, whiche must yelde in degrees, after our former rate 20, from these 20. degrees I maye not abate 52 degrees for our latitude, as I dyd before. [...]

It were againste reason, seynge that the latitude of Wardehouse is greater then our latitude is, and lyeth on the same coaste of the E­quinoctiall: for in the former examples the two places were on the contrarye coaste of the Equinoctiall from vs.

I see it well now, so that by reason I must needes adde it to our eleuation, and so ther amounteth 72. degrees, whiche is one degree more then you did affirme it to haue in latitude, in your former declaration.

The cause is this: that rate of 60 myles to eche degree doth serue in goyng precisely from southe to north, but nother is Wardhouse iust northe from vs, but somwhat towarde the easte. nother yet in the other two examples any of bothe places was directly southe from vs, for the Fore­londe of Affrike beareth towarde the easte, and the Streight of Magellanus bendeth towarde the weste, yet for this tyme it maye serue as well for our purpose, as if it were more pre­cisely doone.

An ordre in teachinge.Yet I thinke in teaching there shoulde bee vsed nothinge but certaine truthe.

What so euer is taught to be retained for a truth, oughte to be a very certaine truth in deede: and they do not well that in suche manner doo teache fyrste vntruthes for truthes. but where inductiō is made by examples, it is often tymes more or at the leaste, no lesse expedient to vse exam­ples not exactly true, then to take only precyse true exam­ples, for thereby it appeareth the proofe to bee of greater force, if it will procede in an example whiche is not precise­ly true. And in these examples we haue so large scope of tri­all, that we neede not sticke for two or thre degrees, for I in­tende not to speake particularly of any citye that is vnder [Page 85] one certain degree, but of whole prouinces, whiche occupi­eth diuers degrees in their latitude: as you vnderstand that the whole isle of Britayne doth occupy from 51 degrees, vn­to 62, which containeth 11 degrees. But now to come to our purpose: thus much you vnderstād, y^t beyond y^e equinoctial, yea and beyond the tropike of Capricorne also, there be in­habitantes.

Yea that ther be, aboue 29 degrees besouthe the tropike of Capricorne: for that tropike is but 23 degrees and a half beyond the equinoctiall: and ther be inhabitants 53. degrees beyond the equinoctiall, as before is shewed.

Well if there dwell men but 6 degrees besouth the tropike of Capricorn (for I sayde before, I would not sticke with you for a fewe degrees, sith I wold make my proofe the more forceable) then I demaund of you, whiche way dooth the sonne stande from them at noonetide?

It must needes be alwaies northe from them at noone, as it is alwaies southe from vs at noone, seynge they are beyonde the southe Tropike, towarde the Southe, as we are beyonde the north Tropike towarde the northe.

Then consider two places that stande iuste south and northe (bicause you like well a precisenes in examples) as Venice that famous citie standeth north almost from the cape of Good hope: Now consider the matter thus: in these two places there is one common meridiane line, sith thei do stand almost iuste southe and north the one from the other: then when the sonne is in the Meridiane line of Venice, is hee not also in the Meridrane lyne to them that dwell at the sayd Cape of Affrike?

Yes trulye.

Then those twoo places haue their noone tydes at one hower.

So haue they.

And at Venice theyr shaddowe goeth alwaies at noone toward the north & neuer toward the southe, bicause [Page 86] it is far north from the northerly tropike, called the tropike of Cancer, and so is the foresaid cape of Affrike far southe, beyonde the southe tropike, whiche is the tropike of Capri­corne: wherefore (as you haue confessed) their shaddowe at noone tyde, must needes go all tymes of the yeare toward the southe.

So I see that those two places haue a contrarye propertye, touchinge their shaddowes.

That is parte of the thinge that I did intende to shewe vnto you: but yet they bothe do agree in this pointe, that all times of the yeare their seuerall shadowes do incline towarde one coaste.

That is true. for at Venice it goeth stil north, and at the cape of Good hope, it runneth alwayes southe.

These sort of people are named of the greke Cos­mographers [...], [...] Heteroscij Single sha­dowed. Heteroscij, bicause their shadowes go­eth styll toward one coaste.

As though there were other people, whose sha­dowes did sometime go southward, and other tymes north­ward: I meane their shaddowes at noone, for els all nations haue in one daye, at diuers houres, much diuersitye in theyr shaddowes.

Ye vnderstand the time well. and you shal perceiue as wel, that ther be such places, which chaung their shadows.

You confesse that men dwel beyond the tropike of Capri­corne southward: and other you know to dwel beyonde the tropike of Cancer northward: & thinke you it not agreable to reason, that betwene these two peoples there do dwell dy­uers nations in so greate a plotte of grounde?

I thinke yes. and I heare saye, by our owne cun­trye men, whiche trauaile to Guinea, that they wente be­yonde the sonne, whiche alwaies I tooke to be a lye of liber­tye permitted to farre trauelers, but now I perceaue it maye be true in one sense.

Ther are 2. places of that name, and both are be­yond [Page 87] the tropike of Cancer, toward the south, and the one of them is almoste directlye vnder the Equinoctiall circle: and bicause you haue named that cuntry whiche our nation doothe well knowe, take it for your example. They of Guinea beeynge nyghe vnder the Equinoctiall, haue the Sonne some tymes northe from them at noone, as when he is in the tropike of Cancer: and other tymes they haue the Sonne southe from them, when hee is in the Tropike of Capricorne. and muste not their shaddowes chaunge in lyke sort?

It can not otherwaies be. And so I see, that when it is midsommer with vs, then doth their shadows go sourth ward, to as many as dwell betwene bothe the Tropikes: and in our myd winter, their shaddowes goeth northward.

[...] Amphiscij Double shadowed.Those people are named of the greekes [...], Amphiscij, bicause the noone shadowes goeth both wayes, sothe and northe.

And farther I gather, that there is no quarter in the Horizont, but their shadowe runneth that waies somtyme in the yeare.

You say truthe. but the chief regarde is here gy­uen to the shadowe at nonetide, wherby you may conceaue, that sometime they haue almoste no shaddowe: for when the Sonne at noone is righte ouer their headdes, then theyr shaddowe is ryghte vnder theyr feete, and not on anye syde.

It muste needes be so. for seeynge the Sonne is some tymes northe of them, and sometymes southe from them, hee muste needes twyse in the yeare bee right ouer their headdes, ones in going southward, and againe in com­mynge northwarde.

To helpe your memory and coniecture take this figure for a presidente and example, where I haue set the line A. C. for the horizont, and D. B. E. for diuers places of the son at noone. Now if you call A. the north point of the hori­zonte [Page 88]

zonte, and C. the south pointe, then when the son is in D. toward the north from their heds, their shaddow goith to F. toward y^e south. And when the sonne is in E. toward the southe, then is their shaddowe in G. bēdig toward y^e north: likewaies the sonne be­ing right ouer their heddes in B, their shaddow must rest in H. ryghte vnder their feete. but I see by your countenāce y^t your mind woorketh in some straung imagination: and I coniecture it to bee for that I haue drawen the shaddowes beneth the Horizonte, as you take it.

You haue truly coniectured my phantasye.

Bicause this place serueth not to declare conclu­sions of bye matters, I wyll exhybite to you this other figure,

where the shaddowes doo run on the Horizonte, a­greablye to your phan­tasye, the letters of demonstration remay­ninge as they were beefore, and bothe these tende to one ende.

But heere are but two shadowes.

Where wolde you haue the third set?

Right vnder the tower that giueth the shaddow.

But it may not reache from the foot of the tower, nother toward one coaste, nor other.

No, that it maye not.

Then the footer of the tower doth couer it so, that you can see no shaddow at all.

That is most certaine.

Yet remaineth ther an other sort of people, which differ in one point from these other twoo sortes, by reason that their shadowe in one daye runneth round about them, and goeth toward all coastes of the horizont wherefore the Greekes do call them [...], Periscij. [...] Periscij. rounde sha­dowed.

Is ther no english nor latin names for these sorts of properties?

The latin men borowed of the grekes, both their knowledge and also many names of arte, bicause there is not the lyke grace of facilitie inborn position, in the latyne tonge, as there is in the greeke tongue, and therefore haue I geuen them no englyshe names, bicause no one woorde can aptly expres these properties, excepte I woulde triflinglye make such an immitation, to call theym, One shaddowes Two shadowes, and Round shaddows: or els, which is not muche vnlyke, ye may call them Single shadowed, Double shadowed, and Round shadowed.

That immitation seemeth straunge yet were it better to make new english names, then to lacke words: therefore I will not refuse to vse them, till I can learn more apt names. but I praye you, where do those men dwell, that haue their shaddowes runnyng so about them?

Within the Polare circles: for all people whose zenith is within 23 degrees and a halfe of anye of bothe the Poles, haue their shaddowes running rounde aboute them. but as I shewed you before, the nearer they dwell vnder the Pole, the longer is theyr daye: and therefore the oftener doothe theyr shaddowes runne about them for where the daye is but 24 houres longe, there the shaddowe runneth but ones aboute: and where it is halfe a yeare longe, there it runneth aboute 183 tymes: and in all other meane places raccodingly.

This is manifest ynoughe by your former de­claration of the lengthe of the dayes, and the course of the sonne. And farther I perceaue that when they that be vnder the Northe pole haue their shadowes thus runninge aboute them, then they that dwell vnder the Southe pole haue no shadowes at all, for it is continuall darkenes with them.

You saye well,Lighte and Darknes vnder the Poles. concerninge the sonne lyght, tou­ching them that dwell directly vnder the Poles, but yet they haue the lyghte of the Mone euery moneth more then 14. dayes togither.

Then do they not wante lyghte (thoughe they lacke the sonne) but only halfe a moneth togither, when the Moone is in that halfe of the Zodiake, which is out of their Horizonte.

That is well considered of you. And yet euerye moneth they lacke not lyghte, thoughe bothe the sonne and the Moone also bee oute of their sighte: for as you see with vs, that we haue lyghte before the sonne rising, and after the sonne setting, so haue they suche a lyghte by the beames of the Sonne 50 dayes continuallye after they haue loste the sighte of the sonne, and so haue they the like lighte 50. daies continuall, before the sonne doth rise to them.

Then they wante not the sonne lyght but only 82. daies, although they see not the sonne in halfe a year, and yet halfe that 82. daies they haue the mone in their sighte, as I perceaue by your former lessons: for seing she goeth about the Zodiake euerye moneth, she must needes bee halfe that tyme in that parte of the Zodiake whiche is alwaies aboue their Horizonte. This contemplation deliteth me muche, to marke places absente, as if I were present, and to see their alterations by reason more certenly, then I can do by sense, if I were there presently.

Yet will I withdrawe you from this matter, tyll an other more conuenient place: and now will I procede to the thirde conclusion mentioned before: that is the generall [Page 91] knowledge of the times of the year, in all parts of the world. When the sonne is at the highest with vs,The thirde conclusion is declared. it is at the lowest with diuers other nations, namelye to all them that dwell other vnder the Equinoctiall circle directly, other southe from it: and therefore all those nations haue mydde winter, when wee haue midde sommer. But amongest them all there is one region, whiche is as farre beyonde the equinoctiall towarde the southe, as we are towarde the northe.

That region is about Magellanus streight, as I gether by the seconde former conclusion.

In deede the streight of Magellanus is in that re­gion, for here I meane by a Region that whiche the Grekes do call a Climate, whiche is in forme lyke to those Zones, whiche I did describe before,A Climate. saue that there are more suche Climates or regions, then there are Zones: for the climates may well be accompted 48 betwene the twoo polare circles,The nōber of climates whiche containeth but three of the Zones. but of those cli­mats I will say no more at this present, but that euery regiō where the longest day is half an hour longer or shorter then it is in anye other region, must bee accompted in a seuerall climate from it: so that vnder the equinoctiall the longest daye is but 12. houres, and with vs in the myddle of En­glande, it is about 18. houres: wherefore we must accompt that the myddle of Englande is in the 12. clymate from the Equinoctiall northwarde, and they that dwell 66. degrees and a halfe north, or southe from the Equinoctiall, bicause their longest day is of 24. houres, that is twelue howers lon­ger, then it is in the myddle of the worlde vnder the Equi­noctiall (from which all those accomptes of Climates do begin) they must be iudged in the 24. Climate.

Then are there 24. climates on eche syde of the Equinoctiall, betwene it and the polare circles, yet I remem brethat the common authors make mention but only of 7. on either side, whiche maketh but 14. in all.

That shalbe answered anone, where I will set out [Page 92] the ordre and reason of the diuer sity of the climates: but for this time it shall suffise that you consider this, that all pla­ces within one Climate, haue the tymes of the yeare alyke exactely,The quali­ties of con­trarye cli­mates. and their dayes styll of lyke quantitie the one to the other, and they that dwell in the contrarye climate, as many degres on the other side of the Equinoctial, the haue bothe the times of the yeare contrary, and also the quantity of the daies disagreable, for when it is sommer in the one climate, it is winter in the other and when the daye in the one dothe increase, the nighte in the other dothe increase after the same quantitie iuste.

Then for example: In the cuntrye about Ma­gellanus streighte, it is sommer when wee haue winter: and when our daye is at the longest then is their nyghte at the longest.

Truthe it is, and when wee haue springe, then is their haruest: and so is it common to all them that dwell a­houe the earthe within those twoo climates, yet is there this difference, that in our climate and theirs also we maye ima­gine four quarters equally distincte: the firste quarter being that which we dwell in,Euery Cli­mate hathe 4 quarters and in the contrary climate, our me­ridian circle limiteth the first quarter, & also the third quar­ter in both places, so y^t in this first quarter in both climates, the times of the day and night at a like: for when it is noone to vs, it is no one to them: and when it is midnight to them, it is midnight also to vs.

Then likewaies when the sonne riseth to them, it riseth to vs, and so setteth at one time in bothe Climates.

Ye are far deceiued, for then of necessitie muste it folow, that their daye and ours at one time should be of (one quantity, which is not true, as I said before, but the reason of that shalbe shewed anone, yet is it true, that their houres agre with our houres if their meridian circle agre with ours. And the same meridian circle vnder ground doth li [...]te in both these climates, the 3 quarter also wher it is noone when we in [Page 93] the fyrst quarter haue mydnyght, and they haue mydnight anour noone. Now may you easilye conceaue by your owne mynd, the places of the other two quarters.

Ordre inforceth them, the one to be in our west, and the other to be in our easte.

That distinction is sufficiente for you at this time, and it is precisely true, if you meane the easte, where the Sonne ryseth at the begynninge of the Sprynge tyme, or of the haruest, wherfore for that time I wyll make myne example: When the sonne riseth to vs in the spring tyme, it is noone with them that dwell aboute Calecut, and when the son is in our Meridian line, then doth he set to them: so that whē the son doth set to vs,Calecut. Peru. it is midnight to them about Calecut; & thē is it noone to the famous cuntry of Peru: Again at that time the son riseth to thē that be in the isles of Molucca.Molucca. wherby you may gether that Peru & Calecut be in 2. con­trarye coastes of the earthe, and therfore seeme to go wyth their feet the one against the other, and their heddes the one from warde the other, whiche sorte of people therefore are called of the Greeks and Latines also [...], Antipodes,Antipodes. as you myght say Counterfooted, or Counterpasers. Now to our purpose. all people that haue mydnight when other haue noone, doo differ in sonder by halfe the compas of the heauens, one waye: yet may they not be called Antipodes, except they differ in distaunce euerye waye a quarter of the skye, and must haue one meridian circle. So that our Anti­podes must be vnder our meridian circle, and must be halfe the compas of that circle from vs.

Then as wee are 52. degrees northe from the Equinoctiall, so muste they bee 52. degrees southe from the Equinoctiall, in that parte of the Meridian circle, whi­che is vnder oure Horizonte, and then haue they mydde­nyghte when wee haue noone: and hereby I perceaue that they haue mydde nyghte when it is noone at Magellanus streighte.

In deede it is daye then at Magellanus streight, but not nighe noone, for Magellanus streight is muche to farre toward our weste: but for examples sake that erroure maye be permitted, and especially bicause there is no lond but sea, where you shoulde meane that noone to bee: so can you giue it no propre name: but retaininge that name for example of the true place, you may consider three fortes of people, that is to saye, our selues, and those that dwell by east Magellanus streight, vnder our Meridian circle, which haue noone when we haue noone,Antipo­des. and the thirde sorte which are vnder the same Meridian, but haue midnighte when we haue noone, and are as farre southe from the Equinoctiall, as we are northe, whome I named our Antipodes, and so ought they to be called in respect to vs, and we are Antipo­des to theym also: But nowe comparinge theym with those other by easte Magellanus straight, they ar called eche to other [...] Perioeci, as you may saye, lyke dwellers, bi­cause they dwell vnder one Meridiane circle, and vnder one Parallele also, and be like in distaunce from the equinoctiall circle.

There are manye places in euerye suche region or climate, but there are but two proprely vnder one Me­ridiane, and the one of them hath midnight when the other hath noone: so the tymes of the daye doth differ with them yet I perceaue that they haue the seasons of the yeare agrea­ble, bicause they dwell on one side of the equinoctiall. Then must it folewe that those whiche vnto vs be Perioeci,Perioeci, likdwellers are An tipodes to them that dwell by Magellanus streighte vnder our Meridian.

You saye well. and we vnto them by easte Ma­gellanus streighte, vnder our Meridiane, are called by the greekes and latines [...] Antichthones,Antich­thones, Counter­dwellers. as you wold say Counterdwellers, or Counterclimates.

And thus haue you three sortes of inhabitauntes by comparing the one with the other, wherof alwaies Perioeci (that [Page 95] is Likedwellers) haue like tymes of the yeare, but not of the daye. Antichthones or Counterdwellers, haue like times of the day, but not of the year. Antipodes or Counterpasers, haue nother the parts of the year, nother of the day agreable togither, but cōtrary in both, how be it ther is a farther cōsi­deration for exactnes of this knowledg, which I will herafter declare to you in place more conuenient: but hereby maye you gather the diuersityes of tymes of the yeare, and also of the dayes, accordinge to the diuersitie of the inhabitauntes comparinge them all other to your owne cuntrye, or one of them to an other, as occasion shall serue, and oportuni­tye of matter. And thus will I ende for this time, if I maye perceaue by your repetition of this thyrde treatise that you remembre all thinges therein declared.

I were els to blame. but as I haue learned in it manye seuerall thinges, so for the ordre of the arte these I note as chiefe matters.

• 1
  The repeti­tion of the thirde trea­tise.
  Firste the distinction of the Plages of the worlde, accordingly as they be sette forthe in the Horizont of the Sphere.
• 2 Then the Paralleles on earthe, agreable to the Paralleles in the skye, of like names, and distaunce proportionable.
• 3 Thirdly the distinction of the. v. Zones, by their qualities and limites, and of their inhabitantes.
• 4 The diuersities of Spheres according to their diuerse inclinations, but twoo are the generall distinctions, that is a Ryght Sphere, and a Bo­winge Sphere.
• 5 Fyftlye, you gaue me a brefe ordre to take the heyghte of the Pole, or any other Starre or Planete.
• 6 Then folowed the diuers alterations of the Horizonte, as wel betwene Easte and weste, as betweene Southe and Northe.
• 7 Seuenthlye, there was declared the causes of the diuersities of the daies, fyrste in diuerse regions, and then in one region.
• 8 The difference betwene a Naturalle daye, and an Artificiall daye.
• 9 The quantitie of the longeste daye in certen partes of the worlde, and namely vnder the Poles of the worlde.
• 10 How by this excellente Arte a man maye measure all the compasse of the earthe, and yet abyde styll in one cuntrey.
• 11 A distinction of sondrye inhabitantes, accordinge to the diuersities of their shaddowes, whiche are three principallye.
• 12 Then lastlye folowed an other distinction of inhabitantes, accordinge [Page 96] to the agreeablenes and diuersities of tymes of the yeare, and the quarters of the daye, and these you named by three seuerall names also, whiche are names of comparison, bicause they take not those names, but in comparison to other nations.

This I remembre to be the summe of this laste treatise.

You remembre it well, and vnderstande it also well, as it may appeare by your repetition. Therfore nowe shall you depart for a time, and you shall reade ouer againe your authors of the Sphere, whiche you did name before, and now marke whether you can vnderstande them, and as your returne, I will instruct you more exactly in all the pre­misses, and other diuers conclusions, whiche nowe I haue omitted of purpose.

I am moste earnestly bound vnto you for your great gentlenes, whiche I pray god to requite, sith I cannot, and who wyll els I knowe not.

Farewell then, and remembre your owne profit▪ Schollar. The author of all profite, continew and increase your profit, that you may haue quiete time to trauaile for the profite of manye.

IF THE INEXPLICABLE BENEFITE of knowledge did not enforce me to for­gette all bashfulnes, I myghte thinke it to muche shame, so often to trouble my Master frome his earnest studies, and to staye him from his profitable trauell with mine importune crauynge of knowledge, namelye sithe I canne not recompence anye parte of hys paynes: yet hys gentlenes is suche, that hee seeketh more the profite of other, then his owne pleasure or peculiare commoditie: and therfore will I boldly entre into his house. Are you at home syr?

I am alwaies at houe for my friendes, if I bee not with them from home: yet some times I can not be at home for my selfe.

The lesse for me and suche as I am, that often trouble you more for our owne commoditye, then for your gayne.

I seeke to gaine no more then competentelye maye serue my necessarye vses, with conueniente regarde to my charges: but if I offende anye wayes in couetinge monnye, I adsure you it is to beare the charges in set­ting forth such monumentes of knowledg, as were meruai­lous profitable for all men, very pleasant to many men, & yet estemed only of wise men. but sith I cānot do the good that I wold, and other want will which haue goodes in excesse, I must do as many other doth, wish good to all men, & helpe [Page 98] them as I canne. And for your parte I looke none other re­compense but this, that you alwayes be thankefull to your Master. and as hee helpeth you freelye, so doo you healpe other againe, and hyde not the knowledge priuately, whi­che may profite many publikely. but now to your matter: haue you perused the authors of the Sphere which ar com­monly readde?

To reade them all, it were to muche for my lyfe tyme, and the profite not so greate, as I heare manye menne saye: for as the noumbre are infinite, so the la­ter wryters doo moste commonlye but repete that, that twoo or three of the auncientes haue written before. wher­fore as I learned that the beste wryters of them for my studye, were Proclus, Ioannes de Sacro bosco, and Orontius the Frenche man, so I haue readde them, and out of them haue I collected a table of theyr moste notable matters, whyche as yet I vnderstande not, or els doo desyre to heare the demonstrations for their proofe.

You haue doone well in bothe pointes. for as the numbre of writers are infinite, so haue I founde great tedious payne in readinge a great multitude of them. Notwithstandyng as you shall hereafter seeke further know­ledge, so muste you reade more wryters in that matter: wherefore amongest a greate noumbre wo orthye the rea­dinge, I wyll name a fewe vnto you, whyche I wishe you to studye: and the resydue I leaue to your owne discre­tion. Cleomedes the greeke authour, is very woorthye to bee often readde: but beste in hys owne tongue, for the latine booke is muche corrupted. Also Euclide his booke entituled Phaenomena, and Stoffler his commentaries vp­pon Proclus Sphere: whyche booke I wishe were well re­cognised (as it hathe greate neede) then myghte it serue in steede of a greate numbre of other bookes. Dyuers Englyshe menne haue written right well in that argument: as Grostehed, Michell Scotte, Batecombe, Baconthorpe, [Page 99] and other dyuers, but fewe of their bookes are printed as yet, therefore I will staye at those three for this tyme. As for Plinye, Hyginius, Aratus, and a greate manye other, are to bee readde onlye of masters in suche arte, that can iudge the chaffe from the corne. and Prolemye that wor­thye writer and myracle in nature, is to harde for younge schollars, except they be fyrste instructed not onlye in the principles of the Sphere, but also well traded in Euclides his Geometrye, and also well exercised in the Theorykes of the Planetes. But nowe let me see the table that you haue collected.

• 1 The ordre and mouinges of the nine Spheres.
• 2 The spaces of their reuolutions by their propre motions.
• 3 The forme of heauen is rounde, and his mouynges circulare.
• 4 The earthe is rounde in forme, and the water also.
• 5 The earthe is in the myddle and Centre of the worlde, and is but as a pointe in comparison to the Firmamente, and doth not moue anye waies.
• 6 The compasse of the earthe, and the diameter of it, what they make in common myles.
• 7 Of the circles in heauen what is theyr iuste quantityes, their numbre, their ordre, their distaunce, and their offices.
• 8 Whye the Zodiake hath that name, and whether anye suche formes bee in the skye.
• 9 The diuers significations of a figure, and the declyninge of them. There are two Horizontes, one sensible, and the other onlye iudged by reason, and what the quantities of them bothe are.
• 10 The Greekes and the Latines doo not agree in the description of the circles Arctike and Antarctike, and what are theyr reasons.
• 11 Whether there bee anye dwellers in the Vntemperate Zones.
• 12 What bee the circles Verticall and circles of Heighte, the circles of ho­wers, and of the twelue houses.
• 13 Of the rysinge and settynge of the Signes and other Starres, bothe in the Ryghte sphere, and also in the Bowing sphere, after the Astro­nomers.
• 14 Of the Latitude of the Sonne and the twelue Signes from the easte and weste.
• 15 Of the risinge and setting of the starres, after the mynd of the poetes.
• 16 Of the diuersitie of Naturall daies, as well as of Artificial daies in di­uers partes of the earthe.
• 17 The diuersities of howers, whereof some ar equall, and other vnequall [Page 100] accordinge to the course of the sonne.
• 18 The heighte of the sonne aboue the Horizonte at all howers, and in all regions.
• 19 The diuersyties of shadowes, whereof some be called Ryght shadows, and other be called Turned shaddowes.
• 20 The distinction of the circles Paralleles necessary in Cosmographye, with the proportion of their degrees, to the degrees of the Equi­noctiall.
• 21 The distinction of Climates and the numbre of them, and howe large in breadth eche of them is.
• 22 Of the Longitude and Latitude of regions and other places, and how bothe these ought to be taken.
• 23 The description of the Mylke waye in the skye, whiche is commonly called Watlynge streete, and what is the cause of that coulour in it.
• 24 The numbre and names of the chiefe signes and figures that be in the skye, and whye they be so called.
• 25 Of the circles and mouinges of the Planetes, and namely of the eclip­ses of the Sonne and the Moone.

These be the titles of such matters as I haue noted in them moste meete for this tyme, syth manye other thynges are sufficiently taughte in the former treatises, and some other thynges, namely in Orontius booke, appertaine to Cosmo­graphye, whiche I perceaue by your sayinges, you mynde to reserue for a peculiar treatise of that matter, and therfore I haue omitted them here.

So myghte you haue doone some other thyn­ges also, whiche you haue noted here: howe be it I will vse my libertye therein, to expresse in conuenient largenes those thinges, that be meet for this place, and the rest will I touch with as conueniente briefnes: referringe the other to theyr more conueniente places.

Syr I know right well, that your iudgement is as well to be folowed in the ordre of teaching, and choise of matter, as it is to be esteemed in the teaching and explicati­on of all doubtefull cases.

In ordre of teaching is more credit to be gyuen to a master, then in affirming of anye doctrine: for the ordre [Page 101] is by longe experience best knowen of such men: but for af­firming of any doubtefull doctrine, no man ought to saye any more then he can shewe good reason, for thapprouyng of the same. And now to your matter. although you follow the ordre of Ioannes de Sacro bosco in many of your pro­positions, yet will I beginne with your thirde proposition, and referre the twoo firste to a more meete place, sythe the proofe of them can not well bee vnderstande, withoute a great numbre of other cōclusions, which must fyrst be pro­ued. And for to begin with the declaration of the ro und­nes of the skye, and his circulare motion, I thynke it good to folowe that ordre whiche mouyd men fyrste to obserue this kinde of arte.

The firste occasion to thinke the worlde to be rounde.At the fyrste beginning of the worlde, when this arte was vnknowen, menne marked the rysinge of the Sonne and the Moone, and other notable starres, as the Broode henne, whiche is called of many men the Seuen starres, and other like: and perceauinge them to rise alwaies aboute the easte, and so to ascende by lyttle and lyttle to the Southe, from whence they dydde descende againe softely to the west, where they dydde continuallye sette: and the nexte daye a­gain they perceaued them to begin their accustomed course and so continued like as before: wherin although they sawe some diuersitye, yet they perceaued that diuersitye to bee vniforme, and after a yeare to retourne to the olde state agayne. by this occasion they beganne to ymagine that thys manner of mouynge coulde not bee but in a rounde and circulerre forme, and also in a rounde and circu­lerre bodye.

The second occasion.Then to vnderstande this matter the more exactlye, they obserued the mouinges of suche starres as neuer go vnder ground, which be about y^e north pole: & ther thei perceaued by diligēt marking of thē, especially in y^e long winter nights, & that at sundry times, y^t thei turned round about one point in the skye: and those starres that were nighe to that pointe [Page 102] dyd make but a lyttle compas in their mouinge, and the far­ther that any starres were from that pointe, the greater was the circle of their reuolution.The thirde occasion. Then thirdelye they marked certaine notable starres, whiche did rise and set, but yet were not farre from those other starres, whiche do neuer rise nor sett, and they might wel perceaue that they did continue but a lyttle while vnder the Horizont out of sight, wher as con­trarye wayes, those starres that were farther from that point or Pole, did remaine longer time vnder the Horizont, out of their sighte, whereby they were inforced to thinke, that these varieties and formes of mouynge coulde bee in none other manner of body then in a rounde forme, and that the same mouynge was circulare and rounde, as it did manifest­lye appeare in the northe parte of the skye, where the starres continually moue rounde aboute one pointe, and do neuer set vnder the Horizont. And that point about whiche they noted this motion to bee, they called (as reason inforced them) the Pole of the worlde.A Pole.

What doth that word signifie?

It hath his name of turning: as you wolde saye, a Turne point. and it doth betoken the ende and extreame pointe of any Axetree, howe be it by speciall prerogatiue the name is appropried to the endes of the Axetre of the worlde.

This picture dooth some

what represent the motiō of the starres aboute the north Pole.

You say truth. howbe it apt­ly it can not be perceaued in flat forme but in a roūd body, as a globe is: but in that point (me thinketh) ther is no bet­ter instrument then the sky it selfe, wher euerye man maye learne that lysteth to marke, and there bee certaine notable starres in that place and namelye Charles wayne, whiche is called also the greate Beare, whose motion [Page 103] is so euidente, that euery childe may marke it:Charles waine. And twise in the yeare, that is in the middle of February and in the mid­dle of August, they serue for a iuste horologe: so that the finger in a clocke doth not more aptely pointe the howers, then doth that figure of Charles waine.

There can hee no more apte declaration of the roundnes of the heauen, and of his circular motiō, then the sight of those stars which moue so roundly, and kepe their quarters in heauen so precisely. and yet I haue hearde of cer­taine great clerks, that in no case thoughte it reas onable to affirme suche a forme of roundnes, or suche a round moti­on in heauen: but moste of all I meruaile of that famous man Lactantius Firmianus, which doth affirme (as I haue hearde) that the heauen is not rounde, but flat and playne.Lactantius Firmianus his erroure.

Many scrupulous diuines by mysse vnderstan­dynge of scripture, haue abhorred the studye of Astrono­mye, and also of philosophye, and often tymes doo more sharply then discretely raile at these bothe, and yet vnder­stande they not any thinge in eyther of them bothe. suche men are to hastye to bee good iudges, that will so quickely pronounce sentence, before they haue anye good euidence, and will determine the case, before they vnderstand the matter. for how can anye man vnderstand well or iudge rightly y^t thing that he knoweth not? yet such drowsy dreamers haue oftentymes deceaued many wise men, with their appearante reasons, but yet none but such, as either were giuen to hate the name of philosophy, or els at least had no time, or none habilitie to gette vnderstandinge in it. By some suche men I may think that Lactantius was seduced: and the more easily, for that he had conceaued a deadly hatred against all philo­sophers and against philosophy it selfe:Lactantius opinion of the forme of heauen. lib. 24. c. 3 but I wil let him and his folowers passe, and retourne to the matter.

Yet if it please you, I wolde gladly hear his rea­sons, that he maketh for approuing his opinion, seyng hee is named so greate an oratour and so famous in learnynge, [Page 104] that many men will beleue him without any reason.

Who so euer wyll beleue him in this point, must do it without reason: for he alleageth no reason for his pur­pose, but taketh it as a certaine truthe, thereby to improue the opinion of the Antipodes, as I will more largely de­clare anone in proouing the roundnes of the earthe. But se­ynge he coulde bring no reason for his opinion, you shall heare some reason against his phantasye, and then iudge as you can.

That the skye is not flatte.Firste I reason thus: If the heauen be flatte and plaine as a borde, then howe so euer it stande, one parte of it muste needes be nearer to the earth then any other parte of it. and that parte by all lykelyhod must be right ouer our heddes, is not that so?

I can not imagin els any forme of situation: and

that doth appeare partly in this figure, where A. B. C. standeth for the skye, and lyeth flatte ouer the earthe, whiche is heere represented by D: and now I see that B, whiche is righte ouer D, is muche nearer to it then A. or C, or anye other poynt in that flatte plaine forme, whiche is sette to represent the flatte skye.

Nowe then what will Lactantius say, or any man for him? doth this heauen moueor not?

He can not deny that which we maye see with our eies, that bothe the Sonne, the Moone, and all Starres doo moue euery hour continuallye.

Yet peraduenture he might saye, as some other like contemners of philosophy haue saide, that the starres and Planetes do moue in the skye, as fishes do swimme in the water: and that they go forwarde thoughe the heauen [Page 105] stande styll.

I remembre I haue hearde of that sayinge, and that a famous writer of late doth maintaine that opinion.

What will they saye then, dooth keepe the starres in suche a iuste ordre and equalitye of distaunce? whiche ne­uer altered any one whitte syth the beginning of the worlde, is it possible that the starres shuld mouein the skye as fishes doo swimme in the water, or as birdes flye in the ayer, as som terme it, but that the starres must stragle in their course, as the fyshes do, and as the byrdes also do?

I haue seene both fyshes in the water, and foules in the ayer, to keepe a meruallous certene course in their fly­ing and swimming, and namely fishes that go in sculles, as herringes commonlye doo, and other fyshes diuers times, and wilde geese also and storkes in their flyinge, whereof I haue often mused.

You maye often see suche notable sightes; yet if you marke them, you shall see muche alteration in their fly­inge, as well as in the swimming of the fishes: whereby you may think their ordre not to be constant, but somtimes one flyeth a lyttle faster, and an other a lyttle slacker: and some­time they swarue on the one side, and somtime on the other. but were it not a sonde ymagination, to thinke that starres doo flye and folowe one guide as byrdes doo, and in 5000. yeare space to keepe their places so precisely, that they varye not one minute of a degree?

In deed it were meruailous, and so are all Gods woorkes.

Yet is there one inuincible reason againste that opinion,The Mylky way called of the gre­kes Galaxia gathered of the figure of the Milkye way in hea­uen, whiche many men in England do call Watlyng streete, comparing it to one of the greate highe waies in Englande that is called Watlyng streete. This Mylkie way, if it serued for none other purpose, yet doth it seeme woorthy the no­ting, for the exact consutation of the saide opinion, and for [Page 106] that cause it myghte seeme to bee made by God, which hath wroughte man ye meanes to leade men vnto truthe. This way is in the skye it selfe, as all men hath confessed, and their eyes doo testifye, and the starres that bee in it are alwayes seene to keepe their places in it: so that it muste needes folowe, that the same wayes doothe mooue with the star­res, and then consequentlye the skye muste needes moue also.

Yet it may be said, that the starres which bee in it doo moue alwaies so certainly in it, that it maye seeme to moue, as though it stande still.

Did you euer marke the same Mylke way?

Yea verily, and that often.

And did you perceaue in it any boughts, corners, partitions, or suche other like markes, wherby you myghte knowe one part of it from an other?

That haue I done also, in so muche that in som places it seemeth to be diuided into two waies.

That is true. And think you if the starres did moue in it, and it stande still, that these starres which now be by the partition of those branches, muste not within foure or fiue howers be passed farre from that place?

It shuld so folowe, yet that is not so: for I haue marked the contrary oftentymes, that they keepe those pla­ces styll.

Then do not the starres moue from their places, but as those places moue with them.

It appeareth now to plaine to bee made doubt­full any more.

Yet will I prooue it better: Dydde you euer marke anye notable place of that Mylke waye at the be­ginnynge of the nyghte in the easte, or in any other coaste of hauen?

Yea for southe.

And haue you marked whether that place hathe gone anye farther westward that nyghte?

I haue marked it well, and haue perceaued that it hathe moued a greate waye from his firste place: and who so euer lysteth to trye it, let him at sixe of the clocke in the deepe winter marke any notable places in it, and at tenne of the clocke the same nyght, hee shall perceaue it to haue gon westward more then a quarter of the skye.

Your woordes are true, meanynge a quarter of the skye aboue your Horizonte: and by this you see, it can not bee auoyded, but that the skye dooth mooue as well as the starres.

It is moste manifestly proued, so that Lactan­tius himselfe can not denye it, onlesse he will deny that hys owne senses may iudge in sensible thinges.

Then if the heauen be flat, as he doth imagyne it to be, and it doth moue westwarde, as all men dooth see, other the muste say that the skie is infinite in length, and that wee neuer see any parte of it againe after it is ones past our sighte: and therby affirme, that there be infinit many sonnes and as many moones, and an infinite numbre also of all o­ther Planetes, and of all seuerall kinde of starres, or els hee must declare whiche wayes that the Sonne, the Moone, and the other starres doo com into the easte againe.

He can not saye that they come backwarde the same waye that they went forwarde, for then wee shoulde see them in their retourninge: and to saye truthe, there can bee none other forme of mouinge, but in rounde forme, that may bringe them into the easte againe: But peraduenture he may say, that though the skie be flat and plain in forme, yet it hath a rounde motion.

Some other man may say so: for he thinketh the contrarie as his woordes importe, for in reprouing Astro­nomers, hee saithe: Ex motu syderum opinati sunt coelum uolui. By the mouing of the Starres they imagined that the heauen doth turne rounde by which wordes hee seemeth to meane that the starres moue, but not the skie

That is fully improued before.

If it were not, I myghte reason with him thus: Seyng he affirmeth as reason inforceth him, that the starres do moue, and will not confesse that the skye turneth round, then (as I declared before) one parte of the skye whiche is ouer oure headdes, is nearer to the earthe then the bothe endes be.

That appeareth plaine, excepte hee wolde saye against all reason, that the earthe were as large as the skye.

an argumēt against the flatnesse of the skye. The maior or maxime. Yet thoughe hee woulde saye so, my reason shall proceede in full strengthe, syth some partes of the skye by his meaninge muste needes bee farther from vs then some other. Therfore I frame my reason thus: All thinges that men can see, seeme greattest when they bee nyghest vnto menne, and the farther they bee from their sight, the lesses they shewe.

I thynke no man so childishe to denye that. for euery hower our sighte doth approue that it is so: if we see a man a farre of, he seemeth no bygger then a lyttle child: and a greate shippe farre in the sea, dooth shewe no bigger then a crow sometimes.

The minor. Then takinge that for a maxime in argumente, I annexe this minor, that the starres mouynge it that ima­gined flat skye, are most nighest to vs, when they bee ouer our headdes: and they are fardest from vs, when they be in the easte or in the weste:The conclusion. wherefore I inferre the conclusion, that the starres muste seeme greatest, when they be ouer our heddes: and they muste seeme muche lesser, when they be in the easte or weste.

This conclusion is plainly false. for our eyes doo testifye the contrary, syth alwaies the sonne, the moone and the starres doo seeme greatest at the rysinge in the east, and at their settinge in the weste. And they shewe smallest, when they be nyghest ouer our headdes.

If the conclusion be false, and the argument good [Page 109] as Lactantius can not comptroll it, then I maye obiecte to him his owne rule: Necesse est falsa esse, quae rebus falsis congruunt. It can not be chosen but those muste be false sen­tences that doo agree with false matters. and so muste they needes bee salfe premisses, that do inferre a false conclusion.

In good faithe I thinke nother Lactantius, no­ther any man els is able to auoide this reason, except he will auoide that fonde opinion of imagining a flatte skye, and the standing of the same vnmouable: yet if anye man wolde saye, that the heauen were square, or of any other forme of diuers angles, as here you se many varieties in these figures.An other reson by auoi ding of em­ptines whi­che nature cannot bere

How might I aptly reproue their opiniō, if thei will affirme farther, that the skye with suche a forme doth moue round? for by saying they mighte auoide the danger of this last inconueniene.

While they mighte seeme to auoide one danger, they fall into an other: as for a proofe. I tourne those figures round, whereby in deed it appeareth, that euery part of them keepe styll theyr owne distaunces vnchangeably frome the centre, but yet is one parte more nerer the centre then an other parte is, and euerye parte in their turning seemeth to describe a circle about the centre, eche circle in bignes according to the distaunce of that parte whereby it is described, and so the greatest circles are made by the extreame angles, of euery figure.

All that is easily perceaued, at the first sighte in tourning the figures aboute.

Then if the heauen bee cornered, it maye haue no lesse roome to moue in, then the compasse of the vtter­moste circle doth require.

That appeareth certaine, for els it woulde staye by those corners, or els break the corners in the tourning, wherof nether is to be fantasied but of fools, whose thoughts are pardonable in all those that refuse not their cōmon fe­lowshippe, but not in other, although for their woorthines they might be Wardens of that company.

Then if for their motion they require so large a circle, as may compas their corners, there appeareth voyde roome against euery side, in which roome what shal be set to auoide emptines, which nature can not beare?

Let them answere that lyketh that phantasy, for I can imagine nothing, except I shuld name Ayre, but that by his nature can not ascend so highe.

You gesse well, that it muste be some subtile and liquide thinge, that might change his place as fast as the heauens do turne: for in turning, the corners will come anone where the emptines is now, and so successiuely eche chaunge place with other. but Ayer you say cā not come thither, sith it may not ascend so highe: the lyke may you saye of fier and water, and muche more of thearth. Againe if they could as­cend, how shuld they pearse through the substance of the heauens? beside that being elementes, and therefore corruptible and subiecte to daily alterations, they are vnmeet to be mat­ched with the vnchangeable substance of the heauens.

This is reason inough against that imaginatiō, sith nature can not suffre it to bee emptye, and nothinge els but part of the skye can supplye it.

The thirde reason for apt mouing Yet considre farther: syth the motion of heauen of all other muste bee iudged the moste swiftest, whiche in 24. howers dooth runne so large a race, that is manye folde greater then the compasse of all the earthe, so that euery ho­wer it runneth many thousand miles, dooth not this swyfte [Page 111] motion require that forme, which is of all other most apte for mouing? & doth it not repugne to such formes as be full of corners, & therfore vnapt to moue swiftly or vniformly?

It appeareth plain madnes to dream ones the contrary.

Then all men know that as cornered bodies be most vnapt for to run, so is a round globe most apt for all other.

Euery cōmon turner can skil in y^t reason, & know y^t a litle altering of the one side, maketh the boul to run biasse waies.

If the reason be so plaine that common artificers can skyll of it, it were to great a folly for learned menne to doubte of it.

They that doubt of it, neuer waied their opinion with any reason, as I maye thinke, for these reasons suffice to persuade any man.

The fourth reason for capacitie. Yet ones againe way this for the for me of heauen. sith it incloseth all thinges, and is the greatest of all other, were it not meete that it shuld haue the greatest forme which is most large and apte to compas and inclose all other?

It is bothe meete and necessary also.

Then is it well knowen of yonge schollars in geo­metry, that as of all flatte formes of like circumference, the circle is the greatest, so of all sounde formes of lyke circuite the Globe is moste largest, and therefore moste aptest for the forme of the skye, whiche incloseth all thynges that man canne see.

I myght be ashamed to demaunde anye more profe for the roundnes of heauen or his circulare motion, yet are the reason so pleasante, that I delite muche in the hearinge of them, and therefore canne bee contente to imploye as muche time in hearing them, as you thinke good to bestow in framynge them.

I coulde occupye you so a greate tyme: but I thinke it not best to staye thereon to longe, syth wee haue many other matters to prooue, and at other tymes we maye talke hereof againe. These reasons whiche you haue hearde [Page 112] do proue not only that the motion of heauen is round, but also that the rounde forme doth best agree to the skye, for largenes of capacitye, for aptenes in mouing, for auoyding of emptines, and for the iuste appearance of the starres in vniforme bignes, whiche I thinke sufficiente for this time.

There be twoo thinges by the waye which I de­sire muche to heare more largely declared: the one is for the appearance of starres, whiche seeme moste greatest at theyr risinge and settynge: the other is, for the auoydinge of emptines, whiche as I haue often hearde, so woulde I gladly ones vnderstande.

The firste of them appertaineth to perspectiue, and the seconde vnto naturall phylosophye, so that bothe doo require an other place and tyme: yet bicause I haue alleaged it for this present matter, although the reasons why it is so, may not well here be repeted, yet that it is so, shall be brefely declared.All thinges shew great through vapoures or myste. In a mystie morning as you walk, all things

that you see, seeme greater through the myste, then in deede they be a pennye in the water seemeth broader then it is, and the deeper that it lyeth, the greater it appeareth: so the Sonne and the Mone and all other stars being nigh to the earth, do shew through the vapours that ascend frō the ground, and therfore appear greater then they be: & if the vapours be many, the starres shew the bigger: the cause is, the interruptiō and reflectiō of the sight beames by the vapours & the water. & liker is the cause in seing throughe glasse which occasioned weke sights to seke aid of spectakles

Many vse that aide, that know not the reason thereof.

Nature ab­horreth emptines. So manye drawe water at a plompe, that knowe not the cause, why the water do the ascend, whiche is onlye [Page 113] natures worke to auoide emptines. And many men vse bel­lowes to blow the fier, whiche know not the reason of their firste inuention, and therefore can not mende them if they be hard to draw. many men also draw waters by fountaines hi­gher then the springe, yet few of them do knowe what is the reason of their woorke, and therefore fewe canne amende it, if the faulte be any thinge doubtefull. A greate numbre of other lyke thinges coulde I shewe, where natures abhorful­nes to permitte any emptines, doth cause straunge effectes, in thinges that are vsed of many men, and well knowen of fewe men. But ass it appertaineth not to this place to dis­course largely in those matters, so an other tyme shall serue for them. And nowe lette vs proceede in oure purposed at­tempte, to see what proofes I can bringe for the roundenes of the earth: wherein I will beginne with a distribution dis­iunctiue, containynge many opinions touching the forme of the earth: and eche of them will I substantially improue,Diuers opinions of the forme of the earthe. saue that onlye whiche affirmeth it to bee rounde, and that will I so fullye approoue, that I doubte not but you shall thynke your selfe fullye satisfied. Som menne consideringe that as for the skie not forme was so meete as a round form, bycause of his swifte mouinge, so for the earthe whiche standeth so steddilye, they iudged no forme so meete as

a Cube forme, which they esteemed moste stable of all other: and therefore manye aunciente Philosophers by the forme of a Cube dydde secretely signifie constancy and stablenes:Why fortun is pictured standing on a globe. and contrarye waies by the forme of a globe they expresse changable alteration, and continuall mouing.

That I may perceaue by the placing of Fortune on a rouling globe, in token of hir inconstancy & voluble changinge. And therefore haue I often phantasied, that dice,Why dice be made in cubik form. whiche is the image of Fortunes inconstancye, and serueth onely for fortunes playes, myghte beste haue been made [Page 114] in forme of a Globe, for they are as vnconstant as fortune hir selfe.

Ther seemeth in Fortune two diuers natures,Diuers for­tune. the one is lyghte and alwaye flickerynge, the other is heauy, and therefore more stable, so that ofte tymes we see them that haue a lyghte and pleasunte fortune, as lightlye leese, that they lyghtly gayned: but where heauye fortune setteth hir foote, seldom can she be remoued, hir steppes are so stayed: but to expres more exactly the nature of the cube resembled in the dice, bothe in forme and in effecte, you shall marke well the meaning of that olde prouerbe: Iacta est alea, The dice is caste. or the lotte is drawen. or fortune is past. by whi­che saying is declared, that the thinge that is ones done, can neuer againe be vndone, although it may be altered, and so cōstancy in that appeareth most certein. for as your chance on the dice beyng ones caste, you muste be content to stand to it: so fortune when it is paste, can not bee altered. And that is the cause why all men vse to saye, when they expresse their stay in lyuing: Suche is my fortune. Yet many learned men put difference betwene chaungable chaunce, and stable fortune, callyng the firste Fortuna, and the other Fatum: so that destiny is stable, though fortune chaung right often. But thus I forget our purposed intent, with so many digres­sions of other bye matters.

I founde no faulte not thought no tyme loste, syth the matter is pleasunte and somewhat to our purpose.

Well, this was their imagination, that thoughte the earthe to be of a cubyke forme, for that they iudged it the most stedfast form.

The second opinion. Then an other sorte deuised a three cornered forme like he rygge of an house where tone syde lyeth flatte,

and the other two leane a slope. And thys forme they iudged better for twoo causes. Firste they thought that it [Page 115] was more steddy then a cube form, bicause it hath a broader foote, and a lesser toppe: and secondly for that they thought it a more apte forme to walke on, and more agreable to the nature of the earth, wher some times there ryseth highe hils, and sometime againe men may see greate vales descendyng.

This imagination is grosse inoughe.

And so grosse is the iudgement of the that fo­lowe not, or searche not for true reason, but content themselues with a lyght conceaued fantasye.

And in this they be deceaued, that they accompt this form more apt to walk on: for the flat of the cube is plainer, & therefore more apte to walk on, then is a slope ground.

If the syxte parte of the earthe were onlye inha­bited, then woulde it appeare so in deede: but if you go any farther, then haue you vnapte plainesse to walke on in theyr imagination, whiche go so downe righte, that they do feare fallynge. Againe they thinke this Rigge forme meetest for the standing of the sea, and for running of riuers: for in the fyrste forme, if the sea should reste on the ouermost plaine, then wolde it ouer runne all that plaine, and so flowe ouer all the earthe: where as in this seconde forme it mighte reste about the foote of the earthe, and yet the slope risyng wyll not permit it to ouer runne all the earthe. And so for riuers if there be no slopenes (as in a cube there is none) then can not the ryuers runne well.

The thyrde opinion. A thyrde secte thinkinge to amende

these bothe, imagined the earthe to be plaine and flatte: for so they fantasied that it wold rest moste steddilye, and so was it very easy to walke on.

We are more beholdynge to those men, for deuising our easy wal­kinge, then we are bounde to them for their wise doctrine.

The fourthe opinion. The fourthe secte, fearyng least by this opinion they shoulde leese the sea and all other waters, imagined the [Page 116]

forme of the earthe more apte to holde water, and deuifed it hollow lyke a bolle.

Those men were verye studious for staying of water, more then they were for framyng of their wittes.

Yet this vaine follye didde seeme to them greate wisedome.

Saue that I do credite your report, I wolde ne­uer haue thoughte, and muche lesse haue beleued, that euer anye suche madde imaginations hadde beene phantesied of anye men.

Who lysteth to see the monstruouse opinions of suche dreaminge doters, maye reade them often touched in Aristotle his naturall bookes, and aboundantly in Plu­tarche his boke De philosophorum placitis, and in Galene and Eusebius in bokes of the same matter peculiarly writen. But these 4 opinions which I haue here rehersed, are briefly noted in the firste boke of Cleomedes sphere, though not in like ordre: and saue that in the seconde opinion I iudge his printe corrupt, and that for [...], I do reade and tran­slate [...]: as it may well be gathered by his owne con­futation, which will not agree so well for confuting al stiple sormes or spire formes, but as mens iudgment ought to be free, so if any mā list to follow y^t print, I wil not withstād him.

Although some of these opinions are so grosse that they neede no confutation, yet I praye you repeate the confutations that Cleomedes doth vse.

I am well content, and better pleased to alleadge them in his owne name, then to ascribe them to my selfe, for diuers causes. Firste he beginneth with the thirde opinion, and reproueth it thus.he reprose of the third opinion. If the earthe were flatte and plaine, then should all nations haue one horizonte: for in a plaine flatte forme, there can be no iuste cause of alteration of the Horizont.

That foloweth moste certenly.

Then must the Sonne and Moone and all other starres rise to all people, when they rise to anye one, and so muste they sette (eche one in his course) to all men at one instante.

That will followe also.

If the Sonne rise to all men at ones, and sette like­wayes at one time, then muste the daye beginne to all people at one, & all nations must haue night at one time precisely.

That is false as all men confesse: for at Hierusa­lem (whiche is well knowen) it is day thre houres soner then with vs, and so is it nyghte sooner by thre howers also. But in Calecut (as learned men affirme, and trauelers thither, do confirme) it is daye 6. howers soner then with vs, and it is night 6. howers soner to them againe then to vs.

Your sayinges are true if they be well taken: but and if this conclusion bee false, as it is in deede, then muste that opinion be false, whereof this conclusion is inferred.

So doth it well folowe, and is fully prooued.

One stronge reason for the varietie of howers is gathered by the eclipses duly obserued, and namely of the Moone,, for as it happeneth at one instance of time, so is it not one hower to all nations. As for example:Examples of eclipses. This year of 1556, the eclipse of the Moone shall be with vs the 17 day of Nouembre at 3. of the clocke in the morninge, and to them at Calecut it shall be at 9. of the clocke in the morning: yea we shall see the Moone in the southwest, and they shall not see her at the same instant, for she will be to them vnder the horizonte in the northwest. like waies in the yeare of 1562. there shall be a great eclipse of the Moone with vs, whiche shall endure aboue three houres and an halfe, and yet shall they at Calecut see no part of it, by reason that the Moone shall be farre vnder their horizont before that eclipse begin. And in lyke manner this laste yeare 1555. was there a greate eclipse of the Moone the fifte daye of Iune, at three of the clocke in the morning, yet in Calecut there was none eclipse [Page 118] seene then, for the Moone was set vnder their horizont two howers almost before the eclipse began. But in the yeare of 1551. when we had the eclipse of the Moone at 9. of the clock at night, the 20. day of February, they at Calecut sawe that eclipse at thre of the clocke in the morning the nexte daye, as the Portingales that were there can testifye. Wherby it is manifest, that their Horizont doth not agree with ours, and thereof doth it folowe that the earth is not flatte. But nowe to returne to Cleomedes againe, (vnto whose wordes I haue added but the examples of the eclipses) his seconde reason against the flatnesse of the earth, is this.

An other re profe of the flatnes of the carthe. If the earth were flatte and plaine in forme, then the Pole must needes appeare at one height to all parts of the world, and the artike circle (which incloseth the starres that neuer set) shuld be but one to all nations. But bothe these thinges appeare plainly false: for as vnto vs about London the Pole is not fully 52. degrees highe, so if you go northward, you shall fynde the Pole to rise higher and higher, till it bee fully 90. degrees highe. and in going southward, the eleuation of the Pole waxeth lesser and lesser, till you come to the middle of the earthe vnder the equinoctiall, where the pole is of no height, but is equall with the Horizont. Also in all these places, you shall haue seuerall arctike circles.

That must needes folow the diuersitye in the ele­uatiō of the Pole, as it hath been sufficiently declared before

As the firste improbation doth reproue the flat­nes of the earth betwene easte and weste, bicause it regardeth chiefly the rising and settyng of the Sonne and other starres, and their course betwene easte and west, so this second con­futation improueth the opinion of plainesse betwene south and north. So doth it folow, that the earthe is flatte nother one way nother other, but bothe waies hath some certain ri­sing, which anon I will proue to be a iuste roundenes.

The thirde confutation A thirde reason is alleged by Cleomedes, touching the e­qualitie of daies to all nations, which shoulde of necessitye [Page 119] follow if the earthe were flatte, and all people had one hori­zonte, but bicause it is so little disagreable from the fyrste reason of one Horizonte, and one tyme of risinge and set­tinge of the sonne, I haue ioyned them both in one, as be­fore it dothe appeare. These thre reasons are plaine inough. The fourth reason whiche Cleomedes doth make, is not so easye, yet is it as certaine as any of the other: and therefore I will shewe you what it is, seyng you desire to heare his owne arguments, although I determined before to allege such rea­sons only, as myght appeare easy to vnderstand.

If it be not ouer muche obscure, it may please you to declare it in the moste playnest forme ye can.

I will only alter his ordre in the propositions, adding that wich is not easye to be gathered, to make it the easier to your vnderstanding. This is it.

The fourth confutation of the plain nes of the Earthe. If the earth were plaine, it shoulde folowe, that the whole diameter of the world from one side of the sky to the other, shoulde be but 100000. furlonges, that maketh 12500 miles, which saying appeareth so absurd, that no man will graunt it. but if any man wold do it, this argument folowing shall cōfute him. First therfore I reason thus. If the earth be plain, then al places in the earth ar as far a sonder, as their Zeniths, or Verticall pointes be in heauen. This maxime must I adde vnto Cleomedes, to make his reason the more plaine.

But this maxime do I not vnderstande, wherfore I beseeke you both to proue it, and declare it.

I am content.

You knowe by the former treatises, that the Zenith is the pointe right ouer the headde of any people, whose Zenith it is: whereof it muste folowe that euerye diuers place in carthe, muste needes haue a seuerall Zenith in the skye.

That is plaine.

Then imagining the earth to be flatte, the lynes that dooth ascende from any twoo places, vnto theyr Ze­niches in the skye, muste needes be paralleles, as here in this [Page 120]

picture doth partly appear. for if the circle be set for the skye, and the flatte square within it for the earthe, then take two places in the earth, as A and B. the zenith to A is C, & must needes be right ouer it, and therfore the line that is drawen from A to C, must be a iust plumb line, & perpendiculare to the flatte earth. And likewaies the ze­nith to B is D, which muste needes be righte ouer it, and therfore the line that goeth frō D to B, must of necessitye be a perpendiculare and plumbe line to the flatte earthe also. Then if bothe those lines be per pendicular to one flatte plaine, or to one line standinge for that plaine flatte, all the angles that they bothe doo make with the thyrde lyne A B, muste bee righte angles, accor­dinge to the definition of a perpendiculer line. Nowe if all their angles be right, then are they all equall accordynge to the fourthe grauntable request in the seconde booke of the Pathway, that all righte angles be equall eche to other. And if all their angles be equal, then must their matche angles be equall of sorce: wherby it doth folow accordinge to the is. Theoreme of the seconde booke of the Pathway, that those two perpendicular lines be paralleles, seyng that on 2 righte lines, as A C and B D, there is drawen a thyrde ryghte line A B, crossewayes, and maketh twoo matche corners of the one lyne, equall wyth the lyke twoo matche corners of the other lyne.

Hereby I haue not onlye gotten the vnderstan­ding of your proofe, but also I perceaue a farther vse in he Theoremes of the Pathway, then I knewe before.

I will prosecute my proofe. Syth those twoo [Page 121] lynes bee paralleles, and equallye distaunte, then is there as muche space betweene A and B, as there is betweene C and D.

Thus is your maxime sufficiently proued, and fully declared: for A B betokeneth the distaunce of the two places in earth and C D, standeth for the distaunce of their zeniths in the skye.

Nowe therefore will I retourne to Cleomedes argument. They that dwell at Lysimachia (in Grece) & thei that dwell at Syene (in the southe parte of Egypte) haue be­tweene them in distaunce 20000 furlonges (that is 2500 mi­les) wherefore it must solowe that their zenithes in the skye be no farther a sonder, seyng they be limited by two perpen diculers equallye distaunte: but it is well knowen by good proofe of instrumentes, that Syene is vnder the Tropike of Cancer directly, and Lysimachia is vnder the hedde of the North dragon, which 2 places in the skye are iustly pro ued to be a sonder the 15 part of the whole compas of hea­uen, that is the first part of the diameter of the skye. Wher­sore if 20000 furlonges be the first parte of the diameter, the whole diameter must be but 100000 furlonges: & the whole compas of the skie muste be but 300000 furlonges, and of these furlonges it is prooued, that the earthe contayneth in compas 250000. so is the heauen lyttle bygger then the earthe in compas whiche absurditie maye easily be con­futed by the Sonne, whiche in comparison to the skye, is a verye lytle parte of it, and yet is bygger than the earthe mannye folde: whereby anye manne maye see what ab­surditye foloweth that opinion, to thynke that the earthe is flatte.

I doo metely well vnderstand this reason, but I shuld better haue conceaued it, if I had knowen the two pla­ces whiche hee alleageth for examples sake.A like rea­son.

Then will I for your pleasure make y^e like argument by example of 2 places which ar better knowen to english men. [Page 122] you knowe the castle of Arundell.

The name is auncient and famous.

And Newe castle vppon Tine is well knowen to you also.

So is it.

To go the next waye betwene these two places it is 270 englysh myles.Arundel castle. And the Zenith of Arundell castle (whiche is the iuste point of the latitude of it) is 50 degrees and 30 minutes, as ones I remembre I tooke note of it in ri­ding that waies. The Zenith also of Newcastle is from the equinoctiall 55. degrees, so is the difference betwene their ze niths 4 degrees and 30 minutes. Now (as I haue declared before) If the earthe be flatte and the perpendicularre lines bee paralleles and equidistant, that go vp from these two places to their zeniths, then is 4 degrees and 30 minutes, iust equal in quantity to 270 myles.

That is true, as it is proued before in the third treatise.

You are farre deceaued: it is declared there, that 270 myles in earthe, muste answere in proportion to foure degrees and an halfe, and not that they are equall togyther.

I perceaue mine owne negligence in markinge the propretye of speache. I shoulde haue sayd, that as foure degrees and an halfe is the eight score part of the whole compas of heauen, so 270 myles is the eighte score parte of the circuite of the earthe.

That is true: but yet these 2 partes are as farre vnequal in quantity as hea­uen & earth ar vnlike in their compas, wherfore to the in­tent that frō henceforth you shall not mistake it againe, I wil by lineary demonstratiō set before your eyes the de­claration and difference of [Page 123] them bothe more plainly then curiously.

Here in this figure you see two circles drawen vppon one centre, their common centre being G, from which there are drawen to the vttermost circle two right lines G A, & G D, these lines do crosse the lesser circle in 2 pointes E and F, fro whiche two pointes I haue drawen twoo paralleles, vnto the circumference of the greater circle, whiche two paralleles be B E, and C F. Nowe may I say, that bicause these two circles be made vpon one common centre, and twoo lynes drawen from that centre to the circumference of the both circles, bicause A G D is one common angle in them bothe, ther­fore are there arche lynes inclosed betweene those two ryght lynes lyke in proportion.

I perceaue it well: so that if the arche lyne A D in the greater circle, be the syxte parte of it, then is E F the arche lyne of the lesser circle, the syxte parte of his owne circle, in lyke manner. but yet that arche of the lesser circle is not so greate as the lyke arche in the bygger circle.

Then what saye you of the arche B C, in com­parison to the arche E F, whiche bothe arches are betweene twoo lines paralleles?

They muste needes bee equall, seynge there is iuste as muche distaunce betweene E F, as there is be­tweene B C.

So maye you nowe perceaue what difference it is to saye, that two arches of two seuerall circles, are like in proportion; and to saye that they are equall in quantity.

Nowe I perceaue it plainly, that although 4 de­grees and an half (as your former reason did import) be like in proportion to the whole circumference of heauen, as 270 miles are in comparison to the compasse of the earthe: yet it foloweth not that they should be equall togither.

But supposynge the earthe to bee flatte, then it foloweth as I haue declared beefore, that they are equalle in quantitye, seeynge bothe beetoken the [Page 124] distant of one couple of paralleles. And thē it foloweth, that seinge 4 degrees & a half is the four score part of the compas of heauen, if I multiply 270 myles (whiche is equall to it) by 80, therof will amounte the numbre of myles that make the compasse of heauen, whiche are 21600 myles. Nowe to know the diameter of it, [...] I take the two receaued numbres for the proportion betweene the circumference of a circle and the diameter of it, whiche are 22 and 7, (as in the Pathway is declared more largely) and by the rule of proportiō I work in saying: if 22. giue 7, what shal 21600 yelde? and there amounteth 6872 8/11, whiche must be y^e whole diameter of the skie, if the earth were flatte.

[...]

That is to greate an inconuenience for any man to affirm. for therby I se it wold folow that if we go any waye from our owne cuntry, 3436 miles, we shal com hard to the sky, which is to childishe a fantasye, sith not only reason, but dayly trauell decla­reth the contrarye. Againe I re­membre that in the thirde treatise you declared that the earthe was so muche in compasse, whiche muste needes bee many fold lesse then the heauens, whiche ar so farre distaunt from the earthe on euery side.

Thus are all Cleomedes reasons against the flat­nes of the earth fully alleaged, & somewhat largely declared: Now wil I proceede to y^e confutatiōs which he vseth against y^e other opiniōs, folowīg his own ordre. wherfore next doth [Page 125] folow the confutation of them which say that the earth is holowe like a bolle.The consu­tation of the fourthe opinion. Against whose phantasticall imagination he reasoneth thus: If the earthe were hollowe as a bolle, then should the Sonne, the Moone and all Starres in their rising appeare soner to them that dwell in the weste, then to them that dwell in the easte: whiche thinge is contrary to daily ex­perience.

For declaratiō of which saying by line­ari demōstration I think good to drawe a figure, wherin you may aptly se the force of his reason. The vttermost circle of y^e figure doth represent the skye, and the inner most half circle stādeth for y^e imagined holow­nes of the earthe, & the halfe roundelet A B, representeth the massy substance of the earth, the right line K L, expresseth the diameter of y^e world, and therfore the right Horizont of the earthe, K beinge the east and L the west. Now for explication of Cleomedes rea­son: If the earthe were holow, as here the forme of it is dra­wen, then when the Sonne is risen, in the easte aboute E, it wold appeare to them that dwell in the west by B, & not vnto them y^t dwell in y^e east by A. for the brow of the holow groūd by C, doth hide the Son yet frō them, so y^t he must ascend as high as F, before they y^t dwel in the east by A may see hym. Again when y^e Son goeth doune, by this opiniō he shuld set to them that dwel in the west by B, as sone as he came to G, by occasion of the browe of the ground by D. and yet they that dwell in the easte by A, should see him a great while longer: for that browe of grounde by D, wyll not yet hynder their sighte, vntill he be descended as low as H. So shoulde they that dwell in the west see the Sonne soonest in the mor­ning, [Page 126] and they that dwell in the east shoulde see him latest at eueninge.

This thinge is so false, that euery chylde kno­weth the contrarye.

Yet of that opinion dooth there folowe farther inconueniency,An other reproofe of the same o­pinion. as Cleomedes doth shew: for by this fanta­sye, they that dwell in the southe should see the northe Pole more higher aboue ground, and so should haue a larger ar­ctike circle, then they that dwell in the northe, as by the same figure it may be declared.

I perceaue it well: for if I make K to be the south, and L the north, then it appeareth in this form of the earth, that they which dwel in the south by A, may see as low as H: and they that dwell in the northe by B, canne see no farther northe then G. whiche is so farre against reason and daylye experience, that it must needs appeare to be a vaine fantasy, that bringeth for the so mad and monstruous conclusions.

Yet an o­ther confu­tatiō of the same opiniō Yet doth there folow more fonde conclusions of it: for by this opinion all nations that dwell within that ho­lownes, should see lesse then halfe the skie, lesse then halfe the Zodiak, and lesse then halfe the Equinoctiall, wherof it wold follow (beside other absurdities) that they shuld haue their nighte commonly longer then their daye, bicause that parte of heauen which they se is lesse (especially to them that dwell in the botome of that holownes) then that part which is vn­der their horizonte: Yea they that dwell in the botome of that holownes, canne neuer haue their daye so longe as their nighte, bicause they do see so litle a portion of the skye. As a man that is in a deepe trenche or in a pitte, can see but a li­tle of the heauens. And thus hath Cleomedes sufficientlye confuted those two opinions: whiche kinde of confutation Ptolomye doth vse also against bothe those opinions.

Then must they needes be good:Ptolemye. for as I heare all learned men say, Ptolemye is the father of that arte, and proueth all his woordes by stronge and inuincible reasons.

No man can worthely praise Ptolemye, his tra­uell being so great, his diligence so exacte in obseruations, and conference with all nations, and all ages, and his reaso­nable examination of all opinions, with demonstrable con­firmation of his owne assertion, yet muste you and all men take heed, that both in him and in al mennes workes, you be not abused by their autoritye,Autority of writers. but euermore attend to their reasons, and examine them well, euer regarding more what is saide, and how it is proued, then who saieth it: for autori­tie often times deceaueth many menne, as here by and by in Cleomedes it shall appeare, whose argumentes in confuting the other two opinions ar nothing substantiall: which chanced other bicause he sawe the fondenes of these opinions so great, that he sought no great reasons to confute them, other els hastinge in his writinge caused him to vse the lesse dili­gence in framynge his reasons. but nowe will I repeat them.

Cleomedes argumente against the first opiniō. If the earth were of cubike forme, then should all nations haue syxe howers daye only, and 18 howers nyght, seing ther be rounde about the cube four sides, so that on eche of them the Sonne shoulde shine 6 howers only: this is a very weake argument.

Yet vnto me it seemeth a strong reason: for se­ing that the Son doth go round about the skie and aboute the earth also iust in 24 howers, it must needs folow that he spendeth only 6 howers in euerye quarter: and a cube hathe but four sydes in his compasse, (althoughe it haue 6 sides in all) wherfore in mine opinion it is well concluded, that euery one of tose four sides, doo see the Sonne 6 howers iustlye.

Often haue I readde in Galene, and more often haue I seen it by experience, that better it is for men to want all arte of reasoninge cleane, then to haue suche confidence in a meane knowledg therof, that may occasion them to de­ceaue them selfe, and to seduce other. You are fully perswa­ded that this argument is good: whereby it appeareth that you espied not the want of that meane proposition, whiche [Page 128] should make the argument good, which muste be this: that euery quarter of the sky, agreeth to one quarter of thearth.

That not only I thinke to be true, but your selfe affirmed it also before this time, as a true sentence.

And so will I do still, affirming it of the true form of the earthe, but not of this imagined cube forme.

Why, is there anye difference in the quarters of any formes? is not a quarter of a cube the fourth part of it, as well as a quarter of a Globe is y^e fourth part of the globe?

Yes, but yet doth not the quarters of the cube so agree with the quarters of a globe, as the quarters of two globes agree togither.

That I vnderstand not.

Then will I declare it manifestly by lineary demon­stration.

Marke these figures. Here you se first for the true opinion, 2. circles drawen one with in the other vpon one centre, and the same are diuided into four quarters ech of them, so that the four quarters of the lesser circle, E F G H, do answere agreably to the four quarters of the greater circle A B C D, but in the secōd figure, where the cube is made in lue of the earthe, the quarters do not agree, as you may perceaue by the draught of the right lines, agreable to eche side of the cube: for euery side of the cube hath almost halfe the circle aboue his horizontall line. Wherfore if you will haue a cube drawen in a globe, in such sorte that the quarter of the one in cōpasse shall agree to the like quarter of the other, that cube muste be so great, that his [Page 129]

corners may touch the globe on eche side, so muste it bee as greate a cube as maye bee made within that globe. And I am sure you will not say that the earthe is so great in comparison to the skye.

Now I se mine owne erroure, and the fault of Cleomedes ar­gument.

And if anye man wold excuse Cleo­medes, he must say, that Cleomedes did make y^t reason against suche as affirmed two errours at ones, that is the cu­bike form of the earth, & the greatnes of it also to bee suche, as mighte touche the skye with e­uery corner: but if this had been his meaninge he might easily haue expressed it so: but what so euer he ment he framed the confutation of the second opinion in the like sorte. for this is his argument.

Cleomedes confutation of the secōd opinion. If the earthe be of a three cornered forme, then shuld the Sonne shew 8 houres iustly on eche side of it, and so wold it be to al people 8 houres day, & 16 houres night: which thing is to appearant false: so can not that opinion be true. for de­claratiō of this argument I haue drawen first a circle for the sky, and then a small triangle forme D E F, vnto whose thre [Page 130]

sides I haue drawen 3 streight lynes, representing three se­uerall horizontes. but it ap­peareth at the firste sight, that eche of those horizontes doo contayne aboue them almost halfe the skye. So that in this quantitye of the earth, Cleo­medes reasō taketh no place, nother generally in any other but one, where the three cor­ners of the earth may touch the skye, for whiche forme I haue drawen the greate trian­gle A B C.

Yet although Cleomedes argumentes bee not sufficient to confute their opinion, that would say the earth were of any of these bothe formes, their opinion is false ne­uerthelesse. thinke you not so?

Yes verely: for a weake confutation of an vntruth doth not make that vntruth to become true. And bicause you shall not thinke that these opinions haue anye sure grounde, I wyll repeate Ptolemye hys confutation of them both, by one vnfallible reason.

Ptolemy his confutation of the firste and seconde You see in bothe these imagined formes of the earthe, that there can be no more horizontes, then there be sides in the fygure.

That is certaine: for all that dwell on one plain side, must needes haue one horizont: wherfore if the forme of the earth wer four square in his compas, then could ther bee but fower Horizontes, that waye: I vnderstande it betweene easte and weste, and in all varieties there canne be but syxe, syth a cube hath but syx sydes: lykewaies in the thre cornered forme, there canne be but three diuers horizonts betwene easte and west.

You saye well. And seeynge all that dwell [Page 121] on one plaine syde haue all one horizonte, they muste haue day all at one instant both for the sonne risinge and also for the setting, so can ther be no more variety in the beginning and ending of daies, then there are sides in the figure of the earthe, whiche by the firste opinion must be but 4, and but 3 by the seconde opinion, where as the contrary is well kno­wen by dailye experience, as well as by reason, that euerye 15 degrees in distaunce westwarde maketh the daye an hour later: and contrarye waies euery 15 degrees of distaunce est­ward, causeth the daye to be rather by one howers space.

That is proued also before, in confutation of the third opinion, and namelye by examples of eclipses. But what if any wolde affirme that the earth were made of many flattes, as of 24 (for an example) betwene east and west, then shuld there be no more horizontes, then there bee howers in one naturall daie, and yet so the difference of howers could not confute them.

You must thinke that learned men canne as well marke the difference in euerye minute of an hower, as the common people can obserue diuersities in howers: yea the learned obseruations are more exactly taken thē the 60. part of a minut of an hower, wherfore seyng it is so well proued by sondry obseruations, and especiallye by eclipses, bothe of the sonne and the moone, that euerye mile distaunce be­twene easte and west, dooth make a seuerall horizonte, there can bee no other forme of the earthe aptlye assigned, but a rounde circular forme. And by the lyke reason, by the or­drely ascending of the Pole, in goinge northward, and by the vniforme descending of it in going southwarde, it must needes appeare that there can bee none other forme of the earthe betweene southe and northe, but a rounde forme also.

Nowe canne I ende your argumente of the di­stribution disiunctiue, whiche maye be framed thus.

The colle­ction of the argumente The earth must haue some forme, either cubike, thre cor­nered, flatte, or holow, or some suche lyke, other els a round [Page 132] forme, but his forme can not be cubike, nor threcornered, nother flatte, nother holow, nor anye suche lyke, as before is fully prooued, wherefore it muste needes be rounde.

It foloweth well. for it is not possible that in any other imagined forme of the earthe, the horizontes should alter toward euery coaste so vniformely, and the dayes differ so proportionably, the Pole to be eleuate so ratably, or to be depressed so ordrely, and all other appearances to answer so agreably.A roller forme. Yet some men (as Ptolemy doth reporte) had inuented an other forme lyke a roller, or a rounde pyller, whose endes shoulde lye north and south, by whiche forme althoughe they thought none of the varieties of appearan­ces myghte bee hindered, yet in that forme the eleuation of any one of the Poles could haue but two varieties for euer more it muste appeare other ouer their heddes, as to them that dwell on the flatte eandes of that roller, or els to all o­ther that dwell about the compas of the roller, it must still appeare in their horizonte, so shoulde ther bee no starres about either Pole alwaies appearant aboue ground, nother all wayes hydde vnder grounde, but all starres should ryse and set to all them that dwell about the roller. And againe they that dwell on the flatte endes of the roller, shoulde haue but one Horizont, so large in distaunce of ground, as the whole thicknes of the earthe is: all whiche imaginations are bothe well knowen to be vaine, & also easye to be confuted by the former reasons, which serue so largely, that you can ima­gine no forme other then round, but those reasons will confute it. wherefore your argument doth proceede well.

That the water is round by diuers profesYet farther for the roundenes of the water also, and name­ly of the sea, you maye frame argumentes by the lyke forme of appearances: for where so euer you bee on the sea, you shall see halfe the skye iustlye, and the farther west that you go, the later dooth the Sonne rise: and contrarye waies the farther easte that you saile, the sooner in the morning will the Sonne appeare to you. whereof I will declare vnto you [Page 133] a notable example, and a iuste proofe.

An exāple of the roūdnes of the sea by a ship­pes ceurse.Imagine a ship swift of saile to be at the cape of Cornwall ready to make sayle towarde the weste directly, and to haue a greate gale of winde, it is possible that she maye run 240 myles in 24 howers: for I haue beene at the triall of a greater course, therefore I speake (as men say) within my boundes: after which rate she shall runne in 16 howers 160 myles. Now let hir hoise saile at the sonne rising, and let the time of the year be somwhat before midsommer, or little after, when the Artificiall day from sonne rising to sonne settinge, is 16 ho­wers longe: by this meanes at the end of 16 howers, she shall be west of the cape of Cornwall where she began her course 160 myles: and then shall the sonne be at setting to their sight that dwell at the saide cape, but the shippe shall haue the Sonne aboue foure degrees hyghe at that instaunte, by reason that she dydde runne with the Sonne, and that the roundenes of the sea doth chaunge the horizont so many degrees in 160 myles.

Althoughe this example bee pleasaunt, yet it passeth myne vnderstandinge, sith that I beleued hitherto, accordinge to your former doctrine, that 160 myles would not haue altered any waies three degrees, seyng 60 myles do answere to one degree.

That sayinge is true all wayes for the eleuation of the Pole, for going betwene south and northe in all pla­ces; but for going betwene easte and weste, it serueth onlye for the myddle of the worlde, that is vnder the Equino­ctiall circle: and in all other places, the farther you bee from the Equinoctiall, the fewer myles answere to eche de­gree, by reason that the paralleles growe lesser styll to­warde the Poles: yet the leaste of theym is dyuided into thre hundreth and sixtie degrees as well as the greatest, whereof hereafter I will instructe you more exactelye. in the meane ceason, you shall vnderstande, that for the lati­tude [Page 143] of the cape of Cornewalle, euerye degree requyreth onlye 37 myles:How many myles aun­swere to a degree at the southe coaste of Englande. whiche beynge multiplied by 4, maketh but 148: and therefore I sayd aboue 4 degrees did answere to 160 myles, as the truthe is.

Nowe I perceaue somwhat better the reason ther of by the proportion of the parallele circles in the Sphere. and surely this proofe is pleasante, and easye inoughe to bee tried.

A lyke example may this be. Suppose at the same tyme of the year when the day is at the longest,A lyke exāple of a shippes course. that there is a swifte shippe at the weste pointe of the isle of Islande, wher the longest day is 20 howers from Sonne rising to sonne set­ting, in those 20 howers, that shippe might sayle westwarde 200 myles. Then considering that at that latitude whiche is aboue 63 degrees, there answereth but 27 miles to a degree. when the ship is at the ende of his course, the sonne will sette to them that bee in Islande; and then shall the shippe haue the sonne 7 degrees and almost a halse, aboue the horizont, (which maketh halfe an hower in time) so that by the roundnes of the sea, they haue chaunged their horizont so much in twentye howers saylinge. Nowe turne his course and let the shippe haue like wind homeward againe the nexte daye, and let him make saile at the sonne rysinge, then shall it bee after sonne set halfe an hower, before she shall ariue at the former porte: by reason that the sonne rysse halfe an hower later to the shippe, where shee was in the weste, then it dyd to them at Islande: and therefore muste it set halfe an hower rather at Islande, so hathe the shippe loste halfe an hower, by comming eastwarde against the sonne.

I vnderstand that. As 15 degrees doth answer to an hower, so 7 degrees and a halfe maketh halfe an hower: wherefore if the shyppe sayle iuste twentye howers, and that artificiall daye is iust 20 howers longe, then shall they come to their port in Island halfe an hour after son setting, bicause [Page 235] it was halfe an hour after Sonne rising in Island, before they began to make saile.

This varietie coulde not happen, except the wa­ter also were rounde as well as the earthe.An other proofe that the water is rounde. And for farther proofe of the roundnes of the sea, daily experience doothe teache vs, if we wold diligently obserue it, howe that when a shippe doth draw towarde londe out of the maine sea, the lowe grounde doth not appeare at the firste vnto the shippe but the toppes of high hilles and cliffes: like waies they that be on the londe and looke to the shippe, they see the toppe of the ship firste, and after that, the mastes, sayles, and shroudes before they can see the hulle, and body of the ship. Now I demaund of them that thinke the water to be flatte, what is it that letteth the syghte, so that it canne not as well see the lowere grounde from the shippe, or the hulle of the shippe from the londe.

They can name nothing but water: for there is nothinge els betwene them, hable to stay the sight. But then peraduenture they will saye, it is the waues of the sea, whiche rise verye highe often times.

That were to childish an answer, sith the lyke doth appeare, and that most exactlye, in a greate calme, when the sea seemeth as plaine and as smothe as a borde: so that they muste shewe som such thing, as is higher between them then any of both theyr syghts, when the sea is as quiete as can be.

Then is there nothinge but water. But then it seemeth to me, that if the water did rise rounde, the farther the shippe were from the lande the higher she should be, and therfore the better myghte be seene.

Your imagination hath small ground of reason: for although the earthe and the water both ioyntlye and se­uerally bee rounde of nature, and therefore haue in deed no place hygher then other in their circumference, yet all vul­gar men shall thinke by apparance that that place is highest wher thei stand, & that frō them on ethe syde ther is a round [Page 136] descente, vntill by imagination they come to the right con­trary pointe where their Antipodes be, whome they shall think to be right vnder thē, wher as those Antipodes haue the contrarye imagination, that they dwell on the highest parte of the grounde, and that their sea is hyghest, and so bothe descendeth compassedlye vnto the contrarye poynte to them againe. and thus euerye other sorte of people think that they dwell on the highest parte of the londe, and also of the sea, (if they dwell on the sea) and they shall thynke that bothe the sea as well as the londe doothe descende from them eche waies.

As in this circularre forme of the earthe and sea, the menne that dwell by A, thinke them selues to dwell hyghest of all other, so that on eche syde of them the londe & sea seemeth to descend, & therefore they iudge the ship that is by B, to bee lower then they, where as that shippe, contrarye waies, seemeth to them that be in it, to bee on the hy­ghest parte of the worlde: and therefore they thinke that the londe by A, is lower then they are. Againe they that dwell by C, and the shippe that is by D, are of like imaginations, eche in his fantasie thinking him selfe hyghest, and the other lower. And so of them that dwell by A and by C, eche meruayleth how the other canne go, and his headde downewarde: yet in deede none is lower then other, sith eche of them is equallye distaunte from the centre of the earthe, whiche is the lowest place of all other. and therfore no waye is accompted lower except it be nearer to that centre. wherby also it may appeare contrary to your sayinge, that although the sea bee rounde, yet shall not the ship seem to ascend still, but rather seem to descend, thoughe in deed it doth none of both, but moueth circularly about y^e [Page 137] centre of the world, so that it can not aptly be called a right motion, but a compassed motion that a shippe maketh, saue that it is tollerably to be borne in vulgare speache, bycause euery small arche of a great circle, seemeth to be a right lyne to the syght of the eye. And in this figure is somwhat repre­sented the declaration how the compassed form of the water doth let the sight to see the ship, and like waies how that thei on the londe may se the toppe of the ship when they can not see the hulle, and they in the bulle of the ship can not se those places on the londe, whiche other in the top of the ship may see, by reason that their sight is aboue the height of the wa­ter. And this may stande for a conuenient proofe.

So dooth it appeare manifestly, now that my former misconceaued fantasye is reproued. And so I remembre when I haue loked after a shyp that departed from the porte where I stoode, first I lost the sighte of the hulle as thoughe it had sonke into the sea, and yet I saw the toppe still: but at lengthe I loste the sighte of it also, as thoughe all had sonke into y^e water. which by your declaratiō I perceaue doth folow of the roundnes of y^e water: for other reason I can find none.

Although you could fynd other reasons neuer so many, yet this reason doth enforce that effect. this is y^e reason that Ptolemy, Cleomedes, and after them Ioannes de Sacro bosco, and other also do alleage,A physicall reason for the roūdnes of the wa­ter. but the same Iohn hathe an other reason more physicall thē geometricall, borowed out of naturall phylosophy, which is this: Seing that the water is a body of vniforme substance, the partes of it must be of lyke condition as the whole bodye is: but the partes of water dooth all wayes couette a rounde forme, (as wee see in euerye droppe that falleth from any thinge, or standeth on anythinge) wherefore of iuste congruence the whole body of the sea and water must needs couet the same forme.

In deede all droppes that fall from the ayer in a mylde rayne, when menne maye marke it, doo fall in a rounde forme, and so the droppes that fall from the [Page 138] eaues of the house, or from any thing els, yea and the drops of dewe that stande vppon anye leaues of herbes, or other lyke thinge.

For a farther experience, fyll anye vessell brym full of water, and you shall perceaue by tryall, that the wa­ter is higher ouer the myddle of that vessels mouth, then it is by the brimmes. And againe pour out water on a borde or on a stone, and you shall soone see that it will shewe in a round forme, and will be deeper in the middle, then it is by the sides.

Erasmus Rheinhold.Yet farther reasons there be alleged, whiche were to tedi­ouse to repeate: but twoo of them I can not omytte, whiche are declared by Erasmus Rheinholt a manne not onlye of greate learning, but also of as greate honesty in seekinge to profite all men by his trauaile, although sometime hee wan­ted leasure to examine some of his writinges, as it may ap­peare by one of those two reasons, whiche is this.

An other reason.By the longe course of euerye greate ryuer (sayth hee) it maye appeare that the water doth couet a rounde forme, els could it not so much rise in roundnes, as it doth in running so longe a course. for example he bringeth the course of the greate ryuer Danubius, which springeth in the Alpes, bee­syde Vlma in Swicerlande, and entrith into the sea Euxine, aboue Constantinople, whiche is from Vlma 312 germanye myles, that is 20 degrees, whiche is the eightenth part of the whole circuite of the earthe: whereby it muste needes folow that the myddle of that ryuer is higher then the fountaines or the mouthe, by 13 germanye myles (that is 52 englyshe myles) in plumbe heighte. for declaration whereof hee ma­keth this demonstration linearye, supposynge A E B C, to be as one of the greatest circles about the earthe, whose cen­tre is D. this circle must be imagined so to passe agreably to the course of Danubius, that A maye represente the foun­taines of it, and B the mouthe of it, so E shall stand for the myddle parte of the riuers course and A E B, for the whole [Page 139]

course. Now is it sayd be­fore, that betwene A and B are 20 degrees, then if you draw a right line from the one to the other, as heere you se A F B, it will be lo­wer vnder the myddle of the arche, by the length of the line E F, whiche is al­moste the 60 parte of the semidiameter of y^e earthe, and maketh iustlye 52 en­glysh myles, sumwhat lesse then 57: whiche is the 60. part of the semidiameter of the earthe.

This reason seemeth pleasaunte, but I perceaue not the reason of the iuste quantitye of the lyne E F.

That dependeth of the arte of Sines and Cordes and is very certaine without any sensible errour, of whiche in an other place ye muste learne the vse. And in deed as you saye, this reason is pleasaunt, and the author muche to bee praysed and loued, and as muche is it to be lamented, that the shortnes of his life would not permitte him to haue re­cognised his workes againe: wherfore that he can not do by preuention of deathe, I truste some of his friendes will do: for althoughe they be but litle faultes, yet pittye it is that in so good woorkes there shoulde remaine any litle spottes, as in this argument there are two, which yet hinder not the ar­gumente. And althoughe it might bee truely sayde that the heighte of the myddle of Danubius is not 52 myle, and is but 36 mile, yet is the forme of his argumente good, for that height is sufficient to proue that the middle appeareth muche higher then the fountaines of it: the cause of this o­uersyght was, that hee did esteeme the course of Danubius to runne by one of the greatest circles of the earth, which is not so: for it hathe in latitude from the equinoctiall 46 de­grees, [Page 140] so must the parallele of his course bee litle more then two third parts of the greatest circle: but as this is somwhat to straunge for you yet beyng vnexpert in the arte of Cor­des and Sines, and in the knowledge of Cosmographye, so I wyll lette it passe with this lyghte admonyshmente, wysshynge that hee hadde also more aptelye expressed hys meanynge, and the vse of his termes, for auoidinge of slan­derouse tongues, for it myghte nowe bee answered hym, that Danubius is no hygher in one place, then in an other, seeynge all distaunce of heighte is to bee accompted from the centre: and the middle of the riuer by E, is no far­ther from the centre D, then is the fontayne A, or the mouthe B.

Marye that obiection is certaine, and therefore is his errour manifest, and his argument of no force.

Erasmus Rheinholt excused.You triumphe to muche before the victory. his argument is better then you do considre it his intent was to proue that the water doth not run by a right line and doun­warde still, as the vulgare sorte doothe imagine, but that it runneth circularlye. wherefore it foloweth well against the vulgare opinion, to say that the water of Danubius is hy­gher in the middle of this his course, by so manye miles in height plumb vpright, then it shuld be by their imaginatiō So is there none other fault in this point, but the want of distinction of the true opinion of highnes and lownes, from the wronge takinge of the same names, wherby those which do not know his great learning, and myght happen to hear his argument, wold iudge that other he were wonderfullye deceaued, other els that he did to much abuse hys tearmes: but if deathe hadde not preuented him, hee woulde haue declared his meaninge, I doubte not, as I haue declared it.

Erasmus Rheinholt his seconde argument.Nowe to hys seconde argument. he proueth that there can be no such holownes in the sea, as there is betweene two hylles for seeynge the sea is a heauye bodye, and presseth towarde the centre of the worlde, euerye parte of it [Page 241] wyll doo the lyke if it be not stayed. And the water beynge a lyquide and fluxible bodye, can not be stayed by his owne partes: wherefore it foloweth that there can remaine no va­lyes nor dales, nor hollowe partes in it, but it shall quickly be fylled with water. and therfore wee see, that nothinge can be more plainer then is the toppe of water, syth euery part so exactly ioyneth with other, in fyllinge vp all vnequalitie: whereof it foloweth, that if the toppe of the water be iuste equall and lyke distaunte from the lowest part of the world, (which hath been often declared to be the centre of y^e earth) then muste the face of the water needes be round, according to the definition of a circle.

Why the water doth not couer all thearth.That foloweth well in deede: for as eche parte of the circumference in a circle is equally distaunt from the eentre, so if all partes of the face of the water be equally distant from the centre, it must needes be circular, as the circumfe­rence of a circle is. But if it be so round, and ought to haue his place aboue the earthe, how doth it happen that it doth not couer the whole face of the earthe? and so shoulde there be no earth seene.

Haue you forgotten what you readde in Ioannes de Sacro Bosco, for to answere that question?

In deede he sayth that the other three elementes doo compas the earthe round about, saue that for the pre­seruation of man and beastes, the drinesse of the earth doth withstande the moysture of the water.

That reason sauoreth more of the determinati­ons theological, then of the demonstrations mathematical, wherfore I will adde therto a proof by good demonstratiō that it can not compasse the earthe rounde:That the water 1. can not cō­pas the arth II. for whiche pur­pose firste I saye, that the water beinge inclosed within the boundes of the earthe, can not be so greate as the earthe is. Againe considering that one portion of water being mixed with 4 tymes so muche earth, wold make it all softe and slab­by, it may not be thought that the water of the sea and of [Page 142] all ryers and springes ioyned togither, is so muche as the firste parte of the earthe.III. Farthermore if you consider the firme stablenes of the earthe, and the vnstable swaruynge of the water, you wolde thinke that if the water were able to matche the twentith parte of the earthe, it woulde make the earthe more vnstable then the nature of the earthe, and the preseruation of earthly creatures could beare. Yea it would be a weak ground to bear so wondrefull a waight as it doth,IIII. if the quantity of water were notable, in comparison to the quantity of the earth.V. Yet now for farther triall, suppose (as I thinke it true) that on the flatte face and circumference of the earthe, there is as muche water as londe, so mighte it ap­peare that the water were as muche as the londe, as manye men doo affirme.

And moste part of learned men (as I haue heard say) do vouche that as a moste certaine truthe.

It is true, as I iudge also, yf they meane lyke cos­mographers that halfe the face of the earthe (as I sayde) is couered with water, but then imagine what depthe maye that sea be of.

No manne can tell.

Yet by triall of mariners it hath been founde in fewe places, a hundreth fathomes deepe, whiche is litle more then the tenthe parte of a myle.

That not withstandinge, it maye bee deeper in some places.

For a supposition, imagine it were in all places a myle deepe, taking one place with an other.

I thinke that to to muche a great deale, consideringe that all knowen partes are not in the deepest, accomptinge one place with an other, as good mariners can testify, aboue 40 fadome, and so groweth shallower still to the shore.

The more that that supposition excedeth truth, the stronger shall the proofe be of the smalnes of the water in comparison to the earthe.

Then for trials sake, I suppose it were so.

How deepe thinke you now the earth to be?

I remembre you saide before, that 57 myle was but the 60 parte of the semidiameter of the earth: then must the whole earth be in thicknes 6840 myles.

That is agreable to that rate: but as I sayde be­fore, the diameter is 6872 8/11. And nowe if you abate one fifte parte of that depthe, the rest will make the side of a cu­bike forme, almoste as great as the globe of the earthe: as it appeareth in the workes of Geometrye.

The fyfte parte of 6872 is 1374. which beyng de­ducted from 6872 there resteth 5498.

That numbre is somewhat to lyttle, but 5541 is very nigh the side of a cube, equal to the globe of the whole earthe, therefore multiplye it cubikly, as you haue learned in Arithmetike, and then shall you see, howe manye miles square are in the whole globe of the earth.

If 5541 be multiplied by it self, it maketh in square numbre 30702681, which being multiplied again by 5541, doth yeld 170123555421: which is the cubike numbre to 5541, and so consequētly must it be that cube whiche is equall to the earthe, in his whole globe. [...]

So is it very nighe. But now for the quantitye of all the sea, this way must you worke. [...]Firste to know all the plat face of the earth, you must multiply his circumference by his diameter, as it is declared in the Pathwaye, and so will there amounte 148450909: whiche is the full platte forme of all the face of the earth: whereof pre­supposing (as the truth doth inforce vs) that halfe the same is sea and water: then dooth it followe, that the whole platte face of the sea and water is [Page 144] 74225454 myles and a halfe in all togither, which is not the 2000 parte of the earthe.

But muste not this numbre be multiplied by the depthe of the sea?

Seynge that depthe is not in one place with an o­ther aboue one myle, and 1 dooth nother multiplye nor di­uide, it will remaine as it is.

Then dare I thinke farther, that the depthe of the sea beynge not a quarter so muche generallye, the earth must nedes bee 10000 tymes so greate as the sea, and all o­ther waters.

Your woordes erre not muche from the truthe: and therfore by this reason it doth appear, that the water be­ing so little in comparison to the earth, can not aptlye com­pas the earthe. And by this it appeareth also how childish­lye they doo erre, that thinke the water to bee tenne tymes so greate as the earthe: for if it were but twise so greate as the earthe, it muste of necessitye couer all the face of the earthe: yea I will saye constantlye, if all the water were as muche as the hundreth parte of the earthe, it would ouer runne all the earthe, and couer it cleane: whiche I maye easilye prooue, but not brieflye: and seeynge the same thinge is all readye declared in the Pathwaye, I will omytte it heere, syth it is a more appropried proofe for Geometrye, then for Astronomye: and nowe will I returne to the prosecutinge of our former matters, accomptynge this sufficiente for the declaration of the roundnes of the earthe and also of the water seuerallye, and now wyll I adde one reason to approue that bothe they do make one perfect rounde globe.That the earthe and water to­gither doo make a per­fect globe.

Euerye grosse and sounde bodye doth gyue a shadow like vnto his owne forme the earth is a grosse and sound body, therefore muste it gyue a shadow lyke hys owne forme: but in all eclipses of the Mone, which are caused by the shadow [Page 145] of the earth, his shadowe is alwaies constantly round, whe­ther the shadow doo runne easte, weste, southe, or any other waies mixtly: wherfore it foloweth, that y^e forme of the earth is round, whiche giueth that rounde shaddow.

How shall a man vnderstand that the shadowe of the earthe is rounde?

In the eclipse of the moone, other all the mone is darkened, or els but one part of hir: If all the mone be dar­kened, then doth the darkenes begin on the easte syde of the moone in circularre forme, and encreaseth still in the same forme, tyll all the whole moone be eclipsed, and then decrea­seth the darkenes againe, so that the weste syde of the mone is darkened, but the darkenes vadeth by lyttle and litle, and yet styll in circularre forme. And if the moone be darkened only in one parte, whether it be the south part, or the north parte, yet still is the shadowe round in forme: where as if the earthe were square or cubike, other three cornered, or of o­ther suche forme, the shaddow wolde so appear in the mone as by the thirde and fourthe figure, you maye partlye perceaue.

That the earth is but a pricke in respecte of the skye.But I will omitte this matter tyll anone, bicause it is not easye to vnderstande without farther explication of other matters incident therto. And bicause I haue begon to speak of the shaddowe of the earthe: I will alleage one argument more, taken by the same shaddowe to approoue the smal­nes of the earthe in comparison to the skie. wherfore thus I frame mine argument.

The Sonne is but a very small portion in comparison to the whole skie, and yet the Sonne is manyfolde bigger then the earthe: wherfore the earthe muste needes bee but a verye small thinge in comparison to the heauens.

Your arguments is good, and the maior is mani­fest to euery mans sight: but how do you proue the minor?

Euery darke body giueth shadow accordinge to the quantitie that it beareth to that shyning body, which gi­ueth the light, so that if the shining body be equall to y^e dark body, thē doth the shadow run in form of a piller, or of a roller, like byg at both the ends: but if the bright body be greater then the dark body, then doth the shadow growe lesser & [Page 247] lesser in spyre forme, or taper fashion, and at lengthe doth ende in a sharpe pointe. Contrarye wayes, if the lyghte bodye be lesser then the darke bodye is, then doth the shad­dow grow greater and greater, still as it goeth from the dark body, and is smallest at the beginning; contrary to the taper forme, whiche is greatest at the beginninge: and this forme maye be called maundforme, or bell forme, bicause it is like a maunde basket, or a bell.

Examples of these thre diuers shaddowes.

A representeth y^e son or other lyght body. B the earth, or any dark body, and C the shadow.

This may stand as a sure maxime, sith both reason & sense doo testify it to be tru.

Then do I infer farther: that if the sonne were lesser then the earthe, the shadowe of the earthe would grow greater and greater, and would be infinite in lengthe: wher­by it wold darkē the most parte of the starres, euery night: & very often it wold shadowe y^e mone, and that for a lōg space togither. as you may gather by this fi­gure,

wher A represēteth y^e son in lesser form then the earth, which is signified by y^e circle marked with G, & y^e shadowe that cōmeth by this form, is marked with D, which occupieth a great part of the skye, and therefore [Page 148] woulde darken all the starres is so muche space of the skye, which is nyghe hande a quarter of that hemisphere that is aboue our horizont. And as the shaddow tourneth about accordyng to the motion of the Sonne, so in four and twen­tye howers all the starres that be nyghe vnto the zodiake, should suffre eclipse: whiche thinge is contrary to dayly ex­perience, for wee see there (about the zodiake and againste the sonne) the starres very bright.

This reason doth suppose, that the starres do re­ceaue their light of the sonne, which thinge was not yet pro­ued by you, althoughe I thinke it to be true, yet in a good argument, no doubtfull sentence may be alleged.

Then seing this place doth not conueniently permit so longe a digression to prooue that, I will vse the mone for an example, which appeareth so manifestlye to borrowe her lyghte of the Sonne, that according as she receaueth the lyghte from him, so dooth shee appeare greater or lesser in lyght, according to hir distance from him. and when so euer she commeth into the shaddowe of the earth, she leeseth her lyght, other fully or in part, accordingly as she passeth and toucheth the shaddowe of the earthe. wherefore as longe as the moone shoulde be within that shaddow, she must needs be in the eclipse: and the shaddowe beinge so great, she shuld be eclipsed not only euery moneth at the full, but she should continue almoste foure dayes to gither in that eclipse, seing that shaddowe dooth occupye as muche of the skye, as shee doth moue by hir propre course in foure dayes.

That absurditie is to manifest to graunt vnto: and yet the greatnes of the shaddow inferreth no lesse, syth it oc­cupyeth so muche of the skie.

The like inconuenience will follow, if the son and the earth were both of one greatnes, as are B & G in the for­mer figure, for so wolde the shaddow run of one bignes like a roller, as is represented by E, and wold darkē diuers stars, and namelye all that bee in the myddle of the Zodiake, and [Page 249] the moone should both oftener be eclipsed (then in deed she is) by the greatnes of the shaddowe, and wold tarry longer in the eclipse, by that same reason, then good reason wold al­lowe. But seing we perceaue no starres directlye against the sonne to be eclipsed, nother yet the mone, in suche forme as that pyllerlyke shaddow would cause, we must needes thinke that the shaddowe is muche abated, beefore it come to the sphere of the moone, and is cleane consumed before it come at anye of the starres, whiche kinde of abatement could not be, but where the light is much greater then is the body that maketh the shaddow, as is C in comparison to G.

So must it followe, that seyng the Sonne is the lyghte body, and the earthe giueth the shaddowe, of neces­sitye the Sonne muste be greater then the earthe.

Yea in deede, and that manye folde.

Then of more force muste the earthe bee a verye small body in respecte to the whole skye, which is infinitely greater then the sonne, as euery childe may perceaue.

Yet haue I farther matter of profe, that the earth is not only a very small bodye in regarde to the skie, but is without anye vewe of greatnes in that comparison.

If the earthe had anye notable quantitye in respecte of the skye,The second reason for the quanti­tie of the earthe. &c then muste the diameter of the earthe haue as greate a quantitie, in comparison to the diameter of the skie. for as in twoo circles the proportion of the diameters is equall to the proportion of the circumferences, so is the proportiō of the shorter to the longer, greater then is the proportion of their two platte formes: but in two globes the proportiō of the shorter diameter to the longer, is muche greater then is the rate of their platte formes: and yet muche more greatter then the proportion of the lesser globe to the bygger.

That is sufficiently proued in Geometry, wher­fore you may proceede with your conclusion.

If the diameter of the earth haue notable quantity in cōparison to the diameter of the skie, then the stars which [Page 150] ar ouer our headdes, be nygher vnto vs by a notable quan­titie, then when they be in the easte, or in the west.

In deede they are nearer by the semidiameter of the earthe: whiche of it selfe muste needes bee accompted a notable quantitie.

But if it shall be so accompted in regarde to the halfe diameter of the skie, then must the stars ouer our heds seeme bigger by a notable quantitye, then when they are in the easte or weste.

That reason is not only approued by Geome­trye, but also by cōmon sight and daily experience, that the nigher any thing is to the sighte, the greater it seemeth: and the farther from the sighte, the lesser it sheweth.

There is no suche diuersity perceaued in the quan­titie of the starres, but that they appeare styll constantly of one bignes: wherfore it must follow, that their distance is all one in all partes of the skye, and then doth not the semidia­meter of the earth make anye notable diuersitie in distance: wherefore it must be thought that the quantitye of it is not sensible in comparison to the semidiameter of heauen, no­ther the circumference of it in comparison to the circumfe­rence of the skye, and muche more may not the whole quantitye of it bee accompted sensible in respecte to the whole quantitie of the worlde.

That foloweth well: for as I learned in Geometry, if the diameters of any two Globes, be in suche proportion that the greater do contain the lesser a thousand times, then be their circumferences in the same rate: but the platte forme of the greater, is 1000000 folde greater then the lesser: and the whole substance of the bigger globe, doth containe the smaller globe, 1000000000 tymes.

Vndoubtedly it maye bee perceaued by sight as well in dialles, as other greater instrumentes made for ob­seruations, that the semidiameter of the sonne his sphere is more then a thousand times longer then the semidiameter [Page 251] of the earthe, els wolde not the shadowes agree so exactly as they do: for they moue as duely and ordrely about the cen­tre of all suche instrumentes, as if their centre were the very centre of the world. which thinge could not be, if those two centres dyd differ notably, in respecte to the sphere of the Sonne. And if it were not, that an introduction dooth not admitte the exacte proofes of the arte, I could herby declare the proportion of these two semidiameters so exactly, that you should confesse that proofe to bee righte certaine and good. But now wil I procede to the declaration of this third reason by linearye demonstration, although it be somwhat obscure, without other helpe.

In this figure, which representeth the three notable circles in a diall,The thirde reason. that bee made by the course of the Sonne, in the thre notable places of the zodiake, that is in the two tropikes and in the equinoctiall, the vtter­moste arke B L C, representeth the tropike of Capricorne, and is heere made no bygger, then the quarter of a circle, by cause the Sonne doth shine but syxe howers vnto vs, when hee is in y^e signe. the equinoctiall is set as halfe a circle, bicause the son being in it, doth shine to vs 12 howers, and is here limited by E I F.

The tropike of Cancer containeth thre quarters of a circle, bicause that when the Sonne is in it, then is there 18 howers from Sonne rising to sonne setting: and that circle here is signified by G K H. The centre of this diall is A, and the stile that giueth the shaddow is D A, whose toppe being D, doth describe those cantylles of circles, in suche precisenes, as if that diall stood in the centre of the earth. and like waies the distinction of the howers is suche exactlye in that diall, as if the centre of the diall, wer the very centre of the world.

I do conceaue good reason of profe hereby, but yet I thinke I shall perceaue muche more, when I shall vn­derstande the iuste vse of those dials, as well as of other se­uerall instruments of lyke vse.

You say truthe: and therefore wyll I passe from this thirde reason, and come to the fourthe proofe, whiche is thys.

The fourthe reason for the smalnes of thearth.If the earthe were of anye bygnes in comparison to the worlde, then shoulde his semidiameter beare some vewe of byggenesse to the semidiameter of the skie. and so conse­quently the horizont that we haue on the ouer parte of the earthe, should not diuide the skie into two equall partes, for that part which shuld be vnder the horizont, would alwaies be the greater, and the lesser parte aboue the horizonte, as in this figure it doth appear.

where A C D B is the circle of the skie, and the lesser cir­cle is the earthe, the centre B, being cōmon centre to them bothe. and E F is the semidi­ameter of the earthe, as E A is y^e semidiameter of the skye. Nowe if E F bee notable in quantitie in comparison to E A, then will the line C F D (beyng the horizonte on the toppe of the earth) differ notably from the line A E B, be­ynge the diameter of the worlde, and the horizonte to the centre of the earthe. And so shall not that horizont C F D diuide the worlde into two equall halues, but the ouer part aboue the horizonte shall be lesser then the other parte that is beneth the same horizonte, whiche thinge is contrary to daily experience, and to all obseruations: for we may see in the longe winter nights those starres that be in the horizont in the easte at the beginning of the nyght, to be in the same horizont in the weste, at the ende of twelue howers; and contrarye [Page 153] waies those starres that did set in the west, when those other did rise in the easte, shall rise againe when the other do do set. And so of the sonne and the moone when they be in contrarye pointes of the Zodiake.

That is at the full of the moone.

In deede then are they right opposite the one a­gainst the other: but if the moone be at the full, long before the sonne setting, then will she rise somewhat after the same: and contrary waies if she be at the ful after the sonne setting, then will she rise somwhat sooner, by reason that she moueth eastwarde euery hower 33 degrees. And although vnto them that be meanly acquainted with the motions of the planets, the declination of the moone and hir latitude, may occasion some doubtefulnes to rise, yet vnto the learned, those many folde varieties in the motion of hyr and thother planets, do confirme the principles of astronomy more adsuredly: but this will I omitte tyll an other more conuenient tyme.

This is well proued nowe, that the earth in comparison to the whole world is but as a pricke or a mote, and lykewaies in comparison to the other spheres.

You muste except the spheres of the thre planets

whiche bee beneth the son. for vnto them the diameter of the earthe beareth a notable quantity: for the semidiame­ter of Venus Sphere, is but 167 tymes so long as the semidiame­ter of the earth: and the semidiameter of Mer­cury his sphere is shor­ter muche, for it is litle more then 64 times the semidiameter of the [Page 154] earthe, but the moone hath hir semidiameter only 33 tymes and a halfe longer then the earthes semidiameter: all which proportions with the residue, I haue set forth in this figure, wherby you may perceaue, that vnto y^e semidiameter of ech sphere, is annexed the numbre that importeth howe often it containeth the semidiameter of the earthe. that is to say: the sonne his semidiameter containeth it 1120 times, Mars 1220 times, Iupiter 8876 tymes, Saturne 14405 tymes an:d the eight sphere or starry skie. 20110 tymes.

I remembre that Faber on the Sphere doth accompt those distances by miles, which is a pleasant matter to read.

In that place Faber foloweth the accompt of Alphraganus the Arabitian, which speaketh of myles much longer then the Italian myles be: for 6 of the Italian miles do make but 5 of Alphraganus miles: of which diuersity at an other tyme I will instructe you, namely in the treatise of Cosmo­graphye: where I wyll set forth diuers varieties and appea­rante repugnances of sondry writers, for the measuringe of the earthe: and proue it to be a disagrement more in wordes then in meaning: and to come by reason of their diuers mi­les, or other in constant measures. And bicause you like that table so well, lo heere is an other drawen accordinge to the rate of 60 myles to eche degree. But heere by the compas is vnderstande the inner concauitie of eche sphere.

And his conuexitie or vtter compas is equall to the conca­uitye of the nexte sphere aboue it.

If the whole circuite of the skye bee 434376000 myles, and the same compasse is 360 degrees, then muste it needes follow, that euery degre of that sky contayneth iust 1206600 miles, as by diui­sion it may be sufficiently well proued. [...] But howe is this supposition of distaunces ap­proued to be true?

That profe dependeth of more knowledge, then this introduction teacheth, and therefore must be referred to a higher treatise. But in the meane cea­son admitting this supposition, you maye easilye tell, howe manye myles the sonne and the moone are in breadthe, see­inge eche of them is accompted about 31 minutes by theyr diameter, eche in the myddle of his owne sphere.

Nowe I vnderstande the forme of woorkinge for tryall of this matter. Fyrste I muste searche how manye myles make a degree in eche of those spheres, and then take a parte proportionable of that nūbre agreable to 31 minutes & a halfe. Ther­fore to begyn with the sonne. [...]As his whole sphere in the middle is in com­pas 25270868 myles, so tryinge it by diuision, I fynde that euerye degree in that sphere doth containe 70197 miles nygh hande. Then say I by the golden rule, if 60 minutes (whiche make one degre) do require 70197, what doo 31 and a halfe make? After iuste multiplication and diuision, as that rule dooth importe, I fynde the whole diameter of the sonne to containe in myles, 36853: where as the earth (as before is noted) dooth containe in his diameter [Page 157] but 6872 myles. So that therby it appeareth, that the sonne is more then 5 tymes so broade as the earthe is ouerthwart.

That is well limited. for els if the flat of the grea­test circle of the whole earthe myght appeare vnto vs, as the flatte forme of the sonne doth, the flatte forme of the sonne ought to be accompted about 29 times so great as the earth is, in lyke forme. And the whole globe of the sonne muste needes be about 155 tymes so greate as the earth in his whole Globe.

I perceaue that dooth followe by twoo rules of Geometrye, wherof the firste is this.

In what proportion so euer the sides of any twoo squares be, those squares are in the square of that proportion: so that if the sides be as 2 to 1, the squares are as 4 to 1: and if the sydes be as 3 to 1, the squares are as 9 to 1. &c. The se­conde rule is this: In what rate so euer the sydes of any cubes be, the cubes do beare the lyke rate cubikly multiplied. as if the sydes be as two to one, the cubes are as 8 to 1: and if the sydes be as thre to one, the cubes are as 27 to 1. &c.

This is well applied of you, that you can frame your common rules in Geometry to suche speciall matters. And nowe may you proue the lyke in the moone.

You say, that the circumference of the sphere of y^e mone is 724604 myles, and 4/7: then diuidyng it by 360, ther wil a­mount the quantitie of one degree: whiche yeldeth in this rate 2012 myles and 71/90: but accomptinge the breadth of the moone 31 minutes and a halfe, the myles that answere vnto it, are but 1057: wherby it foloweth, that the diameter of the earthe being 6872, is 6 times and a halfe greater then the di­ameter of the moone. And therfore the flatte of the earthe in his greatest circle, is aboue 42 tymes so greate, as the like flatte forme in the moone: and the whole globe of the earth is 273 tymes so greate, as the whole globe of the moone.

In this accompt you take the innermost circum­ference of the sphere of the moone, and in the like accompt [Page 157] manye other take the vttermoste circumference, but it ap­peareth more reasonable to take the myddle distaunce bee­tweene them bothe, whiche is 1055302. (as here by example dooth appeare [...]) and in that place of distaunce to take the rate of hir diameter.

So it seemeth most indifferent reason. And then the measure of one degree wyll be 2931 71/180 and of that there will aunswere to the diameter of the mone (being accompted 31 minutes and a halfe) 1539 myles. Nowe if I diuide the diameter of the earthe (whiche is 6872) by it, there wyll be in the quotient 4 and a halfe almost: so wyll it appeare that the diameter of the earth is 4 times and a halfe almoste so longe as the diameter of the moone: and the flat of the earth 20 times so large as the flat of the moone. And the whole earthe nynetye tymes so greate as the globe of the Moone.

Yet according to the common accompt, the earth is but 39 tymes so muche as the moone: but hereof and of many other thynges that seeme aboue the reache of mannes witte, I will an other time instructe you farther. for it is no meete mater for an introduction. And thys is broughte for exaumples sake onlye, that you myghte vnderstande the ordre of suche sorte of woorkynge, and therby learne to trye your authors sayinges. But nowe it is tyme to proceede to other matters, and to declare the true place of the earthe, and to prooue that it standeth in the myddle of the worlde, whiche thinge althoughe it may suf­ficientlye bee gathered by that that is written beefore,That the earthe is in the middle of the worlde. yet I wyll declare certayne inuincible reasons for confutation of them that mysseplace it. And to begyn with all, there can be but three dyuersities of places in generall, without the centre of the worlde: for other it muste bee beside the Axetree of the worlde, and yet equallye distaunte from bothe the Poles, or els it muste bee on the Axe tree of [Page 171] the worlde, and yet nearer to one Pole then to an other: or thyrdlye it muste bee beside the Axe tree of the worlde, and also nearer to the one Pole then to the other. beside these three varieties there is lefte but one more (whyche is the true placynge of it) and that is to be on the Axe tree of the worlde, equallye distaunte from bothe the Poles: wherefore if the firste three opinions bee reproued as false, this fourthe must needes remaine as onlye true. And nowe for the confutynge of the three fyrste opinions I will vse Ptolemyes argumentes, augmentyng them with a larger explication.

The confu­tatiō of the first opiniōIf the earthe were out of the centre of the worlde, and yet stode in the middle betweene bothe the Poles, then shoulde not the Horizonte cutte the skye into twoo equall halues. And thereof woulde followe, that in the righte sphere the daye and the nyghte shoulde not be of one lengthe.

As for example: If you would ima­gine the earthe to stand as L dooth in this figure, then woulde the Horizont be the righte line E L F, and so the parte that is vnder the Hori­zont is greater then the other parte of the skye aboue the Horizonte: wherefore in the ryghte Sphere the nyghte muste needes alwaies be lon­ger then the daye. but if you would imagine the earth to stand where M, is set vnderneth K, which is the verye centre of the worlde, then woulde that Horizonte G M H, whiche answereth to that centre, be vn­der y^e true horizont of the centre of the world, that is y^e right line A K C. And so shoulde the nighte alwaies in the righte sphere be shorter then the daye, bicause the greater parte of the skye is aboue the Horizonte, and the lesser parte vn­der [Page 159] it. And by the like reasons in al other bowing sphers ther shoulde bee no equalitye betweene the daye and the nyght: and if there were any, it should not be in that time when the sonne were in the iuste middle betweene the twoo Tropikes, (that is vnder the Equinoctiall line) bicause that the Equi­noctiall line is not equally parted by the Horizont, but the greater parte is aboue the Horizont, after the one suppo­sition, and after the other supposition it is vnder the Ho­rizont of the earthe.

This I doo vnderstande well, accomptinge the circle A B C D, to represent the Equinoctiall lyne.

And farther you may perceaue (as all men, in all ages, and in all nations do confesse) that the increase of the dayes from the shortest to the meane, and from the meane daye to the longest are not onlye agreeable betweene them selues, but are lyke also exactlye to the decrease of the daies from the longest to the meane, and from the meane to the shorteste. whiche thynge coulde not bee, excepte that the myddle circle betweene the twoo Tropikes (whiche is ryghtlye called the Equinoctiall circle) were equallye dy­uided by the horizonte into twoo iuste halues. And far­ther: seeyng there can be no position of suche obliquity (ex­cept it be righte vnder the Pole) but some one circle of the Sonnes course must be diuided equallye into two partes by the Horizonte, so that when the Sonne were in that circle, the daye woulde be equall with the nyght: which thing as all nations confesse, happeneth at one tyme to all menne, and that is when the Sonne is in the beginning of Aries or Li­bra, precisely vnder the Equinoctiall lyne: wherefore not onlye that circle dooth ryghtly agree with hys name, but also it foloweth that the same Equinoctiall line is equallye parted into twoo iuste partes by the Horizonte. And there­fore the earthe muste needes bee iudged to bee in the cen­tre of the worlde.

Farthermore, if the earthe were supposed to bee to­ward [Page 160] the easte or toward the weste,An other cōfutation of that firste opinion. from the myddle of the world, (as in this figure it is set toward the easte, which is li­mited by A) thē as the space toward the one side is shor­ter thē the space to the other side frō the earth, so the stars woulde seeme bigger in that nearer part, and lesser in that farther parte.

Which thing is before reproued, and by daily ex­perience may be confuted.

Therfore can not it be a true opinion, that inferreth so false a conclusion. And yet there woulde follow of it more absurditie: that from the morning vntill noone should bee shorter tyme, or els lon­ger then from noone vntill nyght.

That must needes folow also, seeyng that noone is that time of the daye, when the sonne is in the circle which goeth right ouer our headdes from south to north, whiche here in this figure is represented by the right line B E D, as I gather by your former doctrine.

An abbrid­ged argu­ment of all the premis­ses.You gesse well. and by the contrarye of all these you may conclude thus: that seyng the tyme before noone is equalle to the tyme after noone, and the starres appeare nother bygger nor lesser in the weste, then they doo in the easte: And that when the sonne is in the Equinoctiall lyne, the dayes are equall to the nightes, it foloweth cer­tainlye, that thee earthe canne bee no wayes out of the Axe tree of the worlde.

And now for the seconde opinion I reason thus.

Against the second opi­nion.If the earthe were on the Axe tree of the worlde nygher to the one Pole then to the other, then woulde the Ho­rizonte onlye in the righte Sphere dyuide the skye into [Page 261] twoo equall partes, and in no forme of bowing sphere, as by this figure you may gather, wher E standeth for the earth, and A E C for y^e right horizont. B E D and F E G for two oblique horizontes, in 2 seuerall bowing sphers: and K limiteth the centre of the worlde.

Here I see mani­festly that only the right horizont dooth diuide the greater circle (whiche is sette for the skie) into 2 equall partes, and none other: wherby it would folowe, that wee whiche dwell 52 degrees northwarde from the Equinoctiall lyne, shoulde see muche lesse then halfe the skye: but that is false, as it hath beene often tymes proued, wherfore I perceaue that opini­on can not be true.

An other argumente against the second opi­nion.Yet an other argumente againste that opinion, may this be. Yf the earthe were nygher to the one Pole then to the other, when the Sonne is in the iuste easte, the shad­dowes of anye thinges in earthe, woulde not runne full weste: but all shaddowes in earthe runne full weste, when the Sonne is iuste easte: (and contrarye wayes) therefore canne not the earthe bee nygher to one Pole, then to the other.

This argumente is good, and the minor is well knowen to euerye sensible man: so is there no doubte but of the maior.

For the proofe of it, I sette this figure.

Wher the great circle A B C D betokeneth the Horizont, and the lesser circle E F G H, standeth for the earthe. The centre of the worlde is E: the east is D: and the weste is B: the southe is A: and the northe is C. In the earthe the lyne F G, standeth as a Parallele, wyth the ryghte [Page 162]

line BED, and the righte line DH rūneth crosse thē bothe, and maketh an an­gle on the centre of the earth, equal to the angle by D: whose largenes is agrea­ble to the imagined distāce of the centre of the earthe frō the centre of the world. wherfore the greater that y^t distance is, the larger is the angle of that declination, and the lesser distaunce, causeth a lesser angle: but yet if the distaunce be any thing, then will that angle of declination be notable inoughe.

The reste is easye to considre: I meane that all shaddowes runne in a right line from the lyght bodye, that causeth that shadow: so that the sonne being in D, which is the iuste easte, wolde cast the shaddowes in the earthe, not to F (which is the west in the earth) but to H, which is almoste northwest: and therefore is your maior duely proued, and the seconde opinion fully confuted: but how may the thirde opinion be answered?

Against the thirde opi­nion.The thirde opinion is, that the earthe standeth out of the axe tree of the worlde, and also nearer to the one pole then to the other: so doth it containe both the other o­pinions: wherfore seyng they both are reproued, this third muste needes see me falser then ony of them bothe, bycause it includeth all the vntruthe of them bothe. And therfore to conclude with Ptolemye, A confir­mation. the increase and decrease of dayes coulde neuer be so ratable and iustly proportioned as they be, if the earthe stoode any where els, then in the very centre of the worlde. And farther more the eclipses of the moone shuld not happē, An other reason. (as now they do) at the precise hour of ful opposition, if the earthe were not in the very centre of the worlde: for considering that all the thre bodies of the Son, [Page 263] the moone, and the earthe muste needes be in one right line (as in the doctrine of those eclipses it is taught) there is no place in the worlde, where the earth may stand in that right line common to all suche eclipses, but only the centre of the worlde:

as for examples sake I haue noted 4 seuerall eclipses of the moone: the first was in y^e year of Chri­stes incarnation 1551, the 20 day of Febru­arye, when the Sonne was aboute the 12 de­gree of Pisces, and the moone aboute the 12 degre of Virgo. The seconde eclipse was in the yeare of 1553, the sonne being in the ele­uenth degree of Leo, and the moone in the eleuenth degree of Aquarius: The thirde eclipse happened on the fifte daye of Iune, 1555, the sonne being in the 23 degre of Gemini, and the mone in the 23 of Sagittary. The fourth eclipse, shalbe this yeare 1556, the 17 daye of Nouembre, at whiche time the sonne shalbe in the fifte degre of Sagittary, and the moone in the fifte degree of Gemini. Nowe if you lyste to take more examples, for farther tryall you maye so doo. yet two seuerall eclipses serue as well for this proofe as 10000. And then drawing lines for eche eclipse frō the place of the sonne to the place of the moone, all those lines muste needes passe by the earthe, and there is none other pointe, whereby they all (or any two of them) can passe, but onlye the centre of the Zodiak, (which is the centre of the world) therefore muste that centre of necessitie bee accompted the place of the earthe. And this may suffice for this time tou­chinge the earthe and his accidentes, principallye appertai­ninge [Page 164] to Astronomye: for althoughe manye other thinges are to bee considered in it, they appertaine rather to philo­sophers or Cosmographers, then to Astronomers, and namely in the doctrine of the principles. Whether the earthe moue or not. As touching the distinction of the zones, I haue sayde somwhat before, & somwhat more wil I say anon. But as for the quietnes of the earth I neede not to spende anye tyme in proouing of it, syth that opinion is so firmelye fixed in moste mennes headdes, that they accōpt it mere madnes to bring the question in doubt. And therfore it is as muche follye to trauaile to proue that which no man denieth, as it were with great study to diswade that thinge, which no man doth couette, nother any manne alloweth: or to blame that which no manne praiseth, nother anye manne lyketh.

Yet sometime it chaunceth, that the opinion most generally receaued, is not moste true.

And so doo some men iudge of this matter, for not only Eraclides Ponticus, a great Philosopher, and two great clerkes of Pythagoras schole, Philolaus and Ecphantus, were of the contrary opinion, but also Nicias Syracu­sius, and Aristarchus Samius, seeme with strong arguments to approue it: but the reasons are to difficulte for this firste Introduction, & therfore I wil omit them till an other time. And so will I do the reasons that Ptolemy, Theon & others doo alleage, to prooue the earthe to bee without motion: and the rather, bycause those reasons doo not proceede so demonstrablye, but they may be answered fully, of him that holdeth the contrarye. I meane, concerning circularre mo­tion: marye direct motion out of the centre of the world, seemeth more easy to be confuted, and that by the same rea­sons, whiche were before alleaged for prouing the earthe to be in the middle and centre of the worlde.

I perceaue it well: for as if the earthe were al­wayes oute of the centre of the worlde, those former ab­surdities woulde at all tymes appeare: so if at anye tyme [Page 165] the earthe shoulde mooue oute of his place, those inconue­niences would then appeare.

That is trulye to be gathered: howe bee it, Co­pernicus a man of greate learninge, of muche experience, and of wondrefull diligence in obseruation, hathe renewed the opinion of Aristarchus Samius, and affirmeth that the earthe not only moueth circularlye about his owne centre, but also may be, yea and is, continually out of the precise cē­tre of the world 38 hundreth thousand miles: but bicause the vnderstanding of that controuersy dependeth of profoun­der knowledg then in this Introduction may be vttered conueniently, I will let it passe tyll some other time.

Nay syr in good faith, I desire not to heare such vaine phantasie, so farre againste common reason, and re­pugnante to the consente of all the learned multitude of Wryters, and therefore lette it passe for euer, and a daye longer.

You are to yonge to be a good iudge in so great a matter: it passeth farre your learninge, and theirs also that are muche better learned then you, to improue his suppo­sition by good argumentes, and therefore you were best to condemne no thinge that you do not well vnderstand: but an other time, as I sayd, I will so declare his supposition, that you shall not only wonder to hear it, but also peraduenture be as earnest then to credite it, as you are now to condemne it. in the meane ceason let vs proceede forwarde in our for­mer ordre, wherin by ordre of your table I should speake of the circles in heauen, both of their numbre, how many they be, and also of their quantities, how great they are, Of the cir­cles in the skye. which is to be vnderstand in cōparison to the Equinoctiall, or some other greate circle. Then of their ordre, and their distance a sonder: and likewaies what is their offices, whervnto they serue. of all whiche thinges, although I haue all ready sayde inoughe for so briefe an Introduction, yet bicause in theyr numbre there may be some disagreement, and in their quantities. [Page 166] distances and ordre there maye bee some varietie, at the leaste in diuers places, therefore I will speake a little of them againe. Equinoctial First for the equinoctiall, there is but one tho­roughe all the world, and he is equally distaunt from eche Pole, and therefore is called the Girdle of the skye: hys office was declared beefore to bee the lymite of the myd­dle of the world, in whiche the Son maketh the dayes equall to the nyghtes. Also hee declareth the true easte and west, and is not onlye the common measure wherby all other cir­cles are iudged in quantitye, but also it is the true measure of motions celestiall, and the very rule to iudge all ascenti­ons by, the tropiks as hereafter more largely shall appeare. Nexte vnto this circle are there 2 Tropike circles, one on eche side of it,

[Page 158] whose distaunce a sonder may well be marked by a quadrant set so in place conuenient, that it may stand iust plumbe with the flatte of the horizont, and be tourned full southe. Then obserue many daies aboute the middle of Iune the hyghest point that the sonne wyll ascend vnto, and shine duely tho­roughe those two sightes in the ruler, mouinge it hygher or lower, as occasion serueth, tyll it stande exactely pointinge the heyghte of the Sonne at no one beynge at the highest. The lyke obseruation shall you make diuers dayes before, at and after the myddle of Decembre, tyll that you be assured of the iuste heighte at noone of the sonne, beynge at the lo­west then toward the southe. The pointes of these two ob­seruations well marked in the edge of the quadrante are the true places of the two Tropikes: and the distaunce of those two markes a sonder by numbre of degrees, is the very true distaunce of the twoo Tropikes. In the iuste myddle be­tween these twoo tropikes is the place of the Equinoctiall circle. Example. With vs, where the pole is 52 degrees highe, the winter tropike wyll be 14 degrees and a halfe aboue the Horizont. the sommer tropike 61 and a halfe. and the Equi­noctiall iuste 38 degrees in heighte. The gretest declination of the sonne And the numbre of degrees that are betweene this Equinoctiall and any one of the tropiks is named the Greatest declination of the sonne, whiche in our time is about 23 degrees and 28 minutes. The other pointes of declination of the degrees in the ecliptike line from the equinoctial circle, bicause they be many in nū­bre and diuerse in vse, I thinke it good to expresse in a table which hereafter shall serue you for sundry vses.

The like table is in Orontius.

Not euen the lyke, as by conferring you maye perceaue: but for the vse of it, take what degree you list of anye Signe, and by this table you maye knowe his decli­nation from the Equinoctiall circle. The Signes are writ­ten partelye on the headde of the table, and partelye on the foote of the same. The degrees in the fyrste [Page 168]

[Page 169] columpne doo serue for the signes that bee on the heade of the table, and the degrees in the laste columpne doo serue for the signes in the foote of the table, and the common an­gle against the signe: and the degree that you seeke for, doth containe the degrees and mynutes of the declination due to it.

I perceaue it well: if I would knowe howe muche the tenth degree of Leo doth decline from the equinoctiall, I must looke in the columpn ouer Leo right against the nūbre oftenne in the laste columpne, where I fynd 17.46.

That is 17 degrees, and 46 minutes, which is the declination of the 10. degree of Leo from the equinoctiall circle.

I must alwaies vnderstande that 60 minutes do make a degree: so these 46 minutes are ¾ of a degree and 1/60 more. But what is the vse of this table?

That shall you knowe in the next treatise. in the meane ceason to procede with the parallele circles: there fo­loweth next, the Arctike and Antarctike circles,The Artik and Antartik circles whiche are in numbre two, and there office is to enclose those starres, whiche euer appeare aboue our horizont, or neuer appeare aboue the same, as before is declared: but bycause euerye seueralle Climate hathe those cyrcles disagreeynge frome other Climates, therefore theyr distaunce frome the o­ther cyrcles Paralleles canne not bee certaine, (but for one region certaine) nother yet theyr quantities, nother theyr ordre: for where the eleuation of the pole is lesse then 66 degrees and a halfe, there are those circles lesser then the tropikes, and are in ordre betwene them and the Poles, beinge alwaies distaunt from the Pole iust so many degrees as the Pole is in height aboue the Horizont in that region.

It canne not bee other waies. And therefore it foloweth, that where the pole is more then 66 degrees and a halfe in heighte, there the Tropike is aboue the Horizonte, as at Wardehouse you declared it to be: and therefore [Page 170] in that climate the Arctik circle is greater then the Tropike of Cancer.

Of the fiuc zones a­gainst the Greekes.Hereby appeareth the ouersighte of moste parte of the Greekes in limiting the Zones: for they appoint the Arctike and Antarctike circles for boundes of the Tem­perate Zones on the one side, and the Tropikes on the o­ther side: whereof neither bounde can be well admitted, after their owne explication of the qualities of the Zones. for if the temperate Zones shall be called those Zones that be in­habited, as they do so name them, then bycause there was knowen inhabitauntes innumerable besouthe the tropike of Cancer, it muste needes followe, that the tropike canne be no bounde of the temperate Zone: but yet otherwaies ac­comptinge the distinction of the Zones, not by that they are inhabited or vninhabited, but by the varietie of the mo­tion of the sonne in respect to them, and by other accidents of shaddowes, there maye be good reason to make the tro­pikes boundes of the temperat zones: mary there is not the like reason for the Arctike and Antarctike circles. for con­futation therfore of that opinion, I make this argument.

An argu­ment in Ferio.No vncertaine and variable boundes can limite anye cer­taine place: the temperate Zones are places certaine, and the Arctike circle with the Antarctike are chaungable, and vn­certain limites, Therfore can not they be the boundes of the temperate Zones.

This is a good argument, made in Ferio, the fo­werth moode of the fyrste figure. And the maior is moste true, sith nothing can more disagree, then certain and vncertain, stable & vnstable, being contraries togither. The minor hathe 2 partes in it, which both seeme as true: for as long as the Sonne keepeth one yearely course, so longe the regions muste remaine as they were, and that is for euer, other styll temperate, other styll vntemperate. And so is that part of the minor true. The other part for the inconstancy & chan gablenes of the circles arctik & antarctik, must needs be true [Page 178] by their definitions, approued of the same Greekes: for eue­ry region hath a seuerall Actike circle. Wherfore I meruaile muche that the Greekes beynge so wise men, and so greately learned, shuld be so muche ouerseen and so foroly deceaued: but peraduenture ther are but few of that opinion, and such as were leaste learned.

Parmenides, Aristotle, Cleomedes and Proclus may not be accompted vnlearned, and yet they with manye other haue written that as truth. But hereby may you per­ceaue what folly it is, whē men receaue any doctrine as true, and do not well weigh it, but credite the autority of the first teacher. So it appeareth in this matter, that bicause Parme­nides, whiche was a great Philosopher, had fyrst taught that whiche was a great Philosopher, had fyrst taught that distinction of the zones, all the reste did folowe his opinion as a plausible doctrine, without examination of it, till Po­sidonius began to espye that errour & to confute it: as Stra­bo dothe declare in his second boke of Geographye, which place in the latine translation is so euell expressed, that no sentence in it importeth anye sence: wherefore as well for the commoditie of you as of other, I will sumwhat amend that place, wisshinge them that haue leasure and learning to help to amend many other faultes of that good booke and other lyke. The Latine translation is this.

A place of Strabo a­mended.Ad Septentriones, ne{que} penes omnes existentem; ne{que} eisdem vbi­cun{que}. Quisnātemperatas quae immutabiles sunt diuideret? Cum igi­tur non penes vniuersos sit septentrionales esse, nihil esset ad argumē­tum. si enim penes habitatores temperatae omnes, ad quos dicitur, so los temperata? Quod autem non vbi{que} eodem modo, sed mutari, bene comprehensum est. ipse autem in zonas partiens, quin{que} ad coelestia quidem vtiles esse asserit. Ex his duas circumstantes subter polos vs{que} ad eas quae septentrionales habent tropicos, diuersarum vmbrarū esse ab alijs duabus, quae deinceps sunt vs{que} ad habitantes sub Polis. Quae vero inter Tropicos est, vtrin{que} vmbras habere.

Other the matter is very obscure, or els there wanteth lyghte in the declaration of it.

Ther is litle sence in all these words: & y^t sence y^t may be gathered of it is very false. And yet is y^e greek boke both vn [Page 172] corrupt (except it be in a worde or two) and full of perfect, sensible and pleasaunt sentences. this is it.

The prited booke hath [...]falsely. [...],The greke booke hath [...]falselye. [...].

Whiche I doo translate thus.

Arcticis verò circulis (vt qui nec apud omnes existant, nec ijdem vibi{que} perseuerent) quis vnquam temperatas Zonas (quae immutabi­les sunt) terminaret? Caeterum illud quod non apud omnes existant Arctici circuli, nihil facit ad reprehensionem. quum satis sit, si modo sint apud omnes incolas temperatae ipsius zonae, ad quos solos tem­perata dicitur. quod verò adiecit, non vbi{que} seruare eos eandem ratio­nem, sed varie mutari, hoc quidem rectè adsumptum est. At{que} ipse Po sidonius dum Zonas destinguit, quin{que} inquit vtiles esse ad coelestes obseruationes. quarum duae, quae Polis subiacent, vmbras circumfluas habent, vndè Perifciae dicuntur: ibi{que} finiuntur vbi tropici ipsi pro ar­cticis circulis habentur. has sequuntur aliae totidem, eò pertingentes, vbi Tropici verticibus incolarum imminent, at{que} in his vmbrae me ridianae in vnam plagam porriguntur semper, hinc Heterosciae vocan tur. quinta verò quae inter tropicos iacet, in vtrun{que} latus vicissim vm­bras mittit, at{que} Amphiscia nuncupatur.

Which words may be englished thus. What man (saith Po­sidonius) wold assigne the Arctike circles to be as bounds to the tempera te zones? seing those circles ar not in euery Cli­mate: nother do they continue vniforme and of one sort to all cuntries. These wordes (saith Strabo) that they be not in euery climate, maketh nothing to the reproofe. for it is suffi­cient that they be incident to all the inhabitants of the tem­perate zone, in respect to whom alone that temperate zone beareth his name: but those other woordes, that they keepe [Page 173] not one vnforme manner in all places, but are diuersly changed▪ that is well alleaged. Also Posidonius him selfe when he distincteth the zones, doth say, that fiue zones are needefull and sufficient for celestiall obseruations: whereof two which be vnder the poles, are caled Perisciae, or Round shadowed, bicause their shaddowes run round about them. And these zones extend to that place; there the tropik circles and the Arctike circles are all one. After these there do follow two other, which reache from thence vnto those partes, that are directly vnder the tropiks: and these haue their noone shad­dowe running one waies styll▪ and therfore are called Hete­rofciae, or Single shadowed. The fift zone lyeth betwene the tropikes, and casteth the noone shadows 2 waies, wherefore the Greekes call it Amphiscion, that is Double shadowed. Scholar. By this translation (which is worth a paraphra­sis) I doo not onlye perceaue the sence of these wordes, whi­che before were darke, partly for the hardnes of the matter, and partlye for the hypallage, in changinge of the speakers person, but also I espye the monstrous shape of the old translation. And by this I gather also that Strabo woulde not haue the Temperat zones to be bounded by the Arctik and Antarctike circles.

His mynde appeareth more manifest anon after where he blameth Polybius, for assigninge those circles as boundes of the zones: whereof one should be inclosed with in that circle, and the other should extend from it to the next tropike then he concludeth thus: that those vnconstant cir­cles, may be no boundes of certentye.

[...]

Dictum enim est, quod per signa transmigrantia, ea quae non mu­tantur, terminate non conuenit.

For I haue sayde before, that chaungable limites may not be appointed as boundes to vnchaungable places.

Thus it appeareth, that the distinction of zones by [Page 174] the Arctike and Antarctike circles were no constant distin­ction. and so is autoritye of one sorte repelled by thaucto­ritie of an other sorte.

You maye not weighe the matter by auctoritye, for so shoulde that former doctrine continue styll, seynge I aleaged for it Parmenides, Aristotle, Polybius, Cleomedes and Proclus, & against them only Posidonius and Strabo, which maye seeme the weaker in numbre: but then considre that the firste sort bring only affirmation for their testimo­ny, and bare autoritye: the other, confute theym by good reason and substantiall argumentes, whiche are farre to bee esteemed aboue anye autoritye.

Then credityng reason against autority, I must say, that the Zones must be otherwaies diuided, peraduen­ture as I dyd learne of you before, agreable to Iohn de Sa­cro bosco his mynde, whom you called the restorer of the Zones.

Yea in deede: for although Posidonius and Stra­bo did teache the like distinction, yet did they not so openly name the true limites, howe bee it in effecte they meane the same: for when Strabo saith, that the Cold zone doth reach to that place, where the Tropike is the Arctike circle, hee dooth meane that there, where this firste Zone endeth, and the temperate Zone beginneth, the Pole is 66 degrees and a halfe aboue the horizonte, and so muste the same Pole bee from the toppe of their headdes in that place 23 degrees and a halfe: in whiche distaunce bicause the Poles of the Zodi­ake do describe a circle, therfore doth Iohn de Sacro bosco call that circle the Arctike circle, in that confounding▪ it in name with an other circle of the Greekes: wherfore I thinke it more reasonable for auoyding confusion, to gyue it a se­uerall name, and call it the Polare circle, and the other to be called styll the Arctike circle,The Polare circles. as the greeks longe before did name it. And this distinction of the zones by the two Tro­pikes, and the two Polare circles doth distinct exactly those [Page 175] three varieties of shaddowes before mentioned. whiche is a certaine and notable difference, not imagined by men whi­che may erre, but wrought by the sonne, which can not erre. But heere muste I admonish you of an other erroure,An other erroure. gathe red not of grounded reason, but of phantasticall imagina­tion, by occasion of whiche, this fonde distinction of zo­nes was imagined.

Bicause the elder Grekes had no trade into the south parts of Afrike, nother the Ethiopians again into Grece, and far­ther by reason the sonne runneth still ouer their headdes, that dwell betweene the tropikes, manye of the Latines as well as of the Grekes phantasied that there did dwell no in­habitantes, neither could dwell there for the vehement heat: wherfore they called it the Burned Zone. And of lyke oc­casion where they moued to accompt two other zones, that be nigh the poles, to be vninhabited for cold, by reason that the sonne doth neuer come nigher to them then the Tropik circles: but how muche herein they were deceaued, it maye be declared not only by reason, and by experience, but also by autority of many of their owne writers, as namely Era­tosthenes, Posidonius, Polybius, and Ptolemye. but as this is a matter more agreeable to the treatise of Geographye or Cosmography, then of the Sphere, so will I ouerpasse it for this time, and will returne to the reste of the circles of the sphere, amongest which the Zodiake as principall,The Zodi­ake. doth of­fre it selfe, as the common theatre and stage of all the planets motion, and of the chiefe signes and celestiall figures.

Are there I pray you suche figures in the Zodi­ake, as Astronomers do describe?

There are some that affirme no lesse, and testifye that they haue in a cleere ayre perceaued them: but for the reste of the forme, I will say nothinge now: onlye this I doo affirme whiche I know, that all the starres whiche astrono­mers do name to be there, maye easily be seene there, and in lyke forme as they doo place them.

If the formes of beasts be not there, why do they call it by that name of Zodiake, whiche name is deriued as many do affirme, of [...], that signifieth a beaste.

The Signes doo beare the names of beastes, and therfore may that circle take the like denomination also: but yet I denyed not that the verye formes were there, but that they are not easilye seene in suche exacte shapes as they be portured, and as some mem write that they haue seene them: but howe so euer it bee, the certenty is, that the 12 signes are contained in that zodiake, and therfore doth Tullye with other latine men call it Signifer, that is, the Circle of the Signes: but whye those names were giuen to euerye signe rather then other, dooth not appertaine so muche to this treatise, as to that Iudiciall arte, whiche hath more ground of reason then many men thinke.

What is to bee in a Signe.When you saye that the Sonne is in anye signe, you do not meane (I am sure) that the Sonne hath lepte so high from his owne sphere, into the sphere of the Fixed star­res, where the zodiake and the signes be, but that the Sonne is directly vnder the same signe, and in a righte line betwene that signe and the centre of the earthe.

You saye well. That is the common vnderstan­dinge, when we speake of the place of the sonne: but bicause other Planettes doo decline from the myddle of that zo­diake, some tymes towarde the north, and other times to­ward the southe, therfore haue all astronomers appointed a conuenient breadth to the zodiake, according to the decli­nation of the Planets: howe bee it proprelye they doo call that the Latitude of the Planetes,The lati­tude of Planetes. Their declination. Their lon­gitude. The second significatiō of a signe. when they swarue frome the Ecliptike line: and the Declination of them is their di­staunce southe or northe from the equinoctiall line: so doo they call the motion of them in Longitude, theyr distaunce by theyr naturall course frome the beginninge of Aries, which is the beginning of the zodiak. And now appointing the latitude of the zodiake to bee twelue degrees (although [Page 177] some planetes may runne in latitude on the one side almost 8 degrees) bycause that quantitie is moste receaued, then is euerye signe twelue degrees broad, and thirtie degrees long. and so maketh a longe square: frome the corners of whiche long square, you may imagin lines to be drawē to the centre of the earth: and what so euer commeth within the boundes of those lines, is accompted to bee in that signe: and this is the second signification of a signe.The thyrde significatiō of a signe. Arcturus. The Pole starre. A third signification ther is, which we vse when we say that the bright starre Arcturus is in Virgine, where as in deed he is aboue 30 degrees north from the Ecliptike line: which is farre out of the breadth of the Zodiake: and so we say that the pole starre is in Taurus, whiche is from the Ecliptike line 66 degrees. and likewayes we name all the starres in the skye to bee in some signe, bee they neuer so farre from the Ecliptike line, and the Zodiak. Therfore to know what is vnderstand by the name of a signe in this signification, you must imagin 6 circles to be so drawen about the Globe, that they may passe by the beginning of all the signes (for euery circle will serue for two signes be­inge contrarye one against the other) and so shall the whole Zodiake and all the globe also be parted into twelue equall partes, yf you haue drawen those circles rightly & that they do passe al by the two poles of the Zodiak. Now mark how those 2 lines that do inclose any signe, ar widest a sonder in y^e myddle of the Zodiake, and from thence toward eche pole of the zodiake they come nearer and nearer, tyll they touch in the Pole it selfe. All the space betweene anye two suche se­micircles from one Pole to the other, is named a sign in the thyrde signification: so that what so ueuer starres bee within that space, are named to bee in that signe which is within the same space: of all these three diuers formes of signes heere maye you see examples. of the fyrste by A, where the Sonne standeth vnder the signe of Cancer. of the seconde forme you haue an example by B, and of the thirde sorte you haue two varieties, one by, C and an other by D. So that what [Page 171]

so euer Planet doth come within y^e boundes of that figure B, is named to be in the signe of Taurus: & what so euer Planete or fixed star is with­in the compas of the figure C, is iudged to be in Cancer: as y^e Moone is ther re­presented to be and all the starres there portured, & so maye you iudge of anye other signe. Nowe this maye suffise for the explication of the zodiake,The co­lures. after whom foloweth nexte the Colures, whiche take their names in Greeke of vnperfectnes, bycause they bee neuer seene all aboue the grounde in any oblique sphere: whereby it ap­peareth, that good Iohn de sacro bosco was much deceaued in comparing them to the cōpassed bowing of a wild bulles tayle, as thoughe they tooke their names thereof: but men must bear with the ignorance of that time, for lack of knowledge in the Greeke tonge. These Colures serue principally for the distinction of the four chiefe pointes in the zodiake, as before is declared. and bycause the pointe of the interse­ction or crossinge of the ecliptike line and the equinoctiall, doothe sufficiently expresse two of those pointes in the be­ginning of Aries and Libra, therfore the greekes do assigne cōmonly but one Colure, for the other two tropike pointes, and none for these equinoctiall pointes. How be it, bycause they serue also for the declinations and latitudes of fixed starres and Planetes, I thinke it better to describe them, then to omitte them. And thus haue I lyghtly touched all the circles [Page 179] that be fixed in the sphere, and moue with it. Nowe re­maineth other two, which stand styll alwaies and moue not, of whiche the fyrste is the Horizonte, and the nexte is the Meridiane. The horizont is of twoo diuers sortes. the one doth extend on euery syde vnto the firmament,The Hori­zonte. The celesti­al horizont and serueth as it were pecularly for the partition of the heauens, and di­uideth the skie iustly into two halues, wherof the one appeareth vnto vs aboue that Horizonte, and the other is hidde from vs, vnder the same horizont: this horizonte hath his name of the skie, and is called the Celestial horizont, and his diameter is as large as the diameter of the eight spher, which is the farthest and highest part of the skye that we canne see: this large horizont our sight doth inforce vs to acknowledg as a iuste horizont, although reason canne fynde in it some wante of exacte precisenes. And therfore Proclus doth not well distincte this horizont from the other, by naminge the other a sensible horizont, and affirming this to be conside­red only by reason, where as in deede we neede reasons helpe more in iudging the other horizont, whiche I thinke moste aptlye to bee called the Earthly horizont,The Earth­ly horizont bycause it serueth for sightes on the earthe and water onlye, and reacheth not vnto the skie: no, his semidiameter excedeth not (as Macrobius saith) 180 furlongs, that is 22 myles and a halfe: and his whole diameter cōprehendeth but only 45 myles in length. So that if any man do stande on a plaine grounde or on the sea, he maye see rounde about him euery waies 22 myles and a halfe: that is in round compas of the whole horizonte 141 miles & 3/7.

I meane that seing the right line A, C, is 45 miles, the whole circle A B C D, must bee accompted 141 3/7 myles in compas. This saynge of Macrobius is more nygher to the truth then Proclus assertion, which is that the diameter shuld be in this [Page 180] horizont, 2000 furlonges, that is 250 myles, wherby he meaneth that a manne may see euery waye in: a playne 125 myles from him: whiche assertion euery maryner dooth knowe to be false: for it is well knowen by often and good obseruati­on, that in plaine ground, or on the sea, they can not discern. well aboue 20 myles, and therefore do all mariners call that distaunce commonly a Kenninge:A kenning. whiche is as muche as a manne maye well see: yet from a hill or highe grounde men maye see farther, and especially they maye see other hilles or clyffes, but that is no certaine vewe, nor iuste kenninge: yet in that sort men may see 60 miles, or at the moste 80 miles: but 125 myles is to greate a distaunce, for to vewe any thing from a high place, and therfore of more force it is to exces­siue a distaunce to vewe any thinge in an equall plaine,A demon­stration a­gainst proclus. as the horizont must needes be, for de­claration wherof, I sup­pose this figure to re­present the whole globe of the earthe,

and the earthly horizont to be expressed by the ryghte lyne F B G: vnto which line ther is an other drawen as a iuste parallele, which is H K L. of lyke lengthe precisely with the earthly horizonte, and two other lines ioyninge them at the eandes, makinge a longe square of all righte angles, so that two of those angles do lyght on the circumference of the circle of the earthe. Then draw I a right line from E which is the centre of that circle, vnto B, and an other from the same centre E vnto G: wherby ther is made two triangles E B G, and E K L. Nowe presupposing that B is the place where we stande on the earth, and H and [...] [Page 181] vnto whiche the Semidiameter of 1000 furlonges of oure earthlye Horizont, dothe extende on bothe sides: and frome the one of them is drawen a right line to the other, that line must needes fall within the circle.

That is true, accordinge to the 47 Theoreme of the Pathwaye.

Then muste the line K E, be shorter then the lyne B E, and so B and K, are notably distaunte.

That is certaine.

And bicause the righte line F B G, is parallele to the righte line H K L, there must be as muche distaunce be­tweene G, and L, as there is betwene B and K.

That foloweth by the definition of Paralleles.

Then as K, is notably vnder B, so must L be no­tably vnder G: that is to say vnder the Horizont, and ther­fore can not be seene.

It is against the definition of an horizonte, that anye thinge vnder it shoulde be seene.

Then if the semidiameter of the Horizonte shall extend no farther then that a meane quantitie maye be seene on the earth, it maye not be so longe as Proclus hath limi­ted it. Also by the two triangles aforesaide, whose angles are like, and therfore their sides proportionable, & other waies diuersly, by the former figure, it may be domonstrate, that the righte line E G is muche longer then E L, whiche is the semidiameter of the earthe, so that the horizont in so much distaunce is farre hygher then the earth is there, and therfore canne not bee aptelye called a Sensible Horizonte, nor an Earthly Horizonte, as Proclus meaneth. But is appeareth that Proclus dydde rather in this doctrine followe some other mennes opinion then hys owne reason, as he dooth also in the declaration of the chaunge of the Horizontes and the Meridianes, for betweene easte and weste, hee saythe that the Meridianes chaunge at the eande of 300 furlonges: but betweene southe and northe hee dooth as­signe [Page 182] no chaung vnto the Horizonts within 400 furlongs. In whiche woordes there are two errours included: the one that the horizonts be not like in chaunge betwene easte and weste, and betwene southe and northe.

Nay he speaketh only of the Meridianes (I trow) betwene easte and west, and not of the Horizontes.

As thoughe we might chaunge the one, and not vniformely chaunge the other.

Truthe it is, that seing the meridiane doth cutte the Horizonte with right angles, they both must needes o­ther stand bothe still, other chaunge bothe a like: wherefore this firste erroure can not be excused.

And the seconde errour is as manifest as it: for therby he supposeth that the Climates do chaunge by equal quantity of furlonges or miles, which errour is to manifest: for nighe vnto the equinoctiall, 2150 furlonges northwarde do cause increase but of a quarter of an hower in the longest daye. And with vs in the southe parte of England, 700 fur­longes north warde dooth cause increase of a quarter of an hower in the longest daye, and in the north partes of Scot­lande, 320 furlonges doo giue as great an increase: in Ise­lande 4 furlonges yeldeth the lyke increase: and so styll the farther northe you go, the smaller space of ground bringeth the like increase in the longest daye.

Hereby I perceaue, that who so euer will trauaile in these sciences with profit, must lean rather to reason, then to authoritye, els he may be deceaued.

That rule is generall in all artes.

And if Proclus rule be not certen, what rule may I haue more certen? M. For the alteratiō of the Horizonte betwene south & north, bicause not only the climats do chāg therwith, but also the quantities of y^e daies, I wil anon before the doctrine of the ascensions, giue you a table generall for all climates in the earthe. And as for the chaunge of the ho­rizontes or of the meridianes betweene easte and weste, you [Page 183]

[Page 184] shall vnderstande that 15 myles difference from easte toward west, doth make the sonne risinge, the none steed, and Sonne setting, to be later by one minut of an houre. and so 30 miles 2 mynutes: 120 myles 8 minutes: 225 myles. 15. minutes. which is a quarter of an hower. And for exaumples sake more then for any other cause I giue you here this table, which you may easylye increase by the lyke fourme, vntyll you haue accom­plysshed the whole 24 howers, yf you lyste. howe bee it hee that is readye in accompte of Arithmetike, needeth not anye suche tables of ayde. This table is calculate on­lye for suche places as dyffer not aboue 1800 myles bee­tweene easte and weste, hauynge no difference or verye lyttle in their distaunces betweene southe and north, as touching this consideration. And it serueth onlye for the middle cli­mate of the worlde vnder the equinoctiall circle. for euerye other climate, yea and euerye degree in latitude of eche cli­mate, must haue a seuerall table, whiche maye not well be set forth in this brief introductiō, but an other time shall serue herafter for it, yf you call on me and put me in mynde ther­of, els the necessitye of prouision for my familye will make me forget suche promises: howe be it by cause you shall not thinke that I haue done more for them that dwell vnder the equinoctiall (or nygh vnto it in Guynea or in Calecut) then for our own cuntrie, I haue drawen the like table for the ele­uation of 52 degrees, whose vse is euen one with the other before. wherefore if I knowe the distaunce of myles bee­tweene anye twoo places vnder this latitude of 52 degrees, or nyghe thereto, as soone as I haue founde out that num­bre of myles in the table vnder that title, in the nexte co­lumpne on the righte hande, I maye see howe manye mi­nutes they do differ in theyr howers.

So that the miles exceede not 1110, for this table hathe no greater numbre.

If you lyste by this president, you may increase the table as muche as you wyll.

Bicause examples do make rules manifest, I pray you let me proue one example. London and Bristow are 94 myles a sonder, and as I haue hearde you saye, they are not muche different in latitude: I desire to know their difference in howers, therfore I seeke for 94 vnder the title of distaunce of myles, and I can not find it there, for 92 and a halfe is to lyttle, and 101 ¾ is to greate.

And in lyke rate is there difference of minutes: for 10 minutes is to lytle, and 11 minutes is to greate. but to gesse moste nearest: as 92 and a halfe is nigher to 94 then 101 ¾: so is 10 minutes more nearer their true difference then 11. And for this time this maye suffise, althoughe I can giue you a precise rule by the part proportionable to fynde oute the iuste parte of euery minute, but that were more curious then profitable in this place: Therfore will I leaue it, and de­clare vnto you, how you may make the lyke table for any la­titude of euen degrees.

I do perceaue by these two tables, that it I haue ones the fyrst numbre which must be set against one minute of tyme, then must I double it for two minutes, and triple it for thre minutes, and so forth, styll multiplying the fyrste numbre of myles by the numbre of minutes against which it shall stende.

You take it well, and therfore seyng you doubte only of the fyrst numbre, I will giue you a table by whiche you may easily find out that firste numbre for all degrees of latitude of any region. And this is it. where in the first co­lumne you see placed the degrees of latitude, and in the se­conde columne are set the myles with their fractions, which serue for one degree of longitude, in eche of those dyuers latitudes. By this table may you make any table for any ele­uation of hole degrees, accordinge to the example of the former two tables.

That do I perceaue nowe very well, and can do it, I doubt not, sufficiently for anye Climate, yf I were as [Page 187]

[Page 188] certaine of their boundes.Of the cli­mates. but that maye I learne by suche tables as Orontius and dyuers other haue sette forthe all readye.

In deede bothe Orontius and other haue set forth suche tables, whiche maye suffice for an Introduction, but Orontius extendeth not his table aboue the latitude of 66. degrees and a halfe, so there resteth vnto the northe Pole 23 degrees and a halfe,The famous aduenture vnto Mos­couia by the northe Ocean. whiche coaste hytherto hath been kno­wen to very fewe men, but nowe of late by the famous ad­uenture of that woorthye companye of our Englishe mar­chauntes for Moscouia, that coast is discouered vnto 75 de­grees of latitude nighe hande: and our hope is that if they doo continue as they haue valiantlye begonne, they shall disclose those vnknowen people whiche dwell directlye vn­der the Pole, or at the leaste waies discouer that climate, suche as it is, to the full satisfaction of that importune desire, whiche hathe forced manye thousandes to wisshe, that whiche not one yet (that we knowe) coulde attayne: whereby they shall not onlye profite their countrie, but shall procure to theim selues greate ryches and treasure: and that whiche is moste to bee desired, immortall same. Wherefore for my parte to further their knoweledge in the atchiuinge of their woorthye attempte, as I haue all readye in this booke giuen some lighte, so wyll I (God wyllinge) hereafter gyue more lighte: and for an earneste thereof I will nowe exhibyte to you a table of the Climates extended to the verie Pole, whereby you maye learne not onlye the beginninge and eande of euerye climate, but also the iuste quantitie of the longest and shor­teste daye in eche of theim, and in all other places to the Pole selfe: the reason whereof you shall better vn­derstande by the diuersities of the ascensions.

But bicause (as I saide beefore) that euerye Climate dif­fereth frome other, by the space of halfe an hower in the quantitye of their longest daye, therfore did the greekes [Page 190] and namely Ptolemye, for a more precisenes make a certain distinction for euery quarter of an howers difference, whi­che he calleth only by the generall names of paralleles, as it doth at large appear in the sixte chapter of the second boke of his Almagestes, wherof at anye other tyme I will more largelye intreate. And for this present time will onlye sette forthe the summe of that matter in a table, whose firste co­lumpne doth containe the numbre of the paralleles as Pto­lemye did distincte them. The seconde columpne contay­neth a more exacte partition of those paralleles accordinge vnto the increase of the longest daye, by a quarter of an hower, whiche Ptolemye obserued not, after hee came to is howers of lengthe: but I obserue styll, vntill 24 howers of length. after which time and place, bicause the increase of the longest daye is greater and greater continuallye, I thinke it not good to make so curious a table for euery quarter of an hower, but (as Erasmus Reynhold doth) to make the distinction thence forthe by halfe a degree of difference in eleua­tion of the Pole, as by the table you maye see.

In this table are sette for the 96 paralleles iustlye: and but 38 by Ptolomies partition: the cause whereof, I will shewe you an other time. Of these paralleles are made 24 Climats betweene the Equinoctiall circle & the Tropike of Cancer. eche differinge frome other by halfe an hower, as the laste columpne of the table declareth. but the elder Greekes dyd not knowe verye well those North cuntries, and therefore did they assigne only 7 climats according as I haue set them annexed to the firste columne of this table.

Howe be it bicause you shall know what names thelder gre­kes dyd giue them (whyche names hath beene retayned euer sith that time) I haue here drawen a lyke table as your other authors haue sette forthe, that you may the better conferre the figure with the table, and the more easilye vnderstande the one by the other. in whiche figure the circle A, B, C, D,

represēteth the Hori­zont, & the righte line A C, stan­deth for the Meridiane line.The names and ordre of the Cli­mates. A is y^e north pole and C, the south pole. B the easte, & D y^e west. B D beto­kening the Equinoctiall, and EF the tropike of Cancer, GH, the tropike of Capricorne. and al the other lines are the boundes of the Climats eche in his order. The first Climat taketh name of Meroe, a famous Iland in Ethiopia vnder Egypt, inclosed by the riuer Nilus. the secōd Climat is named of Syene, a city of Egypt, lying directli vnder y^e tropik of Cancer. The third Climate is called after Alexā­dria, a notable city & an anciēt vniuersity in egypt also, lying on the north shore of it. The fourth climate beareth y^e name of y^e Rodes, an island better knowē then kept, and yet better loste then kepte so derely. The fifte Climate is expressed by the name of Rome, a citye in Italye well ynoughe knowen.

The sixte climate is called after the Euxine sea, commonlye called Ponte. The seuenth Climate reacheth from the pa­rallele that passeth by the mouthe of the riuer Boristhenes, and extendeth to the parallele that runneth by the south partes of Englande, as Ptolemy witnesseth in the second booke of his Almagestes. And although more maye bee saide of the Climates, yet I will reserue it to the treatise of Cosmo­graphye, and at this time will saye no more, but that on the other side of the Equinoctiall towarde the Southe, there are the like Paralleles, and the like Climates,The southe Climates. with the same quantities of distaunce from the Equinoctiall, and the like increase of daies.

The distaunce of anye Climate or Parallele frome the Equinoctiall is equall all wayes with the eleua­tion of the Pole aboue the Horizonte, as I maye easilye coniecture: so that when I knowe the one, I muste nee­des knowe the other: and that maketh me nowe to thinke that yf I knowe anye eleuation of the Pole, I maye by thys table easilye declare howe farre that Parallele whi­che serueth for that eleuation,The vse of the table of Climates. is frome the Equinocti­alle circle: and howe longe the longest daye is in that place: and if it chaunce that the latitude of anye region whyche I doo seeke for, bee not in thys table iustelye ex­pressed, I muste then gesse by the proportion of those twoo numbres, betweene whyche it standeth, what the pre­cise lengthe of the longest daye is.

Thys table it selfe suffiseth for eche quarter of an hower betweene the longest nighte of 24 howers, and the longest daye of 24 howers: but for more exacter partes of tyme, I woulde not wisshe you to trauaile yet, tyll I maye hereafter gyue you full rules for it: especiallye seeynge thys quarter of the hower is the difference of the whole daye, whiche muste be parted into twoo par­tes, and the one halfe quarter to bee assygned to the [Page 194] difference of the Sonne risinge, and the other halfe quarter the difference of the sonne setting.

That difference is more precise then our clocks or dials do serue vnto, and therfore I may well ynoughe bee satisfied with it for this time: wherefore I pray you now pro­ceede to the Ascensions.

The vse of the name of the Ascensions, hathe greate diuersitye in it,Of the As­centions. therfore I muste by diuision and defi­nition distincte so those diuers varieties, that you may iust­ly knowe them eche in his kinde. And fyrst, for the name of Ascension in generall, it doothe betoken the risinge of anye starres or signes (what so euer they be) aboue the Horizont. But nowe is there dyuers obseruations of seuerall persons touching the risinge of the starres, for Astronomers vse to obserue theyr rysinge in fourme, that is to saye, whether they ryse ryghte or obliquely, not regardynge (in that consideration) the difference in the time of the daye: where as the conninge Maryners, and authors of husbandrye, yea and good Physicians also as well as Astronomers do marke their risinge at twoo times principallye, that is when they rise iuste at the Sonne settinge, or els iuste at the Sonne rysynge.

If Astronomers doo nonsider onlye the fyrste forme, then these other formes do not appertaine to thys treatise, whiche is of Astronomye peculiarly.

Althoughe those risinges and settinges of the starres which Physicions and other good writers of husbanddrye and writers also of nauigation, doo ofte times speake of in their writinges, as beynge suche, whiche in aunciente Kalendars haue beene sette forth plainlye for all menne to vnderstande, and so myghte bee at this tyme also, yet he that shoulde well sette theym so forthe, oughte to bee skyl­full in Astronomye, els canne hee not doo it woorthy the readynge, and therefore it belongeth to Astronomers to [Page 195] determine their true times. Howe bee it bycause Poetes haue oftener made mention of suche rysinges, then Astro­nomers haue doone, therefore doothe Ioannes de Sacro Bosco and others also call them Ascensions Poeticall: not as fayned matters, but as thinges often remembred in Poetes bookes. And as I sayde, they putte difference betweene the rysynge of those starres in the mornyng wyth the Sonne, and the risynge of the same at the Sonne set­tynge. The fyrste manner of risinge with the Sonne, they call in Latine, Ortus Cosmicus, Mundanus and Matu­tinus: whiche maye well bee named in Englyshe the Mor­nynge rysinge: the other sorte whiche in English ought to bee called the Euenynge risinge, is named truely in Latine ortus Vespertinus or Acronychus, and not Temporalis or Chronicus.

Yet manye doo call it so, and Ioannes de Sacro bosco sheweth a reason of that name, bicause (sayth he) that Astronomers vse that time after the Sonne settinge best for markinge the course of the starres.

Ignorance of the Greeke tongue hathe hindred muche manye good wittes: whiche maye often appeare not only in good Iohn de sacro bosco, but also in many writers within these 300. yeares especiallye: but wee muste wynke at suche faultes, whiche rather were the faultes of the time, then of the persons. and for this name Acronychus, is easilye tourned into Chronicus. The fyrste name is of­ten readde in Ptolemye and other Greeke wryters, and is named of the begynnynge of the nyghte, whiche name by ignoraunce was tourned into Chronicos in Greeke, and so accordinglye was called Temporalis in Latine, and then an ymagined reason clouted thereto: lykewaies also in the thyrde kinde of rysynge and settinge, where­of the same author doothe make mention, hit appea­reth that hee was somewhat deceaued, for that owghte not to bee called proprelye rysynge of anye Starre [Page 196] when it getteth oute of the Sonne beames, and maye shewe or shine at eueninge or mornynge.The thyrde kinde of settynge. but it oughte rather to be called Apparition or appearynge of that starre. And contrarye wayes when anye starre is so nyghe vnto the Son that the Sonne doothe take awaye or hyde the lyghte of it, it oughte to bee called the Hydynge or occultation of that starre, and not the settynge of that starre, syth settynge and rysynge haue propre relation to the Horizonte, and yet doothe hee and mennye other contrarye to the lear­ned Greekes call the fyrste, the Sonnelye rysynge of the starre, and the other, the Sonnelye settyng of him where as Ptolemye and the learned Greekes call the one [...], that is in Latine Apparitio, the shewynge of the starre. and the contrarye is called in Greeke [...], and in La­tine Occultatio, the darkenynge or hidynge of the starre. whiche chaunce happeneth commonly to any starre being within 15 degrees of the Sonne. this passion is called of ma­ny men Combustion:Combustiō. Oppression. Other contract the name of combu­stion to syxe degrees, and call this Oppression. but of all these, I will an other time declare my full mynde, for the iust knowledge hereof appertaineth to a higher Arte. And so will I hereafter giue you a table declaringe the mor­ninge and euenynge rysynge and settinge of all the moste notable starres, for the matter is not so easye as it seemeth to bee.

I vnderstande it thus: that when the Sonne is in anye parte of a Signe, those starres whiche be in the same parte of that Signe, doo rise with the Sonne, and those whi­che be in the like degree of the contrarye signe, they rise at the Sonne settynge.

Your taking is true, for suche starres as are nigh vnto the Ecliptike line: but yet such starres as be farre from the ecliptike line, may rise or set with the Son, although thei be in an other Signe then the Sonne is, & so may they ryse or set before or after y^e son, although thei be in one degre of any [Page 197] Signe with the Sonne. And here maye you not forgette that the starre that setteth with the Sonne,The eue­ning settig The mor­ning settig is named to haue an euening setting: and the starre that setteth in the weste at the Sonne rising, is iudged to haue the morning setting: wher­by it foloweth, that the starre that hath the morning rising, hath also the euening setting: and he that hath the eueninge risinge, hath the morning setting: thus haue I spoken rude­ly and lyghtly for this time, but in the table of these risinges and settinges, you shall haue a more exacte forme of know­ledge set out for you, touching this matter. And nowe to retourne to those ascensions which be peculiarly called Astronomicall, fyrste, for the definition you muste vnderstande, that Ascension astronomicall is the certaine limitation of som pointe of the equinoctiall circle,Ascentiō a­stronomical whiche riseth iustelye with anye starre, and largely taking the vse of that name. It betokeneth also the arke of the Equinoctiall circle, whiche lyeth betweene the beginninge of the same Equinoctiall at Aries, and extendeth to the iuste degree that riseth with any starre or signe. Thirdly the ascension of a signe or constel­lation (whiche includeth a certaine measure in lengthe,) is that iuste arke of the equinoctiall, which doth passe the Ho­rizont with that whole signe or constellation.

This ascension is commonly dyuided into twoo kyndes, the one is called Ryghte ascension, and the other Ob­lique or Crooked ascension. Ryghte ascension, is defined to bee that,Ryght as­cention. Croked as­cention. with whiche a greater portion of the Equino­ctiall dooth ascende. And that is called Crooked or Ob­lique ascension, with whiche a lesser portion of the Equino­ctiall doth ascende.

I heare you speake of a lesser portion and a grea­ter portion, but where vnto those comparisons ought to be referred, I can not tell, excepte I shall referre the one to the other.

That maye you not doo, for so one ascension [Page 198]

mighte bee called right & croked also, at the least in diuers comparisons: but that can not be, no­ther is it permitted by any astronomers

How may it appeare that suche absurditie woulde follow?

To the intente that I maye alleage nothinge, but that whiche shall not only be certaine and true, but also shall be manifest to you, I will firste instructe you in the vnder­standing of those Ascensions, and after that I will return to the proof of these my woordes. And for the better vnder­standinge of both definitions, I will name vnto you a thirde Ascension, which must be as the rule of those other 2, and that is the Meane ascension, for seyng you can not well refer greater and lesser but other to one common meane, or els eche to other: and I haue said before (and wil proue it anon) that they can not be compared togither,The meane Ascension. therfore must they bee referred and compared to one common meane, whiche I call the Mean ascension, bicause that with it ther ascendeth not so muche of the Equinoctiall, as with the right ascensiō, nor so lytle as doth ascende with the crooked ascension. and for this cause may it well be called a Mean ascension. Again it maye be called a Meane ascension, bicause it is without all excesse: for the portion of the Equinoctiall whiche ascen­deth with it, is equall to it in precisenes of degrees, so that neither of them excedeth other.

It seemeth reasonable that all excesses beinge re­ferred to anye one thinge, do approue that one as a meane betwene them, namely when the excesses decline to both ex­tremities, as more and fewer, greater & lesser do. but in al this kinde of doctrine, the wordes are more easye to bee vnder­stande, then the matter. Therfore excepte ye do with exam­ples [Page 199] declare these varieties of Ascensions, I doubte it wyll be longe before I shall well conceaue them and rightlye di­stincte them.

You haue learned before, that there is two varie­ties of Spheres, a Righte Sphere, and a Bowing sphere: and as in eche of these the Equinoctiall doth kepe one vniforme ascension, that is to say, y^t in 24 houres iustlye all the equino­ctiall doth ascende, and so consequently in euerye hower of the daye 15 degrees of the Equinoctiall doo passe the righte horizont, so the Zodiake whiche is the circle of the signes, by meanes of his obliquitie, dooth not keepe vniforme as­cension anye where in any position of Sphere. for although the whole Zodiake do ascend iustly in 24 howers, yet in eue­ry hower, vnequal portions of it do ascend, and that diuers­ly, according to the diuersities of the Climates.Certain generall rules in a righte Sphere. But in a ge­neraltye of differences, you may take these generall rules.

In the right sphere, euerye quarter of the Zodiak hath an equall or Meane ascension, with euery quarter of the equi­noctiall, beginning the quarters at the 4 principall points, whiche I haue before set forthe: for if you shoulde take three signes in other partes of the Zodiak, their ascensions wyll not agree with a quarter of the Equinoctiall, sith there is no one signe that doth equally agree in ascension with the lyke portiō of the Equinoctial, that is to say, with 30 degres in it.

This rule is in Ioannes de Sacro bosco, and in Orontius also.

Then you beleue it the better.

Yea in deede.

Then tell me whether the ascension of one of those quarters of the Zodiake, ought to be called a Right ascen­sion, or a Crooked ascension.

Neither of bothe, as I do vnderstande their defi­nitions, seeyng the arke of the Equinoctiall that ascendeth with them, is nother greater nother yet lesser then they, as these definitions do importe, but is equal with them, and [Page 200] therfore it seemeth to me more apte to call it a Meane ascen­sion after your definition.

You saye truthe, and therefore is their doctrine imperfecte, that make but two ascensions, where thre ought to be distincte, (and them selues name thre in vse, and but 2 in distinction and definition) namely seyng (as Tullye hath sayd) it is the greatest faulte that can be, to omitte any membre in diuision: but to omitte their faultes in omission, and to retourne to their better declaration. II This second rule do they also approoue, yea and natures ordre doth necessarily inferre the same, that euerye twoo signes or partes of Signes equall in quantitie, and lyke distaunte from anye one of the 4 principall pointes, haue equall ascensions eche to other.

That is to meane, that Taurus, and Aquarius haue equall ascension, bicause they are equally distaunt from the Equinoctiall pointe of Aries.

And so haue Taurus and Leo, bicause they differre equallye frome the Tropicall pointe of Cancer, and so of all the other. But to the intente that you maye the better vnderstande all this that is saide, and the reste that is to be saide, I haue here set forthe in a table the iuste num­bres of degrees of the Equinoctiall circle, which do answer to the degrees of euery signe in their ascensions in the right Sphere. So that if you desire to knowe the ascension of any degree of anye signe, firste seeke out the signe, and then in the firste columne looke for the noumbre of the degree, against whiche in the common corner vnderneth the Signe you may see the numbre of the degrees and Minutes of the Equinoctiall, that do ascende with that degree of the signe. And those degrees be accompted frō the beginning of the Equinoctiall at Aries, and so orderly after y^e naturall course of the signes. wherby you maye perceaue, that Aries, Tau­rus and Gemini all three togither haue for their ascension 90 degrees, whiche numbre agreeth with the quantitie of 3. signes, and therfore is their ascension Meane. Also I maye [Page 201]

[Page 202]

[Page 203] saye, that the laste degree of Gemini, or anye starre in that degree, or in the laste degree of Virgo, Sagittarius or Pi­sces, haue a Meane Ascension, so that the same starre haue no latitude: how be it in the eande of Gemini and Sagitta­rye, althoughe they haue neuer so muche latitude, yet is their ascension meane. whiche prerogatiue those two points haue, bicause the lynes or circles of their longitudes doo touche bothe the Poles of the Zodiake and of the Equino­ctiall, and so dothe no other circle of longitude: wherefore all starres out of those places limited where so euer they be, they haue no Meane ascension, but other Ryghte ascension, or els Crooked.

Thus I perceaue that the twoo tropike pointes haue a priuiledge aboue the two equinoctiall pointes in the ascensions.

It seemeth so in the righte sphere, but in the Ob­lique sphere the Equinoctiall pointes haue the greater pri­uilege: for alwaies in all places where they doo ascende, they keepe their meane ascension, but so dooth not the tropike pointes in anye oblique sphere. no nother anye starres of their longitude, that is to saye in their Colure. for although twoo pointes in the skie, where their Colure dooth cutte the Equinoctiall circle, haue a meane ascension, yet in those 2. places is there no starre that hath beene noted, as hereafter you shall better vnderstand. But that you maye in the mean season knowe what signes doo ascende righte, and which do ascende crokedlye in the righte sphere, you shall marke this lytle table whiche I haue drawen out of the former great ta­ble, where you see that 4 signes agree styll in their ascension, and the firste 4 haue but 27 degrees and 54 minutes of the Equinoctial answering to eche of their ascensions: the other 4 signes haue 29 degrees, 55 minutes for their ascension: and the laste 4 haue 32 degrees and 11 minutes agreeing to theyr rising, which degrees and minutes added togither, do make iuste 90 degrees that is exactlye one quarter of the equino­ctiall [Page 204]

and so are eche ternary of those Signes one iuste quarter of the Zodiake.

And in like case I perceaue, the 6 howers of time that answereth to those whole quarters, is also the iuste quarter of the naturall day, which amounteth by the addition of the three seuerall times agreing to those 3 seuerall ascensions. And as I vnderstand it, the quantitye of tyme is gathered after the rate of 15 degrees ascendinge euerye hower, as you saide before. so that euerye degree asketh 4 minutes of an hower: and 15 minutes of a degree in the Equinoctiall doo ryse in one minute of an hower: for this is alwaies to bee re­mēbred, that a minute is euer more the 60 part of that thyng whervnto it is referred. But now ther commeth to my mind the sayinge of Ioannes de Sacro Bosco, whiche longe hathe troubled my minde, and I can not learne of anye man howe to vnderstande him well: for in mine opinion his woordes import an impossibilitie. he blameth this argument as euel: These two arkes are equall, and they begin to rise togither, and continually ther riseth a greater portion of the one arke then of the other: ergo that arke will bee full risen soonest, whose greater portion did alwaies rise. This argumente see­meth inuincible in mine opinion, and yet Iohn de Sacro bo sco for improuing of it alleageth an example, wherby as he seemeth to intend, the antecedent maye be true, and the con­sequente false: and therefore the argumente muste needes be naught.

Repeat you his example, that we may examine it:

He willeth to take any quarter of the Zodiake, compared with his like quarter of the Equinoctiall, and to begin with that quarter from the fyrste pointe of Aries, to the latter ende of Gemini, alwaies the greater portion riseth of the Zodiake, and the lesser of the equinoctiall, and yet those two quarters ascend fully togither: and the lyke muste you vnderstande of the thirde quarter, from the beginning of Libra, to the eande of Sagittarye. but contrarye waies, in the quarter that lyeth frome the fyrste parte of Cancer, to the laste of Virgo, the portion of the Equin octiall in ry­fynge, is styll greater then the parte of the Zodiake that ri­seth with it: and yet those bothe arkes doo rise iustly to gi­ther at the eande.

Here is a greate fallation by Amphibologye, as Logitians do call it, so that in one sence it maye be true, and in an other it is false. And fyrste for declaration of Iohn his meaning (as I thinke) marke as many partes of those 2 firste quarters as you lyste, and still by the former table, as well as by tournynge the Sphere it selfe, it wyll appeare manyfestly, that the portion of the Zodiake is euer greater then the matche portion of the Equinoctiall.

That is moste true. for with 12 degrees of Aries there ascendeth of the equinoctiall 11 degrees and twoo mi­nutes only of the Equinoctiall, that is 59 minutes lesse: with 30 degrees of Aries there riseth but 27 degrees and 54 mi­nutes, whiche is lesse by two degrees and syxe minutes: also in Taurus, 15 degrees hath for their ascension 42 degres and 32 minutes, that is twoo degrees and 28 minutes to lytle: the laste of Taurus ascendeth with 57 degrees and 49 minutes, whiche shoulde be 60 if it were equall with the degrees of the Zodiake. Againe the 16 degree of Gemini answereth to the ascensiō of the 74 degree and 48 minute of the equinoctial, whiche in equalitye would be 76: and the 29 degree of Ge­mini should haue by ordre of equalitie the 89 degree of the equinoctial, & hath but 88 degrees & 55 minuts, which is lesser [Page 206] by 5 minutes then equalitye requireth, and so doth it appear in all the reste, saue in the verye laste degree of Gemini, wher bothe numbres appeare euen.

Then are the wordes of Iohn desacro bosco true.

This matter troubleth me to muche: for of this am I assured, that if anye two quantities be equall togyther, and a lesser portiō of the fyrste matched with a greater part of the second, then of necessitye that parte that remaineth of the fyrste quantitie, must needes be greater then that that resteth of the seconde.

That is true also: for if you abate vnequall partes from 2 equall quantities, the portions that remaine will be vnequall, and that parte will bee leaste, frome whiche the greater portion was abated.

As that can not be false, so it seemeth to me, that seyng there doth ascende with the whole signe of Aries but 27 degrees, and 54 minutes, there must needes remain 62 de grees and 6 minutes of that quarter, and that is more then the 60 degrees which resteth of the like quarter of the Zo­diake. Now those 62 degrees and 6 minutes will ascend with the 60 degrees of the Zodiake, so that then there dooth not styll ascende a lesser portion of the Equinoctiall: for as the fyrste portion was lesser, so this seconde parte is greater.

Your coniecture is good: and to approue it the better, you may conferre some lesser partes of those 2 quar­ters togither, as from the 20 degree of Taurus, to the 10 degree of Gemini, the degrees betweene them are 20: & to know the arke of the equinoctiall that ascendeth with those 20 de­grees, subtracte the lesser from the greater, and the ascension of those 20 degrees wyll remayne.

[...]The ascension of the 20 degree of Taurus is 47 degrees and 33 minutes: the ascension of the 10 degree of Geminiis 68 degrees, and 21 minutes. wherfore setting those numbres in conuenient ordre, and making subtractiō duly, ther resteth 20 degres; & 48 minuts, so is this portiō of y^e equinoctiall [Page 207] the greater by 48 minutes.

Proue again from the 28 degree of Taurus, to the 28 degree of Gemini: whiche difference is 30 degrees.

With the 28 degree of Taurus there dooth as­cende 55 degrees, and 44 minutes: and with the 28 of Gemi­ni, 87 and 49. and by Subtraction the difference appeareth to bee 32 degrees, and 5 minutes. so is the arke of that Equinoctiall greater by two de­grees and 5 minutes, then the matche arke of the Zodiake. [...]And therefore are not Iohn de Sacro bosco his woordes true.

Prooue yet more before you condemne him. try the arke from the tenth degree of Taurus, to the 22 degre of the same signe, whiche arke includeth 12 degrees of the Zo­diak.

The 10 degre of Taurus, ascēdeth with 37 degrees & 35 minutes of the equinoctial y^e 22 degre of y^e same sign hath for his ascensiō 49 degrees & 35 minuts, y^e difference between them by subtractiō is found to be 12 degres iust: and so that arke of the Equinoctiall is equall with his matche arke in the Zodiake. [...]

Yet ones more proue the arke frō the last degre of Aries to y^e second degre of Gemini, which ark is 32 degrees.

The last degree of Aries riseth with 27 degrees, and 54 minutes: and the 2 of Gemini hath 59 degrees and 54 minutes in his ascension. betwene which 2 numbres, the distaunce is 32 degrees exactly, and so are those 2 arkes equall also, and neither of those 2 examples do make the arke of the Equinoctiall lesser then the matche arke in the Zodiake: so that they make agaynst Iohn de Sacro bosco. [...]

In deede as his woordes be placed in the Present time, they can not be true, but his meaning may be more fa­uourably gathered, by turning the Present time into y^e Per­fect time, & referring the name of ascension to the whole arke [Page 206] that is fully rysen in that quarter, as I dyd in the explication of his wordes occasion you to make proofe: wherfore take anye parte of the fyrste quarter, and accompt from the be­ginninge of Aries: or lykewaies any part of the thyrd quarter, and recken from the beginning of Libra, and so shall you see alwaies that the portion of the Zodiake whiche is ascended, shall be greater then the parte of the Equinoctiall that is risen with it: & so shall it continue euen to the very laste degre of them bothe, and then at length doth both the quarters end their ascensions exactly togither.

As you saye. nowe doo I perceaue it, so that the faulte is rather in his woordes then in his meanynge.

Such meane matters must be winked at in other, but not folowed. And nowe for the ordre of Ascension of y^e other 2 quarters which begin at Cancer & Capricorne, you shall vnderstand the lyke: but that the greater portion y^e as­cēdeth is referred to y^e Equinoctial circle & not to y^e Zodiak▪

So I vnderstand by this former table that with y^e 28 degree of Cancer there ascendeth 120 degrees and 6 mi­nutes of the Equinoctiall, which is two degrees and 6 mi­nutes more then equality woulde yelde: and with the 26 de­gree of Virgo, there riseth the 176 and 20 minutes of the e­quinoctiall, whiche is also more then equallenes by 20 mi­nutes: and so if I take anye degre of any signe in that second quarter, or in the fourth quarter, beginning at Capricorn, I may lyghtly see by the table that the portion of the Equi­noctiall in his ascension is greater then the matche arke of the Zodiake from the beginninge of Aries to that degree. wherby it appeareth that al those 6 signes do ascend right, bicause a greater portiō of the equinoctiall ascēdeth with thē.

Then by the like reason, the other 6 signes Aries, Taurus, Gemini, Libra, Scorpius and Sagittarius do ascēd crokedly, bicause y^e lesser portiō of y^e Equinoctial doth ascēd with thē: after y^e sort of conferēce, which is cōtrary to y^e I said before, y^e 4 signes only do ascend ryght in the Ryght spher: [Page 209] wherefore you muste vnderstande, that for to knowe the as­cension of euerye signe, you must consider that signe alone, and the arke of the Equinoctiall that dooth ascend with it, and so shall you see exactly the ascension of euerye signe se­uerally. And here you shall vnderstande, that all Astrono­mers commonly do call the Right ascension so largely,An other signification of right as­cension. that it extēdeth to the ascensiō of all the signes in a Right sphere: and so they name the Oblique ascension the rising of all the Signes in anye Oblique Sphere, whereby it appeareth that they giue the name of Ryghte and Crooked ascensions, ac­cordinge to the Horizontes or pofitions of the Sphere, and not after the quantities of time in their ascension. And this shall suffice at this time touchinge ascensions in the Righte Sphere: in which also the descensions or settinges vnder the Horizont, are equall with the Ascensions,Of the des­cention of Signes. so that they need not to haue anye peculiare declaration: but in the Oblique Spheres it is not so, but contrary waies. those signes that do ascende righte, doo descende crooked: and they that ascende crooked, doo descend righte: so that the descension of anye signe in an Oblique sphere, is equall precisely to the ascensiō of the contrarye signe.

You meane that the defcending of Aries is equal to the ascendinge of Libra, and the descendinge of Taurus is one in quantity of time with the ascension of Scorpius.

So is it in deed. And in this greate varietie you shall marke one constaunte vniformitie, that the ascension and descension of any signe in any croked sphere ioyned by addition togither, doo make an equall summe of time with the ascension and descension of the same signe in a righte sphere, in lyke sorte ioyned togither: but to the intente that you maye vnderstande all these thinges the better, and also knowe the iuste ascension of euerye signe in this our Climat where the eleuation of the pole is 52 degrees, I haue drawen heere a speciall table for that latitude. in whiche you shall vse the like manner of entringe, as you did in the other, so that [Page 210]

[Page 211]

[Page 212] althoughe the numbres differ, yet the woorke differeth not in this table. the fyrst columne containeth the degrees of the Signes, and the other columnes doo containe the degrees & minutes of the Equinoctiall vnder eche signe, accordingly as they doo answere to the Ascension of the degrees of the same Signes. By this table may you see a great diuersitie in the Ascensions from those in the Righte Sphere: And yet this maye you certainly obserue: that euerye two signes be­inge contrarye to gither, the one lyinge againste the other, as they haue farre vnlyke ascensions, so yet if you adde their bothe ascensions togither, they will be equall to the ascensi­ons of the same twoo signes in the Right sphere.

Then in as muche as the ascension of Aries is in this latitude 12 degrees and 48 minutes, & the ascension of Libra, 43 degrees iust, (abating as I ought 108 degrees) and so they bothe by addi­tion do make 55 degrees, and 48 minutes. [...] And in the right sphere eche of these signes hath for his ascension 27 degrees and 54 minutes (for the contrarye si­gnes there are equall in their ascension) wherefore by addition there will amounte the same summe precisely that was gathered before: [...] and so like­waies of Taurus and Scorpius: their ascensions ioyned to­gyther maketh 59 degrees and 48 minutes: but in the righte sphere, those two ascensions maketh 59, 50. that is twoo mi­nutes only difference in two signes, so is it but one minute in one signe, that is not to be regarded.

Not greately, and especially in an Introduction. But doo you marke here the Signes that ascende ryght, and them that ascende crooked?

Although I see a difference by this table frome the other: I had thoughte that the more croked Sphere had made the more croked ascension onlye: but yet that they al­waies had kepte one name in generall, and not haue chaun­ged it. but by your question only I am admonished of mine [Page 211] errour: for I see that Libra (as it is easilye vewed) dooth as­cend here righte, and hath for his ascension 43 degrees, and in the Righte sphere it dyd ascende crookedly, and had but 27 degrees and 54 minutes for his ascention, and therefore maye I doubte of all the reste, tyll I haue examined theyr as­censions better.

To ease you of payne, lo here is a table of theyr iuste ascensions, which you maye examine at leasure.

By this table you maye perceaue what signes doo rise crokedlye, and whiche doo ascend righte, and that there bee of eche sorte 6. so that from Cancer vnto Capricorne all the signes in direct ordre do ascende ryghte, and frome Capri­corne to Cancer, in naturall ordre of the Signes, all those 6 signes do ryse crokedly. And this rule is generall in all these northe climates, that lye from 30 degrees of latitude (vnder which Memphis and Alcayre are and mounte Sinay: also the yste of Madera, and the parte of the weste Indies, cal­led Terra florida) vnto 66 degrees and a halfe of latitude, in that Climate wher Island lyeth and the north partes of Nor wayes, and namelye Halgoland, where Oht here dwelte, that was the fyrste discouerer of the north viage towarde Mos­couia.

That viage I desire muche to vnderstande, and [Page 214] so do manye other.

An other time shall serue for it, for now we haue an other matter in hande.

Then for this present matter: Is there anye other varietie of ascention betweene the Equinoctiall circle and the Latitude of 30 degrees?Varietes of Ascensions.

Yea, muche diuersitye: for (as you haue hearde) vnder the equinoctiall 8 signes do ascend crokedly, and but 4 ryght: but from the Equinoctiall vnto 10 degrees of lati­tude, 6 signes ascende ryght, (Gemini, Cancer, Leo, Scor­pius, Sagittarius, Capricornus) and other syxe croked, that is Aries, Tarurus, Virgo, Libra, Aquarius & Pisces. And from 10 degrees vnto 30 there are 8 signes that rise right, as Gemini, Cancer, Leo, Virgo, Libra, Scorpio, Sagittarius, and Capricornus: and the other four, Aries, Taurus, Aqua rius and Pisces, rise crokedly. but to the intent that you may haue the better habilitie to iudge of suche varieties, I haue here sette forth diuers tables for examples sake: and namely suche, whiche importe anye varietie of alteration, or helpe to the apte vnderstandinge of the same.