An Explanation of Whole-sale and Retail: Lib. 2. Parag. 8.

Observe in all Commodities [...] where a hundred gross is men­tioned, it is 112 lb usually no­ted with a C. for Centum, as in this Example, where five hundred and three quar­ters is given, which 5 C multiplied by 112 lb and ¾, or 84 lb added unto it, the product with the addition will make the summe of 644 lb for the subtile weight, and the first number; the second number in proportion, is the price, viz. 3273 ⅔ 8: the third number is 1 lb, on which the demand is made: these compound f [...]actions you may reduce into the least denomination, or the least but one, as in the Table; where by the Rule of Proportion in either way you will finde th [...]t one lb of those Wares stood the buyer in 5 ss: 1 d: or as in the Table 5 2/ [...]2 ss: with all ch [...]rges defraid, according to the demand and state of the Question pro­pounded.

An explanation where gain is imposed up­on the parcel: Lib. 2. Parag. 8.

Admit a Draper bought [...] 58 yards of Cloth, which stood him in (with all charges) 13 lb: 1 ss: at what rate by the yard must he sell it for, whereby to gain 1 lb 9 ss: adde the required profit unto the price, the summe will be 14 lb: 10 ss: that is 58 Crowns, or in shil­lings 290: to avoid fractions, the least denomina­tion is usually best: here the fourth proportional found will be 5 ss, the price of one yard according to the gains required, as by the operation in the Table is made evident.

An explanation, where gain or loss is impo­sed upon a part, Lib. 2. Parag. 10.

This Questi­on [...] is stated ac­cording to the Double Rule of Proportion, ei­ther for gain or loss, by change­ing the ex­tremes in the first Rule, viz. in this 10 for 11, the fraction in all such cases making two terms; the Denominator in the first place being Divider, the price of the Wares or Merchandizes the se­cond term, and the summe both of Numerator and Denominator must possess the third place, if for gain; but must be made Divider, if the Propositi­on be for loss: the first number in the second Rule ought to be the quantity propounded, either in Number, Weight, or Measure; and the last Number an Unite on which the querie is made, of [Page 5] gain or loss: or, which is all one, if an improper fraction as in the Table 4/4, the Denominators be­ing made equal, viz. 135/4 and 4/4 and consequently may be omitted, one being a Multiplier, the other a Divider; their Products are these 1150/4 · 115/6 · 44/4 · the first and third Numerators may be reduced by 2, and their Denominators cancelled; they will stand thus, as in the third Table, viz. As 575 to 115/6 so 22 unto 253/345 which is in money 14 ss. 8 d, the price of one yard with the profit required.

The reason is evident; for if 20 ss were the In­teger, the Numerator would have been 2 ss and consequently the proportion as 20 to the middle term, so 228 the summe of Numerator and De­nominator to the gains required. This question may be easily solv'd without a Double Rule, as thus: by the first Proposition you may finde that one yard cost 13 ss. 4 d. 1/10 part of it is 1 ss. 4 d, the summe 14 ss. 8 d. as before: but this may be of good use in other questions, and therefore con­veniently inserted.

An Explanation upon Loss sustained in any Commodity. Lib. 2. Parag. 8.

A Grocer bought 340 lb sub­tile [...] of a Commodity which cost him in ready money with his char­ges 13 lb. 16 ss. 3 d. and by this parcel he lost 1 lb. 1 ss. 3 d. what was it sold for a pound? the loss in the whole subtracted from the price it cost, the remainder or difference is 12 lb. 15 ss. which in pence is 3060 d. so the proportion will be as 340 lb, is to 3060 d, so shall 1 lb be to the price of it; which is 9 d, as in the Table appears: and as for the trial of it, the pro­portion will be as 1 lb is unto 9 d, so will 340 lb be unto 3060 d, or 12 lb. 15 ss. as by the first Proposition.

An Explanation of gain or loss as any [...]ate per Cent. Lib. 2. Parag. 8.

Suppose 1 Gro [...]e bought 4 C [...] weight of Prunes, at 16 ss. 8 d. the hundred, how must he sell them by whole-sale again, and to make of his money 20 lb in the 100 lb. or after that rate? The answer will be 3 ss. 4 d. which if taken from the price at which they were bought, the remain­der or difference is 13 ss. 4 d. and if sold at that price, there will be after the rate of 20 lb in the 100 lb lost: and if 3 ⅓ ss. be added to the price, at which 'twas bought, the summe is 20 ss, and if vended at that rate, it will bring the desired pro­fit.

If this had been Cloth, and the whole Piece had contained yards 28 ½, which co [...]t in money 23 lb. 15 ss: by the first Proposition find the price of one yard (if it must be sold by retail) the answer will be 16 ⅔ ss. now the question at 20 lb per cen­tum will be the same by retail, as was the former [Page 8] in whole-sale. Many of these Questions may be performed without calculation, as in this Example, where 20 lb per cent. is required. The profit in money here is ⅕, and so the gain or losse in the Commodity must also be ⅕: the price in this was 16 ss. 8 d. that is 50 groats, and ⅕ part of it is 10 groats to be added or subtracted accordingly as it is gain or losse.

An Explanation of Gain or Loss sustained, at any rate per Cent. Lib. 2. Parag. 8.

A Draper bought Kerseys [...] at 6 lb. 13 ss. 4 d. the Peece, and sold them all a­gain for 7 lb. 10 ss. how much he gained, and after what rate in the 100 lb [Page 9] is the thing required: the price by which 'twas bought, and likewise the rate at which 'twas sold must be reduced into one denomination, or by the Rule of Fractions, viz. As 20/3 lb the price is to 100 lb, so 15/2 unto 112 ½: by which it is apparent that he gained 12 lb, 10 ss. in the 100 l. or after that rate; for 100 l. thus imployed will return 112 ½ l.

If any question of this kinde should depend up­on Losse, the Price at which 'twas sold must be less then that by which the Commodity was bought at, so the fourth proportional number will be discover­ed by the same Rule; the state of the Question not differing in any thing, either by Whole-sale, or Re­tail, so it requires no Precedent or Rule but this, which will bring your stock short home, as unfor­tunately true, as prosperously with increase.

An Explanation of Gain or Loss in one Parcel, to finde the rest, Lib. 2. Parag. 8.

Admit 15 Clothes or [...] Pieces were sold for 340 l; then was the price of one Piece 22 l: 13 ss: 4 d, as by the first Proposition; in this there was present gain 19 ss. 4 d, upon every Peece, which subtract­ed from the Price 'twas sold at, viz. 22 l. 13 ss. 4 d. the difference is 21 l. 14 ss. for the price it cost: then will the proportion be as 1 whole Cloth is to 21 7/10 l, so shall 15 Clothes be unto 325 l, 10 ss, as in the Table appears.

If this Commodity had been sold to loss, the differences betwixt the prices makes it evident, and then what one Piece, or any pa [...]t had co [...], will be discovered as before, with all the whole losse sustained; and if it should be required after what rate in the 100 l. the last proposition will un­fold it according to the Rule of Trade.

An explanation of Gain or Losse with time at any rate per Cent. Lib. 2. Parag. 10.

Admit a Tradesman [...] had bought a Com­modity at 5 d the pound, and after 6 Moneths time sold it again for 6 d the l. or suppose the Mer­chandize was bought at 5 ss the yard, and sold it presently again for 6 s the yard, but with 6 Moneths given for day of payment, or to abate so much as the inter­est should come unto at 8 l per cent. per annum, by the sixth Proposition, the gain of those Wares will be discovered after the rate of 20 l per cent. if present pay; but here is to be rebate of money, or forbearance of the stock and profit for six Mo­neths: suppose 100 l disbursed for these Wares at first, which would make 120 l if paid down on the nail; but here use is to be considered for that summe, and six moneths time with the encrease to be de­ducted: the interest of which summe is thus found: in this Proposition 'tis six Moneths, and 8 l per centum, as in the first row or rule in the Table; in the second row under 100 l stands the [Page 12] term for a year, in the same denomination with the time given, viz. 12 moneths; and under the third terme, the time limited for payment, viz. 6 Moneths, the products of them (according to the double rule of Proportion) in the third line is, as 1200 to 8 l. so 720. these are again reduc'd in the operation of the fourth Table, as 120 to 8. so 72 unto 4 l. 16 s. and might have been reduc'd again to 5.1.24. which will also produce 4 l. 16 s. that subtracted from 120 l. the remainder will be 115 l. 4 s. which shewes 15 l. 4 s. clear gains in relation to the rate by which twas bought and sold at, with the interest for the forbearance, agreed upon according to custom and contract, but not exactly true.

An Explanation in Gain or losse with Time. Lib. 2. Parag. 10.

A Merchant bought Mace at [...] 6 s. 4 d. the l. ready money, and he sold the same again unto a Grocer for 7 s. the l. at this rate, the Mace was delivered, and upon condition to be payd at the end of 4 moneths next ensuing the receipt thereof; and it is re­quired what gain the Merchant made of his money, and at what rate per cent. per Annum. In all questions of this kinde make the price at which twas bought, and as 'twas sold, of one denomination, the difference shall be the third terme in the first rule, 100 l. the second number, and the price for which 'twas bought, the first term: in the second rule under the first num­ber I place the magnitude of a year, in that deno­mination, in which the time limited is given; as in Moneths, Weeks, or days: in this 'tis Moneths, as the Letter M denotes; the space of time gi­ven for payment is 4 Moneths, subscribe that un­der the third number; then draw a line from thence towards 19 G, and that crosse with another, as from 12 M t 2 G in this Example; these multi­plied crosse-wise (the second rule being reverst) for the lesse time is given for payment, the profit will be the greater: in the third row stand the products in the Rule of 3 direct; and in the fourth Row or Table is plac'd the form of operation, [Page 14] wherein the desired product is discovered to be 31 1 [...]/19 l that is, 31 l: 11 ss: 6 d 1 [...]/19: the profit re­quired at the rate per cent. per annum.

An Explanation in Gain or Loss with time un­known. Lib. 2. Parag. 10.

A Tradesman bought Nut­megs [...] at 8 ss the l, and sold them all again at 9 ss the l, what day of payment must he allow, whereby to gain af­ter the rate of 20 l per cent. per ann. in all such like Cases, as 100 l to 12 Moneths, so 20 l. secondly, as 8 ss the price, unto 1 ss the gain made: the first rule is reverst, the other direct: in the third row of the Table stand the products, and under that again (in the fourth Table) is plac't the opera­tion in a reverst proportion, but may be made direct if you please: the answer to the question here in this, is 7 Moneths and 15 dayes, the time of payment; which makes the gains proportionable unto 20 l per cent. per annum, the thing required: had the Proposition been of losse, the operation is the same, so it needs no example but this.

An Explanation of Gain or Loss in several pay­ments, Lib. 2. Parag. 10.

A Merchant had certain [...] Wares which stood him in 60 l: these goods he sold unto another, who paid him so much money for earnest, as that the Mer­chant made of his money laid out 12 l per cent. per an. yet was to receive it at two several payments, viz. 40 l or ⅔ of his money 2 Moneths after the Wares were delivered; and the other 20 l, or ⅔ at the term of 3 Moneths after the contract: now to [Page 17] find what money the buyer paid down, observe this table, where in the first row stands this propor­tion, as 100 L is to 12 L gains, so 60 L the price of the wares; in the first place of the second rule the term of a year (in moneths) is inserted; lastly ⅓ or 2 [...]/3 moneths, which number is composed by the summe produced of the terms for payment and the money, viz. as 2 moneths, by [...]/3 of the money to be paid, and [...]/3 of the money by 3 moneths, whose summe is [...]/3. these terms multiplied according to the double rule direct, will produce, as in the third table; these three numbers, viz. 1200. 12. 140. which in the fourth table are reduced to 120.12. 14. and maybe made (retaining the same propor­tion) 10. 1. 14. or 5. 1. 7. the quotient will be found by any of these, or reduced unto 1 ⅖ L. that is 1 L. 8 ss. the earnest given, and the rate at 12 L. per cent. per ann. as was required; if there had been more times of payment given, the proportionall summes to be paid, multiplied by their peculiar terms or respite of time given, and those summes collected into one totall, the operation will be as in this last example.

An explanation of gainer loss proportionable to a stock and time. Lib. 2. Parag. 10.

Admit a man employes [...] his money in the way of trade, by which he gains 16 L per cent. how much does he gain with 80 L in the same employment for 3 moneths time? The state of the question, or a­ny of this kind by the first rule, is thus: As 100 L to 16 L the gain or loss, what 80 L in the second rule there is 12 moneths and 3 moneths: their products (according to this double rule of Three) are 1200 and 240, as in the third table, and in the fourth table as 120 to 16 L gains, so 24; or reduced, it will be as 5 to 16, so 1 unto 3 ⅕ L, or 3 L 4 ss, the proportionall gaines made by 80 L in 3 moneths time: if it had been em [...]loyed to loss, then 3 L 4 ss must have been subtracted from the stock, which in this propositi­on was 80 L, the remainder will be 76 L 16 ss; the question solved.

An explanation in equation of payments in gain or losse. Lib. 2. Parag. 11.

Four Grocers did

joyn their stocks to­gether, and bought with it 1656 lb of Pepper, which cost them [...]07 L, whree­of A did take for his part 240 lb B 300 lb, C 516 lb, and D 600 lb; the totall summe of the wares must be the first number, the whole price the second, and each par­ticular the third number, and then A must pay 30 L. secondly, B 37 L 10 ss. thirdly, C must dis­burse 64 L 10 ss. and lastly, D must pay 75 L. and in the same manner it will be proportioned with gain or loss, to each respective part as in the table,

An explanation of Barter, or vending one commodity for another. Lib. 2. Parag. 8.

A Tradesman exchanged [...] Salt at 20 d. the bushel for Su­gar at 15 d the lb, of which commodity he desired 1 C weight gross; how many bu­shels of salt will there be re­quired to be equall in value unto 1 C weight of sugar: by the first table here you will find that 112 lb of sugar at 15 d the pound comes unto 1680 d. then acccording to this rule and in the second table, you may see the pro­portion, viz. if 20 d bought 1 bushell of salt, then 1680 d will buy 84 bushels of salt, being equall to 112 lb of sugar. This trading with one merchan­dize for another is called Barter, derived from Ba­rato, implying an exchange of commodities, the most ancient way of commerce.

An explanation upon the rate Wares made pro­portionable in barter. Lib. 2. Parag. 8.

If 8 Bolts of Hol­land [...] cost 37 L 10 ss, and valued in barter at 40 L, and this to be exchanged for Wooll at 6 L 5 ss the hundred, what must it be ra­ted at in the barter? according to the rule and state of the question, a fourth number will be found (as [...]n the table) 6 L 13 ss 4 D, the rite put upon the Wooll in barter proportionably answering the enc [...]ease, as the Holland is prized, which is the thing required.

An explanation of Tare, Neat and Cloffe in gross weights. Lib. 2. Parag. 8.

Tare is an al­lowance [...] be­twixt the Mer­chant and the Grocer, for all such commo­dities as are weighed in boxes, chests, casks, &c. for which the allowance is agreed upon when they bargain, as from 6 lb to 18 lb in the C, and is called the Tare; which subtracted from the grosse weight (that is, the chest, or cask and wares together) the remain­der is the Neat; as suppose here are weighed four chests of Sugar, the one in gross weight 6 C and 14 pound, the second 7 ¾ C and 10 pound, the third 8 ½ C and 4 pound, the greatest 9 ¼ C, the summe or totall of them in all 31 ¾ C grosse: then the proportion is as 1 C is to the Tare given (which admit 14 lb) so 31 ¾ C unto 444 ½ lb. or by the rule of [Page 24] Three without fractions (as in the table) and then to the fourth number found, viz. 434 lb. adde in the Tare for the parts, as ¾: which is for the ½ 7 lb & for ¼ adde 3 ½, the summe is 10 ½, the totall 444 ½ lb. as before, which divided by 112 l is 3 ¾ C. 24 ½ lb, the true Tare of the grosse weight 31 ¾ C: from whence subtract 3 ¾ C 24 ½ lb, the remainder will be 27 ¾ C 3 3/2 lb, the Neat weight, as in the table appears, and so for all questions of this kind.

As for Cloffe, it is onely an allowance for the re­fuse of the commodity, which hangs upon the chest or cask, for which is usually allowed but 3 or 4 pound in every parcel, with the parts of pounds, if there be any; but yet in this I strike off ⅛ C 3 ½ lb, and there will remain 27 ½ C 14 lb Near: now to find what it is a pound by the whole weight, or the contrary, see Prop. 1.

An explanation of Trett, with reduction of the pound subtle. Lib. 2. Parag. 8.

Here first you are to [...] know, that the custome betwixt the Merchant and Grocer is to weigh all sorts of his wares by the C grosse, which containes 112 pound, for which in some he allowes Tare, as was said before; but in Tobacco and sundry other com­modities, with all Indian and Arabian Spices, their grosse weight is reduced into simple pounds, usu­ally called the pound subtle, and in every such hundred there is commonly four pound allowed, which is called the Trett; that subtracted, is by many called the Neat weight: this is readily found by dividing the whole quantity by 26, accor­ding to the first rule (which produceth the Trett) and that quotient subtracted from the totall of the pounds subtle giveth the Neat of the refined weight. As for example: A Grocer bought 50 [Page 26] pound of Mace subtle, which cost him 18 L 15 ss, what shall the subtle weight of 4 ¾ C 1 lb gross of the same commodity stand him in, with abating 4 lb per cent. for Tret? first the grosse weight of it reduced will be 533 lb subtle, which divided by 26, giveth 20 ½ lb for Trett, and subtracted from 533 lb, the remainder is 512 ½ lb subtle Neat, as in the first and second table; and in the third table the question is stated, if 50 pound of Mace cost 18 ¾ L, then 512 ½ lb will stand him in 192 3/16 L, that is 192 L 3 ss 9 D, as by the operation in the table will appear; and to finde what it is a pound, the first Proposition will resolve the querie.

An explanation of Exchanges betwixt Forreign Coyns.

Exchanges of all Coynes, [...] Weights and Measures of forreign places with one ano­ther are easily performed by the common rule of Three (if first reduced unto any certain proportion) by which means any one thing may be converted into the species of another, in respect of value or quan­tity, as by some few propositions with examples shall be illustrated, and first for this; sup­pose that sixty pound received at a place where one pound is 13 ss 4 D sterling or English, [Page 28] how much must the man receive in London at 20 s the pound Sterling, whereby to make them equall in value: The answer to this proposition will be 800 s or 40 l, as in the table, equall to 60 Marks, the value of one being 13 s 4 d. had the question been stated in any other denomination, the solution would have proved the same with the second term, as 1 l Scotl. to 40 groats, so 60 l Scotl. unto 2400 groats, or in the fraction of a pound Sterling, thus, as 1 l Scotl. to ⅔ l Sterl. so 60 l Scotl. to 40 l. Sterl. Thus sometimes you may ease your self by chan­ging the denominations (all being true) depending upon the seventh Paragraph of my second Book.

An explanation upon return of money after any rate per cent. Lib. 2. Parag. 8.

A Merchant of London was [...] to return money to be deli­vered at Durham, as admit 616 l received by a Carri­er, which to secure and deliver at the place appoin­ted what was to be returned, the Merchant did al­low 2 l 13 s 4 d per cent. upon this abatement, how much was the summe paid at Durham? first adde unto 100 l the money to be abated per cent. the totall in this proposition will be 102 l 13 s 4 d, which must be the first number in the rule of Three [Page 30] direct, and will be in proportion thus, as 102 ⅔ L, or made an improper fraction, viz. [...]0 [...]/3 to every 100 L returned, so 616 L received will be propor­tionable unto 600 L, the Proposition answered.

An explanation of two wayes concurring in one production.

The rate for exchange [...] here in this example is of a forreigne coyne, whereof 1 L 3 ss 4 D is equall to 1 L sterling, how much of that forreigne money will discharge a bill of ex­change for 240 L 13 ss 4 D sterling? in this case 1 L or 20 ss is the first number in the rule, the dif­ference in exchange is 3 ss 4 D, the summe to be exchanged is 240 L 13 ss 4 D. with these 3 num­bers you may finde 40 L 2 ss 2 ⅔ D. which added to the money paid makes 280 L 15 ss 6 ⅔ D, the totall to be received upon exchange: but the more usuall way is according to the table and prescri­bed rule, viz. as 20 ss is to 23 ⅓ or 20/3 ss. so 1 [...]/3 unto 5615 9/ [...] ss. which reduced is 280 L 1586 ⅔ D, as before.

An explanation of Exchanges. Lib. 2. Parag. 7. Axiom 13. and Parag. 10.

As in this example, [...] suppose 350 L of Eng­lish money was delive­red in London to be repaid upon bills of ex­change a year after the receit thereof, and to allow 8 per cent. per an. in that countrey where 24 ss was equal unto 1 L sterl. from hence the proportion is, as 20 ss is to 350 L, so 24 ss: in the second row of the table it is reduced unto 2. 35. 24. and in the third row to 1. 35. 12. by this or any of them you may finde the fourth proportionall number to be 420 L, the summe to be paid in the forreign coyn; and in the fourth row of the table you will find 100 L of that money under 1. and beneath 12 stands 8 L for a years interest; these will make 3 numbers, viz. 100. 35. 96. from whence a fourth proportio­nall number will be produced, as in the fifth table, viz. 33 L 12 ss, the interest due upon 453 L, so the totall to be received is 453 L 12 S, according to the condition and state of the question.

An explanation in reduction of weights, Lib. 1. Parag. 8.

The question here propounded is [...] of a commodity whose grosse weight is 2 C or 16 stone, at 14 pound to the stone, and it is required to find how many stone there are, where custome admits but of 8 pound: the proportion of a stone weight in these two places is as 14 to 8, or as 7 to 4: in this rule the third term is the least, and yet requires a greater number; from whence it is evident the rule must be reverst, and the fourth proportionall [Page 36] found in the table, will be 28 stone, equall to 16 stone at 14 pound to the stone, the thing required.

An Explanation.

This depends upon the last Proposition, and so requires no other rule, but onely to reduce the gross weight into pounds subtle, which are 560 pound, and since 1 pound Aver de pois is equall to 14 ⅗ ounces, what 560 pound: by the rule of Three direct you will finde 8176 ounces, which divided by 12, the quotient will be 681 ⅓ pound Troy; and so for all other questions of this kind.

An explanation in reduction of Measures. Lib. 2. Parag. 8.

An Inne-keeper bought 20 [...] quarters of corn, to be delive­red where the custome of the place required, 8 ¾ gallons to every bushell, how much must the Farmer send in, ac­cording to the Statute mea­sure, containing 8 gallons (commonly called Win­chester, where the Act was made) for to fulfill the condition as the bargain was agreed upon: the state and operation of this question, or the like, dif­fers not in the form from the 29, as in the margin is evident, where 8 ¾ gallons, or 35/4 multiplied by 20 quarters, the quantity propounded in that mea­sure; which divided by the third number, viz. 8 gallons, the quotient will be 21 ⅛, that is, 21 quar­ters and 7 bushels of the lesser measure, equall to 20 quarters of the greater, the thing required.

An explanation in reduction of measures from plura­lity of proportion. Lib. 2. Parag. 10.

In this Proposition [...] there is an equality or proportion derived from divers descents and collaterall lines, and may be continued like a British pedegree: the equality here re­required is betwixt 47 ells of Antwerp and the yards of London that shall be equall to them, if their measures were not known (in any certain pro­portion) but as derived from some other, and that from a third, and so continuing a proportion untill you arrive at one that runs directly from the first. [Page 39] As for example: here is required how much 47 ells of Antwerp will be of London measure; if the proportion were known that four ells of Antwerp were but equall to 3 yards of London measure, there would be no more in it then to multiply the ells propounded, viz. 47 by 3, which product 141 divided by 4, the quotient would have been 35 ¼ yards: but suppose this proporrion not known, but by derivation, to be collected from others, as in this plurality of measures you will find that the ci­ty of London, according to the English standard for measures, hath proportion to the ells of Lyons in France, and those again to Antwerp, in the Low countreys, from whence the proportion will ar­rive (according to the first table) as 20 to 25, so 60; then in the second table, as 100 ells of Ant­werp, to so many yards of London (supposed to be found) what will 47 ells of Antwerp require, to have an equality in their measures: in the third row or table they are both reduced into a single rule, and in the fourth table unto their least denomina­tions, viz. as 4 is to 1, so 141 in proportion to 35 ¼ yards, as it was before, the thing required, and I hope explained, from whence I will proceed to the customary rules used in Factorage.

An explanation of Factorage. Lib. 2. Parag. 8.

If a Merchant intrusts his Fact­or [...] with a summe of money, upon condition he should have half the gains; in this case the Factors person was valued equall to the adventure: but admit ⅓ part of the gaines were to be allowed the Factor, and 1000 L committed to his charge, the Merchants share will be but ⅔, which is in propor­tion to 1000 L, as ⅓ is unto 500 L, the estimate of the Factors person as by the rule and table appears: and if in this employment 2000 L were gained by the adventure (with all charges defrayed) the Fa­ctors share would be 666 L 13 ss 4 D, and the Merchants 1333 L 6 ss 8 D, the one but half the other: if the Factor had been allowed but ¼ of the gains (in this adventure) his person had been va­lued at 333 L 6 ss 8 D, and his gains would have amounted to 500 L; if ⅕ had been his proportional part, then the Merchants had been; and his gains [Page 41] 1600 L, the Factors 400 L, and the estimate of his person in this employment 250 I, &c.

An explanation of Factorage, Lib. 3. sect. 1. cap. 7. table 1.

A Merchant had a due, [...] but doubtfull debt owing him in another Countrey, where he was to employ a Factor, who had letters of credence to demand his money due, and with this condition, to have 13 ⅓ D in every pound sterling, that he should pro­cure of it: the Factor by his industry recovered 1200 L of the debt, what does his salary amount unto? by the rule of Three you will finde 67 L [Page 44] 10 S, and so like wise in the table, according to the rule of Decimals [...] by this you may state other que­stions of Factorage, and in this form.

An explanation of Sea-hazard, or Bottom-ree. Lib. 2. Parag. 8.

Cambio maritimo, some call [...] this rule, wherein the Credi­tor stands to the hazard with the Merchant at Sea, that if the ship be lost he loses the money adventured: the operation of this rule is facile, the interest just, and [Page 45] the explanation short: the money here contracted for (according to the conditions of 26 L for interest per cent.) is 640 L, and the fourth proportionall found will be 166 ⅖ L, or 166 L 8 S, as in the table of the margent does appear, which with the principle makes 806 L 8 S, to be received where the money was payable, or should be due, the ship being arrived with the adventure at the appointed Port of the Countrey or Kingdom, as the voyage was intended.

An explanation of simple interest. Lib. 2. Parag. 8.

Any question of this nature [...] is with facility performed by the common rule of Three, as if 100 L principall forborn a year requires 6 L interest, the 145 L for the same term of time will exact 8 7/10 L, as in the table, that is, 8 L 14 ss. the question answered.

An explanation of simple interest, lib. 2. par. 10.

All questions of this

kind doe consist of 5 termes, viz. 100 L Principall, secondly, the rate for Use, as in this, 8 L. thirdly, the Principall lent, as in the first rule; in the second rule under 100 l is placed the time for which 8 L was due, as at a yeare, or 12 moneths: the fifth number is the term for the principall bor­rowed, viz. 5 moneths, the products of those are 1200. 8 and 1250, and may be reduced (as in the 13 and 14 Axiom, lib. 1. parag. 7.) to 3.1. 25. the quotient here answers the question, viz. 8 L 6 ss 8 D, the proportionall interest, for the summe and time required.

An explanation of simple Interest. lib. 2. parag. 10.

In this double

rule the first term is 100 l. the second its interest for a yeare, the third is the prin­ci [...]al lent: the first term of the second rule 365, the num­ber of dayes in a vulgar year; the last term is 192, the number of dayes terminating the time, accoun­ting 4 weeks to the moneth; the products of these are 36500, and 124800, and reduced will be 365 and 1248. which multi [...]lied by 6 l the interest is 7488, and divided by 365 the quotient will be (in a direct proportion) 20 l 10 ss 3 d 2 34/73, as in the table, the simple interest of 650 l. the time requi­red.

An explanation of this Proposition, lib. 2. parag. 10. quest. 4.

[...]

In the first rule, as 8 l interest is to 100 l princi­ple, what 8 ⅓ the interest received: in the second rule stands the terms of time, viz. 12 mo. and 5 m. which multipliers and the 2 dividers encreased re­ciprocally by one another, they will produce these 3 numbers, viz. 40. 100. 100. all questions of this nature are made either direct or reverse, according­ly as the products are placed; but by either way the quotient will be discovered, 250 l the princi­pal lent, as in the table; the proposition solved ac­cording to demand.

An explanation of interest money by the rules of practise: Lib 2. Parag. 9. Que [...]t. 4, 5, & 6.

The encrease

of any mixed summe will be thus discover'd; first place your proposition ac­cording to the demand made, as here viz. if 100 L requires 6 L interest, what shall the principall given, as 265 L 13 ss 4 ¼ D in this, 6 is the multiplier, with which encrease the principall, as in lib. 1. sect. 1. parag. 4. exam. 9. and the product will prove 1594 L 0 ss 1 ½ D. here draw a line as in the table, cutting off two places on the right hand, a [...] 94, because 100 is the divisor, the quotient 15 L secondly, the remainder 94 or 94/100 reduce into. shillings, by the multiplication of 20 the product will be 1880, and being no shilling left in the last operation, sever 2 places with the line, the quoti­ent is 18 ss, the remainder 80, which by 12 reduce into pence, and adde to it 1 D remaining in the first product, cut off 2 figures on the right hand, viz. 61, so on the left hand there will be 9 D. the 61 reduced into farthings by 4, produceth 244, to which adde the ½ D remaining yet in the first pro­duct, the summe is 246, that is 2 Q. and 46/100. so [Page 55] the totall interest for a year of 265 L 13 ss 4 ¼ D at 6 L per cent. comes unto 15 L 18 ss 9 D 2 2 [...]/50 Q, as by the operation in the table is conspicu­ous.

An Explanation.

To solve any que­stion

of this kinde, state the propositi­on as in the head of the table, then take the greatest deno­mination of the in­terest allowed, as in this example, 5 L. which multiply through all the de­nominations of the principall here sta­ted, according to sect. 1. parag. 4. examp. 9. the product will prove 4781 L 17 ss 6 D. had the in­terest been 6 L, the product would have contained [Page 56] the principal once more; but being 17 ss 6 d, di­vide it into proportional parts, lib. 2. parag. 9. quest. 4. as in the table at A, viz. 10 ss. 5 ss. and 2 ss 6 d. for the 10 ss take ½ the principal, that is half of 956 l 7 ss 6 d, which will be 478 l 3 ss 9 d. next for 5 s take ¼ part of the principal, or ½ the last, which is 239 l 1 s 10 ½ d, and the half of that again is 119 l 10 s 11 ¼ d. the total of all these is 5618 l 14 s 0 ¾ d. this done, divide the greatest denomination by 100 l, or cut off two places on the right hand, and you will find 56 l and 81 remaining, with which proceed as before, and you will discover (as in the table) the interest to prove 56 l 3 s 8 d 3 5 [...]/100 q. the simple use for a year, as was required: and thus may all other propositions be expeditely solved by this operation, and the rules of practise.

An Explanation.

State the question

as in the head of the table; that multipli­ed by the interest al­lowed in this 5 l, the product is 3226 l 13 s 4 d. now being the money is to be continued but 11 moneths, take pro­portional parts, as in the table at A, 6 M. 3 M. and 2 M. for the 6 M. take halfe the first product, then ¼ and ⅙. or thus, ½ of 3226 l 13 s 4 d. is 1613 l 6 s 8 d for 3 Months, the ½ of that is 806 l 13 s 4 d. lastly. 2 moneths ⅓ part of the former, which is 537 l 15 s 6 ⅔ d. this done, proceed as in the last, or by 42 proposition, and you will discover the interest money to be 29 l 11 s 6 d 2 66/100 q. the demand performed, and if it had been required for any longer forbearance, finde the interest for the term of years by the former propositions, and the parts of a year by this.

An Explanation.

The propositi­on

being stated (as in the head of the table) multi­ply the principal by the greatest denomination of interest, viz. 5 L, as in the table at A, according to the prescribed rules of practise, lib. 2. paragr. 9. quest. 4. for the 10 ss take half the principall, and for the 2 ss 6 D ⅛ or ¼ part of the last, so you will produce these 3 numbers 2718 L 6 ss 8 D. secondly, 271 L 16 ss 8 D. and thirdly, 67 L 19 ss 2 D. the totall is 3058 L 2 ss 6 D to be divided by 100 L, if forborn a year; but the term of time here is but 9 moneths, as in the table at B, which I divide into two parts, viz. 6 M. [Page 59] and 3 M. then take half the totall, that is, 1529 L 1 ss 3 D, and for 3 moneths the half of that 764 L 10 ss 7 ½ D. the totall is 2293 L 11 S 10 ½ D, to be divided by 100 L. now proceed according to the former examples, and you will find the interest de­manded 22 L 18 S 8 D 2 ½ Q. the proposition solved.

If this question had depended on moneths, weeks, and dayes, you must have taken proportio­nall parts, and proceed, as before is specified; so there needs no more examples for the ingenious, to whom all other questions (in the rules of pra­ctise) will be direct, and indirect for others, to in­cumber their understandings with multiplicity of wayes in this kind, therefore I will onely shew you the discount of money, and proceed to Decimall Tables of compounded Interest.

An explanation of this rule in discount, or rebate of money, lib 2. parag. 8.

Admit the interest were [...] 6 l per cent. per ann. which added to 100 l makes the summe 106 l to be rebated: for if this principal were due at the term of 12 mo­neths, it were worth 100 l present pay, because at 6 l per cent. it would encrease in a years space unto 106 l again: from hence this rule of antepayment is framed, and all questions of this condition (if terminated by a year) are solved, as in this example; suppose 546 l shall be due at the term of a year, and desired presently, rebating at 6 l per cent. per ann. the proportion is evident, viz. as 106 is unto 100, so shall 546 be to 515 09 [...]/1000 l, which decimal fra­ction is 1 s 10 ½ d. so 546 l, which should have been due at a yeares end, is worth upon discount present pay 515 l 1 s 10 ½ d, as in the table is de­monstrated by a decimal, and in a natural fraction, it will be 515 5/53 l.

An explanation of discount or rebate of money, for dayes, weeks, moneths, &c.

In all questions upon re­bate [...] of mony at simple inter­est for the space of a year, ob­serve the last proposition: but if for a greater or shorter term of time, viz. moneths, weeks, dayes, &c. or dayes, weeks and moneths; in all such cases you ought to find a proportional interest for those annual parts, because the money due at several payments is terminated therein, [Page 62] as the other in a year. As for example: there is a Le­gacy of 1000 l bequeathed to T. W. at equall pay­ments, viz. 500 l to be paid at the end of 6 months, and the other 500 l at the period of a year: what is it worth present pay, rebating at 10 L interest per cent. per ann. as for the last payment, form the rule of Three according to the last proposition, viz. as 110 L is to 100 L, so 500 L will be in proportion to 454 L 6/11 L. now for that due at 6 moneths end, find a proportionall intere t for the time (ac­cording to the rate allowed) as by the first of these tables in the margent, which is 5 L. and by the se­cond tables operation you will find for the fourth proportionall number 476 4/21 L, the value of the first 500 L present pay: the summe of both pay­ments 930 170/231 L, 930 L 14 sh 8 48/77 D. the Legacy as valued present pay upon rebate at 10 L per cent. per ann. simple interest, which in the first table re­quired no rule to discover it, but many other pro­positions may, therefore it was inserted by me, and made plain as it is generall; if the respite of time had been for more or fewer moneths, with weeks and dayes, the manner of operation is the same in effect, therefore to write ane more of this would prove superfluous unto the ingenious Arith­metition; so of simple interest I will here con­clude.

Many rules do seem originally derived from Truth, or extracted from Art, but if well observed, they are easily detected, being erroneously reered upon falacious grounds, and their derivations from imaginary principles, viz. as in interest, dis­count of money, Equation in payments relating to [Page 63] Time and Interest, &c. These I have inserted to please some, but not to delude any, the wayes be­ing common in generall received customes, plain, easie, and of good use, the errours not being great or considerable in small summes, or in a short for­bearance, as in Bonds, they rarely pleading pre­scription of years, or exeeding an annual revoluti­on, upon forfeiture in transgressing a penal Law; whereas rebate or discount of Mony often depends upon long terms, involv'd with multiplicity of ante­dated years, as in purchasing of Leases, Pensions, An­nuities, Reversions, &c. therefore these were com­posed so compendious as I could, since there be better rules extracted from Artificial numbers, and Decimal Arithmetick in compound Interest, as those following.