shillings be 60 shillings what will 24 shillings make If 6 sheepe cost 58 shillings how many shall I buy for 124 pound multiply 124 by 58 makes 7192 which diuide by 6 makes 1198 sheepe 2 ∶ 3. Or otherwise diuide 58 by 6 makes 9 2 ∶ 3 by which multiply 124 makes 1198 2 ∶ 3 as before Example A Merchant at Siuill deliuereth 1500 Rialls to receiue for euery 11 being a ducat in London 5 shillings 10 pence sterling money how much must he receiue If 11 Rialls be 70 pence what are 1500 Rials At 13 pound in the 100 pound profit of what stocke came 3274 pound Answer diuide 3274 pound by 113 pound makes 2897 pound 39 ∶ 113 of a pound adde two cyphers to the giuen number A Merchant receiued for principall and gaine 328 wherein he found he had gained cleare 56 pound what did he gaine vpon the 100 pound Answere multiply 100 by 56 the gaines makes 5600 which diuide by 328 and the Quotient is 17 pound 3 ∶ 41 in smallest termes If 112 pound cost 7 pound 6 shillings how may I sell to gine 10 pound vpon the 100 pound Answere Take the tenth part of 7 pound 6 shillings or of 146 shillings which is 14 shillings 3 ∶ 5 of a shilling which added to the price makes 8 pound 7 pence 1 ∶ 5 of a penny If 100 pound exchange be 7 pound 2 shillings what is one pound Answere 71 ∶ 100 parts of a pound wherefore multiply 71 by 240 and diuide by 100 makes 17 pence 12 ∶ 5 of a penny If 107 ells of cloth cost 17 pound 12 shillings what will 321 ells cost at that rate Here if you consider the proportion betweene the first number and the third you shall find the third number doth containe the first exactly three times wherefore you need not to multiply the second by the third and diuide by the first number but only take the second number and multiply by 3 makes 52 pound 16 shillings for the price that 321 ells will cost behold the worke at large If 107 ells of cloth cost 17 pound 12 shillings what will 321 ells How to find whither that your numbers giuen be proportionall or not Diuide your third number by the first and if the quotient be an euen number and nothing remaine of your diuidend then the first and third numbers are euen proportionall in whole numbers as in the last example the first number was 107 and the third number 321 so that in deuiding the third nuÌ„ber by the first the quotient is 3 0 remaines wherefore I conclude that the first and third numbers are proportionals in whole numbers and that the third doth containe the first iust three times and so often must the fourth number sought for containe the second and I conclude that three times 17 pound 12 shillings which is 52 pound 16 shillings is the fourth proportionall number sought as appeareth by the ordinary forme of worke in the last example If 36 elles of cloth cost 13 pound 4 shillings 1 penny what will 432 elles cost at that rate diuide 432 by 36 makes 12 by which multiply your second number 13 pound 4 shillings 1 penny makes 158 pound 9 shillings A. doth lend vnto B. 600 pound for 8 moneths the question is how much B shall lend vnto A. for 12 moneths to recompence him not reckoning compound interest Answere If 8 moneths require 600 pound what will 12 moneths require the reason is lesse then 600 pound wherefore diuide 600 pound by 12 makes 50 which multiply by 8 makes 400 pound Or otherwise by proportion as 8 is to 12 so must 600 bee to 400 pound 2 ∶ 3 parts of 600 pound If the number bee not exactly proportionall yet there is a great abreuiation to bee made of the worke of Reduction Multiplication and Diuision in the working of most examples in the Golden Rule as for example If 19 Barrels of Figgs cost 16 pound 12 shillings what shall 58 barrels cost here diuiding 58 by 19 the Quotient is 3 and 1 will remaine wherefore I take 3 times 16 pound 12 shillings for 57 barrels and I haue to worke but for the one remaining which is but to diuide 16 pound 12 shillings by 19 makes 17 shillings 9 ∶ 19 of one shilling the totall is 50 pound 13 shillings 9 ∶ 19 shillings If 356 elles of Holland cost 124 pound 2 shillings 3 pence what will 7259 elles cost at that rate Reduce 124 pound 2 shillings 3 pence into pence makes 29787 pence which multiply by 7259 makes 216223833 pence which diuide by 356 make 607370 which diuided by 240 pence makes 253 pound 170 pence or 14 shillings 2 pence Example A second way more briefly to worke this question or any other of like nature is this multiply the third number by the pounds and primes or shillings and pence and diuide the product by the first number and the quotient will be the fourth number sought In the last example 7259 elles was the third number which multiply by 124l 1 prime or 2s makes 900841 l. 9 primes then also 7259 by 3 pence makes 21777 pence which diuided by 240 makes 90 pound 14 shillings 9 pence then adde those two sums into one totall makes 9009326 primes 9 pence leaue out 9 and then diuide the residue by 356 makes 2530 pound 7 primes and 54 ∶ 356 which with the 9 d. brings out the two pence as in the last example Example If 24 pieces of Raysons cost 25 pound 8 shillings what will 324 pieces cost multiply 324 by 25 pound 4 primes makes 8229 6 primes which if you diuide by 24 the Quotient will be â—42 pound 9 primes or 18 shillings without Reduction as in the example following Example If 25 pound gaine 1 pound 8 shillings what will 725 pound gaine at that rate Multiply 725 by 1 pound 4 primes makes 10150 which diuided by 25 makes 40 pound 6 primes or 12 shillings And in this sort may diuers other questions bee wrought in pounds and shillings without Reduction which I thought good to giue a taste of but I will proceed here no further because I purpose in the second part of this Booke to speake of them at large in the Treatise of Decimal Arithmatick whereby all manner of questions are to bee wrought of Multiplication and Diuision in pounds shillings and pence without Reduction as shall appeare in their seuerall places following And now I will proceede to speake something of the Rule of Three Direct and Conuerst in Fractionall operations wherein I will be as briefe as I may not intending to increase this little Treatise intended for a pocket booke into ouer large a volume The Rule of 3 in Fraction If your three numbers giuen be all fractions multiply the third by the second and diuide the product by the first and the quotient will be the fourth proportionall number sought for Example If 3 ∶ 4 of a yard of Holland cost 4 ∶ 5
of your Ginger into pence makes 9072 pence which diuide by 14 pence makes 648 pound of Sugar which must be giuen for 756 pound of Ginger at 12 pence the pound 2. Example Two Merchants will barter one hath Raysons of 34 shillings the hundred readie money and in barter hee will sell them for 40 shillings the other hath Nut megs of 4 shillings the pound ready money how shall he set his Nut megs to make the like profit Put your coyne into pence and say If 408 d. be 480 d. what is 48 d. Multiply 480 by 48 and diuide by 408 makes 56 d. 2â—â—5â— of one penny for the price of the Nutmegs vid. 4 s. 8 d. 1 ∶ 2 of a pound 3. Example Two Merchants wil barter one hath Holland of 2 shillings 7 pence the ell ready money which he will sell in barter for a shillings 10 pence the ell and yet he wil gaine priuately 10 pound in 100 pound ouer that gaine at what price must hee then set his Holland Answere Set downe 2 shillings 10 pence in pence makes 34 pence of which take the tenth part which is 3 pence 4 ∶ 10 or 2 ∶ 5 and adde to 34 pence makes 37 pence 2 ∶ 5 of a penny for the price to sell one ell to make that gaines Now the other Merchant hath wooll at 7 shillings a Todde ready money how shall he set his wooll to make like profit that he be not deceiued in the bargaine If 31 pence be 37 pence 2 ∶ 5 what is 84 pence Multiply 374 primes by 84 makes 31416 which diuide by 31 makes 101 pence 3 ∶ 10 penny or 8 shillings 5 pence 3 ∶ 10 of one penny which is the price for him to sell his wooll to make like profit Example 4. Example Two Merchants will barter one hath Sugar of 6 pound 4 shillings ready money and he will sell it for 7 pound the hundred The other hath Ginger of 4 pound 6 shillings the hundred and in barter he will sell it for 5 pound the hundred now the question is at what rate each of them doth gaine per cent ' and which hath the aduantage of the other First if 6 pound 2 primes gaine 8 primes what will 100 pound gaine Multiply 8 primes by 100 makes 800 primes then ad 2. or 3 cyphers more to it which diuide by 6 ∶ 2 primes makes 12 l. 9 primes 10 ∶ 31 of a prime or neare 12 l. 18 shilling 8 pence which the first man doth gaine per centâ— Secondly if 4 pound 3 primes gaine 7 primes what will 100 pound gaine Multiply 7 primes by 100 and adde 2 cyphers more makes 70000 which diuide by 4 ∶ 3 primes makes 16 pound 2 primes 34 ∶ 43 of a prime from which subtract 12 pound 18 shillings 8 pence rests 3 pound 6 shillings 2 pence which the second man hath gained more then the first gained 6. Example Two Merchants barter one hath a certaine number of pieces of Sakkins at 18 shillings a piece for the which the other doth giue him 1806 ells of linnen Cloth at 16 pence the ell and yet 30 pound in readie money the Question is how many pieces of Sakkin he had First find what 1806 ells of linnen Cloth cost by Practice makes 120 pound 8 shillings to the which adde 30 pound makes 150 pound 8 shillings then diuide 150 pound 4 primes by 18 shillings or 9 primes makes 167 pieces of Sakkin and 1 ∶ 9 of a piece Example 6. Example Two men will barter one hath Pepper of 22 pence the pound ready mony but in barter hee will sell it for 27 pence the pound the other hath Sinamond of 3 shilling 6 pence the pound readie monie and in barter hee will sell it for 4 shilling the pound the question is how much sinamond wil pay for 384 pound of Pepper at that rate First 384 pound of Pepper at 27 pence the pound is 43 pound 4 shillings which diuide 43 ∶ 2 primes makes 216 pound Sinamond which he must giue 7. Example If 4 English ells make 5 yards and 13 yards makes 50 Pawnes at Geanes how many Pawnes is in 100 ells English If 5 be 4 what is 13 makes 10 2 ∶ 5. Secondly if 10 2 ∶ 5 be 50 what is 100 480 10 ∶ 13 8. Examples Euery 4 ells at Antwerpe maketh 5 at Frankford and 25 there makes 24 Braces at Luques the question is how many braces is 100 in Antwerpe If 25 bee 24 what is 5 makes 4 4 ∶ 5. Secondly if 4 bee 4 4 ∶ 5 what are 100 makes 120. 9. Example If 3 yards at London be 4 ells at Antwerpe how many yards at London make 84 ells at Antwerpe If 4 be 3 what 84 makes 63 ells 10. Example At Roan 112 ells make but 98 and 100 ells at Roan is 112 at Siuil how many of ours in 100 ells of Siâ—ull If 98 Roan be 112 ells what 100 Roan makes 114 ells 1 ∶ 7 of an ell Secondly if 112 ells be 114 1 ∶ 7 what is 100 Siuill makes 102 19 ∶ 25. 11. Example If 67 yards at London bee 100 in Venice how many are 7894 multiply by 67 makes 5288 yards 98 ∶ 100 parts 12. Example A Merchant doth deliuer 400 pound sterling in London by exchange for Antwerpe at 23 shillings 5 pence the pound sterling the question is how much Flemish money hee shall receiue at Antwerpe put your 23 s. 5 d. into pence makes 281 pence which multiply by 400 makes 112400 pence which diuide by 240 makes 468 pound 6 shillings 8 pence which he must receiue at Antwerpe Example 13. Example If 100 pound starling be 134 pound 6 shillings 4 pence Flemmish what is one pound starling worth Reduce your coine 134 l. 6 s. 4 pence into pence makes 32236 which diuided by 100 makes 322 pence 9 ∶ 25 pence or 26 shillings 10 pence 9 ∶ 25 of one penny for one pound sterling If one pound sterling be 1 pound 14 shilling 7 pence ob Flemish how much sterling money is in 100 li. Flemmish Reduce 100 pound into pence makes 24000 pence then put it into halfe pence makes 48000 halfe pence then put 1 pound 14 shillings 7 pence ob into half pence makes 831 by which diuide 48000 makes 57 pound 15 shillings 1 penny almost and so much sterling money is in 100 pound of Flemish money at that rate Of Gaine and Losse IF 13 pieces of Canuas cost 17 pound 12 shillings how may I sell them to gaine 8 pound in the hundred Multiply 176600 by 8 makes 19 pound 19008 or two pence almost and so much must he sell them for to gaine 8 pound in the hundred If 17 pound 12 shillings gaine 1 pound 8 shillings 2 pence what will 100 pound gaine Multiply 1 pound 8 shillings 2 pence in Decimalls by 100 and diuide by 17 pound 6 primes makes 8 pound in the 100 the proofe Example A Merchant hath lent 630 pound at interest for 10 pound
of the first figure of your quotient As if you will diuide 13 pound 95 seconds by 45 or which is all one if you shall say if 45 pieces of figgs cost me 16 pound 19 shillings what did one piece cost Diuide 1395 seconds by 45 makes 31 seconds or 6 shillings 2 pence 2 ∶ 5 of a penny for the price of one piece And in this sort the price of any number of yards ells or pounds being giuen in diuiding it by the number of yards elles or pounds the quotient will bee the price of one and by this Rule you saue a labour of Reduction alwaies diuiding the price by the number giuen the greater by the lesser or the lesser by the greater Example 6. Example If 456 ells of cloth cost 575 pound 7 primes what will one ell cost Diuide 575 pound 7 primes by 456 ells makes 1 pound 2625 fourths or in Coyne 1 pound 5 shillings 3 pence for the price of one ell Reduction in Decimals If you will reduce 75 pound 12 shillings 9 pence into Decimals enter your Decimal Table and for 12 shillings find 6 primes then looke for 9 pence and you shall find 375 fourths so the totall is 75 pound 6375 fourths and are now fit and apt for any Decimall operation If you multiply or diuide 84 pound 13 shillings 6 pence by 17 pound 3 shillings reduce them into Decimals by the Table makes for 84 pound 13 shillings 6 pence 84 ∶ 675 and for 17 pound 3 shillings 17 ∶ 15 and are now fit to be multiplied or diuided one by the other If you will reduce 189 ∶ 756 parts of one pound into Decimals diuide 189 adding 3 cyphers to it by 756 makes 25 seconds for that fraction in Decimalls and now for example If 158 ells of cloth 189 ∶ 756 parts of an ell cost 79 pound 2 shillings 6 pence what will 640 ells cost at that rate Now according to vulgar Arithmatick either I must reduce 158 ells 189 ∶ 756 parts of an ell into 756 parts or otherwise I must Reduce the fraction into his least termes makes 1 ∶ 4 then I multiply or reduce 158 ells into fourths makes 633 fourths for the first number in the Golden Rule Secondly reduce 79 pound 2 shilling 6 pence into pence makes 18990 pence for the second number then put 640 ells into fourths makes 2560 fourths then multiply â—8990 by 2560 makes 48614400 which diuide by 633 makes 320 pound Example The same example wrought by Decimalls If 158 ells 1 ∶ 4 ell cost 79 pound 2 shilling 6 pence what will 640 ells cost at that rate Place them in Decimals thus If 15825 seconds cost 79125 thirds what 640 ells Multiply 79125 thirds by 640 makes 50640000 which diuide by 15825 makes 320 pound the quotient Example Or otherwise Diuide 15825 by 79125 adding one cypher makes 2 primes for the Quotient wherefore I conclude that one halfe of 640 pound which is 320 pound is the answere to the question demanded Also diuide 7912â— by 15825 the quotient is 5 primes by which multiply 640 pound makes 320 pound for the answere to the question as before If a Phillips Dollar be worth 4 shillings 8 pence what are 465342 Dollars worth in sterling money Answer multiply 465342 by primes which is 4 shillings and take the sixth part of that product and adde into it makes 1085798 primes for the answer Or otherwise multiply by 2 primes and 1 ∶ 3 of a prime because 8 pence is 1 ∶ 3 of a prime and both wayes will produce the same answere Example If a common Dollar be worth 4 shillings and a Princes Dollar bee worth 4 shillings 6 pence how many Princes Dollars will pay for 7584 common Dollars Multiply 7584 by 4 shillings and diuide by 4 shillings 6 pence makes 6741 Dollars and 7 seconds and 5 thirds will remaine which is 18 pence so that I conclude 6741 Princes Dollars at 4 shillings 6 pence a piece will pay for 7584 common Dollars and there will remaine 18 pence Example In 654 pound how many Dollars of 3 shillings a piece Adde two Cyphers to 654 makes 65400 because 3 shillings hath 2 fractions in Decimals viz. primes and seconds which is 1 prime and 5 seconds by which diuide 65400 makes 4360 Dollars at 3 shillings a piece Example In 756 pound how many Dollars of 3 shillings 9 pence a piece Adde 4 Cyphers to 756 makes 7560000 which diuide by 1875 which is 3 shillings 9 pence in Decimals makes 4032 Dollars Behold the example following Example If I doe sell 346 yards of Veluet for 298 pound 8 shillings 6 pence how doe I sell one yard Answere diuide the price by the quantitie of yards in decimals makes 8625 fourths or in Coyne 17 shillings 3 pence for the price of one yard Example Makes 17 s. 3 d. a yard A Merchant would buy seuerall sorts of Spices of seuerall prices to wit of 3 shillings a pound of 2 shillings of 2 shillings 3 pence of 1 shillings 7 pence and of 2 shillings 2 pence a pound and would haue of each a like quantitie for 324 pound the question is how many pound hee must haue of each First adde all the prices into one summe makes 11 shillings by which diuide 324 pound makes 584 pound 1 ∶ 11 of a pound and so many pound must he haue of each sort A Goldsmith sent his seruant to the Tower of London to fetch him 415 pound 18 shillings 9 pence in pieces of 6 pence of 4 pence of 3 pence of 2 pence of 1 penny and of one halfe penny and bad him bring of each sort a like quantitie First adde all your Coyne makes 16 pence halfe penny which in Decimals is 6875 fifths by which diuide 4157375 fourths makes 6050 pieces of each sort Example Rules of Practice in Decimalls Set your price giuen in the Decimall Table of a vnite be it yard ell piece or pound and by the price giuen multiply the number of yards ells pieces or pounds and the product will bee the summe that you seeke if you doe but marke out the prime line as shall appeare by examples following 1. Example If one pound weight of small Ginger cost 7 pence half-penny what will 112 pound waight cost Find for 7 pence half-penny 3125 fifths which multiply by 112 pound makes 350000 from which cut off fiue figures to the right hand by the prime line and the summe is 3 pound 5 primes or 3 pound 10 shillings because your multiplicand hath 5 fractions Example How to find the price of any vnite in any place of 10 or 100 or 1000 the price of one being giuen If the price of a vnite bee giuen at any rate and from thence you desire to know what 10 or 100 or 1000 or 10000 will cost at that rate or otherwise if you desire to know if you doe gaine any rate desired by the pound and would know at what rate it will be in the 100 pound or
vpon exchange from place to place the exchange of one pound being giuen you desire to know what 100 pound will amount vnto Place your rate or gaines giuen in Decimalis by helpe of the Table and then adding of one two three or more Cyphers cutting off your prime line you shal know your desire marking the denominations of your fractions if the least to the left hand be primes seconds thirds fourths fifthes cutting off your prime line so many figures from the right hand 2. Example If one pound sterling be 1 pound 14 shillings 3 pence Flemish what is 100 pound sterling worth Place 1 pound 14 shillings 3 pence in decimals makes 17125 fourths then because 100 pound hath 2 Cyphers makes 1712500 then cutting off 4 figures to the right hand you shall find 171 pound 5 shillings for 100 pound sterling to make as appeareth before If one ell of Cambrick cost 7 shillings 6 pence â— farthings what will 100 ells cost at that rate Place 7 shillings 6 pence 3 farthings in Decimals makes 378125 fixths and adding two Cyphers for 100 makes 37812500 from which cut off 6 figures to the right hand makes 37 pound 16 shillings 3 pence for the summe that 100 elles will cost Makes 37 l. 16 s. 3 d. If one pound or piece cost 1 pound 2 shillings 3 pence what will 1000 pieces cost Set 1 d. 2 s. three pence in Decimalls makes 11125 fourths to the which adde 3 Cyphers because 1000 hath 3 Cyphers and from the totall cut off 4 figures makes 1112 pound 10 shillings as is in the 4 example aboue If one ell of Holland cost 3 shillings 3 pence what will 343 ells cost Multiply 343 by 3 shillings 3 pence in Decimalls which is 1625 fourths makes 55 pound 14 shillings 9 pence If one yard of Veluet cost 15 shillings 6 pence what will 972 yards cost Find for 15 shillings 75 seconds then for 6 pence find 25 thirds total is 775 thirds by which multiply 972 makes 753 pound 6 shillings as aboue in the sixth Example If one yard of Veluet cost 17 s. 7 d. 3 q. what will 857 yards cost First find 17 â— to be 85 seconds then 7 d. 3 q. makes 322916 totall is 8822916 which multiply by 857 makes 756 l. 2 s. 5 d. 3 q. If one Dollar be worth 4 shillings 9 pence what are 758 Dollars worth in sterling money Multiply 4 shillings 9 pence which is 2375 fourths by 758 makes 180 pound 6 pence as in the eighth example aboue The price of any number of yards ells pieces or pounds giuen to find the price of a vnite If the price of any number of yards ells pieces or pounds be giuen set them downe in Decimals adding one two or more Cyphers if neede require and diuide that sum or price by the number of the yards elles pounds or pieces and the quotient is the price of a vnite in whole numbers primes seconds and thirds without reduction as shall appeare by examples following and in this manner you may know what summe of money was lent if the principall and interest be giuen at any rate in the hundred or you may know if the rate of one pound exchange be giuen for any place you may know the value of 100 of that Coyne in that money giuen and by this Rule is to bee abreuiated almost al operations of Arithmatick by finding the value of a vnite in any place desired If â—42 ells of cloth cost 22 pound 4 pence half-penny what cost one ell at that rate Diuide 2201875 fifthes by 542 makes 40625 sixths or in Coyne 9 pence 3 farthings for the price one ell cost 1. Example If 345 pound gaine 76 pound 12 shillings what doth one pound gaine Diuide 76600000 by 345 pound makes 222028 sixth or in Coine makes 4 shillings 5 pence half penny almost that 1 pound doth gaine as in the example following 2. Example If 756 pound 3 quarters 24 pound of sugar cost 4421 pound 12 shillings what did one pound waight cost accounting 112 pound to the hundred Reduce 756 pound 3 quarters 24 pound into pounds suttle accounting 112 pound to the hundred makes 84780 poundâ— then diuide 4421 pound 12 shillings by 84780 makes 5215 fifths or 12 pence half-penny one pound 3. Example If I sell 1000 pieces of Cambricke for 700 pound how doe I sell one piece Diuide 1000 by 100 makes 1 pound 42857 fifthes 1 pound 8 shillings 6 pence 3 farthings as in the Example following 4. Example If one pound starling be 1 pound 14 shillings 3 pence Flemish what is one pound Flemish worth Diuide one pound with Cyphers by 17125 makes 11 shillings 8 pence 1 farthing almost 5. Example If 1 l. sterling be 1 l. 14 s. 7 d. ob Flemish what is 100 l. Flemish worth in sterling money Diuide 100 by 173125 fifths which is 1 l. 14 s. 7 d. ob in Decimals makes 57 l. 15 s. 3 d. 6. Example The Golden Rule in Decimalls If the number giuen be pounds shillings and pence set them out in Decimals and also your number of yards ells pieces pounds or any other numbers set them out also in Decimals and then without reduction multiply the third number by the second and diuide by the first according to the instructions of multiplication and Diuision in the former part of this booke and the uotient will be the third number sought 1. Example If 34 ells of Canuas cost 1 pound 4 shillings what will 756 ells cost at that rate Multiply 756 by 1 pound 2 primes makes 9072 primes which diuided by 34 adding Ciphers makes 266823 fourth or in Coine 26 pound 13 shillings 8 pence Example If 112 pound of Indico cost 34 pound 17 shillings what cost 789 pound subtill accounting 100 pound to the hundred Multiply 3485 seconds by 789 makes 27496 pound 65 seconds which diuided by 112 pound makes 245 pound 5058 fourths or 10 shillings 1 penny farthing Example If 981 ells of Cloath cost 94 pound 13 shillings 6 pence what cost 2943 ells at that rate Diuide the third number by the first and by the quotient multiply the second and the product will be the answere sought If 112 pound of Sugar cost 5 pound 3 shillings 9 pence how many pounds will 124 pound buy at that rate Diuide 51875 fourths by 112 pound to find the price of 1 pound makes 46316 sixths or in Coyne 1â— d. 1 ∶ 10 of a penny almost for the price that one pound cost Secondly diuide 124 pound by the price of one pound viz. by by 46316 sixths makes 26773 primes and so many pound he shall haue for 124 pound If one yard Broad Cloath cost 16 shillings 9 pence how many yards shall 56 pound buy at that rate Diuide 56 pound by 16 shillings 9 pence the price of one yard makes 66 yards 9 ∶ 10 almost Example If 7 yards 1 ∶ 2 of cloth cost 9 shillings what will 8 yards 1 ∶ 3 of a yard cost
interest vpon interest 450 pound 19 shillings 6 pence which was for money lent at 8 pound in the hundred for three yeeres now the Question is what was the summe lent Place 450 pound 19 shillings 6 pence in Decimals and you will find your third quotient will be 358 pound wanting some few seconds which prooues the work good 3. Example A Merchant lent 112 pound for 6 months at 17 pound in the hundred for 12 months the question is what he shall receiue Put your money into pence makes 26880 pence marke out your prime line as in the former examples and adde two cyphers then multiply by 17 and take halfe that product for 6 moneths interest and adde into the principall and the totall is the sum of pence which hee shall receiue for principall and interest at 6 moneths end Example Makes 121 li. 10 s. 4 d. 4 ∶ 5 of a d. 4. Example If a pound of Sinamond cost 4 shillings ready money how may it be sold to gaine 12 pound in the hundred to giue 6 moneths time Set your 4 shillings in pence makes 48 pence then adde 2 Cyphers and multiply by halfe the interest and adde them into one summe and the product will bee 50 pound 88 seconds or 4 shillings 2 pence 2 ∶ 25 of one penny for the price to sell one pound to gaine 12 pound in the hundred for 6 moneths time 4. Example Makes 50 pence 9 ∶ 10 of a penny almost 5. Example If 112 pound waight of Clouâ—s cost 33 pound 12 shillings how may I sell them to gaine 14 pound in the hundred and giue 4 moneths time First set downe 33 pound 6 primes then adde 2 Cyphers and multiply by 14 makes 4 pound 704 thirds of which take the third part because 4 moneths is the third part of one yeare which is 1 pound 568 thirds which added into one totall makes 35 pound 3 shillings 4 pence halfpenny for the price to sell 112 pound to giue 4 moneths time and to gaine 14 pound in the 100 in 12 moneths 5. Example 6. Example If I gaine 8 pound 15 shillings in 100 pieces of Linnen cloth what doe I gaine in the 100 at that rate when as the 100 pieces are sold for 52 pound 10 shillings First subtract 8 pound 15 shillings from 52 l. 10 s. and there will remaine 43 l. 15 s. then say If 43 pound 15 shillings gaine 8 pound 15 shillings what will 100 pound gaine Diuide 8750000 by 43 pound 15 shillings or 43 pound 75 seconds and the quotient will be 17 l. 14 s. 4 d. in the 100. 7. Example If in 112 pound waight of Sugar sold for 7 pound 12 shillings ready money there were gained 11 pound in the hundred what did one pound cost at first penny First di 7 pound 6000000 by 111 pound which is the principall and interest giuen and the quotient is 6 pound 84684 fifthes which 112 pound cost ready money Secondly diuide that quotient by 112 pound makes 61132 sixths or 14 pence 3 farthings for the price that one pound cost at first penny 8. Example If 300 pieces of Lawne cost 321 pound 4 shillings how may I sell them to loose 15 pound in the hundred First take the rate what one cost by diuiding 321 pound 2 primes by 300 makes 1 pound 0706666 seuenths or 1 pound 1 shilling 5 pence almost for the price that one piece cost Secondly take the interest of 10706666 seuenths at 15 pound in the 100 and subtract it and then makes 91006 sixths or 18 shillings 2 pence 2 ∶ 5 of a penny for the price to sell one piece to loâ—osse 15 pound in the 100 ready money Thirdly for the proofe of this work say If one piece cost 910067 sixths what will 300 pieces cost at that rate Multiply 910067 sixths by 300 and cut off 6 figures to the right hand makes 273 pound 5 pence almost for the sum receiued for 300 pieces to loose 15 pound in the 100. Fourthly for a second proofe take the interest of 321 pound 2 primes at 15 pound in the hundred losse and deduct it from 321 pound 2 primes and there will remaine 273 pound 5 pence almost which doth proue all the other workes to be truely wrought Example 9 Example If in one ell of Cloth sold for 3 shillings 2 pence half-penny there were gained 10 pound in the hundred ready money what did that ell cost Answere set 3 shillings 2 pence ob in decimals makes 38 pence 5 primes then diuide 38 pence 5000 fourths by 110 pound makes 35 pence the price that one ell cost Example 10. Example If in one ell of Cloth sold for 35 pence 19 seconds there were gained 7 pound in the hundred ready money what did that ell cost when there was 6 moneths time giuen Diuide 35 pound 1900 fourths by halfe the interest adding one 100 which is 103 pence 5 primes and the quotient is 34 pence the price that the ell cost 11. Example A Merchant lent money at 10 pound in the hundred for 100 pound profit for 12 moneths and at the end of 6 moneths he receiued principall and interest 356 pound the question is what was the summe lent Diuide 356 pound by 105 pound which is the halfe yeares Interest and principall and the quotient is 305 pound 5 ∶ 105 of a pound for the summe lent Example 12. Example If 17 pound loose 12 shillings what will 100 pound loose Diuide 60000 fifthes by 17 makes 3 pound 529 thirds or 3 pound 10 shillings 7 pence in the hundred pound 13. Example If 37 yards of veluet cost 32 pound how must one yard bee sold to gaine 9 pound 10 shillings in the hundred First 32 pound the price at 9 pound 5 primes the hundred makes 35 pound 4 seconds which diuide by 37 makes the price of one yard to bee 94702 fifthes or 18 shillings 11 pence ob to sell one yard to gaine 9 pound 10 shillings in the hundred Example Exchange in Decimalls 1. Example IF one pound sterling be 1 pound 14 shillings 6 pence Flemish what is 783 pound sterling in â—emmish money Set out 1 pound 14 shillings 6 pence in Decimalls makes 1 pound 725 thirds which multiply by 783 pound makes 1350 pound 675 thirds or 1350 pound 13 shillings 6 pence Example 2 Example If one pound exchange be 5 shillings 6 pence what is 783 pound Set 5 s. 6 d. in Decimals makes 275 thirds which multiply by 783 makes 215 pound 325 thirds or 215 pound 6 shillings 6 pence which added to the last example is 1566 pound and so much is the double of the summe giuen viz. of 78â— pound because the two prices giuen makes iust 2 pound and this by working a second question in exchange the first is prooued to be truly wrought as appeareth in the example aboue 3. Example If one pound exchange be 1 pound 17 shillings 7 pence half-penny what is 1000 pound at that rate Set 1 pound 17 shillings
7 pence half-penny in Decimalls makes 1 pound 88125 fifthes then because 1000 hath Cyphers adde 3 Cyphers and cut off 5 figures and the answere is 1881 pound 5 shillings 4 Example A Merchant doth receiue 134 pound 6 shillings for the exchange of one hundred pound sterling from Middleborough what was one pound sterling in Flemmish mony Place 134 pound 6 shillings in Decimalls is 134 pound 3 primes then because 100 pound hath 2 Cyphers cut off two figures more to the left hand and it wil be 1 pound 343 thirds or in Coyne 1 pound 6 shillings 11 pence farthing for the exchange of one pound at that rate 5. Example A Merchant doth receiue 645 pound 12 shillings for exchange money at 1 pound 7 shillings 6 pence for one pound sterling the question is how much sterling money he did deliuer Diuide 645 pound 6 primes by 1 li. 375 thirds or 1 pound 7 shillings 6 pence makes 4695268 fourths or 469 pounds 10 shillings 6 pence 1 farthing for the sterling money deliuered 6 Example If 1 l. sterling be 1 l. 7 s. 6 d. Flemmish what is 110 l. Flemmish in Sterling Coine Diuide 100 pound by 1 pound 375 thirds makes 72 pound 72727 fifths or 72 pound 14 shillings 6 pence â—b that 100 l. makes 7. Example If the exchange bee from Rome to London at 69 pence sterling one Duckat how many Duckats shall bee deliuered at Rome for to receiue 356 pound 16 shillings sterling at London Answere Diuide 356 pound 8 primes by 2875 fourths which is 69 pence and the quotient will bee 1241 Duckats 3 pence 8. Example If the exchange bee from London vnto Antwerpe at 23 shillings 5 pence 3 farthings Flemmish the pound sterling how much money must be deliuered at London to receiue 146 pound 14 s. 10 pence 3 q. in Flemmish money Answere Diuide 146 pound 744775 sixthes by 1 pound 3 shillings 5 Pence 3 farthings which is 1 pound 1739582 seuenths and the quotient is 125 pound and so much must he deliuer at London to receiue 146 pound 14 shillings 10 pence 3 farthings in Flemmish Coyne at that rate Example 9. Example A Merchant doth deliuer at Antwerpe 200 pound Flemmish by exchange for London at 22 shillings 10 pence Fleminish for one pound sterling how much must hee receiue at London Answere diuide 200 pound by 1 pound 141666 sixths which is 22 shillings 10 pence makes 175 pound A generall Rule for exchange in Decimals If the price of a vnite be giuen then alwaies diuide the summe of money whereon the question dependeth by that vnite in decimalls and the quotient is the answere to the question 1. Example A Merchant doth deliuer 100 pound sterling by exchange for Rome at 72 pence sterling for one Duckat De Camera the question is how many Duckets he must receiue at Rome for his 100 pound sterling Heere the price of one Ducket is giuen to bee 72 pence which is 6 shillings or 3 primes wherefore I diuide 100 pound by 3 primes and the quotient is 333 pound 1 ∶ 3 of a pound or 6 shillings 8 pence for answere to the question 2. Example A Merchant doth deliuer 756 pound sterling at London to receiue Duckets at 66 pence sterling the price of one Dueket the question is how many Duckets he must receiue at Venice Diuide 756 pound by 66 pence which is 275 thirds and the quotient is 2748 Duckats and 300 ∶ 2750 of one Ducket for the Answere 3. Example A Merchant at Venice doth deliuer 1000 Duckats to receiue at London 287 pound 10 shillings sterling what is one Ducket Set downe 287 pound 5 primes and diuide by 1000 Duckets makes at 5 shillings 9 pence for one Ducket Makes 5 s. 9. d. one Ducketâ— 4. Example A Merchant at Venice doth deliuer 800 Duckats by Exchange for London at 64 pence b. the ducket sterling money the question is how much sterling he must receiue at London Set out 64 pence half-penny in Decimals makes 26875 fifthes which multiply by 800 and cut off 5 figures because your fractions are 5 and the product will be 215 pound sterling Makes 215 pound sterling 5. Example A Merchant doth deliuer 1000 duckets by Exchange for London at 71 pence sterling for one ducket how much must hee receiue sterling money at London Set out 71 pence in decimalls makes 2958 fourths 1 ∶ 3 and adde 3 Cyphers for 10â—0 and cut off 4 figures makes 295 pound 8 primes 1 ∶ 3 or 295 pound 16 shillings 8 pence for the answere Makes 295 l. 8 primes 1 ∶ 3 6. Example One penny Flemmish is 3 ∶ 5 of one penny sterling and one pound Flemmish is 3 ∶ 5 of one pound sterling or â—2 shillings wherefore to conuert Flemmish money into sterling Coyne multiply your Flemmish mony by 3 ∶ 5 which in decimals is 6 ∶ 10 or 6 and the product will bee the value of your Flemmish money in sterling Coyne In 345 Flemmish how much sterling Coyne Multiply 345 by 6 primes and the product is 207 pound sterling 7. Example In 756 pound 18 shillings sterling how much Flemmish coyne when one penny Flemmish is â— 5 of a penny English Denide 756 pound 9 primes by 6 primes makes 1201 pound 5 primes or 10 shillings Reduction of Measures from one place to another IF you will reduce the measure of one Country into the measures of another As if you would reduce the measures of Antwerpe Gaunt Brudges Siuill Roauen or of any other Countrey into the measures at London learne first the order of measuring of all sorts of commodities in both places either out of the experience of Merchants and Tradesmen in those places or out of the best and latest approued Authors that haue written Tables to that effect and note that 4 ells at London makes 5 yards and 100 ells at London is at  Ells. Antwerpe 166â— â— Gaunt short measure 164 Gaunt long measure 154 Brudges 164 Arras 165 Calice 157 Lisse 166 Mastrichâ— 173 Cullen 208 Franckfort 208 Norâ—mberge 174 Daâ—tringe 139 Roâ—â—â— 103 Paris 95 Licons 100 Genna 480 â— â— Palmes Millian 214 Braces Florence 188 Braces Venice for Silke hath 196 Ells. Venice for Linnen hath 180 Ells. Rome 56 Cana. Lisbâ—â—â—â— 100 Varras Madera 104 Varras Seuile 135 Varras These I haue taken out of Mastersons Arithmatick The difference of one hundred Ells Palmes Varras or Braces being found of any place from London if you would conuert the measures of any of those places to London measure as for example If you would conuert 356 ells of Brudges measure into ells at London you shall find in the Table that 164 ells make 100 at London then by the Rule of Three say 1. Example If 164 be 100 what are 356 ells Multiply 356 by 100 and diuide by 164 makes 217 ells 12 ∶ 164 of an ell which 356 at Brudges will make in London But according to the order of decimalls if you will bring the measures of other places
is pounds and so you haue pounds shilling and pence Example In 785697 pence how many pounds shillings and pence makes 3273 pound 14 shillings 9 pence If you will bring farthings into pounds shillings and pence diuide first by 16 and the remainer is farthings alwaies lesse then 16 or one groate and then againe by 6 makes pounds shillings and pence as before cutting off the prime line Example In 8735672 farthings how many pounds â—hillings and pence Reduction of Waights In 8756 hundred 3 quarters 24 pound 12 ounces Haberde poyce 16 ounces to the pound and 112 pound to the hundred how many pounds and ounces Example In 1569â—492 ounces Haberdepoyse how many hundreds quarters pounds and ounces finde how many ounces makes 112 pound in multiplying 112 pound by 16 ounces makes 1792 ounces by which diuide makes as in the example following Reduction of Measures In 2356 Acres 3 Roodes 27 Perches how many Perches in all Example In 765437 Perches how many Acres Roodes and Perches diuide by 160. Example Reduction of Time In 356 yeares 24 dayes 36 houres and 22 minuts how many dayes houres and minutes Example The Proofe In 187150342 minuts how many houres dayes yeares and minutes Reduction of Motion In 11 Signes 34 degrees 25 minutes 36 seconds 24 thirds how many fourths Example The proofe In 4722971040 fourths how many signes degrees minutes seconds thirds fourths Example Questions by Reduction 1. Question In 389 pound Starling how many Dollars of 4 shillings 8 pence or 14 groates a piece Reduce 389 pound into groats in multiplying them by 60 makes 23340 groats which diuide by 14 groats makes 1667 pound and 8 pence Example 2. Question In 300 pound starling how many Angels at a 11 shillings a piece Reduce 300 pound into shillings makes 6000 shillings which diuide by a 11 makes 545 angels and there will remaine 5 shillings Example 3. Question In 3012 pound how many Ryals of plate at 7 pence a Ryall Reduce 3012 pound into pence makes 722880 pence which diuided by 7 makes as in the example Example 4. Question If one Dollar be worth 4 shillings 8 pence how many Dollars is in 108579 pound 16 shillings starling Multiply your pounds by 60 makes 6514740 then reduce 16 shillings into groates by 3 makes 48 groates which added into one total makes 6514788 which diuided by 14 makes as in the example Example In 465342 Dollars of 14 groats a piece how much starling money multiply your Dollars by 14 makes 6514788 groates which diuide by 60 makes 108579 pound 16 shillings Example 5. Questions If I receiue 8060 French Crownes at 6 shillings a piece in France how much Starling must I pay for them at 6 shillings 1 penny a piece multiply 8060 by 73 pence the number of pence in one French crowne makes 588380 pence which diuided by 240 pence makes 2451 pound 11 shillings 8 pence Example 6. Question If 564 yards of cloth cost 124 pound 12 shillings how may I sell a yard to gaine 22 pound 7 shillings by the whole Summe Answere adde 22 pound 7 shillings to 124 pound 12 shillings makes 146 pound 19 shillings which reduce into pence makes 35268 pence which diuided by 564 makes 5 s. 2 d. ½ 6 47 of a farthing for the price to sell one yard for to gaine 22 pound 7 shillings by the bargaine Example 7 Question If 156 ells of cloth cost 124 pound what will one ell cost Reduce 124 pound into shillings makes 2480 shillings which diuide by 156 makes 15 shillings 4 pence 26 156 q. Example 8. Question If I sell 342 yards of Veluet for 241 pound 17 shillings how doe I sell one yard reduce your 241 pound 17 shillings into shillings makes 4837 shillings which diuided by 342 yards makes 14 shillings 1 penny 43 â—57 of a penny Example 9. Question A certaine Nobleman sent his seruant to the Tower of London with the Kings Maiesties Warrant to the Mint-master for 3408 pound 15 shillings willing him to bring it in pieces of 12 d. of 9 d. of 6 d. of 3 d. of 2 d. of â— d of 1 oh commanding him to bring him of each sort a like quantity or number of pieces the question is to know how many of each sort hee shall bring vnto his master to make the said sum of 3408 li. 15 s. reduce your mony into half pence and also your seueral pieces of Coyne into half pence and diuide the greater by the lesser as in the example Example VVhat Progression Arithmaticall is and the Rule PRogression Arithmeticall is nothing else but a briefe summing colecting or gathering together of diuers numbers increasing by equall proportion into one totall summe As for example 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. c. or also 3. 4. 5. 6. 7. 8. c. or 2. 4 6. 8. 10 12. c. or else by 3 as 5. 8. 11. 14 17. 20. 23. 26. c. or of all such like kinds of Progrission which doe increase equally by 2. 3. 4. 5 or 6 or any other greater increase and such kind of Progression is called Arithmeticall 2. To find the summe of a Progression Marke first how many seuerall places there be in your Progression and note that downe then adde the first number of the Progression to the last then multiply halfe those two numbers by the whole number of the places or else halfe the number of the places by the whole number of the first and last terme added into one summe and both waies will produce the totall summe of that Progression Example There is a Progression beginning at 4 and is continued vnto 44 increasing by 4. First set downe the numbers of that Progression beginning at 4 and ending at 44. Termes 4. 8. 12. 16. 20. 24. 28. 32. 36. 40. 44. Places 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. Here the first terme is 4 and the last is terme is 44 which added together makes 48 the one halfe which is 24 multiplied by a 11 the whole number of places makes 264 the totall Example First Question A certaine man gaue to his daughter in marriage the first day of Ianuary 1 pound and the second day 2 pound the third day 3 pound and so increasing euery day 1 pound vntill 31 dayes were expired the question is what he should receiue in the whole sum First 31 dayes is the number of places and 31 li. is the last payment adde the first terme 1 to the last terme 31 makes 32 which multiplied by 15 one halfe which is halfe 31 or take 31 and halfe 32 and the product wil be the totall Summe of his wiues portion Example How to find the latter terme of a Progression If you would know the latter terme of a Progression of 100 termes increasing by 3 and beginning at 10 take one terme from 100 termes there will remaine 99 which multiply by 3 the excesse or difference of the increase makes 297 to the which if you adde
pence the elle Canuas what will 7848 elles cost adde a Cypher and diuide 78480 by 240 and the Quotient will bee 32 pound 7 primes which multiply by 17 pence the price makes 555 pound 9 primes or 18 shillings Example At 3 shillings 5 pence an ell of Holland what will 702 elles cost diuide 7020 by 240 makes 2 pound 9 primes and there will remaine 6 which multiply by 41 pence the price of â—e ell makes 118 pound 9 primes or 18 shillings and then the 6 elles makes 1 pound 6 pence the totall is 119 pound 18 shillings 6 pence Example At 19 pence the elle of Holland what will 32544 elles cost diuide 325440 by 240 makes 1356 which multiply by 19 pence the price of one elle makes 2576 pound 8 shillings The Golden Rule Of single proportion Direct or the Rule of three called The Goulden Rule IN this Rule of 3 Direct there is alwaies three termes giuen and a fourth required and it is called the Goulden Rule in regard of the excellency of this Rule aboue all others The difficulty of this rule consisteth in the right placing of the three numbers giuen set the terme next your right hand whhereupon the question is moued and a terme of the same nature towards the left hand the third terme in the middle Then multiply the second nuÌ„ber by the third and diuide the product by the first and the Quotient is the fourth proportional number sought or desired to be found out whose denomination is euer like vnto the middle number 1. Example If 90 yards of Cloath cost 23 pound what cost 346 yards If 124 pound gaine 37 pound 12 shillings what will 758 pound gaine How to worke this last example and all other after a more briefe and exact manner Diuide the third number by the first and by the Quotient multiply the second and the product is the answere Example If 356 elles cost 137 pound 12 shillings 9 pence what cost 2848 elles First diuiding 2848 by 356 the Quotient is 8 by which I multiply 137 pound 12 shillings 9 pence the products are 1096 pound 96 shillings 72 pence then diuide 72 by 12 is 6 shillings which added to 96 shillings makes 102 shillings or 5 pound 2 shillings the totall is 1101 pound 2 shiliings as before 2. Example If 124 yards cost 17 pound 10 shillings 1 penny what cost 744 yards If 32 pieces of Raysons cost 19 pound 2 shillings 2 pence what will 112 pieces cost at that rate 3. Example If 356 pieces cost 137 pound 12 shillings 9 pence what will 2848 pieces cost at that rate Example Example How to know whether any question giuen be to be answered by the Rule Direct or Conuersed By these notes following you shall find whether any question propounded be to be answered by the Rule of 3 Direct or conuersed for alwaies the third number is the number whereon the question dependeth and is distinguished from the other two by some one of these notes following And the answer is alwaies more or lesse so that if it bee more then the lesser of your two extreame numbers is the diuisor if lesse then the greater of your two extremes is your diuisor If the number whereon the question bee depending be your Diuisor theÌ„ the answer is by the conuerse Rule and you must multiply your two former numbers for Diuidend If the first number be the Diuisor then the question is answerable by the Direct Rule and the product of the two latter numbers is your Diuidend Example If 13 Cannons spend 358 pound of powder what will 5 Cannons spend now here the question is what 5 Cannons will spend I answere lesse then 13 Cannons wherefore by this rule the greater of the two extreames 13 is the diuisor wherefore I multiply 358 by 5 and diuide by 13 makes 137 pound 6 ∶ 13 that 5 Cannons will spend 2. Example If 13 Cannons spend 358 powder what will 5 Cannons spend 2. Example I lent my friend 115 pound for 7 moneths and when I came to him to require the like kindnesse he could lend me by 54 pound the question is how long hee should forbeare that 54 pound to make requitall or to equal my time and kindnesse If 115 pound require 7 monthes what will 54 pound require here the answere in reason is that 54 pound must bee longer time forborne then 115 pound and so the answere is more times then 115 pound so that I find the lesser of my exteames 54 is my Diuisor and the question answerable by the Rule conuersed so that I multiply 115 by 7 makes 805 which diuided by 54 makes 14 moneths 49 ∶ 54 of a moneth or 14 moneths 25 dayes 23 ∶ 25 Example 4. Example A Captaine of a Band of men is besieged in a Citie hauing with him 7200 men and his victuals will serue the whole Company but 7 moneths but there is no hope left to haue any fresh victuals vntill 16 moneths the question is how many men he shall send away to make the victuals serue for 16 moneths Answere lesse then 7200 men If 7 moneths require 7200 men how many will 16 moneths aske When Wheate was sold at 3 shillings 8 pence the bushell the penny loafe of bread waighed 6 ounces what shall the same loafe of bread waigh when Wheat is sould for 2 shillings the bushell I answere more then a 11 ounces If 44 pence giue 6 ounces what will 24 pence giue If 356 men digge a trench in 24 dayes in how many dayes will 200 men make the same Answere in more dayes 42 dayes 17 houres 7 ∶ 25. If 356 men require 24 dayes how many will 200 men require Or thus Considering the numbers 200 may be had in 156 once therefore for 200 take 24 dayes then for 150 take 18 dayes totall 42 dayes then there will remaine 6 to bee multiplied by 24 makes 144 ∶ 200 parts of a day as before If 112 pound cost 3 pound 5 shillings 5 pence what will 3136 pound cost diuide 3136 by 112 makes 28 which multiply by 3 pound 5 shillings 5 pence makes 91 pound 11 shillings 8 pence If 100 pound gaine 7 pound what summe of money will gaine 85 at that rate Answere If 7 pound require 100 pound what will 85 pound require Or otherwise diuide 85 by 7 makes 12 1 ∶ 7 by which multiply 100 makes 1214 pound 2 ∶ 7 of a pound Or otherwise diuide 100 by 7 makes 14 2 ∶ 7 by which multiply 85 makes 1214 pound 2 ∶ 7 Example Carseys at 54 shillings the piece are put in Barter at 3 pound the piece how shall Wooll worth 24 shillings the Tod be set in Barter to make the bargaine equall If 54 shillings be 60 shillings what shall 24 shillings make Answere for more then 24 shillings and lesse then 54 so that 54 is the diuisor and multiplying 24 by 60 makes 1440 which diuided by 54 makes 26 shillings 2 ∶ 3 or 8 pence If 54
in 8 moneths Take the tenth part of 336 which is â—â— li. 6 primes or 12 s. makes 369 li. 12 s. Secondly if 12 moneths gaine 33 pound 6 primes what will 8 moneths gaine I answere lesse then 33 pound 6 primes wherfore multiply by 8 and diuide by the greater extreme 12 makes 22 pound 4 primes or 8 shillings the answere If 120 Pioners in 6 dayes cast 300 rods of Trench how many shall 600 men cast vp in 4 dayes If 120 giue 300 what will 600 giue Answere 1500 Rods. Secondly if 6 dayes giue 1500 rods how many will 4 dayes giue I answere lesse multiply by 4 and diuide by 6 makes 1000 Rods. If 112 pound in 12 months gaine 100 li. what wil 340 li. gaine in 7 months Answer 303 li. 4 ∶ 7. Secondly if 12 moneths gaine 303 li. 4 ∶ 7 what will 7 moneths gaine Example A generall Rule Put alwaies your diuisor into the same fraction of your diuidend and your quotient will be of the same denomination that your diuidend was as in the last example 12 moneths was turned into seuenths and also 303 pound 4 ∶ 7 was turned into seauenths of pounds and so the quotient of that diuision was pounds and the fraction of a pound remaining If 7 pound in 13 months gaine 3 pound in how long time will 340 pound gaine 60 pound First if 7 pound Gaine 3 pound what will 340 pound gaine makes 145 pound 5 ∶ 7 of a pound Secondly if 145 pound 5 ∶ 7 or 1020 ∶ 7 ask 13 moneths what will 60 pound or 420 ∶ 7 gaine Multiply by 13 and diuide by 1020 makes 5 months 6 ∶ 17 of a month If 600 great Horses in 5 dayes doe spend 1125 Bushels of oats how many bushels wil serue 1400 Horses for 22 Dayes First say if 600 giue 1125 what 1400 makes 2625 bushels Secondly if 5 spend 2625 bushels what will 22 dayes spend Multiply by 22 and diuide by 3 makes 11550 bushels How to worke the double Rule at one operation This last question or any other of like nature which is wrought by the double Rule at two seuerall operations may be answered at one in this manner multiply the three latter numbers to make your diuidend one into the other then multiply the two former numbers for to make your diuisor and then diuide the diuidend by the diuisor and the quotient will be the same as in the last example 1125 being multiplied by 1400 makes 1575000 which againe increased by 22 makes your diuidend 34650000. Then multiply your two former numbers 600 by 5 makes 3000 for the Diuisor and then diuiding your diuidend by your diuisor 3000 the quotient will bee 11550 bushels as before at two operations Example If 35 s. in 7 months gaine 6 s. in how long time will 340 l. gaine 100 l. First if 35 s. gaine 6 s. what will 340 l. require Reduce 340 l. into pence and multiply by 6 makes 40800 which diuided by 35 makes 1165 s. 5 ∶ 7 s. Secondly if 1165 â— 5 ∶ 7 require 7 moneths what will 100 l require Makes 12 moneths 8 ∶ 816 parts of a moneth Fellowship without Time This Rule differeth very little from the Rule of three for in this Rule the summe of all the moneys disbursed is the first number in the Golden Rule Then the gaines or losse is the second number the third number is each seuerall partners money disbursed so that the Rule must bee seuerally wrought for each seuerall Partners portion Example Foure Merchants made a company together the first viz. A. put in stock 74 pound B. put in 90 pound C. put in 100 pound and D. put in 120 pound and they found that they had gained 84 pound now the question is what each man must haue of the gaines according to the proportion of his money disbursed First adde all the moneys disbursed into one totall summe viz. 74 90 100 120 totall is 384 for the first number in the Golden Rule Then the second number is 84 pound the gaines and the third number is each particular mans stock then worke as followeth If 384 pound gaine 84 pound what will A. B. C. D. summs gaine to them The like reason is in losse as is in gaines Example A certaine ship being in a tempest on the sea was forced to cast ouer board so much of her lading as amounted vnto the summe of 642 pound then there is great reason that all the ventures should beare part of that losse according to the proportion of his stocke which hee ventured As suppose A. ventured 700 pound B. 530 pound C. 640 pound D. 800 pound totall is 2670. Then say If 2670 pound loose 642 pound what will each of A. B. C. D. loose as in the example following Example If 2670 pound loose 642 pound what will A. B. C. D. summes loose to them fioure Merchants bought a ship which cost them 3600 pound whereof A must pay one third part of the money B. one fourth C. one fifth D. one sixth the question is what each man must pay of the saidsumme Answere Seeke a number wherein the like parts may bee had which is 60 and take the like parts of that number for the numbers that you seeke for to find each mans portion of the money which he should pay First 1 ∶ 3 of 60 is 20 the 1 ∶ 4 is 15 the 1 5 is 12 the 1 ∶ 6 is 10 which adde into one totall makes 57 for the first number in the Golden Rule Example If 57 be 3600 what will bee the summes of A. B. C. D. The said ship made a Voyage to Sea and hath gotten all charges deducted out 240 pound the question is what each man must haue of the gaines Answere If 57 gaine 240 what will A. B. C. D. summes gaine to them Foure Merchants made a Company A. put in 320 pound 13 shillings 3 pence B. put in 840 pound 16 shillings 6 pence C. put in 560 pound 18 shillings 9 pence D. 1000 pound and in one yeare they found they had gained 400 pound 18 shillings 6 pence the question is what each man must haue of the gaines First the totall summe of all their moneys makes 2721 pound 8 shillings 6 pence or 653142 pence for the first number Then reduce each seuerall mans money disbursed into pence for the third number the second is the gaines also reduced into pence and then worke according to the Rule Example If 2721 pound 8 shillings 6 pence gaine 400 pound 18 shillings 6 pence what will A. B. C. D. summes gaine to them Rules of Fellowship with diuersitie of Time Multiply each mans money disbursed by the time that it continued in stock and gather the totals as in the last Rule to make the first terme in the Golden Rule and the gaines or losse is the second and then each mans product of money and time for the third terme in the Golden Rule and worke as followeth Example Three men
in the 100 for 3 yeeres interest vpon interest the Question is vnto what summe it will amount vnto at the end of the terme Answere Take the tenth part and adde it into one totall 3 seuerall times makes 838 pound 10 shillings 7 pence 1 ∶ 5 of a penny for principall and interest at the rate giuen to bee paid at the end of three yeares Example 2. Example A Merchant receiueth for principall and interest 838 pound 10 shillings 7 pence 1 ∶ 5 of a penny at 10 pound in the hundred compound interest which was for money deliuered out for 3 yeares now the Question is what was the summe of money that was lent To doe this or any other the like question diuide the summe of mony receiued by 110 three seuerall times and the three quotients will shew the yearely increase of the money lent and the last quotient will be the answere to the question or the money disbursed as in the example following which is the proofe of the former question Example 3. Example A Merchant lent 100 pound for 7 yeares at 10 pound in the hundred Compound Interest the Question is what he shall receiue at the end of the terme Example Makes at 7 yeares end 194 li. 17 s. 5 d. How to worke Compound interest at any rate per cent What is the principall and interest of 352 pound put out at 8 pound in the hundred compound Interest to be paid at the end of two yeares Adde two cyphers to 352 pound makes 35200 then place your Interest 8 vnder the lowest cypher next the right hand and multiply 352 by 8 placing the product vnder the line and that will be the Interest which added into the summe lent makes the totall of the principall and interest and so worke for the second third and fourth yeare as in the Example First I multiply 35200 by 8 makes 2816 which I adde vnto 35200 makes 38016 then I multiply 3801600 by 8 makes 4105728 or 11 shillings 5 pence abating 4 figures for the 4 cyphers which I added to the summe for to find out the prime line as appeareth in the example and so of any other summe or rate in the hundred At 17 pound the hundred per annum compound interest what wil 879 pound amount vnto to bee all forborne vnto the end of 5 yeares Adde 2 cyphers to your summe giuen and multiply by your Interest 17 and adde into the principall and so worke 5 yeares and the last product will bee the summe of money to bee receiued viz. 1927 pound 3 shillings 5 pence Example If a Merchant buy a parcell of Holland at 3 pound 6 shillings the piece and another parcel at 4 pound 2 shillings the piece the third sort at 4 pound 10 shillings the piece the fourth sort at 5 pound the piece how may he sell 40 pieces of each sort 10 pieces to gaine 18 pound in the hundred and giue 9 moneths time for the payment as in the Example following Example 10 Pieces at 3. 6. a piece 33. 0. 10 Pieces at 4. 2. a piece 41. 0. 10 Pieces at 4. 10. a piece 45. 0. 10 Pieces at 5. 0. a piece 50. 0.   The summe is 169. 0. Take the 3 ∶ 4 of the interest makes 191 pound 16 shillings 3 pence 3 ∶ 5 of one penny to sell to gaine 18 pound in the hundred for to giue 9 moneths time A Merchant sold 300 quarters of wheat cost him 352 pound ready money and lost 7 pound in the hundred what did one quarter cost him and at what rate did he sell a quarter to loose 7 pound in the hundred Take the interest at 7 pound in the hundred which is 24 pound 12 shillings 9 pence 3 ∶ 5 which subtract from 352 li. makes 327 pound 7 shillings 2 pence 2 ∶ 5 of a penny and diuide the remainer by 300 makes 1 pound 1 shilling 10 pence for the price sold secondly diuide 352 pound by 300 makes 1 pound 3 shillings 5 pence ob for the price which it cost him Rie sold for 3 shillings a bushell looseth 20 pound in the hundred what will then be lost if it bee sold for 3 shillings 6 pence a bushell If 3 shillings be 80 pound what is 3 shillings 6 pence Multiply 80 pound by 3 1 ∶ 2 or by 3 shillings 6 pence makes 2800 which diuide by 3 makes 93 li. 1 ∶ 3 Or otherwise if 36 pence bee 80 pound what is 42 pence Multiply 80 by 42 and diuide by 36 makes 93 pound 1 ∶ 3 of a pound as before If in one ell of Cloth sold for 3 shillings 2 pence there were gained after the rate of 10 pound in the hundred what did that ell of cloth cost diuide 385 or 38 penny 1 ∶ 2 by 110 makes 35 pence that the ell cost If one yard of Holland cloth cost 2 shillings 11 pence how many yards shall I buy for 34 pound 6 shillings put it into pence makes 8232 pence which diuide by 35 pence makes 235 yards 1 ∶ 5 yard How to gaine any rate in the Hundred you desire Put your price that one yard ell pound or piece doth cost you into pence and then for 10 pound in the hundred take the tenth part of that summe which is the same number placed one place nearer to the right hand and that is the profit or Interest which added vp into the price giuen makes the price to sel one yard pound ell or piece to gaine 10 pound in the hundred ready money Example If one ell of Holland cloth cost 3 shillings 9 pence how may I sell to gaine 10 pound per cent ' ready money Put 3 shillings 9 pence into pence makes 45 pence then take the tenth part of 45 pence which is 4 pence 5 ∶ 10 or one half makes 49 d. 1 ∶ 2 for the price to sell an ell to gaine 10 li. per cent Example If your price you would gaine bee not 10 pound in hundred then adde 2 Cyphers to your number of pence giuen and multiply that number by your Interest omitting to multiply by the cyphers and the product vnder the line is your Interest or gaine which added vp into one summe makes the price to sell one yard ell pound or piece to gain according to the rate desired example If one pound of Cloues cost 4 shillings 10 pence how may I sell to gaine 9 pound per cent ready money Put 4 s. 10 d. into pence makes 58 d. then ad 2 cyphers makes 5800 which multiply by 9 makes 5 ∶ 22 or 5 pence 22 ∶ 100 parts of one penny which added vp to the vpper numbers is 63 pence 22 ∶ 100 parts of one penny or 5 shillings 3 pence 1 ∶ 5 of a penny for the price to sell one to gaine 9 pound in the hundred If one piece of Raysons cost 18 shillings 9 pence how may I sell to gaine 18 pound in the hundred ready money put your money into pence makes 225 pence
to which adde 2 cyphers makes 22500 which multiply by 18 makes 40 ∶ 50 or 40 pence ob which added into the price makes 265 pence ob for the price to sell one piece to gaine 18 pound in the hundred Example A Merchant lent wares for 10 pound in the hundred profit for 12 moneths and at the end of 6 moneths he receiued principall and interest 356 ls the question is what was the summe lent Answere adde 2 cyphers to 356 pound and diuide by 105 pound which is 6 moneths interest and principall makes 339 pound 1 ∶ 21 parts of a pound for the sum lent Example Equation of Payment The Rule of payment is to bring diuers paymenâ—s due at seuerall dayes to be payed at one intire payment AMerchant is to pay at diuers payments 600 pound viz. 200 pound present 200 pound at 8 moneths 140 pound at 6 moneths and 60 pound at 2 moneths now hee is willing to pay all at one payment what time must be giuen The ready mony being omitted set the rest as numerators thus 200 ∶ 600 140 ∶ 600 60 ∶ 600 partes which in their least termes abreuiated makes 1 ∶ 3 7 ∶ 30 and 1 ∶ 10. Now multiply 1 ∶ 3 by 8 makes 2 and 2 ∶ 3 secondly 7 ∶ 30 by 6 makes 1 and 2 ∶ 5 thirdly 1 ∶ 10 by 2 makes 1 ∶ 5 totall is 4 moneths and 4 ∶ 15 of a month for the time sought Examples A Merchant hath owing him 752 pound to be payd 200 pound content 200 pound at 3 moneths 130 pound at 5 moneths and the rest at 12 moneths now at what time ought this money to be payd all at one payment Example A Merchant hath owing vnto him 782 pound 12 shillings to bee paid 1 ∶ 3 at 4 moneths 1 ∶ 2 at 7 moneths the rest at 12 moneths what time must it bee all at one payment Makes 6 moneths 5 ∶ 6 of a moneth VVines worth 14 pound ready money are sold for 16 pound to pay 1 ∶ 3 at 3 moneths 1 ∶ 2 at 4 moneths and the rest which is 1 ∶ 6 at 12 moneths the question is what is gained in 100 pound in 12 moneths Makes at 5 pound in the hundred Sugars worth 21 pound ready money are sold for 25 pound to pay 1 ∶ 5 ready money 1 ∶ 8 at 4 moneths 3 ∶ 10 at 7 moneths 3 ∶ 8 at 15 moneths the question is at what rate per cent per annum they were sold Makes 8 pound 9 ∶ 40 per cent Alligation Mediall ALlegation is an ArteÌ„ teaching to combine or knit together diuers things vnequally prised and thereby to find an equall price of any part of the said mixture Alligation Mediall is that which by the augmenting the quantitie of euery seueral portion to be mixed by his owne price and diuiding the summe of all the products by the totall of the seuerall portions to bee mixed findeth the thing sought Example Three seueral sorts of Barly are to be mixed viz. 34 bushels at 18 pence and 76 at 20 pence and 100 at 22 pence the Question is what one bushell of that mixture will be worth First multiply each number by his price viz. 34 by 18 76 by 20 and 100 by 22 makes 612 1520 and 1200 the totall is 4332 then adde the number of bushells into one summe makes 210 by which diuide 4332 d. makes 20 pence 132 ∶ 210 of one penny for the price of one bushell so mixed 2. Example If you will mixe 30 gallons of Sacke at 4 shillings a gallon with 150 gallons of White Wine at 2 shillings the gallon what will a gallon of that mixture bee worth Multiply 30 by 4 makes 120 shillings also 150 by 2 shillings makes 300 shillings totall is 420 shillings then adde 30 and 150 makes 180 gallons by which diuide 420 shillings makes 2 shillings 1 ∶ 3 of a shilling or 2 shillings 4 pence for the price of one gallon so mixed 3. Example Admit there were 6 portion of Siluer of 7 ounces fine 12 of 8 ounces fine and 25 of 10 ounces fine which are to bee mingled with 10 pound of Copper what is a pound of that mixture worth For answer multiply 6 by 7 makes 42 also 12 by 8 makes 96 and 25 by 10 makes 250 the totall is 388 which being diuided by 53 the totall of 6 12 25 and 10 makes 7 ounces 17 ∶ 53 of an ounce and so much fine is a pound of that mixture 4. Example A Merchant hath 6 seuerall sorts of Spices of which he will sell of each an equall quantitie of seuerall prices for the summe of 323 pound 8 shillings viz. Sinamond large at 4 shillings 6 pence a pound Nutmegs Case at 3 shillings 8 pence a pound Large Maces at 8 shillings a pound and Pepper Case at 2 shillings 2 pence a pound Pepper Callico at 22 pence the pound and Ginger large at 10 pence a pound the Question is how many pound he must haue of each to make the iust summe of 323 pound 8 shillings Answer first put your money into shillings makes 6468 shillings secondly put all your prices of the Spice into one summe and by that summe which is 21 shillings diuide 6468 makes 308 pound which he must sell of each Example Alligation Alternat ALligation Alternat is that which altereth the places of such excesse as commonly fall betweene the meane price and the extremes in which counter-change if the extremes be equall then the difference betweene the meane price lesser extreme is to be set against the greater extreme and of the contrary if otherwise 1. Example White Wine of 20 pence the gallon is to be mixed with Sacke of 3 shillings a gallon so that there must be mixed 300 gallons to make the price to bee but 2 shillings 4 pence the gallon the question is how much of each sort must bee taken The numbers set downe as in this example thus the difference of 20 the lesser extreme from 28 is 8 also the difference of 36 the greater extreme is also 8 so that I find you must take as many of one sort as of the other to make this mixture viz. 150 gallons of each sort 2. Example White Wine of 16 pence a gallon is to be mixed with Sack of 40 pence the gallon how many gallons must bee taken of either sort so that 120 gallons may be of 30 pence the gallon The numbers being set downe as in this example the difference of 16 the lesser extreme from 30 the meane price there wil remaine 14 which I plate against 40 then take the difference of 40 the greater extreme from 30 the meane price there will rest 10 to be linked with the lesser extreme whereby I find that so often as I take 14 gallons of Sacke I must take 10 gallons of White Wine to make the mixture 3. Example A certaine Clothier is desirous to mingle 144 pound of wooll of 4 sorts viz. blew wooll of 10
shillings the stone red wooll of 11 shillings the stone greene wooll of 12 shillings white wooll of 9 shillings the stone how many stones of each shal he take that one stone of the mixture may be worth 14 shillings The counter-change being made according to the Rule as is in the Margent it is plaine that so often as you take 5 of Blew you must take 3 of Greene and 2 of Red and 2 of VVhite Therefore if 12 bee 144 what The end of the first Booke THE SECOND BOOKE Containing a Treatise of Decimall Arithmatick Wherein is taught how to work all manner of operations in Decimall Arithmatick more speedy and easie then by vulgar Arithmatick and first of the Decimall Table LONDON Printed by Augustine Matthewes dwelling in the Parsonage-house in Saint Brides lane neere Fleetstreet 1623. THE VSE OF THE Decimall Table THe Decimall Table following doth begin from one Farthing vnto a Prime or two Shillings so that if you haue a Decimall Fraction giuen which doth containe 90625 sixths search it in the Decimall Table and you shall find it ouer against 21 pence three farthings and that is the value of that fraction giuen Or if you would know how to set out 16 pence halfe-penny in Decimalls search in the Table against 16 d. 2 g. and you shall find 6875 fifthes for the decimall sought But if you would set out any number of shillings from one shilling vnto one pound or â—o shillings search in this little Table following and you shall find your desire As if you would set out 15 shillings in Decimalls you shall find 7 primes 5 seconds for 15 shillings and so of any other summe as in the example following Example â—â—ill 1. 2. 1 05 2 10 3 15 4 20 5 25 6 30 7 35 8 40 9 45 10 50 11 55 12 60 13 65 14 70 15 75 16 80 17 85 18 90 19 95 20 1 li. q 1. 2. 3. 4. 5. 6. 7 q. 1. 2. 3. 4. 5. 6. 7 1 0010416 0 025 2 0020833 1 0260146 3 003125 2 0270833   3 028125 1 0041666 7 0291666 1 0052083 1 0302083 2 00625 2 03125 3 0072916 3 0322916 2 0083333 8 0333333 1 009375 1 034375 2 0104166 2 0354166 3 0114583 3 0364583 3 0125 9 0375 1 0135416 1 0385416 2 0145833 2 0395833 3 015625 3 040625 4 0166666 10 0416666 1 0177082 1 0427082 2 01875 2 04375 3 0197916 3 0447916 5 0208333 11 0458333 1 0218746 1 046875 2 0229166 2 0479166 3 0239582 3 0489584 6 0â—5 12 05 q. 1. 2. 3 4. 5. 6. 7 q. 1. 2. 3. 4. 5. 6. 7 12 05 18 075 1 0510416 1 0760146 2 0520833 2 0770833 3 053125 3 078125 13 0541666 19 0791666 1 0552083 1 0802083 2 05625 2 08125 3 0572916 3 0822916 14 0583333 20 0833333 1 059375 1 084375 2 0604166 2 0854166 3 0614583 3 0864583 15 0625 21 0875 1 0635416 1 0885416 2 0645833 2 0895833 3 065625 3 090625 16 0666666 22 0916666 1 0677082 1 0927082 2 06875 2 09375 3 0697916 3 0947916 17 0708333 23 0958333 1 0718746 1 096875 2 0729166 2 0979166 3 0739582 3 0989584 18 075 24 1000000 THE SECOND BOOKE CONTAINING A TREATISE of Decimall Arithmatick The declaration of the parts of the Decimall Table FIrst the Decimall Table in the left Margent containes certaine numbers in great and small letters first from 1 farthing vnto one prime or tenth of a pound or two shillings Then from one prime for euery shilling vnto one pound starling or 20 shillings First beginning in the left margent is set downe one farthing in the vttermost paralell to the left hand in the first paralell of the Table and so continuing from one farthing to one prime or 2 shillings and ouer against euery number in the left side in a right line towards the right hand is contained the numbers in decimals answering vnto euery farthing from one farthing to one prime or 2 shillings and in the vpper margent in the head of the Table is contained the true denominations of the said are all numbers in primes seconds thirds fourths fifths sixths and seuenths which are small enough to worke any question exact to a small fraction of one penny in a summe of great value as shall appeare by examples following But here you shall note that all the numbers in the said Table cannot be exact and perfit To find the value of a Decimall fraction in the parts of Coyne Suppose the number giuen to bee 2 seconds 4 thirds 5 fourths and 7 fifthes and you desire to know the true value thereof in coyne set downe your numbers as in the example following and marke your prime line and then multiplie the fraction by 240 the pence in one pound and the numbers that arise by multiplication ouer the prime line are the summe of pence the value of that fraction giuen and the remainer on the right hand of the prime line is the fraction of one penny Example Here by multiplication of 2457 fifthes by 240 pence I find 5 pence is gone ouer the prime line and there remaines 82080 100000 parts of one penny Now to know the value of that fraction in farthings multiply the same by 4 and so many as goe ouer the prime line are farthings the rest is the fraction of a farthing Example Numeration in Decimals If you haue a number to be expressed in Decimals of money or Coyne sterling learne first by the Decimall Table how to expresse your Coyne from one penny vnto one pound sterling or from one farthing to one pound sterling for which the Table going before was calculated If you would know the manner how to calculate the said Table diuide 1 pound adding 7 cyphers vnto it by your part you would know how to set forth in Decimals as if you would know how a farthing will stand in Decimals diuide 1 pound with cyphers by 960 the number of farthings in one pound sterling and the quotient will be the numbers in Decimals signifying one farthing Example So that I find that diuiding of 1 pound by 960 farthings the Quotient is 1 third 0 fourth 4 fifths 1 sixth and 6 seuenths for if you should haue proceeded adding more Cyphers the Quotient would haue been alwaies 6 because I see the number remaining to be the same it was at the last that is 64. And although a farthing cannot bee set out exact in Decimals yet it will serue in Multiplication and Diuision for in 10000 yards or ells it wil not differ 1 penny as shal appeare afterwards by examples in their places How to set out a penny in Decimalls Diuide 1 penny with Cyphers by 240 the number of pence in one pound sterling and the quotieÌ„t wil be a penny in decimals 2. Example Here seeing that after I find the first quotient 6 and the remainer 16 as before I cease Diuision as needlesse any further knowing it will produce 6 in the quotient infinitely and therfore I put as
them as in the last example and from the product cut off the 3 figures for the 3 fractions and the totall is 284 pound 5 shillings the sum that 758 ells will cost at 7 shillings 6 pence an ell c. Example If you will multiply fractions by fractions in decimals as to multiply 5 primes 2 seconds 6 thirds 3 fourths by 7 primes 2 seconds 5 thirds set them as before and cut off 7 figures 4. Examples Makes 7 s. 7 d. ob If you will multiply in Decimals by 10 or by 100 or by 1000 c. set downe your numbers and marke how many fractions there bee in your multiplicand and then ad so many cyphers as your multiplier hath to the right hand and cut off your prime line and the worke is ended as in this example Example How to change any fraction giuen into Decimalls Admit there be a quotient of a diuision which is 358 pound 126 ∶ 255 of one pound which fraction you would turne into Demalls adde a cypher to your numerator of your fraction makes 1260 but because your number will not be euenly diuided by your denominator 255 therefore adde more cyphers and then diuide the number by 255 makes 49411 fifths in Decimals to be ioyned with the whole numbers 35849411 fifthes and are now fit for multiplication and diuision in Decimals 5. Example Admit there be a fraction to be set out in Decimals thus it is required to know what 156 yards of cloth will cost at 196 784 of a pound one yard Adde to 156 2 3 or more cyphers and diuide by the denominator 784 makes 25 seconds by which multiply 156 yards makes 39 pound 6. Example 7. Example For the proofe of this worke multiply 156 by 196 makes 30576 which diuided by 784 makes 39 pound as before CHAP. V. Diuision in Decimalls IF you will diuide any number in Decimals either whole numbers by fractions or fractions by whole numbers or whole numbers and fractions by whole numbers and fractions set them downe according to the Rules in Decimalls in the operations before going As for example a certaine Merchant bought as much cloath as cost him 284 pound 5 shillings at 7 shillings 6 pence an ell the question is how many elles he had for his money To doe this or any other the like question diuide your summe of money 284 pound 5 shillings by 7 shillings 6 pence and the quotient will shew you what number of ells and parts of an ell if any bee were bought for that money 1. Example How to Diuide the smaller number by the greater If you will diuide 34 pound 6 shillings amongst 36 men place your numbers adding 3 or 4 or 5 cyphers and then diuide by 36 makes 95271 fifthes or in Coyne 19 shillings 0 pence ob for euery mans portion 2. Example What is the quotient of 724 pound Diuided by 3 ∶ 4 of a vnit or 15 shillings Answer diuide 724 by 75 seconds makes 965 1 ∶ 3 for triall whereof multiply 965 1 ∶ 3 by 15 shillings or 75 seconds makes 724 as in the Example 2. Example This last question is in effect no other but as the former for if I shall say a merchant buyes Broad Cloth costs him 724 pound at 15 shillings or 3 ∶ 4 of a pound one yard the question is what number he had for his money and by Diuision I find he had 965 yards and one third part of a yard as is proued in the example and so diuiding 724 by 3 ∶ 4 the quotient is 965 1 ∶ 3 3. Example If you will diuide the product of the second example in multiplication which was 559â—â—53125 seuenths by 16325 for the proofe of that worke which ought to bring out the multiplicand 34â—2625 or rather if you will diuide 559 pound 6 shillings 8 pence ob almost by 16 pound 6 shillings 6 pence the quotient will be 34 pound 5 shillings 3 pence Example How to find the Prime line in any Diuision decimall or to find the true denomination of of the Quotient In any diuision decimall alwaies marke out your prime line in your diuidend with a streight do vne line with the pen then set your Decimall fractions in primes seconds thirds fourths c. beyond the line also do the like in your diuisor and then mark how often you may remoue your diuisor that the whole numbers of your diuisor may stand vnder the whole numbers of your diuidend and so many figures shall your quotiont haue in whole numbers the rest are to bee marked with prickes in the quotient for primes seconds thirds c. If you will diuide 93861375 fifthes by 34 pound 35 seconds then place them with pricks as in the example following I find hauing placed my diuisor vnderneath my diuidend that I may remoue my diuisor twice vnder the whole numbers of my diuidend and therefore I conclude the first two numbers of my quotient wil be whole numbers which I marke from the rest of the numbers in the quotient with a line and then diuiding according to the former instruction you shall find the quotient will bee 27 pound 3 primes 2 seconds and 5 thirds Example 2. Example If you would diuide 15554 pound 2 primes 5 seconds or 5 shillings by 45 pound Place them as in the Example following and you shall find that there will be in the quotient 3 figures in whole numbers and the rest will be primes and seconds so that diuiding of 15554 pound 5 primes by 45 pound the quotient is 345 pound 13 shillings Example 3. Example If the greatest number of your Diuisor be primes then the figures of your whole numbers in the quotient will be once greater in value then the times you can remoue your Diuisor as if you would diuide 241 pound 5 primes by 7 primes then whereas you can remoue your diuisor by two times vnder the whole numbers 241 yet you shall haue 3 numbers in the quotient in whole numbers because your first figure of your diuisor is primes so that in diuiding 241 pound 5 primes by 7 primes I find the quotient will be 345 pound or integers and so many yards at 14 shillings a yard which is 7 primes wil 241 pound 10 shillings buy Example 4. Example If you will diuide 16 pound 875 thirds which is 16 pound 17 shillings 6 pence by 375 thirds which is 7 shillings 6 pence or which is all one imagine there is as much cloth of 7 shillings 6 pence a yard as cost 16 pound 17 shillings 6 pence the question is how many yards was bought for that money placing your numbers as in the example following I find 45 yards is the answere to the question Example 5. Example If you will diuide whole numbers and fractions by whole numbers place the whole numbers and fractions vppermost and marke out your prime line and then set your diuisor vnder-neath and the lowest figure in valew of your diuisor will shew you what is the denomination
93 pound 12 shillings 6 pence makes the answere to bee 94 pound 10 shillings 9 pence and so here in stead of multiplying 3120833 sixths by 515 and diuiding by 17 I haue saued more then halfe the worke Example 3. Example If 7 pound buy 100 pound waight of Sugar how many pound waight will 156 buy me at that rate Diuide 156 by 7 makes 22 2 ∶ 7 by which multiply 100 makes 2228 pound 4 ∶ 7 4. Example If 356 pieces of Callicoes cost 300 pound 15 shillings how much will 917 pieces cost at that rate Diuide 917 by 356 makes in the quotient 2 therefore take the price giuen twice and there will remaine after your diuision 205 by which multiply 30075 seconds makes 6165375 seconds which diuided by 356 makes 173 pound 18 seconds or 173 pound 3 shillings 8 pence to bee added to the former summe 601 pound 10 shillings makes 774 pound 13 shillings 8 pence for the Question The same question wrought without Reduction in Decimals If 356 cost 30075 seconds what 917 Multiply 30075 second by 917 makes 27578775 seconds which diuide by 356 makes 77468 seconds or 774 pound 13 shillings 8 pence as before the proofe Example 5. Example If 179 pound of Indico cost 60 pound 13 shillings 5 pence what will 716 pound cost at the same rate diuide 716 by 179 makes 4 in the quotient and nothing wil remaine wherefore I conclude that 4 times 60l 13 ◠5 d. which is 242l 13 s. 8 d. and is the answere to the question demanded 6. Example If 36 pound of Cloues cost 11 pound 6 shillings how many pound shall I haue for 354l Diuide 113 primes by 36 makes 31388 fifths which multiply by 354 cutting of figures for the 5 fractions makes 111 pound 11352 fifthes or 3 pound 2 shillings 2 pence 3 farthings for the answere Fellowship in Decimals To worke the Rule of Fellowship in Decimals gather the whole number of all the moneys disbursed into one summe and then diuide the money gained or lost by that summe and multiply that quotient so found by each seuerall partners stocke disbursed and the products will be each seuerall mans gaine or losse 1. Example Foure Merchants made a company A. put in 60 pound B. 80 pound C. 120 pound D. 140 pound and they gained 72 pound the Question is what part each Merchant must haue of the gaines First the totall summe of all their moneys disbursed was 400 pound wherefore according to the rule I diuide 72 pound adding Cyphers vnto it by 400 and the quotient is 1 prime 8 seconds by which I multiply each seuerall mans Stock disbursed and I find A. shall haue 10 pound 16 shillings B. 14 pound 8 shillings C. 21 pound 12 shillings and D. 25 pound 4 shillings totall is 72 pound as in the example Example 2. Example Foure Merchants made a company and set forth a ship to sea which cost them 3616 pound 13 shillings A. must pay 1 ∶ 3 of the money B. 1 ∶ 4 C. 1 ∶ 5 D. 1 ∶ 6 the question is what each man must pay of the said summe Take a a number wherein the like parts may be had which in the former book of vulgar Arithmatick I find to bee 60 whereof 1 ∶ 3 is 20 and 1 ∶ 4 is 15 and 1 ∶ 5 is 12 and 1 ∶ 6 is 10 the totall is but 57 wherefore I deuide 361665 by 57 and the quotient is 63-45 seconds which I multiply by 20 and I find A shall pay 1269 pound then I multiply by 15 and B. shall pay 95175 second and by 12 and C. shall pay 7614 primes and by 10 and D. shall pay 6345 primes the totall is 361665 seconds the proofe of the worke Example 3. Example ◠Three Merchants made a Company A. put in 566 primes B put in 398 primes C. put in 1204 primes and they gained 58 pound 16 shillings or 58 pound 8 primes what must each man haue of the gaines first the totall disbursed is 216 pound 4 primes by the which I diuide 58 pound 8 primes the quotient is 27197 fifthes for one pound gaines which I multiply by each seuerall mans money disbursed and I find A. shall haue 15 pound 7 shillings 10 pence half penny B. 10 pound 14 shillings 3 pence 3 farthings C. shall haue 32 pound 13 shillings 9 pence 3 farthings the totall is 58 pound 16 shillings the proofe Example 4. Example Three Captaines agree together to deuide a spoyle or bootie which they had taken containing 7851 li in this sort A. is to haue 1 ∶ 2 B. 1 ∶ 3 C. 1 ∶ 4 the question is what each mans share shall be Find a number which hath such parts in it viz. 12 whereof 1 ∶ 2 is 6 1 ∶ 3 is 4 and 1 ∶ 4 is 3 which in one summe makes 13 therefore diuide 7851 adding cyphers to it by 13 and the quotient will be 603 pound 92307 fifthes which multiply by 6 4 and 3 and you shall find A. shall haue 3623 pound 5384 fifths B. shall haue 2415 pound 69228 fifths C. shall haue 1811 pound 76921 fifths the Totall is 7850 pound 99991 fifths which doth want but 1 fourth of 7851 pound which in value is but 3 125 parts of 1 penny and this example is to bee wrought without the Golden Rule Behold the proofe of the worke Example The same example wrought another way After you haue diuided 7851 pound by 13 find in your Decimall Table what the quotient is in Coyne makes 603 pound 18 shillings 5 pence ob which multiply by 6 4 and 3 and their totall in one summe is the answere as before These three seuerall products added into one sum makes 7850 l. 19 s. 11 d. wanting but one penny in the whole sum which is the defect of the Decimals which cannot be exactly set out in coyne but it wil serue to answere a question of one million with one penny errour at the most 5. Example Three men made a stocke together and they gained 244 pound 8 shillings A. put in 315 pound 7 moneths B. 408 pound 10 moneths C. 500 pound 3 moneths now the question is what each man must haue of the gaines First multiply each mans stocke by his time and gather all the totals into one summe and they make 7785 by which diuide your gaines 244 pound 4 primes and the quotient will bee 31393 sixths which multiply by the seuerall products of each mans money and time and the totall of each seuerall product is the summe desired for each mans part of the gaine Example Position in Decimals The Merchants bought a parcell of Linnen Cloth cost them 757 pound 17 shillings whereof A. must pay 1 ∶ 4 B. 1 ∶ 5 C. 1 ∶ 8 what must each man pay of this sum I take 20 for a number wherein I can haue those parts viz. 1 ∶ 4 of 20 is 5 and 1 ∶ 5 of 20 is 4 and 1 ∶ 8 of 20 is 2 pound 5 primes
or 2 one halfe their totall is 11 pound 5 primes or 11 1 ∶ 2 by which I diuide 757 pound 85 seconds and the quotient is 65 l. 9 primes which I multiply by 5 for A. makes 329 pound 10 shillings B. 263 pound 12 shillings C. 164 pound 15 shillings the totall is 757 pound 85 seconds 1. Example 2. Example A Ship-carpenter bought 300 timber trees of a Gentleman and was to pay for the first 100 a summe of money vnknowne for the second twice asmuch as for the first 100 and for the third 100 of trees hee was to pay thrice asmuch as he paid for the first and the whole â—00 of trees cost him 7â—4 pound 12 shillings the question is what each hundred cost him seuerally To work this question or any other of like nature suppose a vnite or one pound for the first 100 then he must pay 2 pound for the second 100 which is twice as much and then also he must pay 3 pound for the third hundred which is three times as much as the first but yet 1 pound 2 pound and 3 pound makes but 6 pound and it should be 724 pound 12 shillings so that now whereas in the former Booke I taught you to resort to the Golden Rule for the answere saying If 6 pound cóme of my position 1 pound of what comes 724 pound 12 shillings Now alwaies supposing a vnite for your first number you shall saue multiplication and so diuiding of 724 pound 6 primes by 6 I find the first 100 of Trees cost him 120 pound 15 shillings 4 pence and the second 100 cost him 241 pound 10 shillings 8 pence and the third 100 cost him 362 pound 5 shillings the total makes 724 pound 12 shillings behold the worke Example 3. Example Foure Merchants consent to build a ship cost them 541 pound 16 shillings whereof A. must pay a certaine summe of money vnknowne B. must pay twice as much as A C. must pay twice as much as B and D. must pay as much as all the other three viz. as A. B. and C. now the question is what each man must pay of this summe I suppose A. must pay 1 pound then B. must pay 2 pound which is twice as much as A. doth pay and C. must pay 6 pound which is thrice as much as B. doth pay and then D. must pay 9 pound which is as much as all the other three doe pay but their totall is but 18 pound and it should be 541 pound 16 shillings wherefore I diuide 541 pound 8 primes by 18 and the quotient is 30 pound 1 prime or 2 shillings for the first part Then B. must pay 60 pound 4 shillings C. 180 pound 12 shillings and D. 270 pound 18 shillings their totall makes 541 pound 8 primes behold the worke Example 4. Example A Cesterne of water containing 600 gallons is filled with water and hath 4 seuerall Cocks to emptie the same whereof if they be all set open at once the Cesterne will be empty in 24 houres now the second Cock will auoyde twice as much as the first Cock in 24 houres and the third will auoide three times as much as the first and the fourth Cocke 5 times as much as the first the question is how many gallons each Cocke doth auoide in 24 houres of the said 600 gallons I suppose the first Cock will auoyde one gallon then the second must auoyde 2 and the third 3 and the fourth Cock 5 but yet they are but a 11 gallons and they should be 600 gallons wherefore diuiding of 600 by 11 the quotient is 54 gallons and 6 ∶ 11 of a gallon for the first Cocke Behold the worke in the example following Example Of Gaine and Losse in Decimals If a Broad Cloth 28 yards long bee sold for 14 shillings a yard and the seller doth gaine 10 pound in the 100 ready money what cost that broad Cloath First by Practice find the price of the 28 yards at 14 shillings a yard makes 19 pound 6 primes or 19 pound 12 shillings diuide 19 pound 6 primes by 110 pound makes 17 pound 81818 fifthes or in Coyne 17 pound 16 shillings 4 pence 3 farthings 1. Example Secondly if 28 yards cost 17 pound 81818 fifthes what did one yard cost at that rate Diuide 17 pound 81818 fifthes by 28 yards and the quotient will be 63636 or in Coyne 12 shillings 8 pence 3 farthings for the price that one yard cost Example Thirdly for the proofe of this worke say If one yard cost 63636 fifths how may I sell it to gaine 10 pound in the hundred ready money Take the tenth part of 63636 fifths makes 63636 sixths which added into one Totall makes 69999 fifthes which doth want but one fifth of 7 primeâ— or 14 shillings which proues all the former works to be true Example 2 Example A Merchant doth deliuer money at interest for 9 months after the rate of 12 pound in the hundred for 12 moneths simple interest and at the end of 9 moneths doth receiue for interest 87 pound the question is what was the summe lent Answere because the interest of 9 moneths at 12 pound in the hundred is 9 pound deuide 8700000 by 9 pound and the quotient is 966 pound 6666 fourths or 966 pound 13 shillings 4 pence the summe lent Example 3. Example If 13 pieces of Canuas cost 17 pound 12 shillings how may I sell them to gaine 8 pound in the hundred Multiply 17 pound 6 primes by 8 adding two cyphers makes for 19 pound 8 thirds or 19 pound 2 pence almost The proofe of the former example if 17 pound 12 shillings gaine 1 pound 8 shillings 2d what will 100 pound gaine at that rate Multiply 1 pound 8 shillings 2 pence or in Decimals 1 pound 408 thirds by 100 makes 140 pound 800 thirds which diuide by 17 pound 6 primes makes 8 li. for the rate that 100 pound will gaine which shewes the former worke to bee truely wrought Example 4. Example If in one ell of cloath sold for 3 shillings there bee gained after the rate of 12 pound in the hundred for 12 moneths how should that ell haue been sold to gaine 17 pound in the hundred for 12 moneths Multiply 17 pound by 3 shillings which is 1 prime 5 seconds and diuide the product by 12 makes 2125 fourths or in coyne 4 shillings 3 pence and so much must it haue been sold for to gaine 17 pound in the hundred Example Secondly if 3 shillings giue 12 pound what will 4 shillings 3 pence giue Multiply 2125 fourths by 12 and diuide by 15 seconds and the quotient is 17 pound the proofe of the last example Example 5. Example A Merchant sold 24 Clothes which cost him 342 pound wherein hee lost after the rate of 10 pound in the hundred and tooke in exchange 560 pieces of Raysons at 24 shillings the piece wherein hee gained 10 pound in the hundred ready money now the question is what his gaine
or losse was and what summe of money hee was to pay for the Raysons First 560 pieces of Raysons at 24 shillings a piece is 672 pound from which subtract 342 pound leaâ—es 330 pound to pay for the Raysons Secondly 672 pound at 10 pound in the hundred is 67 pound 4 shillings for his gaines by the Raysons Thirdly 342 pound lesse 10 in the hundred is 34 pound 4 shillings to be deducted from 342 pound and then take 34 pound 4 shillings from 67 pound 4 shillings leaues his gaines more then his losse to be 33 pound Example 6. Example A Merchant receiueth for principall and interest 352 pound wherein he gained 9 pound in the hundred for one yeare now the question is what was the summe of money lent Diuide 35200000 by 109 pound makes 322 pound 9357 fourths oâ— 322 pound 18 shillings 8 pence half-peny for the summe leâ—t 6. Example 7. Example A Merchant hath owing vnto him 540 pound to be paid at the end of three yeares now his debtor will pay him ready money if he will abate him 9 pound in the hundred Diuide 540 pound with Cyphers by 109 three times one after the other and the third quotient will be the summe that hee shall pay in ready money abating 9 pound in the hundred interest vpon interest Behold the worke following 7 Example The proofe is made by multiplying the last quotient by 9 and that product againe by 9 and thirdly againe by 9 makes 540 pound wanting but one fifth which is but 3 ∶ 1750 parts of 1 penny or 6 ∶ 875 parts of one farthing 8. Example A Merchant hath owing vnto him 632 pound to be paid at the end of 12 monthes now his debter will pay him ready money if he will abate him 12 pound in the hundred per annum Diuide 632 by 112 pound and the quotient will be the summe of money that will discharge the debt abating 12 pound in the hundred Example 9. Example 324 pound was receiued for interest money lent a Merchant Aduenturer at 17 pound in the hundred one yeare what was the summe lent Answere diuide 32400 by 17 makes 1900 pound and 1 ∶ 17 of a pound 10. Example If 358 ells of Holland cast 124 pound 16 shillings how shal it be sould an ell to gaine 12 pound in the hundred ready money First multiply 124 pound 8 primes by 12 adding two cyphers makes 139 pound 776 or in Coyne 139 pound 15 shillings 6 pence Secondly diuide 139 pound 776 by 358 makes 3905 fourths or 7 shillings 9 pence 3 farthings for the price to sell one ell to gaine 12 pound in the hundred Example 11. Example If one ell of cloth cost 18 pence how shall I sell 358 ells to gaine 7 pound 10 shillings by the bargaine and at what rate in the hundred doe I gaine First 358 ells at 18 pence an ell makes 26 pound 17 shillings to the which adde 7 pound 10 shillings the gaines makes 34 pound 7 shillings for to sell 358 ells to gaine 7 pound 10 shillings by the bargaine Secondly diuide 7 pound 500000 sixths by 26 pound 85 seconds and the quotient is 27 pound 9346 fourths or 27 pound 18 shillings 8 pence farthing which is the rate gained by the 100 pound of money Example 12. Example How much Indicoe of 6 shillings 3 pence a pound wil pay for 73 broad clothes at 16 pound one cloth and to pay 60 pound in present money First 73 broad clothes at 16 pound a cloth makes 1168 pound from which subtract 60 pound there will remaine 1108 pound which diuide by 6 shillings 3 pence or 3125 fourths and the quotient is 3545 pound 9 ∶ 10 of one pound and so much must he giue of Indicoe for the clothes Example 13. Example How many pounds of Cloues at 6 shillings a pound and small Sinamond of 3 shillings a pound must bee giuen for 36 Carseyes at 4 pound 3 shillings a piece to haue of each a like number of pounds Answer 36 Carseys at 4 pound 3 shillings a piece makes 149 pound 8 shillings which diuided by the price of both viz. 9 shillings makes 332 pound of each sort The proofe 332 pound of Cloues at 6 shillings a pound makes 99 pound 12 shillings then 332 pound of Sinamon at 3 shillings a pound makes 49 pound 16 shillings the total is 149 pound 8 shillings the giuen price of the 36 Carseys Example 14. Example Of what principall came 1000 pound principall and interest at compound interest in three yeeres at 6 pound in the hundred Diuide 1000 pound three seuerall times by 106 makes 839 pound 61 seconds or 839 pound 12 shillings 3 pence almost which was the summe lent at first Example 15. Example If 34 Tun of wine cost 544 pound how may a man sell a Tun to gaine 12 pound vpon the hundred ready money First find the price of one Tun diuiding 544 by 34 makes 16 pound for the price of one Tun which it cost then multiply 1600 by 12 pound makes 17 pound 92 seconds or 17 pound 18 shillings 4 pence 4 ∶ 5 of a penny for the price to sell one Tunne of that Wine to gaine 12 pound vpon the 100 pound How to worke gaine and losse in pence and parts of Pence or Farthsngs Set out your number of pounds shillings pence and farthings in pence and in tenths of one penny and for one farthing set out 2 primes 5 seconds which is one fourth of a penny and for two farthings set out fiue primes which is one halfe penny and for three farthings set downe 7 primes 5 seconds which is three quarters of one penny and then they are apt for decimall operations both for multiplication diuision or any other worke of Arithmatick without reducing them into farthings and there wil bee a great deale of labour saued in these kinds of operations as shall appeare afterwards by the examples following 1. Example What is the interest and principall of 100 pound put forth at 10 pound in the 100 compound interest for the space of 7 yeares to bee all receiued at the end of the terme First put your 100 pound into pence maker 24000 pence then worke as in this example following and you shal find it will amount vnto 46769 pence and 1 ∶ 5 of one penny which diuided by 240 pence makes 194 pound 17 shillings 5 pence 1 ∶ 5 of a penny which is the summe that 100 pound will amount vnto at interest vpon interest in 7 yeares at 10 pound in the hundred Example 2 Example A Merchant deliuered 358 pound at interest for three yeares for 8 pound in the hundred compound interest the question is what it wil amount vnto at the end of the terme Put your money into pence makes 85920 pence which multiply by 8 adding 2 Cyphers and worke for three yeares as in the example following Example The proofe of the former example in Decimals A certaine Merchant receiued for principall and
â— Â 864  1 46932800 5     8  1 16640000 2  1175462   8      93312  1 5868743 6     8  1 25971290 3 1 7138242 7  8      16077696     1 36048896 4    In this manner you may proceede infinitely and thus much shall suffice for making of these Breuiats The Breuiat of 8 pound in the hundred per annum Compound Interest for 30 yeares Yeeres 1. 2. 3. 4. 5. 6. 7. 8 Yeeres 1. 2. 3. 4. 5. 6 7. 8. 9 1 10800000 16 342594260 2 11664000 17 370001800 3 12597120 18 399611940 4 13604889 19 431570100 5 14693280 20 466095710 6 15868743 21 503383370 7 17138242 22 543654040 8 18509302 23 587146360 9 19990046 24 634118070 10 21589249 25 684847510 11 23316389 26 739635320 12 25181701 27 798806140 13 77196237 28 862710630 14 29371936 29 931727480 15 31721691 30 100626506 In this sort you may gather all the Tables or Breuiats for any rate in the hundred which I will here omit in this small vollum intending afterwards to publish this and diuers other operations in my second Edition of my Booke of Decimall Arithmatick shortly to come forth The vse of these Breuiates and Tables and of all others of like nature in working of questions of Interest and Annusties Rule 1. To find what 1 pound due at any number of yeares is worth at the end of the terme Enter the Table of 10 pound in the hundred and find in the left Maâ—gent the number of yeares and from that number so found cut off seuen figures the answere is in pounds primes seconds thirds fourths c. for the answere to the question demanded 1. Example What is one pound put forth at interest compound at 10 pound in the hundred worth to be paid at the end of 18 yeares Find the eighteenth number in the Breuiat which is 55599173 from which cut off seuen figures to the right hand and the answere is 5 pound 11 shillings 2 pence q. Example Makes 5 l. 11 s. 2 d. 1q 2. Example What is 100 pound due at 7 yeares end worth to be paid at the end of the terme at 10 in the hundred compound Interest Find the seuenth number in the Table of 10 l. in the hundred makes 19487171 to the which adde two Cyphers because 100 pound hath two Cyphers and cut off seauen figures to the right hand and the sum is 194 pound 87171 fifthes for the Answere 3 Example What will 758 pound for 6 yeare make at 10 pound in the hundred compound Interest to bee paid at the end of the terme Finde the sixth number in the Table of 10 pound in the hundred which is 17715610 which multiply by 758 the money named in the question and the product cutting off 7 figures to the right hand makes 1342 pound 16 shillings 10 pence ob almost Rule 2. How to find what any yearely Annuitie will make to bee paid all at the end of the terme First find the number of yeares of the annuitie giuen and from the number answering deduct a vnite in the first place to the left hand and adde a Cypher to the last figure to the right hand and cut off seuen figures to the right hand and the answere is found 1. Example What will 1 pound annuitie make to be payd for at the end of the terme of 16 yeeres at 10 pound in the hundred compound interest Find the sixteenth number in the Table of 10 pound in the hundred and subtract a vnite from the first figure to the left hand adding a Cypher to the right hand makes 359497290 From the which cut off 7 figures to the right hand makes 35 pound 18 shillings 11 pence 3 farthings 2. Example What will 1000 pound annuitie yearely amounteth vnto to be all forborne vntill the end of the terme of 5 yeares at 10 pound in the hundred compound interest Find the fifth number in the Table of 10 pound in the hundred and subtract a vnite from the first figure adding a Cypher in the last place makes 61051000 then because 1000 pound hath 3 Cyphers adde 3 Cyphers and cut off seuen figures makes 6105 pound 2 shillings for the answere 3. Example What will 142 pound annuitie make to be paid at the end of the terme of 10 yeares Find the tenth number in the Breuiat of 10 pound in the hundred and subtract a vnite in the first place adding a Cypher to the last makes 159374240 which multiply by 142 pound the annuitie named and from the product cut off seuen figures to the right hand and the answere to the question is 2263 pound 2 shillings 2 pence 3 farthings 3. Rule How to find what any summe of money due at the end of any number of yeares is worth in ready money at 10 pound in the hundred compound interest Enter the Table of 10 pound in the hundred with your number of yeares and the numbers which doth answere in the Table is your Diuisor then adde seuen Cyphers to your summe of money giuen to make your diuidend then diuide your diuidend by your Diuisor and the quotient adding more Cyphers will be your answere in pounds primes seconds thirds c. 1. Example What is 1000 pound due at 7 yeares end worth in ready money at 10 pound in the hundred compound interest Find the seuenth number in the Table of 10 pound in the hundred which is 19487171 this is your Diuisor Then adde seuen Cyphers to 1000 pound makes 1000000000 or adde more Cyphers marking out your prime line in your diuidend to find out how many figures your quotient will haue in whole numbers and the rest will bee primes seconds and thirds this is your diuidend and then diuide by your diuisor makes 513 pound 3 shillings 2 pence Hauing found what 1000 pound due at 7 yeares end is worth in ready money if you will find what 100 pound or 10 pound or 1 pound is worth in ready money place your quotient in decimalls and marke out your prime lines cutting of one figure for 100 pound â— for 10 pound or 3 for 1 pound the answere is as followeth Example 2. Example What is 750 pound due at 5 yeeres end worth in ready money at 10 pound in the hundred compound interest Find the fifth number in the Table of 10 pound in the hundred which is 16105100 for diuisor then place 10 Cyphers before your number giuen 750 pound and marke out your prime line and diuide by your Diuisor and the quotient will be 465 pound 13 shillings 10 pence for the answere to the question giuen Example Makes 465 pound 13 shillings 10 pence 3. Example What is 847 pound due at 21 yeares end worth in ready money at 10 pound in the hundred compound interest Find the 21 number in the Table of 10 pound in the hundred for Diuisor which is 74002499 then set 10 Cyphers to your numbers giuen makes 8470000000000 for your diuedend then diuide and the quotient will be 144 l. 9 s. 1 d. 1 ∶ 5 of 1 d. the answere Example Makes 114 l. 9 s. 1 d. 1 ∶ 5 of a penny 4 Rule How to find what any yearely Annuities for any number of yeares is worth in ready mony at 10 pound in the hundred compound interest Enter the Table of 10 l. per cent with your number of yeares giuen and from the numbers found subtract a vnite in the first place and place a Cypher in the last for your diuidend which diuide by the number found in the Table against your yeares giuen and the quotient is the answere to the question 1. Example What is 100 pound per annum annuitie for 21 yeares worth in ready money at 10 pound in the hundred Compound â—nterest Looke in the Table of 10 pound in the hundred for 2â— yeares and subtract a vnite in the first place and adde a Cypher in the last makes 6400 4990 Diuide this by 74002499 the 21 number adding Cyphers and marking the prime line and the quotient is 864 pound 17 shillings 4 pence â— farthings for the answere to the question demanded Example 2. Example Hauing found what 100 pound annuitie will amount vnto if you would know what 10 pound or 1 pound annuitie will amount vnto or 1000 pound in 21 yeares place it in Decimalls and cut off 1 2 or adde 3 Cyphers to the last or remoue 3 places and you shall find your demand Example 3. Example What is 546 pound yearely annuitie for 14 yeares worth in ready money at tenne pound in the hundred compound interest Find the fourteenth number in the Breuiate of 10 pound in the hundred from it subtract a Vnite in the first place and adde a Cypher makes 279749830 which multiply by 546 makes 152743407180 which diuide by 37974983 the 14 number in the Breuiate makes 4022 pound 4 shillings 2 pence 3 farthings Makes 4022 l. 4 s. 2 d. 3 ∶ 4 1. Example There is a Debt bought for 513 pound 3 shillings 2 pence ready money which was due at 7 yeares end now the question is what the debt was at 10 pound in the hundred compound interest Set your money paid in Decimalls makes 513158 which multiply by 19487171 the number against 7 yeares cutting off 10 figures makes 999 pound 999 thirds wanting but one third of 1000 pound wherefore I conclude the debt was 1000 pound which was due at 7 yeares end 2 Example There was a Debt bought for 600 pound which was due at 4 yeeres end what was that debt at 10 pound in the hundred compound interest Multiply 600 pound by the numbers against 4 yeares which are 14641000 makes 878 pound 4600000 seuenths or in Coyne 878 pound 9 shillings 2 pence 2 ∶ 5 of 1 penny for the summe of that debt Makes 878 l. 9 s. 2 d. 2 ∶ 5 of a penny I haue set no exampies of the Table of 8 pound in the hundred nor of no other rate bectuse I intend shortly to speake more at large of this subiect in another volume if God please to giue mee time and health in which I intend to speake more at large of the Grounds Reasons and proofes of these kind of Operations and here I will finish this small Treatice of the second Booke FINIS
of broad Cloth of three seuerall prices of each a like quantitie and he was to pay halfe as much more for the second sort as he payed for the first and twice as much for the third sort as he payed for the second now the question is what each sort cost him and at what price euery yard was rated vnto him I suppose the first sort cost him 4 pound then the second sort must cost him 6 pound which is halfe as much more as the first and then the third sort cost him 12 pound which is twice as much as the second the totall is but 22 pound but it should be 248 pound wherefore if 22 pound come of 4 pound of what number comes 248 pound Example The first cost him 45 pound 1 ∶ 11 of a pound then the second sort cost 67 pound 7 ∶ 11 of a pound the third sort cost 135 pound 3 ∶ 11 of a pound total is 248 pound then diuide 384 by 3 and you shall find hee had 128 yards of each sort and by Practise you shall find the first sort cost 7 shillings 1 ∶ 2 d. a yard the second sort cost 10 shillings 7 pence a yard almost the third sort cost 21 shillings 1 penny 1 ∶ 2 d. Double Position The Rule of double Position SVppose a number at pleasure as in the last Rule of single Position and proceed as if you had found the right number and if by working you find the true number then your Position was the right number which doth seldome happen First if by your working there commeth out more then the true number then note it thus + with a crosse if lesse then thus − with a long line which doth signifie lesse Secondly suppose another number greater or smaller and worke as before vntill you doe find the true number sought which if you doe not find see the difference also from the true number sought and note it with the signe + or − as it shall bee found Then thirdly set your suppositions with their errours more or lesse as in the examples following Fourthly multiply crosse the first position by the seconds errour and the second position by the errour of the first and then if the signes be both alike + or − abate the lesser from the greater and the remaines shall be the diuidend Also the lesser error abated from the greater leaues the diuisor but if the signes be contrary one + the other lesse add both together to make the diuidend and adde the two errors to make the diuisor and lastly diuide the diuidend by the diuisor and the quotient is the true number desired 1. Example A certaine man seeing a purse in his friends hand saith vnto him It seemeth vnto me that there is 100 Crownes in your purse To whom the other answered Nay quoth hee there are not 100 Crownes but saith he if they were increased 1 ∶ 2 and 1 ∶ 3 and 1 ∶ 4 and lastly one Crowne ouerplus then would they be iust 100 crownes I suppose there were 12 Crownes in his purse to which if I adde one half of 12 which is 6 and one third of 12 which is 4 and one fourth of 12 which is 3 and lastly one Crowne more the totall will be but 26 Crownes but they should be 100 Crownes so that this errour is two little by 74 Crownes which I note thus 74 − 12 Secondly I suppose he had 24 Crownes to which I adde 1 ∶ 2 of 24 which is 12 and 1 ∶ 3 which is 8 and 1 ∶ 4 which is 6 and lastly one Crowne ouerplus the totall is 51 but it should bee 100 Crownes so that this is an errour of 49 too little which I also note thus 49 − 24 The answere is that hee had 47 pound 13 ∶ 25 parts of a pound in his purse The proofe followeth 2. Example Twenty yards of Sattin and 12 shillings is equall vnto 12 yards of veluet lesse 10 shillings the price of either sort is required To answere this or any other like question take any number for the price of a yard of the lesser number which here is veluet which at 20 shillings a yard lesse 10 shillings amounteth vnto 230 shillings Now admit a yard of Sattin at 14 shillings so 20 yards and 12 shillings amounteth vnto 292 shillings from which subtract 230 shillings rests 62 s. more then the truth Againe rate a yard at 12 shillings so the 20 yards and 12 shillings makes 252 shillings from which take 230 shillings rests 22 shillings more then the truth also Now multiplying 22 by 14 and 62 by 12 the productes are 308 and 744 and the difference of those numbers is 436 then take 22 from 62 rests 40 for diuisor by which diuide the difference makes 10 shillings 9 ∶ 10 shillings for the price of a yard of Sattin Example 3. Example Otherwaies if 40 the difference of errors gaine a the difference of positions then 62 the first error yeelds 3 and 1 ∶ 10 Or if 40 yeeld 2 what 22 makes 1 and 1 ∶ 10 this taken from 12 or 3 1 ∶ 10 from 14 leaues 10 9 ∶ 10 for the price as before 4. Example A Carpenter was hired to work 20 daies at 12 pence a day but euery day that hee was idle hee was to abate 18 pence of his wages and in the end he receiued but 8 shillings now the question is how many daies he wrought First suppose he wrought 12 daies which commeth to 12 shillings then must the 8 dayes that hee played come to 12 shillings at 18 pence a day also but this question saith there came due to him 8 shillings Behold an error of 8 shillings too little Againe I say that he wrought 14 dayes amounting to 14 shillings then 6 dayes that he played at 18 pence a day commeth to 9 shillings this taken from 14 shillings leaues 5 shillings and it should bee 8 shillings which is an errour of 3 shillings too little Now multiplying 12 by 3 and 14 by 8 the products are 36. and 112 and the excesse is 76 which being diuided by 5 the difference of the errours quoteth out 15 1 ∶ 5 for the number of working dayes and 4 dayes 4 ∶ 5 for the number of playing dayes 12 − 8 5 14 − 3 Otherwayes If 5 the difference of errours yeeld 2 the difference of positions what 8 the first errour makes 3 1 ∶ 5 to be added to 12. Or if 5 be 2 what is 3 makes 1 1 ∶ 5 to be added to the second position 14 whereby all three wayes the numbers of the Dayes he wrought are found out Barter or Exchange TWo men barter one hath Ginger of 10 pence a pound ready money in barter hee will sell it for 12 pence a pound The other hath sugar of 12 pence a pound ready money but in barter hee will sell it for 14 pence a pound the Question is how much Sugar will pay for 756 pound of Ginger First put your price