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A Grocer bought 5 ¾ C grosse weight of Wares, which lay him in (with all charges defraid) 163 lb: 13 ss: 8 d. sterling: and it is demanded what one lb cost: or how to sell it by the pound without gain or loss.
As the quantity of any one Commodity or wares is unto the total price with the cost and char∣ges, so will a l, or an unite of the first denomination be in proportion unto the rate it may be sold for.
Observe in all Commodities 〈 math 〉〈 math 〉 where a hundred gross is men∣tioned, it is 112 lb usually no∣ted with a C. for Centum, as in this Example, where five hundred and three quar∣ters 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 pro∣pounded.
How to sell a••y Wares or Commodities by retail, the pr••ce or value of the whole par••el being known, and to gain a certain su••me of money in the whole quanti••y requ••red.
As the quantity of the whole Commodity bought is unto the summe of the price and gain re∣quired, so will 1 C. 1 lb; or 1 yard of the first denomination be proportional unto the price it must be sold at.
Admit a Draper bought 〈 math 〉〈 math 〉 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 shil∣lings 290: to avoid fractions, the least denomina∣tion 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.
A Tradesman bought a whole piece of Cloth con∣taining 28 ¾ yards, which did stand him in (with all charges defraid) 19 lb: 3 ss: 4 d. sterling, how
should he sell it, whereby to gain 1/10 part in every yard, or forc'd unto so much loss in retail.
RULE 1. As the Denominator is to the price known, so the fractions summ.
As the quantity given,
RULE 2. so an Unite of the same.
This Questi∣on 〈 math 〉〈 math 〉 is stated ac∣cording to the Double Rule of Proportion, ei∣ther for gain or loss, by change∣ing the ex∣tremes 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 se∣cond term, and the summe both of Numerator and Denominator must possess the third place, if for gain; but must be made Divider, if the Propositi∣on 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
gain or loss: or, which is all one, if an improper fraction as in the Table 4/4, the Denominators be∣ing 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 In∣teger, the Numerator would have been 2 ss and consequently the proportion as 20 to the middle term, so 228 the summe of Numerator and De∣nominator 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 con∣veniently inserted.
How a Commodity must be sold by retail, upon a∣ny certain loss of money in the whole parcel or quan∣tity.
As the quantity of any Commodity or Parcel is to the difference betwixt the Price and Losse, so shall 1 C, 1 lb, or one yard of the Commo∣dity it self be proportionable unto the rate it must be sold at.
A Grocer bought 340 lb sub∣tile 〈 math 〉〈 math 〉 of a Commodity which cost him in ready money with his char∣ges 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 pro∣portion 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.
Ʋpon the price of any Commodity known, how to sell 't by whole-s••le or retail, with gain or loss,
at any rate in the 100 lb that shall be requi••ed.
As the summe of 100 lb sterling is in propor∣tion unto the price of the Wares, so shall the rate in money for gain or losse be in proportion to a fourth number, which added to the price of the Commodity, gives the gain, and subtracted from it, shews the losse sustained at the rate required.
Suppose 1 Gro••e bought 4 C 〈 math 〉〈 math 〉 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 remain∣der 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 pro∣fit.
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 cen∣tum will be the same by retail, as was the former
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.
The price of any Wares or Merchandize by which the said Commodity was bought and sold: what gain was made, or loss sustained in the 100 lb: or after what rate or proportion.
As the price (by which any Merchandize was bought) shall be in value or proportion unto 100 lb sterling, so will the price of the Wares by which they were sold, be in proportion to the true gain or losse sustained.
A Draper bought Kerseys 〈 math 〉〈 math 〉 at 6 lb. 13 ss. 4 d. the Peece, and sold them all a∣gain for 7 lb. 10 ss. how much he gained, and after what rate in the 100 lb
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 up∣on 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 discover∣ed by the same Rule; the state of the Question not differing in any thing, either by Whole-sale, or Re∣tail, so it requires no Precedent or Rule but this, which will bring your stock short home, as unfor∣tunately true, as prosperously with increase.
By the Price which any Wares or Merchandizes were sold at, with the rate of Gain or Loss in one Peece, how to discover what the whole Commodity cost.
As 1 Peece, 1 Hund. 1 Yard, or 1 Pound weight, &c. shall be in proportion unto the price thereof, so will the number of Peeces, or quantity sold, be proportionable to the price of them all together.
Admit 15 Clothes or 〈 math 〉〈 math 〉 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 subtract∣ed 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 un∣fold it according to the Rule of Trade.
To finde the Gain or Losse upon Merchandizes bought and sold, with time agreed upon betwixt the Debitor and Creditor for payment of the money at any rate per cent. per an.
Admit a Tradesman 〈 math 〉〈 math 〉 had bought a Com∣modity at 5 d the pound, and after 6 Moneths time sold it again for 6 d the l. or suppose the Mer∣chandize 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 inter∣est 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 Mo∣neths: 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 de∣ducted: 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
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.
By the price of any Wares bought and sold, with the time limited for payment, to finde the gain made, or losse sustained, and at what rate per cent. per Annum.
A Merchant bought Mace at 〈 math 〉〈 math 〉 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 re∣quired 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 num∣ber I place the magnitude of a year, in that deno∣mination, 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 gi∣ven for payment is 4 Moneths, subscribe that un∣der 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 multi∣plied 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,
wherein the desired product is discovered to be 31 1••/19 l that is, 31 l: 11 ss: 6 d 1••/19: the profit re∣quired at the rate per cent. per annum.
A Grocer bought Cloves at 4 ss 3 d the l. and after 6 Moneths time sold them again for 4 ss the l, what losse did the Grocer sustain, and how much per cent. per ann. by the last proposition you will find his losse to be 11 l. 15 ss. 3 9/17 d.
By the difference of prices in any one Commodity bought and sold, by whole-sale, or retail, to finde what time must be allow'd for to gain after any rate per Centum per annum that shall be assigned.
A Tradesman bought Nut∣megs 〈 math 〉〈 math 〉 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 af∣ter 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 opera∣tion 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.
If 124 l of Cynamon cost 20 l sterling, and that sold again for 23 l what day of payment was there given, when the Merchant made after the rate of 16 l per cent. per ann. of his money so laid out? this question will be solved by the last Proposition, and
found that the day of payment was at the term of 11 Moneths and ¼ of a Moneth.
With the price and quantity of any Wares on Merchandize, to finde how they must be sold, upon several days of payment, either in Gain or Losse, at any rate given per cent. per ann.
A Merchant had certain 〈 math 〉〈 math 〉 Wares which stood him in 60 l: these goods he sold unto another, who paid him so much money for earnest, as that the Mer∣chant 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
find what money the buyer paid down, observe this table, where in the first row stands this propor∣tion, 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 propor∣tion) 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.
By the gain made, or losse sustained per cent. per ann. to finde what any other s••••me must gain or ••••se in any part of a year.
Admit a man employes 〈 math 〉〈 math 〉 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 a∣ny 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 propositi∣on was 80 L, the remainder will be 76 L 16 ss; the question solved.
By the profit of a small stock in money, and a short time to find what gain is made in the hundred per ann. or the contrary in loss.
To solve this, and prove the last, I will reverse the former proposition; and suppose a Tradesman employed 80 L for the space of 3 months, in which time he gained 3 L 4 ss. and here it is required to find after what rate it was per cent, per ann. the state of the question will be as 80 L to 3 ⅓ L the gains, so 100 L, and if in 3 moneths, what in 12 moneths, or a year? The answer to this will be as in the last Prop. 16 L per cent. per an.
Divers tradesmen joyn their stocks together, with which they buy a Commodity, whose price and quanti∣ty is known, from whence they take unequall shares, what part then must every one pay?
As the whole quantity of any Merchandize:
Is in proportion unto the whole price thereof,
So shall each particular mans part or share
be proportionable to the money he must pay.
Four Grocers did
| lb | L | ss | |
| A 240 | 30 | 00 | |
| lb L | B 300 | 37 | 10 |
| 1656 207. | C 516 | 64 | 10 |
| D 600 | 75 | 00 | |
| The totalls | 1656 | 207 | ••0 |
In whole-sale, or by retail, if the price of any two com∣modities be known with the price and quantity of the one to finde what quantity of the other shall be equiva∣lent to it.
As the price of any Wares (the quantity un∣known)
Shall be in proportion unto 1, or a unity of it,
So the price of that whose quantity is known,
Will be to a parcel of the first, and equall to the other.
A Tradesman exchanged 〈 math 〉〈 math 〉 Salt at 20 d. the bushel for Su∣gar at 15 d the lb, of which commodity he desired 1 C weight gross; how many bu∣shels of salt will there be re∣quired 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 pro∣portion, 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 merchan∣dize for another is called Barter, derived from Ba∣rato, implying an exchange of commodities, the most ancient way of commerce.
The worth of any wares in ready money, if valued at a greater price in barter, how to set a rate upon the price of any other commodity to be bartered for it, that shall be proportionable to the first.
As the price of any Merchandize in ready money
Is unto the value of the same Wares in barter,
So the second Wares (in the first denomination)
Shall be proportionable to the price of it in barter.
If 8 Bolts of Hol∣land 〈 math 〉〈 math 〉 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 ra∣ted 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.
In any grosse weight, as Sugar, Currens, &c. up∣on the allowance of Tare, to find the Neat weight, and the price of it; and if there be Cloffe allowed to find also the Neat and the price, by knowing what the grosse ••o••ind was valued or bought at.
As 100 grosse weight of any Wares or Merchan∣dizes
Shall be in proportion to the pounds allowed for Tares,
So will any gross wares that are known or weighed
Be unto the allowance given for the Tare there∣of.
Tare is an al∣lowance 〈 math 〉〈 math 〉 be∣twixt the Mer∣chant and the Grocer, for all such commo∣dities 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 remain∣der 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
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 re∣fuse 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.
Upon any Indian Spices sold by whole-sale, with the allowance for Trett, to find the subtle weight Neat, and how much it is a pound; or by the pound subtle of one sort, to find what any other quantity did cost.
As 26 pound weight of any Indian Spices
Is in proportion unto 1 pound for the Trett,
So shall any quantity of the same Wares
Be proportionable unto the Trett thereof.
If 50 lb weight subtle of any Spice propounded
Did cost a certain and known summe of money,
What is the price of another quantity of the same,
When 4 pound per cent. shall be allowed for Trett.
Here first you are to 〈 math 〉〈 math 〉 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 com∣modities, with all Indian and Arabian Spices, their grosse weight is reduced into simple pounds, usu∣ally 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, accor∣ding 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
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.
If 1 pound of Cloves cost 3 ss 6 D, what is the price of 676 pound, deducting 4 pound in every hundred for Trett?
The subtle weight here propounded is 676 lb, and abating 4 lb per cent. for Trett, which comes unto, by the last Proposition, 26 lb, which deduct∣ed from 676 pound, there will remain 650 pound, then by the first Proposition, if 1 pound cost 3 ½ ss, what shall buy 650 pound? the answer to this question will be 113 L 15 S, and so for any other of these kinds.
A man delivers unto a Merchant a certain summe of money to be received of his Factor upon Bills of Ex∣change in a forreign Countrey and Coyn, the rate and proportion of the moneys in both places being known.
As a unite, or any one piece of a known Coyn,
Is in proportion unto a Coyn of another value,
So any summe of money delivered in the first Coyn
Unto the quantity, to be received of the second.
Exchanges of all Coynes, 〈 math 〉〈 math 〉 Weights and Measures of forreign places with one ano∣ther 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 quan∣tity, as by some few propositions with examples shall be illustrated, and first for this; sup∣pose that sixty pound received at a place where one pound is 13 ss 4 D sterling or English,
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 chan∣ging the denominations (all being true) depending upon the seventh Paragraph of my second Book.
Any pieces of Coyn, if equal unto some one piece of another, and that equivalent to a third, to be ex∣changed with the first; how much money of the one will discharge a bill of the other.
This differs not essentially from the last; as ad∣mit 10 Ryalls were equall to one Ducat, and one of them worth 5 s 6 d, how much money Sterling will discharge a bill of Exchange for 4500 Ryals? the proportion will be: As 10 Ryals is to 5 ½ ss. what 4500 Ryals? the answer 2475 s, that is 123 l 15 s sterling, the question solved: for if A be made equall to B, and B = to C, then A and C are equall, as by the second Axiom. Lib. 2 par. 7.
If upon return of money a certain rare per cent. shall be required, to find in any summe of money how much must be abated, at the rate propounded, upon such exchange or return of money.
As the summe of 100 l with the allowance per cent.
Shall be in proportion to 100 l where it is to be paid,
So will any summe of money received of a Mer∣chant
Be proportionable to the money that shall be delivered.
A Merchant of London was 〈 math 〉〈 math 〉 to return money to be deli∣vered at Durham, as admit 616 l received by a Carri∣er, which to secure and deliver at the place appoin∣ted what was to be returned, the Merchant did al∣low 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
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 propor∣tionable unto 600 L, the Proposition answered.
Observe in any proposition made, the true state of the question, and whether it be customary, or of that predicament; if customary, it is something to∣lerable in small summes, although a little errone∣ous; this caveat concerns other propositions, only note well the difference of these, in the last, the Assurancer was to have so much money out of the summe delivered to him, as should but discharge the money he returned, which the last rule does solve, where the Assurancer had 16 L out of the 616 L, so answers the question in the rate requi∣red, which admit imposed upon every pound sterl. the proportion will be: as 1 L is to the rate given, so will the summe to be returned, unto the money due upon it for the assurance. And for the probat of this, suppose (as in the last proposition) 600 L were to be returned from Durham to London, allowing the assurancer 6 ⅖ D upon every pound sterl. the rule is as 1 L to 32/5 D, so 600 L shall be in proportion to 3840 D, that is 320 ss, or 16 L, as before, due for the securing of 600 L, and not 616, as in the last proposition, which is erro∣neous, though allowed of by many.
As any one pound sterl. or other piece of money,
Is in proportion to the difference of Exchanges,
So will any summe propounded of the first money
Be proportionable to the coyn where it is payable.
The rate for exchange 〈 math 〉〈 math 〉 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 ex∣change for 240 L 13 ss 4 D sterling? in this case 1 L or 20 ss is the first number in the rule, the dif∣ference in exchange is 3 ss 4 D, the summe to be exchanged is 240 L 13 ss 4 D. with these 3 num∣bers 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 prescri∣bed 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.
By knowing the money paid unto a Merchant; and likewise the summe received upon bills of exchange in a forreign coyn, to find how the exchange went between those places.
This proposition is but the former reverst, and so requires no rule (but that of proportion) nor exam∣ple but the last, where the first money paid is 240 l 13 s 4 d; the forreign money received upon bills of exchange was 280 l 15 s 6 ⅔ d, the middle num∣ber here in the rule of Three must be 1 l sterling, or 20 s, if you please: the former numbers redu∣ced into improper fractions will stand in the rule of Proportion thus, viz. As 14440/3 ss is to 20 ss, so will 50540/9 ss be to 1 l 3 s 4 d, the rate which the Exchange went at, according to the former Propo∣sition, enucleated in this.
In all these questions, or any others (appertain∣ing onely to the exchange of money) there is no∣thing more required, from the value or estimate of any known Coins, to finde what summe of the one, shall be equall or in proportion unto the same quantity of the other, as if 1 l sterling were equall in value unto 25 s of some other coyn, the proportion of equality would be, viz. As 1 l ster∣ling, or 20 s is to 25 s, so any summe of the first coyn to an equall quantity of the second, or which is all one (••ib. 2. parag. 1. Aziom 13.) as 4 to 5, so any quantity of the first to an equal summe of the
second, and likewise the contrary to these, viz. as 5 is to 4, so any known summe received of the first coyn, will be equal in quantity to the summe of the second due to be repaid in exchange, which is the sole scope of this rule, or the mark that is ••imed at in the exchange of money, as for the profit, ex∣perience in trading will discover it.
A Merchant delivers so much money, with this condition, to be repayed in a forreign Coyn and Coun∣trey, within any limited time, as a year, and at any rate per cent. per an. for interest allowed of there.
As in this example, 〈 math 〉〈 math 〉 suppose 350 L of Eng∣lish money was delive∣red in London to be repaid upon bills of ex∣change 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 proportio∣nall 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.
To reduce weights that are customary in one, or di∣vers Countreys, to an equality from one denomination into another, or the weight of any ponderous body being known, to find the quantity of a greater or lesser weight.
As the proportionall parts of 1 ounce, 1 pound, 1 stone, 1 C weight, &c.
Shall be to any quantity propounded in that weight,
So will the weight of any other place, towne, or countrey
Be proportionable to the weight thereof deman∣ded.
The question here propounded is 〈 math 〉〈 math 〉 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
found in the table, will be 28 stone, equall to 16 stone at 14 pound to the stone, the thing required.
How many hundred or pounds of Troy weight will there be found in 5 C Aver de pois, when as 1 pound 2 ounces 12 penny Troy, is equal unto 1 pound or 16 ounces of the Civil, or Merchants weight.
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.
The customary measure of any place being known, with the quantity of one propounded, to find how much it will make by a greater or lesser measure of another place.
An Inne-keeper bought 20 〈 math 〉〈 math 〉 quarters of corn, to be delive∣red where the custome of the place required, 8 ¾ gallons to every bushell, how much must the Farmer send in, ac∣cording to the Statute mea∣sure, containing 8 gallons (commonly called Win∣chester, 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, dif∣fers 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 mea∣sure; which divided by the third number, viz. 8 gallons, the quotient will be 21 ⅛, that is, 21 quar∣ters and 7 bushels of the lesser measure, equall to 20 quarters of the greater, the thing required.
How many yards or ells of any one place propounded will be equall, or make a given number in some other, which hath proportion to the measures of a third place, &c. and that in any known quantity unto the first.
| I | II | III | IV | V |
| Antwerp | Antwerp | = Lyons: | Lyons | = London |
| = 47 ells: | 100 ells | = 60 ells: | 20 ells | = 25 yards |
In this Proposition 〈 math 〉〈 math 〉 there is an equality or proportion derived from divers descents and collaterall lines, and may be continued like a British pedegree: the equality here re∣required 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 pro∣portion) 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.
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 ci∣ty 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 ar∣rive (according to the first table) as 20 to 25, so 60; then in the second table, as 100 ells of Ant∣werp, 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 denomina∣tions, 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.
In the first place you must consider what the Mer∣chant allowes his Factor in lieu of his pains, and the adventure of his person; as whether ½, ⅓, ¼, ⅕, &c. that proportionall part taken from an integer, the re∣mainder
is the Merchants, the other shews the value of the Factors person.
As the proportionall part of the Merchants adven∣ture
Shall be to the whole stock adventur'd in his charge,
So will the proportional part allowed to the Factor
Be to the estimate of his person in the employ∣ment.
If a Merchant intrusts his Fact∣or 〈 math 〉〈 math 〉 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 propor∣tion 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 Fa∣ctors 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 va∣lued 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
1600 L, the Factors 400 L, and the estimate of his person in this employment 250 I, &c.
If a Merchant shall deliver unto his Factor any summe of money, and does agree for to allow him 2/7 parts of his gain, with this proviso, that he em∣ployes such a stock of his own as shall be mention∣ed in the contract between them, what shall the Factors person be valued at, and how much will his gains amount unto? find by the last Propositi∣on what the proportionall parts are unto the Mer∣chants adventure, and from the Factors part sub∣tract his stock adventured, the remainder will be the estimate of the Factors person, and the 2/7 parts of the whole gain will produce his profit. As for example, Suppose a Merchant delivers to his Fact∣ors charge 2000 L, conditionally that he employs 300 L of his own in the same adventure, the pro∣portion wil be, viz. as 5/7 is to 200 L, so will 2/7 be unto 800 L, from whence subtract 200 L, the re∣mainder is 600 for the estimate of the Factors per∣son in the employment; and admit the gains at his return were 3675 L 8 ss 9 D, the 2/7 parts of it will be found 1050 L 2 ss 6 D, and the Merchants share will be 2625 L 6 S 3 D. both Propositions answered.
A Merchant did condition with his Factor, to al∣low him for the adventure of his person a part of his stock, and according to that proportion of the whole adventure, he should share in the gaines, from hence to discover what the Factors person was valued at, and the proportion of his pro∣fit is the thing required. To explain this, sup∣pose a Merchant intrusts his Factor with 1680 L, and with this condition, that if he gained so much money he should have 240 L for his pains, and so proportionally for a lesse or greater encrease: in all questions of this kind reduce the two summes (like fractions) into their least denominations, viz. 240/1680 which will be 1/7, then by the 33 Proposition, as 6/7 is to 1680, so 1/7 to 280 L, the estimate of the Factors person in this imployment; and suppose he gained (all charges defray'd) 1481 L 7 ss 6 D, what must he have for his pains? The answer will be 211 L 12 ss 6 D (lib. 2. parag. 9. quest. 6.) that is ••/7, according to the Articles of Agreement made.
A Merchant conditions with his Factor to allow him, out of his gains, a certain profit in the pound ster∣ling, by which it is required to find what the facto∣rage will amount to in any summe propounded.
As 1 L sterling, or any other summe of money given
Shall be in proportion to what is allowed for fa∣ctorage,
So the gains of the adventure in the first denomi∣nation
Will be proportionall to the gaines for the Fa∣ctors share.
A Merchant had a due, 〈 math 〉〈 math 〉 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 pro∣cure 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
10 S, and so like wise in the table, according to the rule of Decimals 〈◊〉〈◊〉 by this you may state other que∣stions of Factorage, and in this form.
A Merchant takes up money to fraight his ship, with condition to allow 26 L per cent. and that to be paid where the goods should be landed, with this provi∣so, that the Creditor shall stand to such hazards as belongs to sea, viz. Ship-wrack, or Pirats, &c.
If the summe of 100 L sterl. or any other money
Shall require upon adventure 26 L for interest,
Then any greater or lesser summe of the first mo∣ney
Will be in the same proportion to the required gain.
Cambio maritimo, some call 〈 math 〉〈 math 〉 this rule, wherein the Credi∣tor 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
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.