The welspring of sciences, which teacheth the perfecte worke and practise of arithmeticke both in vvhole numbers & fractions, with such easie and compendious instruction into the saide art, as hath not heretofore been by any set out nor laboured, : Beautified vvith most necessary rules and questions, not onely profitable for marchauntes, but also for all artificers, as in the table doth plainely appere..

¶The tenth Chapter treateth of the rule of Fellowship, wyth∣out any time limited.

THe rule of felowship is thus: you must set down eche mās summe of money that he lai∣eth into company,* 1.1 euery one directly vnder the other, y^e which you shall adde altogither, & the totall sum of all their whole stocke beyng thus assembled, shalbe your common diui∣sor, to the finding out of euery mans part of y^e gaine. Then shall you mul∣tiplye the gaine, or the losse, by eche mans portion of money that he layde in, & diuide the products by the sayde diuisor: so shal you haue in your quo∣tient euery mans part of the gaine, or else of the losse, if any thing be lost.

¶Example

1. Twoo Marchaunts haue made companye togither, the first laide in 500. li. The seconde put in 300. li. and w^t occupying thei haue gained 64. li. I demaunde how much eche mā shal haue of the same gaines according to the money that he laide in. Aunswere: Adde 500. & 300. both togither, which

are the percels that they laide in, and therof commeth 800. for your diuisor: then say by the rule of three, if 800. li. (which is their stock) do gaine 64. li. what shal 500. li. gaine? (which is the fyrst mans money that hee laied in) multiplie & diuide and you shall finde 40. li. for the firste mans parte of the gaine: then say if 800. giue 64. what will 300. giue? Multiplye and diuide, and you shal finde 24. li. for y^e seconde mans part of the gaine.

500
300	800	64	500.
800
	800	64	300.

Or otherwise, put 500. li. which is the fyrst mans money y^t hee layed in, ouer the 800. li. which is the whole, stocke, and you shall haue 500/800 which being abbreuiated, do make ⅝, & such part of the gaine shal y^e fyrst mā take, y^t is to say ⅝ of 64. li. which is 40. li.

And consequentlye, by the same ma∣ner, the seconde shal take the ⅜ of 64. which is 24. pound for his part of the gaine as before.

5	00	3	00
8	00	8	00

2. Twoo Marchaunts haue com∣panied togither, y^e fyrst put in 640. li. and he taketh ⅝ partes of the gaine. I demaunde what the seconde Mar∣chaunt layed in? Aunswere, Seing that the fyrst Marchaunt taketh ⅝ of the gaine, it followeth that y^e seconde must haue ⅜ which is the rest, & ther∣fore say by the rule of three, if ⅝ of the gaine, which the fyrste man taketh, did lay into the stock 640/1. How much shall the ⅜ of the gaine laye in, which is the seconde mans gaine? Multi∣ply and diuide, & you shall find 384. li. so much ought the second man to lay into company.

3. Twoo Marchauntes haue com∣panied

togither, the fyrst man layed in 640. li. and y^e seconde hath layed in so much, that he must haue 60. li. for his part of 100. li. which thei haue gai∣ned. I demaunde howe much the se∣conde man did laye into companye? Aunswere: seing that the second man taketh 60. li. of the gaine, it followeth y^t the fyrst must haue but 40. pounde. Therefore say by the rule of three, if 40. li. do lay in 640. li. what shal 60. li lay in? Multiply and diuide, and you shall finde 960. pounde, so much did the seconde marchaunt lay in.

4. Two marchaunts haue com∣panied togither, the first laide in 83. li. 6.s. 8.d. y^e seconde put in 170. duckets: & thei haue gained 100. li. of the which the fyrst man muste haue 60. li. I de∣maund what the ducket was worth? Answere, seing that the first mā must haue 60. li. it followeth y^t the seconde must haue 40. li. therefore say by the rule of thre if 60. li. of gaine y^t the first

man taketh did lay in 83. li. 6.s. 8.d. of principall, howe much shall 40. li. of gaine put in, multiplye & diuide, and shall find 55. li. 5/9: so much are the 170. duckets worth. Then put 55. li. 5/9 into shillings, and you shall haue 1111.s. 1/9 thē to know what y^e ducket is worth, saye by the rule of three, if a 170/1 gyue 1111. 1/9, what will 1/1 giue? Multiplye and diuide, & you shall fynde 6.s. 6.d. 22/51, so much is the ducket worth.

5. Two Marchauntes haue com∣panied togither, the seconde mā laide in more by 30. li. than did the first mā: and they gained 120. li. of the which y^e first man ought to haue 50. li. I de∣maund what eche of them did lay in. Answere, from 120. li. abate 50. li. and there resteth 70. li. for y^e second mans part: so that by this meanes y^e seconde mā (bicause he laide in 30. li. more thā the first man did) taketh 20. li. more of y^e gaine: & therfore say by y^e rule of 3. if 20. li. of gaine did lay in 30. li. of prin∣cipall, how much shall 50. li. lay in?

Multiplye and diuide, and you shall finde 75. li. so much did the firste man lay in, and consequentlye the seconde layd in 105 li.

6. Two marchaunts haue compa∣nied togither, the second hath layd in twise so muche as the firste man dyd, and 10 li. more: and they gayned 100 li. of the which, the firste ought to haue 32 li. for his part: I demaūd how much eche of them dyd lay into company?

Answere, If it were not for the 10 li. that the second man layd in more: he should haue had but 64 li. of the gain which is the double of the first mans parte. But bicause he layd in 10 li. more, hee hath foure pounde more of the gayne, and therefore saye by the rule of three, if 4 li. of gayne did laye in 10 li. of principall, (which was ouer and aboue the double of the first mā∣nes laying in) what shall 32 li. of gay∣nes lay in? which is the firste mannes parte of the gaynes that hee taketh.

Multiplye and diuide, and you shall finde 80 li. for the first mannes laying in: and consequently 170 li. for the se∣cond mans portion that he layed in.

7. Two marchaunts haue compa∣nied togither, and they haue gayned 100 li. of the which the first must haue after the rate of 10 vpon the 100 li. and the second must haue after the rate of 15 li. vpon the 100 li. I demaunde how muche eche of them oughte to haue? Aunswere, Put 10 li. for the fyrst mans laying in, and 15 li. for the second mā∣nes laying in. Adde 10 li. and 15 li. togi∣ther, and they make 25 li. Then put 10 ouer 25. and it is 10/25 which being abbre¦uiated are ⅖. Therfore he that taketh 10 li. vpon the 100 li. must haue the ⅖ of the gayne, which is 40 li. Then put 15 ouer 25. and it is 15/25 which being ab∣breuiated are ⅕. Therefore the second must haue ⅗ of the 100 li. which is 60 li.

8. Twoo Marchauntes haue com∣panied

togither, y^e fyrst laide in 46. li. 18.s. and the seconde laide in 33. li.2.s. so they haue gained 30. li. I demaund how much euery man shall haue for his part of the gaine? Answere: Adde 46. li. 18.s. and 33. li.2.s. both togither and you shall finde 80. li. for your cō∣mon diuisor: then say if 80. li. which is all their stocke do gaine 30. li. what will 46.9/10 gaine, which is the fyrste mans laying in: Multiplie & diuide, and you shall finde 17. li. 11.s. 9.d. for the first mans part of the gaine. Thē say again, if 80. li. do gaine 30. li. what will 33. li. 1/10 gaine, which was the se∣conde mans, laying in: multiply and diuide, and you shall fynde 12. li. 8.s. 3.d. for the seconde mans part of the gaine.

And after the same maner shall you doe, in case there were three or foure Marchaunts that would com∣panye togither: Adding all theyre summes of money (which they laye into the stock) into one total summe:

which shalbe your common Diuisor: and then worke with the rest, as is taught in the former Questions of y^e rule of companie.

9. Three Marchaunts haue com∣panied togither, the first laide in I know not how much: the seconde did put in 20. peeces of cloth, and y^e thirde hath layde 500. pounde. So at y^e ende of their cōpany, their gaines amoun∣ted vnto a thousand pounde, wherof y^e fyrst man ought to haue 350. pound, and the seconde must haue foure hū∣dred pounde.

Now I demaunde how much the first mā did lay in, and for how much the 20. peeces of clothe were put into company?

Aunswere.

Seing that the fyrste and the se∣conde marchaunts must haue 750. li. for their parts of the gaine. Then the thirde man must haue the rest of the thousande pound which is 250. li.

And therefore say by the rule of thre, if 250. of gaine, become of 500. li. of principall: of howe much shall come 350. li. of gaine? which the fyrst man taketh, multiplye and diuide and you shall finde 700. li. So muche did the first man laye in: then say if 250. li. of gaine be come of 500. li. principall, of howe much will come 400. li. which is the gaine y^t the seconde mā taketh. Multiply and diuide, & you shal finde 800. li. For so much were y^e 20. peeces of cloth layde into company.

10. Three Marchaunts haue gai∣ned 100. li. the fyrst muste haue the ½, the seconde must haue ⅓: And y^e third must haue ¼. I demaund how much euerye man must haue of the gaine? Aunswere, Reduce ½, ⅓, ¼, into a cōmon denominatiō, after the order of the second reduction in fractions, & you shall finde 12/24, for the ½: 8/24, for the ⅓: and 6/24, for the ¼: Then take 12 for y^e first mans laying in, 8. for y^e se∣cond

mannes laying in: and 6 for the thirde mannes laying in. The which three numbers being added together shall be your common diuisor, which do make 26. 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 finde 46 li. 2/13 for the fyrste mannes part of the gaine. 30. li. 10/13 for the second mannes parte: and 23 li. 1/13, for the third mannes parte.

11. Two marchaunts haue gayned 100 li. the firste muste haue ½ and 5 li. more: the second must haue ⅓ and 4 li more: I demaunde how muche eche of them shall haue? Aunswere, From 100 abate 5 and 4. so ther wil remayn 91. then take the ½ of 100. li. which is 50 li. for the first mans laying in: Like∣wyse, 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 which number adde 5, and all is 59. li. ⅗ for y^e first mans part. Likewyse multiplye. 91. by 33. ⅓: and diuide by 83. ⅓, & you shal finde 36. li. ⅖ vnto the which adde 4: and you shal haue fourty pound, ⅖ for the seconde mans part.

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

Likewise multiplie 106. by 33. ⅓ and diuide by 83 ⅓ & you shall finde 42. li. ⅖: from the which abate 2. li. lesse and there remaineth 40. pounde, ⅖ for the seconde mans part.

¶The Rule of Felowship with time.

THe money that euery mā lai∣eth in, must be multiplied by the time that it remaineth in company: and of that which commeth therof you shal make their new layings in for eche of them: and then multiplye the gaines by euery one of them seuerally, the which you shall diuide by all their new layings in added togither, and you shall haue proporcionally eche mans part of the gaine according to his laying in.

¶Example.

1. Two Marchaunts haue compa∣nied togither, the first hath put in the fyrst of Ianuary 450. pounde, the se∣cond did lay in y^e 2. of May. 750. pound

And at the yeres ende, they had gay∣ned 100 li. I demaunde howe muche eche of them shall haue of the gayne? Answere: forasmuche as the firste dyd put 450 li. the fyrste of Ianuary: hys money remained in company 12. mo∣nethes, and therefore multiply 450. by 12 monethes, and therof commeth 5400. for his newe laying in. And the seconde layed in his 750 li. but at the first daye of Maye: so that his money remayned in companye but 8 mone∣thes. Therefore multiplye his 750 li. by 8. and therof commeth 6000 for hys new laying in: Then adde 5400. with 6000. and they make 11400 for youre common diuisor: Then multiply 100 li. which is the gaynes by 5400, and diuide the product by 11400. and ther∣of commeth 48 li. 7/19 for the first man∣nes part of the gayne. Likewise mul∣tiplye 100. by 6000, and diuide the pro∣ducte by 11400. and you shal finde 52 12/19 & so much must the second man haue for his parte of the gayne.

2. Two marchaunts haue compa∣nied togither, the first hath put in the first of Ianuary 640. li. The seconde can lay in nothing vntil the first of A∣prill. I demaunde how much he shall then laye in, to the ende that he maye take halfe the gaynes? Answere, Mul∣tiply 640 li. by 12. monethes that his money abideth in the companye, and therof cōmeth 7680 li. for his laying in. And so muche oughte the seconde mannes laying in to be, for bycause he taketh ½ of the gaine: But for that, that he putteth in nothing vntill the first of Aprill, his money can be in cō∣pany no lōger than 9 monethes. And therefore diuide 8680 by 9, and ther∣of commeth 753 li. ⅓ So much ought the seconde marchaunt to laye in the first of Aprill, to the ende that he may take the one moyty of the gaynes.

3. Three Marchauntes haue com∣panied togither, the firste layed in the firste of Marche 100 li. The se∣conde

laide in y^e first of Iune so much money, that of the gaine, hee must haue the ⅓ parte: and the thirde laide in y^e fyrst of Nouember so much mo∣ney, that of the gaines he must haue likewise ⅓ and thei continued in com∣pany, vntil y^e next Marche folowing. I demaunde howe much the seconde and the thirde Marchaunts did laye in? Answere, Multiply 100. which the firste man did lay in, by 12. monethes that his money continued in compa∣nie, and therof commeth 1200. for hys laying in: and so much ought the se∣conde and the thirde marchaunt eche of them to lay in: Bicause they parte the gaynes by thyrdes. But for that, that the seconde Marchaunt putteth in nothing tyll the fyrst of Iune, hys money can bee in companye but nine monethes. Therefore diuide 1200. by nine monethes, and therof commeth 133. ⅓. And so much ought the seconde Marchaunt to laye in: Then, foras∣much as the thirde Marchaunt, dyd

laye in nothing vntil the fyrst of No∣uember: His money abideth in com∣panye but the space of foure mone∣thes. Therefore diuide 1200. by 4. and thereof commeth three hundred pounde. And so much ought the third marchaunt to lay into companye.

4. Three marchauntes haue com∣panied togither, the fyrste layde in the fyrst of Ianuary a hundred Duc∣kettes. The seconde hath layed in fyftie pounde, the fyrste of Marche: And the thyrde put in a Iewell the fyrste of Iulye: And at the yeares ende, they had gained foure hundred crownes: of the which, the fyrste marchaunt must haue fifty crownes, and the seconde muste haue 80. I de∣maunde what y^e Ducket was worth, and at what price the Iewell was valued, whych the thyrde Marchaūt layde in?

Aunswere: the firste mannes money is 1200 as afore is sayde, and hee ta∣keth 50 crownes of the gayne: there∣fore say, if fifty crownes of gayne be come of 1200, which was his stock, of how muche shal come 80. crownes of gaine that the seconde man taketh? multiplye and diuide, and you shall finde 1920. for the second marchaunts laying in. Then say again, if 50 crow∣nes bee come of 1200. stocke: of howe much shal come 270. crownes, which the thirde man taketh of the gayne? Multiply and diuide, & you shall finde 6480. for the third marchauntes lay∣ing in. Then diuide 1920, whiche is the seconde mannes laying in, by 10. monethes that his money did conti∣nue in company, and you shall finde 192 Duckets, which are worth 50. li. bicause he layed in 50 li. Then diuide 192 Duckets by the sayde 50. li. (being reduced into shillinges) and thereof commeth 5. shillings 2. pence, ½. So muche was the Ducket worth: Fi∣nallye,

diuide 6480. (which is the third mannes laying in) by 6. mone∣thes that his Iewell remained in cō∣panye, and you shall finde 1080 Duc∣kets: and for that price was y^e Iewell put into company.

5. Three Marchauntes haue com∣panied togither: the first layed in the first of Ianuary 100 li. and the firste of Aprill he hath taken backe againe 20. li. The second hath layed in the firste of Marche 60 li. and afterward he dyd put in more 100 li. the first of August. The third layd in the first of Iuly 150 li. And the first of October he did take backe agayne 50 li. And at the yeres end, they found that they had gained 160 li. I demaunde how muche euery man shall haue? Answere, Multiply 100 li. which the first man layed, by 12 monethes, and therof commeth 1200. li. from that number abate 9 times 20 which are 180. and there wil remaine 1020. for the first mans laying in. Thē

multiplie 60. which the seconde man layde in, by ten & you shall haue 600. vnto the which adde 5. times one hū∣dred, which are 500. so all amounteth to 1100. for the second mans laying in: Afterwardes, multiplie 150. pounde, which the thirde man hath layed in, by 6. monethes, and therof commeth 900. from y^e which number abate thre times 50. and they are 150: so there resteth 750. for the thirde mans lay∣ing in. Then procede with the reste, as in the first Question of the rule of felowship with tyme, in adding 1020, 1100. and 750. altogither, which shall be your Diuisor: Then multiply 160 by 1020. by 1100. and by 750, & diuide at euery time by your Diuisor, which is by all theyr layings in added togi∣ther, and they make 2870, so you shall fynde 56. 248/287: for the fyrst man, 61. 93/287 for the seconde, and 41. 233/287 for the thirde man.

6. Two Marchaunts haue compa∣nied

togither, the firste hath put in 960. pounde, for the space of 12. mon∣thes, and he ought to haue 8. pounde vpon the hundred pounde of y^e gaine. The seconde hath layed in 1120. li. for y^e space of eight monethes, & he ought to haue after 12. pounde vpon the 100. pound of the gaine.

And at the yeres ende, they haue gained eyght hundred pounde. I de∣maunde how much eche of them shal haue of the gaine. Answere, multiplie 960. that the first mā did lay in, by 12. monethes, and the product thereof, multiplie againe by 8. and you shall haue 92160. for the fyrst mans laying in: then multiplye the 1120. that the second hath layed in by eyght mone∣thes, and that which commeth therof you shall multiplie againe by 12. and you shall finde 107520. for the seconde mans laying in: Then proceede with the rest, as in the first Question of the Rule of Felowshippe, and as in the laste Exaumple, and you shall

finde 399 3/13 for the first man: and 430. li. 10/13 for the second man.

¶ The rule of company, be∣twene Marchaunts and their Factours.

7. The estimation of the bodye or persone of a Factour, is in suche pro∣portion to the stocke, which the Mar∣chaunt layeth in: as the gayne of the sayd Factour is vnto the gayne of the sayd Marchaunt. As thus: if a Mar∣chaunt do put into the handes of hys Factour 200 li. to employe, and he to haue halfe the profite, the persone of the sayd Factour shal be esteemed 200 li, And if the Factour do take but the ⅓ of the gaine, he should haue but ½ so much of the gaine as the Marchaunt taketh, which should take ⅔ wherfore the persone of the Factour is estemed but the ½ of that which the Marchant layeth in, that is to say 100 li.

And if the Factour did take the ⅖ of the gayne, then the Marchaunt shall take the residue, which are ⅗ of y^e gain wherefore the gayne of the Mayster vnto that of the Factoure is in suche proportion as 3 vnto 2. Then if you will knowe the estimation of the per∣sone of the Factour, say if 3 giue me 2 what wil 200 giue? Multiplie 200 by 2 and diuide by 3 so you shall finde 133 ⅓ Otherwise, consider that the Fac∣toure taketh the ⅔ of that whiche the Marchaunte taketh. And therefore take the ⅔ of 200, and you shall fynde 133 ⅓ as before: and so much is the per∣sone of the Factoure esteemed to bee worth.

8. And if the Marchaunt should de∣liuer vnto his Factoure 200. li. and the Factour would laye in 40 li. and his person, to the ende he might haue the halfe of the gain: I demaund for how much shal his person be estemed Ans. abate 40 li. from 200 li. and ther

will remaine 160. li. And at so much shall his person be estemed.

And if the factour woulde take the ⅔ of the gaine, his person with his 40 pounde, shall bee estemed twise as much as the stock that the marchant layeth in, which shoulde haue but ⅓ of the gaine: for ⅔ vnto ⅓, is in double proportion. Therefore double two hundred pounde, therof cōmeth 400. li. from the which abate 40. li. & there will remaine 360. li. And if the Fac∣tour would take but the ⅓ of y^e gaine, that shall bee but the ½ of ⅔ which the marchaunt taketh: then the estima∣tion of his person, with his laying in should be estemed but the halfe of y^e which the marchaunt layeth in: take therfore the ½ of 200. li. which is 100. li. from the which abate fourty pounde, and the rest which is 60. li. is the esti∣mation of his person.

9. If it so chaunce that for to make traffick of 240. li. the person of y^e fac∣tour should be so estemed, y^t he shuld

haue but the ¼ of the gaine, & yet hee would haue the ⅔, I demaunde how much he shoulde put in of ready mo∣ney, besides hys person? Aunswere, seing that his person gaineth the ¼, al the whole laying in, shall gaine the rest that is to saye the ¾: nowe for bi∣cause ¼ is the ⅓ of ¾ therfore his person shalbe estemed the ⅓ of all the laying in. Take then the ⅓ of 240. and you shall haue 80. for the estimation of his person, and for that, that he wil haue the halfe of y^e gaine, you shal adde 80. with 240. li. and therof commeth 320. of the which take the halfe, which is 160. and from the same you shal abate the 80. and there wyll remaine other 80. which he ought to lay in of readye money, and the marchaunt must lay in the ouerplus, which amounteth to 160. li.

10. A marchaunt hath deliuered to his Factour 1200. li. to gouerne them in the trade of Marchādise vpon such condition that hee for hys seruice

shal haue the ⅓ of y^e gaine if any thing be gayned, or of the losse if any thing be lost: I demaund for how much hys person was estemed? Answere, seeing that the Factoure taketh the ⅓ of the gain, hys persone ought to bee estee∣med as muche as ½ of the stock which the Marchaunte layeth in, that is to say the ½ of 1200 li. which is 600 li. The reason is, bycause the ⅓ of the gayne that the Factoure taketh, is the ½ of the ⅔ of the gaine that the Marchaunt taketh.

11. A Marchaunt hath deliuered vn∣to his Factour 1200 li. and y^e Factour layeth in 500 li. and his person: Now, bicause he laieth in 500 li. and his per∣sone, it is agreed betwene them that he shal take the ⅖ of y^e gayn: I demaūd for how much his persone was estee∣med? Aunswere, Forasmuch as the Factour taketh the ⅖ of the gaine, he taketh the ⅔ of that which y^e Marchāt taketh, for ⅖ are the ⅔ of ⅗: and there∣fore

the Factours laying in ought to be 800. pounde, which is the ⅔ of 1200. pound, that the marchaunt layed in: Then abate 500. pounde, which the Factour did lay in, from 800. pounde, which should be hys whole stock and there remaineth thre hundred poūde for the estimation of hys person.

12. More, a marchaunt hath deliue∣red vnto his factour a thousand poūd vpon such conditiō, that the Factour for hys paines and seruice, shall haue the gaines of 200. pounde, as though he layde so much in of ready money: I demaunde what portion of y^e gain, the saide Factour shal take? Answere: See what parte the 200. li. (which the Factour layed in) is of 1200. which is the whole stocke of their company, & you shall finde that it is the ⅙, and such parte of the gaine shall the Fac∣tour take.

But in case, that in making the co∣uenauntes, it were agreed that the

Factour shoulde haue the gaine of two hundred pound of y^e stock, which the marchant layeth in, that is to say, of the thousand pound. Then should y^e Factour take the ⅕ part of y^e gaine. For 200. li. is the ⅕ of a 1000. pounde.

Notes

• * 1.1

  A Rule.