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.

¶ Example.

1. Twoo Marchauntes haue made companie together, the firste laied in fiue hundred pounde. The second put in three hundred pounde, and with oc∣cupiyng thei haue gained. 64. pound: I demaunde how muche eche mā shal haue of thesame gaines, accordyng to

the money that he laied in. Aunswere: Adde. 500. and. 300. bothe together, which are the percelles that thei laied in, and thereof commeth. 800. for your diuisor: then saie by the rule of three, if 300 .li. (whiche is their stocke) do gain 64 .li. what shall. 500 .li. gain? (which is the first mānes money that he laied in) multiplie and deuide, and you shal finde. 40 .li. for the first mans parte of the gaine: then saye if. 800. giue. 64. what will. 300. giue? Multiply and di∣uide, and you shall finde 24 .li. for the seconde mannes parte of the gaine. 〈 math 〉〈 math 〉

Or otherwise, put 500 .li. which is the first mans money that he laied in, ouer the 800 li. whiche is the whole, stocke, and you shal haue 509/800 which be∣ing abbreuiated, do make ⅝, and suche part of the gain shal the first mā take, that is to say ⅝ of 64 .li. which is 40 .li.

And consequentlie, by the same man∣ner, the seconde shal take the ⅜ of 64. which is 24. pound for his part of the gaine as before. 〈 math 〉〈 math 〉

2. Twoo Marchauntes haue com∣painied together, the first put in 640 .li. and he taketh ⅝ partes of the gaine. I demaunde what the seconde Mar∣chaunte layed in? Aunswere. Seeyng that the first Marchaunt taketh ⅝ of the gaine, it followeth that the second must haue ⅜ which is the rest, and ther fore saie by the rule of thrée, if ⅝ of the gaine, whiche the first manne taketh, did saie into the stocke 〈◊〉〈◊〉. How muche shall the ⅜ of the gaine laie in, whiche is the seconde mannes gaine? Multi∣tiplie and diuide, and you shall finde 384. pounde, so muche ought the se∣conde man to laie into companie.

3. Twoo Marchauntes haue com∣panied together, the first manne laied in. 640. pounde, and the seconde hath

laied in so muche, that he muste haue 60. pounde for his part of. 100. pounde whiche thei haue gained. I demaunde howe muche the seconde man did laie into companie? Answere: seyng that the seconde man taketh. 60. pounde of the gaine: it followeth that the firste must haue but. 40. pounde. Therfore saie by the rule of. 3. if. 40. pounde doe laie in. 640. pounde, what shall. 60. pounde laie in? Multiplie and diuide, and you shall finde. 260 .li. so muche did the seconde Marchaunt laie in.

4. Twoo Marchauntes haue com∣panied together, the firste laied in. 83. pounde 6. shillinges. 8: pence, the se∣conde put in. 170. duckettes: and thei haue gained 100. li of y^t which the first man must haue 60 pounde. I demaūd what the ducket was worth? Answer seyng that the first man must haue 60 pounde, it followeth that the seconde muste haue. 40. pounde, therefore saie by the rule of three, if. 60. pounde of gaine that the first man taketh did lay

in. 83 .li. 6 s. 8. pence of principall, how muche shall. 40 .li. of gain put it, mul∣plie and diuide, and you shall finde 55 .li. 5/9: so muche are the 170. duckets worth. Then put 55 .li. 5/9 into shillings and you shall haue 1111. s. 5/9 then to knowe what the ducket is worth, saie by the rule of thrée, if a 〈◊〉〈◊〉 giue 1111. 〈◊〉〈◊〉, what will 〈◊〉〈◊〉 giue? Multiplie and de∣uide, and you shall finde 6. s. 6. d. 12/51, so muche is the ducket worth.

5. Twoo Marchauntes haue com∣panied together, the second man laied in more by 30. poundes then did the firste man: and they gained 120. poun∣des of the whiche the firste man ought to haue 50. pounds. I demaund what eche of thē did laie in. Aunsware, from 120. pound abate 50. pounde and ther resteth 70. pound for the second mans parte: so that by thys meanes the se∣conde manne (because he laide in 30. pound more then the first man did) ta∣keth 20 .l. more of the gain: & therfore say by the rule of 3. if 20 .li. of gaine

did laie in. 30. pounde of principall, how muche shall. 50. pounde laie in Multiplie and diuide, and you shall finde. 75. pounde, so muche did the first man laie in, and consequently the se∣conde laied in. 105. pounde.

6. Twoo Marchauntes haue com∣panied together, the second hath laied in twise so muche as the first man did, and. 10. pounde more: and thei gained 100. pounde, of the whiche, the firste ought to haue. 32. pounde for his part: I demaunde how muche eche of them did laie into companie? Answere. If it were not for the. 10. pound that the se∣conde manne laied in more: he should haue had but. 64. pounde of the gaine, which is the double of the first mānes parte. But because he laied in. 10 .li. more, he hath ••ower pounde more of the gaine, and therfore saie by the rule of. 3. if. 4. pound of gaine did laie in 10 pound of principall (whiche was ouer and aboue the double of the first man¦nes laiyng in) what shall 32 .li. of gai∣nes

laie in? whiche is the first mannes part of the gaines that he taketh. Mul¦tiplie and diuide, and you shall finde 80 .li. for the firste mannes laiyng in: and consequently. 170. pounde for the second mannes portion that he laid in.

4. Twoo Marchauntes haue com∣panied together, and thei haue gained 100. pound of the which the first must haue after the rate of 10 vpon the 100 pound, and the second must haue after the rate of 15 pound vpon the 100 .li. I demaunde howe muche eche of theim ought to haue? Answere. But 10 .li. for the first mannes laiyng in, and. 15 li. for the second mannes laiyng in Adde 10 .li. and. 15. pound together, and thei make 25. pound. Then put 10. ouer 25 and it is 10/25, whiche beyng abreuiated are ⅖. Therefore he that taketh 10 li. vpon the 100. it must haue the 2/•• of the gaine, whiche is 40 .li. Then put. 1••. ouer 25. and it is 15/25, which being abre∣uiated are 3/••. Therfore the second must haue 3/•• of the 100 .li. which is. 60 .li.

8. Twoo Marchautes haue com∣panied together, the first laied in 46 .li. 18. shilling. and the seconde laied in 33. pounde 2. s. so thei haue gained 30. pound. I demaunde how much euerie man shal haue for his part of the gain Answere: Adde 46. pound 18. shilling and 33. pound 2. shilling both togither and you shall finde 80. pound for your common diuisor: then saie if 80. pound which is all their stocke do gain 30 .li. what wil 46. 6/10 gaine, whiche is the firste mans laiyng in: Multiplie and deuide, and you shall finde 17. pounde 11. shillyng 9. pence for the firste mans part of the gaine. Then saie again, if 80. pound do gain 30. pound what wil 33. pound 1/10 gain, whiche was the se∣conde mans laiyng in: multiplie & de∣uide, and you shall finde 12 .li. 8. s. 3. d. for the seconde mans part of the gain.

And after the same maner shal you doe, in case there were three or foure Marchauntes that woulde companie together: Addyng al their summes of

money (which thei lay into the stocke) into one totall summe: whiche shal be your common deuisor: and then work with the reste, as is taught in the for∣mer questions of the rule of company.

9. Three Marchautes haue compa∣nied togither, the first laide in I know not how muche: the seconde did put in 20. peeces of clothe, and the thirde hath laide 500. pounde. So at the ende of their companie, their gaines amoun∣ted vnto a thousande pounde, wherof the firste manne ought to haue 350. pounde, and the seconde muste haue foure hundred pounde.

Now I demaunde how muche the first man did laye in, and for how mu∣che the twentie péeces of clothe were put into companie?

Aunswere.

Seeyng that the fyrste and the se∣conde Marchautes must haue 750 .li. for their partes of the gain. Then the thirde manne muste haue the reste of the thousande pound which is 250 .li.

And theerfore saie by the rule of. 3. 〈◊〉〈◊〉 250. of gaine, be come of 500. pound of principall: of how muche shall come 350 pounde of gaine? whiche the firste man taketh, multiplie and diuide, and you shall finde 700. pound. So muche did the first mā laie in then saie if. 250 pound of gaine be come of. 500. pound of principall, of how muche will come 400. pounde, whiche is the gain that the second man taketh. Multiplie and diuide, and you shal finde. 800. pound For so muche were the. 20. peeces of clothe laied into companie.

10. Three Marchauntes haue gai∣ned. 100 .li. the firste must haue the ½, the seconde must haue ⅓: and the third must haue ¼. I demaunde how muche euery manne must haue of the gaine? Answere: reduce ½, ⅓, ¼, into a commō denomination, after the order of the second reduction in fractions, and you shall finde 12/24, for the ½, 8/24, for the ½: and 6/••••, for the ¼: Then take twelue for the firste mannes laiyng in, 8. for the se∣cond

mannes laying in: and 6 for the thirde mannes laying in. The whiche three nombers beinge added together shall be your common diuisor, whiche do make 25. Then multiply 100 by 12 for the firste man, by 8, for the second man, and by 6 for the third man. And diuide euery multiplication by 26. So shall you fynde 46 li. 2/13 for the fyrste mannes part of the gaine. 30 .li. 10/13 for the second mannes parte: and 23 li. 1/1••0 for the third mannes parte.

11. Two marchauntes haue gained 100 li. the firste muste haue ½ and 5 li. more: the second must haue ⅓ and 4 li. more: I demaunde howe muche ethe of them shall haue? Aunswere, From 100 abate 5 and 4. so ther wil remain 91. then take the ½ of 100 l. which is 50 li. for the first mans laying in: Like∣wise, take ⅓ of 100 li. for the seconde mans laying in, which is 33 li. ⅓. Then adde 50 li. and 33 li. ⅓ togither, and you shall haue 83 li. ⅓ for youre com∣mon

diuisor, then multiply 91. pound by 50. and diuide by 83. ⅓: and thereof cōmeth 54 pound, ⅗ vnto the whiche nomber adde 5, and all is 59 .li. ⅗ for y^e first mans part. Likewise multiplye. 91. by 33. ⅓: and diuide by 83. ⅓: and you shal finde 36 li. ⅖ vnto the which adde 4: and you shal haue fourty pound, 〈◊〉〈◊〉 for the seconde mans part.

12. Two Marchauntes haue gay∣ned a hundred pound, the firste muste haue the ½ lesse by 4 pound, the second must haue ⅓: lesse by 2 pounde. I de∣maund how much eche of them shall haue? Answere, Adde 4 & 2. with 100. & they make 106. Thē take as before is saide ••0 pounde, for the first man, & 33. ⅓ for the seconde, adde them bothe togither, & they be 83. ⅓ whiche shalbe your diuisor. Then multiplie 106. by 50. and diuide the product by 83 ⅓, so thereof commeth 63 .li. ⅗. From the whiche abate the foure pounde lesse y^t the fyrste mā taketh, and then is there remaining 59. pounde, ⅗ for his parte.

Likewise multiplie 106 by 33. ⅓ and diuide by 83⅓ & you shall finde 42 .li. ⅖: from the which abate 2 .li. lesse and there remaineth 40. pounde, ⅖ for the seconde mans part.