The vvell spryng of sciences whiche teacheth the perfecte woorke and practise of arithmeticke, bothe in whole nombers and fractions, with suche easie and compendious instruction into the said arte, as hath not heretofore been by any sette out nor laboured. Beautified with moste necessary rules and questions, not onely profitable for marchauntes, but also for all artificers, as in the table doeth partlie appere: set forthe by Humfrey Baker citezeine of Lo[n]don.

¶ The 11 Chapiter treatteth of the Rules of barter.

TWoo Marchaunts will chaūge their marchandise, the one with the other. The one of them hath clothe of 7. s. 1. d. the yarde to selle for readie money, but in barter he wil sel it for 8. s. 4. d. The other hath Sina∣mon of 4. s. 7. d. the li. to sell for readie money. I demaunde how he shall sell it in barter to the ende he be no loser? Aunswere, saie, if 7. 1/12 (whiche is the price that the yarde of clothe is worth in readie money (be solde in barter for 8. ⅓ for what shal 4. 7/12 be solde in bar∣ter which 4. 7/12 is the price that the l. of Synamon is worth in readie money, reduce the whole numbers in to their

broken, and then multiply and diuide, and you shall finde 5. s. 4. d. ••2/1•• parts, of a penie, and for so much shall he sell the pounde of Synamon in barter.

2. Two Marchaunts will chaunge their marchaundise the one with the other, the one of them hath Chamlets of two pounde 18. s. 4. pence the péece to sell for ready money, and in barter he will sell the péece for 4 .li. 3, s. 4. d. the other hath fine cappes of 35. s. 10. d. the dossen to sell in barter. I demaund what the dosen of caps did cost in redy money? Answere: saie if 4 .li. 3. s. 4. d. whiche is the ouerprice of the péece of Chamlet, become of 2 .li. 18. s. 4. pence whiche was the iust price of the same, of what shal come 35. s. 10. d. whiche is the ouerprice of the dossen of cappes? Multiplie and deuide, and you shall finde 25. shil. 1. d. and so muche are the dossen of caps worthe in redie money.

3. Two Mharchants will chaunge their marchaundise the one with the other: the one of them hath Fustians

of 18. s. 4. d. the peece to sell for readye money, and in barter hee will sell the pece for 26. s. 8. pence. The other hath tapistrie of 15. d. the ell to sel for readie money, and in barter he will sell it for 20. pence the ell: I demaunde whiche of them gaineth, and how muche vp∣pon the hundred pounde of money?

Aunswere: saye if 18. s. ⅓ (which is the iuste price of the peece of F••itian) bee solde in barter for 16. s. ⅔: for howe muche shall 1. s. ¼ (whiche is the iuste price of the ell of Tapistry) be solde in barter? Multiplie and diuide, and you shall finde 21. d. 9/11. And he doeth ouer∣sel it but for 20. d. so that of 21. d. 9/11: bée maketh but 20. d. And therefore saye by the rule of three, yf the seconde marchaunte, of 21 9/11, do make but 20/1 how muche shall he lose vpon the 100/1? Multiplie and deuide, and you shall find 21. ⅔, the which being abated from a hundred there wil remaine 8. ⅓. And after the rate of 8. ⅓. doeth the seconde marchant lose vpon the 100. And con∣sèquently

the firste marchant, of 20. d. maketh 21. d. 9/11: and therfore say again by the rule of thre, if the first marchāt of 10/11, doe make 21. 9/11 how much shall he gaine vpon 100/1? Multiplie and di∣uide, and you shall finde 102 .li. 1/11. Thus the firste gaineth after the rate of nine pounde. 1/11 vpon the hundred pounde of money.

For your better vnderstandyng of these questions, you muste note that when one Marchante gaineth of an other after the rate of ten pound vpon the hundred pounde hee gaineth the 〈◊〉〈◊〉 of his owne principall, and the other whiche loseth after the rate of 9. 1/11 vp∣pon the hundred he loseth the 1/11 of his principal. And it may be proued thus: When one marchaunt will sell hys wares vnto an other, whiche wares stand him but in 100 .li. and he wil sel thē for 110 .li. he of his 100 .li. maketh 110 .li. wherfore he gaineth after 10. li vpon the 100. whiche is the 1/1•• of his principall, and the other whiche byeth

wares for 110 .li. that coste but 110 .li. of the 110. poūd he maketh but 100 .li. And therfore say by the rule of three, if 110. become of 100. of howe muche shall come 100? Multiplie and deuide, and you shall finde 90. 10/11, the whiche abate from 100: and there resteth 9. 1/11 whiche is the 1/11 of his principall that y^• second leseth vpon the 100. as afo•••• is saied. And therefore, who so that will know what one marchant gaineth of another, either after the rate of tenne vpon the hundred, whiche is the 1/11 of hys principall, or else after the rate of twentie vpon the hundred which is the ⅕, or of anye other parte, and that he would likewise knowe what parts the other loseth of his principall: hee muste take for the numeratour of the broken number of hym that loseth, as much as for him that gaineth, then adde the numerator and the denomi∣nator (of the broken number of hym that gaineth) both togither, and make therof the denominator of the broken

number of hym that loseth, and then shall you haue the parte of hym that loseth, as by example, of him that gai∣neth after ten pound vpon the 100 .li. which is the 1/10 of his principall: take the numerator whiche is 1. and make that the numeratoure of the broken number of hym that loseth, then adde 1. whiche is the numerator of the fra∣ction of hym that gaineth with tenne, whiche is his denominator, and you shall haue 11. for the denominatour of the fraction of hym that loseth. Then put one ouer the 11. and you shal haue 1/11. Thus it appeareth when one mar∣chaunt gaineth of an other after ten vpon the hundred, he gaineth the 1/10 of his principall, and the other loseth 9. 1/11 whiche is the 1/11 of hys principall. And if he woulde gaine after twentie vppon the hundred whiche is the ⅕ of hys principall, the other shoulde lose sixtine ⅖ whiche is the ⅙ of hys princi∣pall, and so is to bee vnderstande of al other fractions.

4. Two marchaunts wil chaunge their marchaundise the one with the other, the one of them hath Seies of 20. s. & 10. d. the peece to sel for readie moneye, and in barter he will sell the peece for 23. s. 4 d. and yet he wil gain moreouer after ten pounde vppon the hundred pounde. The other hath wol of 50. s. the hundred to sell for readye money. I demaunde how he shall sell the C. of woll in barter; Answere: say if 20. s. 10. d. whiche is the iuste price of the peece of Seye, be solde in barter for 23. s. 4. d. for how much shall 50. s. (which is the iust price of y^• C. of woll) be solde in barter? Multipliye & diuide, and you shal finde 56. s. Then for be∣cause the first marchant gaineth after 10. li vpō the C .li. he maketh of his c .li. 110 .li. and consequently the second marchant maketh of 110 .li. but 100 .l. And therefore saie, if the seconde mar∣chaunt of 110. doe make but 100 how much shal he mak of 56: Multiply and diuide & you shal finde 50. s. 20. d. 10/12 of

a penie, and for so muche shall he selle the hundred of woll in barter.

5. More, two Marchauntes wyll chaunge their marchaundise, the one with the other, the one of theim hath Taffeta, of 16 crownes the peece to sell for readie money, and in barter he will sel the peece for twenty crownes, and yet he wyll gaine moreouer after ten pounde, vpon the hundred pound. The other hath ginger of 3. s 9. d. the pounde waight, to sell in barter. I de∣maunde what the pounde did coste in readie moneye? Answere: saye if twenty crownes which is the surprice of the peece of Laffeta, become of 16. crownes the iuste price, of how muche shall come. 3. s. 9. d. whiche is the price of the ouerselling the pounde of Gin∣ger? Multiply and diuide and you shal finde 3. s. Then, for because that the Marchaunt of Laffeta will gaine af∣ter the rate of ten vppon the hundred▪ say if 100. doe giue 100. what shal 3. s. giue? Multiplie and deuide and you

shall finde thre shillinges thre pence 〈◊〉〈◊〉 and so much did the pound of Ginger coste in readite money.

6. More twoo marchauntes will thaunge their marchaundise the one with the other, the one of theim hath Worsteds of 25 shil. the péece to sel for ready money, and in barter he wil sell the péece for 33. shill. 4. pence and yet he loseth after ten vpon the hundred: the other hath waxe of 3 pound 6. shil. 8. pence the hundred to sell for readye money. I would know how he should sell his ware in barter? Aunswere: say if 25. shil. whiche is the iuste price of the peece of Worsted be solde in bar∣ter for three and thirtie shill. 4. pence, for how much shall thre pound 6. shil. 8. d. be solde, whiche is the iust price of the hundred of waxe. Multiply and di∣uide, and you shall find foure pound 4/9 whiche is eight shillinges ten pente, ⅔ then for because that the Marchaunt of Worsteds, loseth after ten vppon the hundred: Of a hundred he maketh

but sixtie. And thererefore, saie: If ninetie geue a hundred what giueth foure pounde. 4/9? Multiply and diuide, and you shall finde foure 76/81 whiche is worth eightine shillinges nine pence 5/27, and for so much shall he sell the one hundreth of Waxe in barter.

7. More, twoo Marchauntes wyll chaunge their marchaundise the one with the other, the one of them hath Worsteds of 5. pounde six shillinges, eight pence the peece to sell for readie moneye, and in barter he will sell the peece for 6. pounde, 13. shillinges. 4. d. and yet he loseth after tenne vpon the hundred, and the other hath Muske of two shillings. nine pence ⅓ the pound waight, to sell in barter? I demaunde what the pound did cost in readie mo∣ney? Answere: say if 6 pound. ⅔ whiche is the ouerprice of the peece of Wor∣sted, become of 5. pound, 1/9 whiche is the iust price of the same, of how much shall come twoo shillinges 9. pence. ⅓.

Multiplye and deuide and you shall finde 2. 2/9. whiche is twoo pence ⅔ then for because that the marchaunte of Worsteds loseth after tenne vpon the hundred, of a hundred he maketh but 90. and therfore saie if a hundred giue but 90. how muche shall 2. s. 2/9 giue? Multiply and diuide and you shal find twoo shillynges and so muche coste the pound of Muske in readie money.

Other Rules of Barter, wherein is giuen some parte in readie money.

WHen a Marchaunt ouersel∣leth hys marchaundise and he will giue also some part of hys ouerprice in readie money as in the ½ the ⅓ or the ¼ &c. He must substract the same part of money from the iuste price, and also from the ouerprice of his marchandise: and the two numbers that remaine after the substraction is made, shalbe that twoo firste numbers in the rule of three and the iuste price of the second marchant

shalbe y^• thirde, to know how much he shal ouersel the part of his marchādise

8: Two Marchaunts wil chaunge their marchaundise the one with the other the one of theim hath fine woll at fiue pounde the hundreth, to sell for readie moneye, and in barter hee will sell it for sixe pounde, and yet hee will haue the ••/3 in readye money. The other hath clothe of 13. shillinges four pence to sel for ready money. I would knowe howe he shall sell the same in barter? Aunswere: take the ⅓ of 6 .li. whiche is the ouerprice of the 100. of wolle, and you shall haue 2. pound the whiche abate from 5 .li. whiche is the iust price of the 100. of woll and from 6 .li. which is the ouerprice, and there shal rest 3 .l. and 4 .l. for the 2 first num¦bers in the rule of thrée, then take 1••. s. 4. d. whiche is the iust price of a yarde of clothe for the thirde number: Then multiplie and deuide and you shall finde 17. shill. 9. d. ⅓. for so muche shall the seconde selle his clothe in barter.

9. More, twoo Marchauntes will chaunge their marchaundise the one with the other, the one of them hath waxe of thrée pound. 6. s. 8. d the C. to sell for readie money, and in barter he will sell the same for 4 .li. 3. s. 4. d. and yet he will haue the ¼ in ready money, and the other hath fine Crimson sat∣tine of 15. s. the yarde to sell in barter. I demaund what it is worth in ready money. Aunswere. Take the ¼ of 4 .li. 3. s. 4. d. and abate it from 4 .li. 3. s. 4. d. and from thrée pounde 6. s. 8. pencs, and there resteth 3 .li. 2. s. 6. d. and 2 .li. 5. shillinges 10. pence for the two first numbers in the rule of thrée, and 15. s for the thirde number whiche is the ouerprice of the yard of sattine. Then multiply and diuide, and you shal find 11. shillinges. And soe muche did the yarde of sattine cost in readie money.

10. Two Marchants will chaunge their marchandise the one with the o∣ther, the one of them hath tinne of 50. shillings the hundred to sell for ready

money, and in barter he wil sell it for three pounde 6. s. 8. d and he wil gaine after ten vppon the hundred, and yet he wil haue the one half in readie mo∣ney: and the other hath leade of 3. half∣pence the li. to sell for readie money. I demaund how he shall sell the pounde in barter? Aunswere: See first at tenne vpon the hundred, what the thre poūd ⅓ will come vnto, and you shall finde that they will come to 3 .li. ⅔, which is 13. s. 4. d. of the which, the halfe which he demaundeth in readie money, is 36 shillinges and 8. pence the whiche be∣yng abated from fiftie shillinges, and also from three pounde 13. shillinges four pence, there shal rest 13. shillings foure pence, and one pound sixtine. s. eight pence, for the twoo first numbers in the rule of three, whiche you muste put al into halfepence, and thre halfe∣pence for the thirde number, and then multiplye and diuide, and you shall finde 4. pence ⅛, and for so muche shall hée sell the pounde of leade in barter.

11. More twoo marchauntes will chaunge their marchaundise the one with the other, the one of theim hath steele of 16. s. 8. d. the hundred waight to sell for readie money, and in barter he wil sell it for 25. s. and yet he loseth after tenne vpon the hundred, but hee will haue the ½ in readie moneye, the other hath yron of 6. shill. 8. pence the dundred to sell in barter, I demaunde what it did coste in readye money?

Aunswere: saie if a hundred come but to 90. how muche shall 25. s. come to? Multiplie and deuide, and you shall finde 22. s. 6. d. of the whiche number, take ½ which is 11. s. 3. d. and substract it from 22. s. 6. d. and from 16. s. 8. d. and there shall rest 11 s. 3. d. and 5. s. 5. pence for the two first numbers in the rule of thrée, and 6. shil. 8. pence which is the ouerprice of a hundred of yron for the thirde number, then multiplie and deuide, and you shall finde. 3. s. 2. pence, ½4/7: and so muche did the hun∣of yron coste in readie moneye.

12. More, twoo marchauntes wyll chaunge their marchaundise, the one with the other, the one of them hath sayes of 200 shill. 10 d. the pece to sell for ready money, and in barter he wil sell the pece for 21 shillings, and he wyll haue the ¼ in readie money: The other hath cappes of 35 shill. the dosen to tell for readye money: but he wyll gayne after 10 vppon the 100. I de∣maunde howe he shall sell the same cappes in barter? Aunswere, saye, if 100 be worthe 110: What shall 35. shill. be worthe, which is the iust price of the dosen of cappes? Multiplye and diuide, and you shall fynd 38 shill. 6. d. Then take the ¼ of 25. whiche is 6 sh. 3. d. and substracte it from 20 shill. 10. d. and from 25. sh. and there shall rest 14 sh. 7. d. & 18 shill. 9. d. for the two firste numbers in the rule of three, and 38 shill. 6. d. whiche is the iuste price with his gaine of the dosen of cappes, for the thyrd nomber: then multiplie and diuide, and you shall finde 49.

shill. 6. d. and for so muche shall he sell the dosen of cappes in barter.