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 thyrde parte treateth of certaine briefe rules, called rules of practise, with di∣uers necessarie questions pro∣fitable for Marchaunts.

The first Chapter.

SOme ther be, which doe call these rules of practise briefe rules, for that by them ma∣ny questions may be done wyth quicker expedition, than by the rule of three. There be others which call them the small multiplication, for bicause that the product, is alwaies lesse in quan∣titie, than the number whiche is to bee multiplied. This practise com∣meth not in vse, but onely amonge small kindes of numbers, whiche haue ouer them, other numbers that are greater. And thys beyng well considered, is no other thyng

but to conuert lesser and particu∣ler kindes of number, into greater, the which maye be done by the mea∣nes of diuision, in taking the halfe, the thirde, the fourth, the fift, or suche other partes of the summe, which is to be multiplied, as the multiplier is part of hys greater kinde, and that which commeth thereof is worth as muche (not in quantitie, but in his owne forme) as if you did multiplye simplie the two summes, the one by the other: And for the better vnder∣standing of suche conuersions, you must haue respect to one of these two considerations. The first is, whē one woulde demaunde this question. At 6.d. the yarde of Cotton, what are 18. yardes worth by the price? It is ma∣nifest that they are worth 18. peeces of 6. pence the peece, or 18. half shillings, which must be turned into shillings, in taking y^e halfe of 18.s. & they make 9.s. Or otherwise you must cōsider, that at 1.s. the yarde, the 18. yardes

are worth 18.s. wherefore at 6.d. they shall be but halfe so much, for 6.d. is but the ½ of 1.s. Therefore you must take the ½ of 18. and they make 9.s. which are worthe as much as 108.d. that is to say, as 18. times 6. pence.

2. First, if you will multiplie anye number after thys maner by pence whereof the number of y^e same pēce, doe not extende vnto 12. and therof to bring shillings into the product: you must know the certaine partes of 12. which are these: that is to say, 6.4.3. 2. and 1. For 6. is the ½ of 12. and 4. is the ⅓ of 12:3. is y^e ¼:2. is the ⅙: and 1, is the 1/12. Then for 6.d. which is the halfe of 1. shilling, you must take the ½ of al the number which is to be mul∣tiplyed. And that which commeth thereof, shal be shillings, if there doe remaine 1. it is 6. pence.

For foure pence you muste take the ½ of all the number that is to bee multiplyed: and if anye vnities doe remaine, they shall bee thyrdes

of a shilling, euery one being in value 4. pence.

For 3. pence you must take the ¼ of al the summe: if anye vnities doe re∣maine, they shall bee fourthes of a shilling, euery one being worth thre pence.

For 2. pence you must take the ⅙ of all the summe, and if any vnities doe re∣maine, they shall be sixte partes of a shilling, being euerye one of them worth two pence.

For d. take the 1/12 of the whole sūme, if anye vnities remaine, they are 12. partes of a shilling, eche of them be∣ing in value 1.d. as by these examples following doth plainely appere.

j.

At 6. Pence the yarde.

What 59. yardes.

29. shill. 6. Pence.

ij.

At 4. Pence.

What 82.

27. shill. 4. Pence.

iij.

At 3. Pence.

What 927.

24. shill. 3. Pence.

iiij.

At 2. Pence.

What 346.

57. shil. 8. Pence.

v.

At 1. Pence.

What 343.

28. shil. 7. Pence.

Here you may see in the fyrst exam∣ple that 59. yardes, at 6. pence y^e yarde is worth .29. shil. 6.d. in taking the ½ of 59. And in the seconde example, y^e 82. yardes at 4. pēce the yarde, is worth, 27.s. 4.d. in taking the ⅓ of 82.

Likewise, in the thyrde example, 97. yardes, at three pence the yarde, bringeth 24. shil. 3. pence, in taking the ¼ of 97. Also in the fourth exam∣ple, 346. yardes, at 2. pence the yarde, maketh 57. shillings eyght pence in taking the ⅙ of 346. And fynal∣ly

in y^e fift example .343. yardes, at 1.d. the yarde, amount to 28. shil. 7.d. in taking the 1/12 of 343. And so is to bee done of all such lyke, when the num∣ber of the pence, is any of the certaine partes of 12.

But if the number of the pence be not a certayne parte of 12. you muste reduce them into some certayne par∣tes of 12. and after the foresayd maner you shal make two or three productes as neede shal require, and adde them togyther into one summe as 5.d. may be reduced into 4. & 1. or els into 3. & 2: wherfore if you wil work by 4. & by 1: you must for 4.d. take fyrst the ⅓. of y^e number, that is to be multiplied, and for 1.d. take the 2/12, or rather for 1.d. ye may take the ¼ of the producte which did come of the 4.d. bycause that 1.d. is the ¼ of 4.d. But if you wyl worke by 3, and 2, you shal take for 3.d. the ¼. of the number which is to bee multi∣plied: and likewyse for 2.d. the ⅙ of the same number, adding togyther both

the productes. The totall summe of those two numbers shall be the solu∣tion to the question. And in like ma∣ner is to be done of all other. As by these formes folowing may appeare.

j.

At 5. d. the yarde.

What 49. yardes?

16. shil. 4. d.

4. shil. 1.

20. shil. 5. d.

ij.

At 7. d.

What 5••?

18. shil. 0

13. shil. 6

31. shil. 6. d.

iij.

At 8. d.

What 40?

13. shil. 4

13. shil. 4

26. shil. 8. d.

iiij.

At 9. d.

What 73?

36. shil. 6

18. shil. 3

54. shil. 9. d.

v.

At 10. d.

What 32?

16. shil. 0

10. shil. 8

26. shil. 8. d.

vj.

At 11. d.

What 27?

9. shil. 0

9. shil. 0

6. shil. 9

24. shil. 9. d.

Here in this same first exaumple where it is demaunded (at 5. pence y^e yard) how much are nine and fourty yardes worth? Fyrst for foure pence,

I take y^e ⅓ of 49.s. and thereof cōmeth 16.s. 4.d. thē for 1.d. I take the ¼ of the same product, that is to say, of 16.s. 4. d. and that bringeth .4. shil. 1.d. these twoo sūmes added togither, do make 20.s. 5.d. And so much are the 49. yar∣des worth at 5.d. the yard.

For 7.d. take the ⅓ and the ¼ of the whole summe which is to be multi∣plied, and adde them togither, that is to say, for 4.d. the ⅓ and for 3.d. the ¼: bycause 4.d. is the ⅓ of 12.d. and 3.d. is the ¼ as in the second example before doth appeare: Where the questiō is thus, at 7.d. y^e yard what are 54. yar∣des worth? Fyrst for 4.d. I take the ⅓ of 54: and they make 18.s. Likewyse for 3.d. I take the ¼ of 54. and they are 13.s. 6.d. Then I adde 18.s. and 13.s. 6. d. togither, so both amount to 31.s. 6.d and so much are the 54. yardes worth at 5.d. the yarde.

Otherwyse for 7.d. take first the ½, of the whole sūme for 6.d. Then for 1.d. take the ⅙ of thesame product, and

adde them togither, so shall you haue the lyke summe as before.

For eight pence you must first take ⅓ of the whole sūme for 4. pence, and another ⅓ for other 4.d. and adde thē togyther as in the example doth eui∣dently appeare. Where the question is thus, at 8.d. the yarde, what are 40 yardes worth? Fyrste for 4.d. I take the ⅓ of 40. which is 13.s. 4.d. Againe, I take another ⅓ for the other 4 pence whiche is also 13. shillings & 4. pence. These two summes being added to∣gither, do make 26. shillings 8. pence, and so much are the 40. yards worth at 8. pence the yard as in the third ex∣ample abouesayd doth appeare.

Otherwayes, for eyght pence you mai take first the ½ of the whole sūme for 6.d. Thē for 2.d. you shal take the ⅓ of the product, which did come of the sayd ½, and adde them togither, so shal you haue likewise the solution to the question. As in the same third exāple of 40. yardes, I take first the ½ of 40.

for 6.d. and thereof commeth 20. shil. then for 2.d. I take ⅓ of the saide pro∣duct, that is to say of 20.s. which brin∣geth 6.s. 8.d. these two summes (20.s and 6.s. 8.d.) I adde togither & they make 26.s. 8.d. as before.

For 9.d. you must take the ½ & the ¼ of the whole sūme, and adde them togither: or else for 6.d. take fyrst ½ of the whole summe, then for 3.d. take y^e ½ of the same product, bicause 3.d. is y^e halfe of 6.d. And 6.d. added with 3.d. bringeth 9.d. as by the fourth exam∣ple, where it is demaunded after this sort: at 9.d. the yarde, what are 73. yardes worthe. First for 6.d. I take the ½ of 73. and therof commeth 36.s. 6.d. then for 3.d. I take ½ of y^e same 36. shil. 6.d. which is 18.s. 3.d. these two summes doe I adde togither, & they make 54. shil. 9.d. as in y^e saide fourth example is euident.

For 10.d. take first the ½, then y^e ⅓ of the whole sūme, & adde thē together

For 11.d. take fyrst ½ for 4. pence, se∣condely,

another ⅓ for other 4.d. and thirdely ¼ for 3.d. of all y^e whole sūme: and adde them togither.

Or else for 11.d. take first the ½ then the ⅓ of the whole summe, and final∣lye the ¼ of the laste product, adding them togither.

3. Lykewise by the same reason, when you wil multiply (by shillings) anye number that is vnder xx.s. you shall haue in the product poundes, if you knowe the certaine partes of 20: which are these: 10.5.4.2. &. 1. For 10. is the ½ of 20. 5 is the ¼ part: 4 is the ⅕:2. is the 1/10: and 1. is the 1/20.

Then for 10.s. which is the ½ of a pounde: you muste take the ½ of the number, which is to bee multiplied, and you shall haue poundes in y^e pro∣duct. If there doe remaine 1, it shalbe worth ten shillings.

For 5. shillinges you muste take the ¼ of the number whiche is to bee multiplied, & if there do remaine any vnities, they shall be foure partes of

a poūd, euery one being in value 5.s.

For 4.s. you must take the ⅕ of the number which is to bee multiplied. And if there do remaine any vnities, they shal be fift parts of a pound eue∣ry one being worth four shillings.

At 10. shillings the Peece.

What 75. Peeces?

37. li. 10. shil.

At 5. shil.

What 89.

22. li. 5. shil.

At 4. shil.

What 93.

18. li. 12. shil.

For 2. shillings you must take the 1/10 of the nūber that is to be multiplied. Wherefore, if you wyll take the 1/10 of any number: you muste seperate the last figure of the same number which is nerest your ryghte hande, from all

the other fygures. For all the other figures which doe remayne towarde your lefte hande, from the same fy∣gure, which is seperated, shall bee the sayde 1/10 of a pounde: and that sepera∣ted fygure, towarde your right hand shall be so many peeces of 2. shillings the peece: the which fygure muste be doubled, to make therof shillings, as by these examples appeareth.

At 2. shil.

What 9/8.

9. li 16. shil.

At 2. shil.

What 40/3.

40. li. 6. shil.

Herevpon dependeth another exact way for to multiply by shillings (if y^e number of shillings be euē) which is thus: you shal take ½ the nūber of the same shillings, and conuert them in∣to peeces of 2. shillings. Then by the

number of this halfe, you must firste multiply the last figure toward your right hande, of the nūber which is to be multiplied: And if ther be any ten∣nes in the same product, those must ye reserue in your minde: But if (wyth the same or els without the same) you doe finde any diget number, the same diget number shall you double, & put it in the place of shillings: Thē muste you proceede to the multiplication of the other figures, adding vnto y^e pro∣duct the tennes which you before re∣serued: and therof shal come pounds.

Now, for your better vnderstan∣ding of this which hath bene said and by the way of example, I wil propone vnto you this question.

At 8. shillings the grosse, what are 97. grosse worth after the rate?

Firste in this example I take halfe the number of Shillinges, as before is taught, that is to say of eighte shil∣lings, which is foure shillinges: this 4. shil. I put apart, behinde a crooked

line righte againste 97. towardes the left hand, as here you may see and as here after apereth by diuers exāples.

At 8. shil. the Grosse.

4) What 9/1

38. li. 16. shil.

At 6. shil.

3) What 9/9

29. li. 14. shil.

At 12. shil.

9) What 34/5

207. li. 0 shil.

At 14. shil.

7) What 21/0

127. li. 0. shil.

Now in the first example, where it is demaūded, at 8.s. the grosse, what are 97 grosse? First the ½ of 8.s. which is 4.s. being set apart behind the cro∣ked line, as before is sayd: thē I mul∣tiplye y^e 97 by 4. saying first, 4. times 7. is 28. I double y^e diget nūber 8. and

that maketh 16, the which 16, I do put vnder the line, in the place of shillīgs & I kepe y^e tennes in my mind, which here are 2. For 20. are two times ten: Then secondly, I multiply 9, by the sayd 4, and thereof cōmeth 36: wher∣vnto I adde the 2, tennes, which be∣fore I dyd reserue, and they make 38. Therefore I put 38, vnder the lyne in the place of poundes, and the whole summe wil be 38. li. 16.s. Thus much are the 97. grosse worth, at eight shil∣lings the grosse: the like is to be done of all other. As of 12. shillings in mul∣tiplying by 6. Likewise of 6. shillings if you multiply by 3, also of 14. if you multiply by 7. And so of all euen nū∣bers after the same manner.

For 1. Shilling you must take the ½ of the 1/10 parte of any number that is to be multiplied.

At 1. shil.

What 35/0

17. li. 10. shil.

And if any thyng do remayne, they are shil. Thus by this manner shil.

are conuerted into poundes: for it is euen lyke, as if you did diuide thē by 20.s. as by this exāple in the margent doth appeare. Wher it is demaūded at 1.s. the yard, the peece, or any other thing, what are 350. worth?

First I seperate the laste fygure of 350. nexte to my ryght hand, which is the 0 wyth a line betweene it and the figure 5. Then I make a line vnder the 35/0, and I take the ½ of 35, after this maner: saying the ½ of 3. is 1. and 1. remayneth, which remayn signifieth 10. in that second place. Then I put 1. vnder the line agaynst 3, & I proceede to the rest, saying: the halfe of 15, is 7. (which 15. came of the 1. that remay∣ned, and of the 5. in y^e first place) I put 7. vnder the line right agaynst 5, and they make 17. li. The 1, which did last remayne, is 10.s. Therfore I put 10.s aparte vnder the line, and the whole summe is 17. li. 10.s. so muche are 350. worth at 1.s. the peece.

But when the number of shillings

is not some certayne parte of 20. shil. you muste then conuert the same nū∣ber of shillings, into the certayn par∣tes of 20. and make twoo or three pro∣ducts, as nede shal require, the which muste bee added togyther after thys maner following.

For 3. shillings you must firste take for 2. shil. the 1/10 of the number that is to be multiplied, then for 1. shillīg you must take the ½ of the producte which did come of the same 1/10 part: and adde those twoo sūmes togither, as appea∣reth by this example following.

At 3.s. the peece of any thing, what shall 684 peeces coste mee after the rate. Firste, for 2 shillings I take the 1/10 of 684, which is 68:

At 3. shil.

What 68/4?

68. li. 0. sh

34. 4.

102. li. 12. sh

in seperating the laste figur 4, which I must double, and they be 8. I set eyghte shillings aparte from the place of poundes, and then I haue 68. poū∣des 8.s. for the 1/10 parte, that is to say,

for the 2.s. secondlye, for 1. shil. I take the ½ of the product, that is to saye: of 68. li. 8.s. which is 34. li. 4.s. and I put the same vnder the 68. li. 8. shil. Then finally, I adde those two sum∣mes together, y^t is to saye, 68. li. 8.s. and 34. li. 4. shil, so they make 102. li. 12.s. and so much are the 684. peeces worth at 3. shillings y^e peece, as may appere in the margent.

For 6. shil. take 3/10 of the number which is to be multiplied: that is to say, first 1/10, then double the product of the same 1/10 and adde them togither. Or otherwise for 4.s. take fyrst y^e ⅕ of y^e nūber that is to be multiplied, thē take the ½ of the product which is for two. s. and adde them togither.

Or else take for 5. shil. the ¼ of the whole summe, then for 1. shil. the ⅕ of the product and adde them togither.

Likewyse for 7. shil. take fyrst for 5. shil. the ¼ then for ••. shillings take the 1/10 of the number which is to be mul∣tiplied, and adde them togither.

For eyght shillings take the ⅖ at two sundry tymes, that is to say, first ⅕ for 4. shil. and then as much more for o∣ther 4. shil. and adde them togyther.

For 9. shil. take first the ¼ and lyke∣wise the ⅕ of the number that is to be multiplied, and adde them togither.

For 11. shil. take first ½ for 10.s. Thē for 1. shil. take the 1/10 of the producte, & adde them togither.

For 12. shil. take first the ½ for 10. shil then for 2.s. take the ⅕ part of the pro∣duct, and adde them togither.

For 13. shil. take the ¼ then the ⅕, & agayne another ⅕ of the nūber which is to be multiplied. And adde the pro∣ductes togither, that is to say: fyrste for 5. shil. take the ¼, then for 4. shil. take the ⅕. And agayne, another ⅕ for the other 4. shil. and assēble the three productes, the like is to be done in al others, when the price of the thing which is valued, is onely of shillings. And as by these examples following doth playnly appeare.

At 6. shil.
Whas 67.
13. .8
6. .14
20. li. 2. shil.
At 7. shil.
What 347.
86. .15
34. .14
121. li. 9. shil.
At 8. shil.
What 540.
108. .0
108. .0
216. li. 0. shil.
At 9. shil.
What 230.
57. .10
46. .00
103. li. 10. shil.
At 11. shil.
What 159.
79. .10
7. .19
87. li 9. shil.

At 12. shil.
What 349.
174. .10
34. .18
209. li 8. shil.
At 13. shil.
What 267.
66. .15
53. .8
53. .8
173. li. 11. shil.

4. Likewise in multiplying by pence you shal haue (at the first instāt) poū∣des in the product, in case you knowe the certayne partes of the 1/10 of a poūd or of 24. pence, which are these 12, 8, 6, 4, 3, and 2. For 12, is the ½ of 24: 8. is y^e ⅓: 6 is the ¼: 4 is the ⅙: 3 is the ⅛: and 2. the 1/12: but for 12.d. which is 1. shil. we haue before made mencion thereof.

For 8.d. you muste take the ⅓ of the 1/10 and the rest which are the peeces of 8.d. must be doubled to make of them peeces of 4.d. And of the same num∣ber being doubled, you must take the

⅓ which wil be shillinges, & if there do yet remayn any thing, they are thirds of a shilling beeing in value 4. pence the peece.

For 6.d. take the ¼ of the 1/10, and of that which remayneth you must take the ½ which shall be shillings, if there do yet remayne 1, it shall bee in value 6. pence.

For 4.d. you must take the ⅙ of the 1/10 and of that which resteth, take the 1/•• to make therof shillings, if any thing do yet remayne, they are thirdes of a shilling, being in value 4.d. the pece.

For 3.d. take the ⅛ of the 1/10, and of that which remayneth, take the ¼, to make of them shillings: if any thing do yet remaine, they are fourthes of a shilling, euery one of them beeing worth 3.d.

For 2.d. take the 1/12 of the 1/10: and of that which resteth take y^e ⅙ the which are shillings, if there do still remayne any thing, they shall be sixt parts of a shilling, euery one being in value 2.d

For 1. d. it is not possible with ease, to bring of pence, poūds (into the pro∣duct) vpon the total summe: But first you must bring thē into shillings by y^e order of the secōd rule of this chapter, and then afterward you shal conuert thē into poūds, if nede so require. As by this exāple following may apeare.

At	8. d.
What	59/5.
	19. li. 17. shil. 4. d.
At	6. d.
What	67/8.
	16. li. 19. shil.
At	4. d.
What	93/4.
	15. li. 11. shil. 4.d.
At	3. d.
What	57/1.
	7. li. 2. shil. 9.d.
At	2. d
What	36/4.
	3. li. 0. shil. 8. d.

At	1. d.
What	66/5.
	5••5.	00. shil.	4.d.
	2. li.	16. shillings.	4.d.

But if the number of pence, be not a certayne parte of 24. pence. Then must you bring them into the certain partes of 24. and make therof diuers productes, which must be added togi∣ther, as shall hereafter appeare.

For 5. pence you shall firste take for 3. pence, then for 2. pence, and adde them togither, according to the in∣struction of the last rule. Or else firste take for 4. pence, and then for 1. d.

For 7.d. firste take for 4. d. then for 3. d. and adde them togither:

For 9. d. fyrste take for 6.d. then for 3. d. adding them togither.

For 10. d. fyrste take for 6. d. then for 4. d. and adde them togither.

For 11. d. take first for 8. d. then for 3. d. & adde them togither: as by these examples following doth appeare.

At	5. d
What	92/7.
	11.	.11.	.9
	7.	.14.	.6
	19. li.	6. shil.	3. d.
At	7. d.
What	51/2.
	8.	.10.	.8
	6.	.8.	.0
	14. li.	18. shil.	8. d.
At	9. d.
What	54/6.
	13.	.13.	.0
	6.	.16.	.6
	20. li.	9. shil.	6. d.
At	10. d.
What	27/3.
	6.	.16.	.6
	4.	.11.	.0
	11. li.	7. shil.	6. d.
At	11. d.
What	26/4.
	8.	.16.	.0
	3.	.6.	.0
	12. li.	2. shil.	0. d.

5. If you wil multiply any number by shil. and pence, being both togither you must take first for the shil. accor∣ding to y^e instructiō of the rule of this first chapter, then take for y^e pence af∣ter the order of the fourth rule before mencioned: but if ther be any certayn partes of 1. li. cōtayning both shil. and pence, thē for such parts you shal take the like part of the number that is to be multiplied, as the nūber is part of 1. li. the which certain parts are these, 6. s. 8. d: 3. s. 4. d: 2. s. 6. d: & 1. s. 8. d. For 6. s. 8. d. is the ⅓ of a li. 3. s. 4. d. is y^e ⅙ of a li. 2. s. 6. d. is the ⅛: & 1. s. 8. d. is the 1/12. then for 6. s. 8. d. you must take the ⅓ of the nūber that is to bee multiplied: & if ani thing do remain, they are thirds of a li. euery one being worth 6. s. 8. d

For 3. s. 4. d. you must take y^e ⅙ if ani thing do remain, they are sixt parts of a li. euery one being in value 3. s. 4. d.

For 2. s. 6. d. you must take the ⅛: if any thing be remaining they ar eight parts of a li. ech one beīg worth 2.s. 6.

For 1. shil. 8. d. you shal take the 1/12 if there do any thing remaine, they are twelfth partes of a pounde euery one being valued at 1. shil. 8.d.

At 6. shil. 8. d

What 647.

215. li. 13. shil. 4. d.

At 3. shil. 4. d

What 220.

36. li. 13. shil. 4. d

At 2. shil. 6. d

What 47.

5. li. 17. shil. 6. d

At 1. shil. 8. d

What 400.

33. li. 6. shil. 8. d

6. Heere shall you accustome youre selfe, to multiply by all sortes of sum∣mes, being compoūd of shillings, and pence, which mai come to practise. As thus, for 1. s. 1. d. for 1. s. 2. d. 1. s. 3. d. for 1. s. 4d. Likewise for 2.s. 1.d. 2.s. 2.d. 2.s. 3. d. 2. s. 4. d. And so of all other: consi∣dering moreouer, many subtile ab∣breuiations, which happen oftētimes

that are easy to be cōceyued. As thus at 11. s. 3. d. after that I haue takē first the ½ for 10. s. Then for 1. s. 3. d. I take the ⅛ of the product, bycause 1. s. 3. d. is the ⅛ of 10. s. in taking the sayd ⅛ of the product. And by this meanes, whē ye haue taken one product, ye may oftē∣times vpō y^e same, take another more briefly thā vpō y^e sūme y^t is to be mul∣tiplied, which thing you must foresee.

At 11. shil. 3. d.
What 53.
26. .10. .0
3. .6. .3
29. li. 16. shil. 3. d.
At 6. shil. 3. d.
What 58.
14. 10. .
3. 12. 6.
18. li. 2. 6. d.
At 12. 8. d.
What 64.
32. 0. .
6. 8. .
2. 2. 8.
40. li. 10. shil. 8. d.

7. But if you wil multiply, by poūds, shillings and pence being altogither. Firste you muste wholy multiply by poundes. Then take for the shillings and pence, as in the fifte rule of thys chapter is plainly declared. And as by these examples folowing may apere.

At	3. li.	6. shil.	8. d.
What	49.
	147.	.0	.
	16.	.6	.8
	163. li.	6. shil.	8. d.
At	5. li.	18. shil.	4. d.
What	543.
	2715.	.0.	.
	271.	.10.	.
	135.	.15.	.
	90.	.10.	.0
	3212. li.	15. shil.	0. d.
At	2. li.	7. shil.	4. d.
What	927.
	1854.	.0.	.
	185.	.8.	.
	154.	.10.	.
	2193. li	18. shil.	0.d.

8. So these rules do serue both to bye and sel, at such a price the elle, the yard, the pece, the poūd waight, or a∣ny other thing: how much such a thīg Lykewyse they are very necessary to cōuert al peces of gold and syluer in∣to poundes: for I may as wel say, at 4. shil. 8. d. the French crowne, what are 135. crownes worth?

9. When anye one of the summes (which is to be multiplied) is cōpoūd of many denominatiōs: & the other is of one figure alone: thē shal ye mul∣tiplye all the Denominations of the other summe, by the same one figure begīning first wyth that sūme which is least in value towardes your right hande, and bring the product of those pence into shillings, and the producte of the shillings into poūds, as by this example doth appeare

At 3. li. 9. shil. 8. d.

What 7.

24. li. 7. shil. 8. d.

10. But (if in any of y^e nūbers which are to be multiplied) ther be with it a broken number, you must (according to his denominator) take one or ma∣ny partes of the other nūber, as neede doth require: and set the nūber which cōmeth thereof, vnder the productes, adding thesame togither. As thus: At 5. li. 7. s. 8. d. the grosse, what shall. 34. grosse ½ cost? First

At 5. li. 7. sh. 8. d

What 34 1/7.

170. .0

11. .6. .8.

1. .14. .0

2. .13. .10

185. li. 14. shil. 6. d

you shall multiply 5. li. 7. sh. 8. d. by 34. grosse, saying 5. ty∣mes 34. doe make 170. li. then for 6. sh 8. d. take the ⅓ of 34 which is 11. li. 6. shil 8. d. Thirdely, for 1 sh. take 34. shillings, which is 1. li. 14. shillings 0.

Lastly, for the ½ grosse, you must take ½ of the 5. li. 7. s. 8. d. which is 2. li. 13. s. 10 And then adde them all togither, so you shall finde that the 34. grosse ½ at 5. pound 7. shillings 8. pence is worth

185. pound, 14. shillings 6. pence, as a∣peareth in the margent.

And as in this last exaumple, you did take the half of the money, (which one grosse was worth) for the ½ grosse Bycause that 1. grosse beeing worth 5. pound 7. shillings 8. pēce, the ½ grosse muste bee worth halfe so muche. So likewise, if you haue ⅓ of a grosse, or of any other thing, you muste take the ⅓ of the price, that one grosse is worthe. Semblably, for the ¼ of any thing you shal take the ¼ of the price, also if you haue ⅔, take the ⅔ of the price that one is worth, and of all other fractions, as by these examples folowing doth ap∣peare.

At 4. li. 6. shil. 8. d.

What 46. ½.

184. .0. .0

15. .6. .8

2. .3. .4

201. li. 10. 0.d.

At 8. li. 0. shil. 9. d.
What 54. ⅓
432. .0. .0
1. .7. .0
0. .13. .6
2. .13. .7
43. li. 14. shil. 1. d.
At 3. li. 16. shil. 8. d.
What 17. ¾
51. .0. .0
8. .10. .0
5. .13. .4
. .19. .2
68. li.. 00. shil. 10. d.

11. If you will make the proofe of these rules aforesayd, you must first abate the sūme of money (which the fractiō of the multiplicatiō doth import) frō the totall sūme. And diuide the rest of the poūds of the sayd total summe, by the whole multiplicand, the fraction only accepted. And if any thing do re∣main after the diuision is made, that remaine shal be multiplied by 20. and vnto the product of that multiplicati∣on,

you shall adde the shillings which remained of the rest of the total sūme Agayn, if any thing do remaine after the same diuision, you must multiply thesame by 12, & vnto the product adde the pence of the total summe that re∣mayned, if any be left. And thus if ye haue truly wrought, you shal find a∣gain the higher sūme of your questiō that is to say, the price that one grosse or any other thing is worth, whereof you demaund.

Or otherwise reduce the remayne of the totall summe (the value of the moneye that the fraction is worthe, beeing fyrste deducted) all into pence, in multiplying the pounds by 20, and the shillings by 12. adding thereunto, the shillings and pēce, which are ioy∣ned wyth the remayne of the sayd to∣tall sūme, if any such be, then diuide those pence by the foresayde number that is to be multiplied, the fraction of the same number beeing also aba∣ted. So shall you finde the price that

one peece, one Grosse, or any other thing is valued at. As in the firste ex∣ample going before, where the totall summe is 201. pound 10. shillings, frō the which I doe first abate the price of the half grosse, which is 2. li. 3. s. 4. d, the rest is 199. li. 6. s. 8. d. which beeing reduced into pens bringeth 47840. d. I diuide the same by 46. and thereof commeth 1040. pence. Then I diuide that 1040. pence by 12. and they bring 86. shillings 8. pence, that is to say, 4. li. 6. shillings eyght pence, whiche is the price that one grosse, or any other thing did cost, as in that fyrste exam∣ple doth appeare.

12. The lyke is to be done of any manner of thinge that is solde by the hundred or by the Kyntall.

As thus: at 12. pound 7. shillings. 6. d the 100. pounde wayghte: what shall 374. pound wayght cost? You shall fyrst multiply twelue pounde, seuen shillings, sixe pence, by three: that is to saye, by three hundreth. Then for

50. li. waight, you

At. 12. li. 7. sh. 6. d

What 3/74.

37. .2. .6

6. .3. .9

2. .9. .6

0. .9. .10. ⅘

46. li. 5. sh. 7. d. ⅘

shall take the ½ of 12. li. 7. s. 6. d. bi∣cause 50. li. is the ½ of 100. li. Like∣wise for 20. pound waight, which is the ⅕ of 100. li. take the ⅕ of 12. li. 7. shil. 6. d. lastly for 4. li. waight take the ⅕ of the laste product. This done, you muste adde all these productes into one summe, which will make the summe of 64. li. 5.s. 7. d. ⅘, as by this exāple aboue writ∣ten doth appeare.

The proofe is made by reducyng the totall summe into pence. And to diuide y^e product by the number y^t is to be multiplyed, y^t to to saye by 374. likewise diuide y^e quotient produced of that first diuisyon by 12. so shal you finde againe the higher summe 12. li. 7. shil. 6. d. which is the price of 100. li. waight, as before.

13. Also the like maye be done of

our vsuall waight here in Englande (which is 112. li. for euerye hundred pounde waight) in case you knowe the certaine parts of a hundred, that is to say, of 112. li. waight, which are these 56. li. 28. li. 14. li. 7. li, For 56. li. is the ½ of 112. 28. li: is the ¼ of 112. li: 14. li. is the ⅛, and 7. li. is the 1/16.

Therfore, for 56. li. take the ½ of the summe of money, that the 112. pound waight is worth.

For 28. li. take the ¼ of the summe of money that the 112. li. is worth.

For 14. li. take the ⅛ of the summe that the C. is worth.

For 7. li. take the 1/16 of the summe of money that the C. is worth.

As thus: at 3. li. 6. s. 8. d. the hun∣dreth pounds waight, that is to saye, the 112. li. What shall 24. C. 3. quar. 21. li. cost after the rate?

Fyrst, you shall multiply 24. hun∣dreth by 3. which is the 3. li. & thereof cōmeth 72. li. then for 6. s. 8. d. which is the ⅓ of 20. s. you shal take y^e ⅓ of 24

which is 8. li. for

At 3. li. 6. sh. 8 d.
What 26. .3. 21. li.
72. .0. .0
8. .0. .0
1. .13. .4
. .16. .8
. .8. .4
. .4. .2
83. li. 2. sh. 6. d

24. nobles ma∣keth 8. li. after∣warde, for the 3. quarters of y^e C. you shal first for y^e 56. li. take the ½ of 3. li. 6. s. 8. d. bicause 56. li is the ½ of the C. & thereof cōmeth 1. li. 13. shil. 4. d. then for 28. li. (which is the quar. of a C.) you shall take the ¼ of 3. li. 6. s. 8. d. or else the ½ of the product, which came of 56. li. which is 16. s. 8. d. likewise for 14. li. take the ⅛ of 3. li. 6. s. 8. d. which is 8. s. 4. d. or else the ½ of the product of 28. li. which is al one: lastly for 7. li take the 1/16 of 3. li. 6. s. 8. d. or else the ½ of the product, that came of 14 li. and therof cōmeth 4. s. 2. d. Then adde al these products togither: & the totall summe wil be 83. li. 2. s. 6. d. so muche are y^e 24. c. 3. quar. 21. li. waight worth after 3. li. 6. s. 8. d. y^e C. as appereth in

the margent.

The proofe hereof is made, lyke to the other proofes aforesaide, sauing that wher in those proofes, you abate the price of the money, that the frac∣tion was worthe, from the totall summe: here in thys example (and in such other like) you muste abate the price of money, that the odde waight amounteth vnto (ouer and aboue the iust hundrethes) from the saide totall summe, the rest thereof shall you cō∣uert into pence, diuiding the product of y^e multiplication by the iust nūber of the hundrethes, so shall you finde the pence y^e one hundreth is worthe, which you shall bring into poundes by the order of diuision, & so all other.

¶The seconde Chapter treateth of the rule of three compounde, which are foure in number.

THere belongeth to the fyrste & seconde partes of the rule of thre compounde alwaies fyue numbers: wherof (in the fyrst

part of the rule of three compounde the seconde number and the fift, are alwaies of one semblaunce, and like denomination: whose rule is thus, multiply y^e first nūber by the seconde, & that shalbe your diuisor: then mul∣tiplye y^e other three nūbers the one by the other to be your diuidende. Exā∣ple, of this first part: if 100. crowns in 12. monthes, do gaine 16. li. what will 60. crownes gaine in 8. monthes? Aunswere, first multiplie 100. crownes by 12. monthes, & therof cōmeth 1200. for your diuisor: then multiply 15. li. by 60. crownes, & by 8. monthes, & you shall haue 7200. diuide 7200. by 1200. & therof cōmeth 6. li. so many li. wyll 6. crownes gaine in 8. monthes: thys questiō may be done by y^e double rule of 3. y^t is to say bi y^e rule of 3. at 2 times: yet this rule of 3 cōpoūd is more brief

Crownes.	monthes.	poūds.	crownes.	monthes.
100.	.12.	.15.	.60.	.8.
	1
	72	00
	12	00	(6. li.

2. In the seconde part of the rule of thre compound, the 3. number is like vnto the fift, wherof the rule is thus: multiplie the 3. number by the 4, the product shalbe your diuisor: thē mul∣tiply the first number by y^e seconde, & the product therof by the fift, y^e which number shal be your diuidend, or nū∣ber y^t is to be diuided: as by example.

When 60. crownes in 8. monthes do gaine 6. li. in how many monthes wil 100. crownes gain. 15. li. Aunswere: Multiply the thirde number 6. by the fourth nūber 100: & therof cōmeth 600 then multiplye y^e firste number 60. by the secōd nūber 8. & by y^e fift nūber 15. thereof will come 7200. then diuide 7200. by 600. & the quotiēt wilbe 12: in so many monthes will 100. crownes gaine 15. li. This question may lyke∣wise be done by the double rule of 3.

Crownes	monthes.	pounds.	crownes.	pounds.
60.	.8.		.6.	.100.	.15.
	1
	72	00	monthes.
	66	00	(12

3. In the thirde part of the rule of 3. compound, there may be 5. numbers or more: & in this rule y^e first nūber & the last are alwayes dissemblaunt y^e one to thother: & the questiō is from the last nūber vnto the first, wherof y^e rule is thus: multiply that number which you would know by those nū∣bers which do giue y^e value, & diuide y^e product of the same, by y^e multiply∣cation of the nūbers which are alrea∣dy valued, as by exāple. If 4. deniers Parisis, bee worthe 5. deniers Tour∣nois, & 10. deniers tournois, be worth 12. deniers of Sauoy, I demaūd how many deniers Parisis are 8. deniers of Sauoy worth? Aunswere: Multi∣ply 8. deniers of Sauoy (which is the nūber y^t you would knowe) by 4. de∣niers parisis, & by 10 deniers tournois which are the nūber y^t giue y^e value, & they make 320: then multiplie 5. de∣niers tournois, by 12 deniers of sauoy (which are y^e nūbers already valued) & thei make 60: lastly diuide 320. by 60

and you shal finde 5. deniers ⅓ parisis, so muche are the deniers of Sauoye worth.

Parisis.	tournois.	tournois.	sauoy.	sauoy.
4. d.	.5 d.	.10 d.	.12 d.	.8 d.
	32	0	par.
	6	0	(5. d. ⅓.

4. In the fourthe parte of the rule of thre compounde: the fyrst number and the last are always semblant and of one denomination, and the questiō of this rule, is alwayes from the last number to y^e last sauing one. Where∣of there is a rule which is thus. You must multiplye that number which you woulde knowe, by the numbers that are alreadye valued, and diuide the product of the same, by the multi∣plication which commeth of the nū∣bers that giue y^e value, as by exāple.

If 4. deniers Parisis, bee worth 5. Deniers Tournois, and 10. Deniers Tournois, be worthe 12. Deniers of Sauoy, I demaunde how many De∣niers

of Sauoy, are 15. Deniers Pa∣risis worth. Aunswere: Multiplye 15. Deniers Parisis that you woulde knowe, by 5. Deniers Tournois, & by 12. Deniers of Sauoye, which are the numbers alreadye valued, and thei make 900. Diuide the same by 4. times 10. which are the numbers that doe giue the value, and you shal finde 22. Deniers ½ of Sauoye, so much are the 15. Deniers Parisis worth.

Parisis.	tournois.	tournois.	Sauoy.	Parisis.
4. d.	.5 d.	.10 d.	.12 d.	.15 d.
	12
	90	0	Sauoy.
	44	0	(22. d. ½

The thirde Chapter treateth of questions of the trade of Marchaundise.

IF 31. Deuonsh. dosēs do cost me 100. li. 15. shil. What shall 4. do∣sens cost? Aunswere: fyrst bring the 100. li. 15. shill. all into shillings,

in multiplying y^e 100. li. by 20. adding to the product the 15. shill. and thereof commeth 2015. shill. then multiplye 2015. by the thirde number 4. and di∣uide the product by 31. and the quoti∣ent wilbe 260. s. The which diuide a∣gaine by 20. and therof commeth 13. li.

Dosens.			Dosens.
31.	100. li.	15. sh.	4. d.
	20
	2015
	4
	8060.
	1
	28
	8060 (260.
	3111
	33

If foure Dosens be worth 13. pound. What are 31. Dosens worthe by the price? Aunswere: Multiply 31. by 13. and therof cōmeth 403. The which you shall diuide by 4. and thereof com∣meth

and thereof commeth 100. li. ¾, which ¾ are 15.s. and so much are 31. Dosens worth as before.

Dosens.	li.	Dosens.
4.	.13.	.31.
		13
		393
		1
		403.
	403
	444 (100. li. ¼

If 49. elles be worth 2. li. 4. s. 11. d. what are 18. elles worth by the price? First you must bring 2. li. 4. s. 11. d. all into pence, in multiplying 2. li. by 20. maketh 40. adde thereto 4. shil. they make 44. s. y^e which multiply by 12. d & thei make 528. d. whereunto adde 11. d all is 539. d. the which 539. d. muste be your second nūber in y^e rule of 3. then multiply 539. by 18. & therof commeth 9702. diuide y^e same by 49. & you shal haue in your quotient 198. d. y^e which diuide by 12. & you shal finde 16. s. 6. d. so much are the 18. elles worthe.

Elles:		Elles.
49.	.2.li. 4. sh. 11.d. .18
	20	539
	44	162
	12	54
	99	90
	44
	539	9702

13	1
427	76
386	198 (16. sh. 6.d
9702 (198.	122
4399	1
44

If 18. elles be worth 16.s. 6.d. what are 49. elles worth by y^t price? Auns. bring 16.s. 6.d. into pence, in multi∣plying 16. by 12. and thereof commeth 198.d. with the 6. d. added to it, then multiplye 198 by 49. the product will be 9702. The which diuide by 18. elles and therof commeth 539.d. Then di∣uide 539.d. by 12. and the product ther∣of by 20. So shall you haue 2. li. 4. sh.

11.d. so much are the 49. elles worth.

Elles.		Elles.
18.	.16. sh. 6. d.	.49
	12	198
	32	392
	166	441
	198	49
		9702

17	1
446	151
9702 (539.	••39 (44. shill.
1888	122
••1	1

If a yarde of Veluet cost 19.s. what shall ¾ of a yarde cost? Aunswere: sette down your numbers thus. If

1/1

19/1

¾

. Then multiplye 1. times 19. by 3. and therof cōmeth 57. for your diuidende, or number to be diuided. The which 57. you shall diuide by 1. times 1, foure times, which are 4, and your quotiēt wil be 14.s. ¼, which ¼ is worth 3.d. so

much are the ¾ of a yarde worth after 19. shil. the yarde, as by practise follo∣weth.

1/1	19/1	¾	11
			57 (14. sh. ¼
			44

Or otherwise by the rules of prac∣tise: first for 2/4 of a yarde which is ½ of a yarde, you muste take the ½ of 19.s. which is 9.s. 6.d. then for ¼, take the ½ of the product, that is to saye, of 9.s. 6.d. and therof cōmeth 4.s. 9.d. adde these nūbers togither, &

19. shil.

9. sh. 6.d.

4. .9.

14. .3.d.

you shall haue 14.s. 3.d. as aboue is said, and as appeareth here in the margent.

If ¾ of a yarde of Veluet do cost 14. shil. 3.d. What shall 1. yarde coste set your numbers downe thus: if

¾

14

¼

1/1

. Reduce 14. ¼ into a fraction, and they wil be 57/4 thē multiply 57. by 1.4. times, & thereof cōmeth 228. for your diuidend. Likewise multiply 1. times

4.3. times, & therof cōmeth 12. for your diuisor: then diuide 228. by 12. & your quotient wil be 19. shil. so much is the yarde of veluet worth.

	57		1
¾	14 ¼	1/1	10
			228 (19. shil.
			122
			1

Or otherwise by y^e rule of practise: you shall take the ½ parte of 14. sh. 3.d. and adde it with the same 14. sh. 3.d. and you shall haue 19. shill. as before.

14. shil.	3. d.
4.	.9. d.
19. shil.	.0. d.

If one ell of Hollande clothe be worth 5.s. what are ⅔ worth after the rate? Aunswere, say thus if

1/1

5/1

⅔

. Then multiply 2. times 5. one time, and therof commeth 10. for your diui∣dende: likewise multiply thre times 1. one time, thei make 3. for your diui∣sor, then diuide 10. by 3. & thereof com∣meth 30.s ½ which ⅓ is worth 4. pēce, &

so much are the ⅔ of an ell worth.

1/1	5/1	⅔	1
			10	(3. shil. ⅓
			3

Or otherwise, by the rule of prac∣tise: take first the ⅓ of 5.s. for the ⅓ of an ell, which is 1.s. 8.d. Likewise, for the other ⅓ of an ell take againe ano∣ther ⅓ of 5.s. which is also 1. sh. 8.d. and adde them together, and so shall you haue 3.s. 4.d. as before.

5. shill.
1.	.8
1.	.8
3. shill.	4 d.

If ⅔ of an ell of Hollande cloth doe cost me 3.s. 4.d. what shal the el cost? Aunswere: set down your sūme thus, if

⅔

3 ⅓

1/1

. First reduce 3 ⅓ all into thirdes, and it will be. 10/3. Then mul∣tiply 1. times 10.3. times, and thereof cōmeth 30. for your diuidēd. Likewise multiplie 1. times 3.2 times, youre quotiēt wil be 6. then diuide 30. by 6. & you shall haue 5. s. so much is the ell

of Hollande clothe worth.

	10		30
2	3 ⅓	1/1	6 (5. sh.

Or otherwise by practise, take the ½ of 3.s. 4.d. which is 1.s. 8.d. & adde it to the same 3.s. 4.d. and therof wyll come 5.s. as before. For the ⅓ of 5.s. is as much as the ½ of

3. sh.	4.
1.	8.
5. sh.	0.d.

3.s. 4. d. which was the price that the ⅔ of an elle did cost, as ap∣peareth.

If one ell cost me 17.s. what shal. 15. elles ⅛ part coste? which ⅛ is halfe a quarter of an elle. Aunswere: saye, of

1/1

17/1

15. ⅛.

. First reduce 15 ⅛ into eight partes, and they make 121/8 then mul∣tiplie 121. by 17.1 time, and thereof commeth 2057. for your diuidende. Likewise multiply 8. times 1. 1. time, and your quotient wyll bee 8. for your diuisor, then diuide 2057. by 8. and you shall fynde 257. sh. ⅛, whiche is 12. li. 17. shil. 1.d. ½ and so muche are

the 15 elles ⅛ worth, as by practise doth appeare.

		121
1/1	17/1	15 1/8

Or otherwise, for 10 sh. take y^e ½ of 15 which is 7 li. 10 sh. then for 5 sh. take the ½ of 7. li. 10.s. which is 3. li. 15.s. thirdly for 2.s. take y^e ⅕ of 7. li. 10.s. bi∣cause y^e ⅕ of 10. sh. is 2. sh. Fourthlye, for the ⅛ of y^e ell, you shal take the ⅛ of 17.s. which is 2.s. 1.d. ½. Lastlye, adde all these summes togither, and thē shal you find 12. li. 17.s. 1.d. ½ as before, and as appeareth more plainly in the margent.

15.	. ⅛.
17.s.
7.	.10.	.
3.	.15.	.
1.	.10.	.
	2.	1 ½.
12. li. 17.s. 1.d. ½

If 25. elles be worthe 2. li. 3.s. 4.d. what are. 18 elles ¾ worth by y^t price? Aunswere: first put 3.s. 4.d. into y^t part of a li. and you shal haue ⅙ then say, if 25/1 giue me 2. li. ⅙ what shall 18 ¾ giue: put y^e whole number into his brokē, and then multiplie 1. times 13. by 75. y^e product will be 975. the whiche you

shall diuide by 25. times 6.4. times, which maketh 600. Then diuide 975. by 600. and your quotient will be 1. li. and 375. remaineth, y^e which 375. you shall multiplie by 20. thereof cōmeth 7500. diuide y^e same by 600. your quo∣tient wil be 12.s. and 300. remaineth y^e which abbreuiated bringeth ½ which is 6.d: thus y^e 18 elles ¾ are worth 1. li. 12.s. 6.d. as by practise appeareth.

	13	75
25/1	2 ⅙	18 ¾.

Or otherwise by the rules of prac∣tise: for bicause that 12. elles ½ is the ½ of 25. elles, therfore take the ½ of 2. li. 3.s. 4.d. which is 1. li. 1.s. 8.d. then for 6. elles ¼ take ¼ of 2. li. 3.s. 4.d. or else the ½ of the last product (that is to say of 1. li. 1.s. 8.d.) which is all one, & adde them togither, so shal you haue 1. li. 12.s. 6.d. as before.

.2.	.3.	.4.
.1.	.1.	.8.
	.10.	.10.
1. li.	12.s.	6.d.

If 15. yardes be worth 32.s. what are halfe a yarde or halfe a quarter or else ⅝ of a yarde worth. Aunswere: say, if 15/1 giue 32/1 what wyll ⅝ giue? Mul∣tiplie 1 times 32. by 5. and diuide the product by 15. times 1. shil. and 4. re∣maineth, which is ⅓ of a shil. that is to say 4.d. and so much are the 5/2 of a yarde worth.

15/8

32/1

⅝

Or otherwise, se what the yarde is worth after the maner aforesaid in y^e other examples, & you shal find y^t the yard is worth 2.s. 1.d ⅗ of y^e which nū∣ber take first y^e ½ for 4/8 which is 1.s. 0 d. ⅘, of the which nūber, take the ¼ for y^e other ⅛ which is 3 d. ⅕, adde these two nūbers togither, and you shal finde y^e ⅝ to be worth 1.s. 4.d. as before is said

2. sh.	1.d.	⅗.
1.	0.	⅘.
1. sh.	4.d.	0.

If 13. els ⅚, be worth 27.s. what are 10. elles ⅔ worth by y^t price? Aunswere: say if 13. ⅚ giue 27/1, what shal 10. ⅔ giue: put the whole nūbers into their bro∣ken, & you shall finde 83/6, 27/1, & 32/3. Thē multiplie 6. times 27. by 32. & thereof commeth 5184. the which nūber you shall diuide by 83. times 1. thre times, and you shall finde 20. sh. 68/83 which is worth 9.d. 69/83 part of a penny.

83		32
13 ⅚	27/1	10 ⅔

If two yardes ½ be worth 4.s. 8.d. what are 8. yards ¼ worth? Aunswere: put the 8.d. into the part of a shilling, which wilbe ⅔ then reduce the whole numbers into their broken, and they will stande thus. 5/2, 14/3, 33/4, then multi∣plie two times 14. by 33. and diuide y^e product by 5. times 3.4. times, & you shall finde 15.s. 4.d. ⅘, so much are the eyght yardes ¼ worth.

5	14	33
2 ½	4 ⅖	8 ¼

If one kersey bee worth 2. li. 6.s. 8.d. how many kerseys shall I bie for 36. li. 3.s. 4.d. after y^t rate? Aunswere: put 6s. 8d. into the part of a li. & you shall haue 2. li. ⅓ for the first number in the rule of 3. and 1. ell for the second number: then put 3.s. 4.d. into the part of a li. and you shall finde 36. li. ⅙. for the third number, then will your 3. nūbers in the rule of 3. stande thus.

2. ⅓

1/1

36 ⅙.

. Therefore reduce the whole numbers into their broken, & you shal haue

7/3

1/1

217/6

. Then multi∣ply 3 times 1. by .217. & therof will cōe 651. for your diuidende. Likewise, multiply 7 times 1. by 6. & the product therof will be 42. Then diuide 651. by 42. and you shall finde 15. ½. So many kerseys of 2. li. 6.s. 8.d. the peece, shall you haue for 36. li. 3.s. 4. d.

7	217
2 1/7	36. ⅚

¶The 4. Chapter treateth of losses and gaines, in the trade of Marchaundise.

If 13. yards ⅓ be worth 22. li. 10.s. how shall I sel the yarde to gaine ⅓, or to make of 3.4? which is all one? Auns. say by the rule of 3. if 3. be come of 4. or if 3. yelde 4. what will 22. ½ yelde: multiplie & diuide and you shal fynde 30. li. Then say gaine by the rule of 3. if 13. yardes ⅓ doe giue 30. li. aswell of principal as of gaine: what wil 1. yard be worth by the price? Multiply and diuide, and you shall find 2. li. 5.s. and for that price must the yarde be solde to gaine the ⅓, or to make of 3.4.

		45	40.
5/1	4/1	22 ½	13 ⅓ 30/1	1/1

Or otherwise, take the ⅓ part of 22. li. 10.s. which is 7. li. 10.s. that shall you adde with 22. li. 10.s. and you shal haue 30. li. as be∣fore.

22.	.10. s.
7.	.10.
30.	.00.

Then di∣uide 30. by 13. ⅓, & you shall fynde 2. li. 5.s. as aboue is said.

If one yarde bee worth .27. sh. 6.d. for how much shal 16. yards ⅔ be solde to gaine 2.s. vpon y^e pound of money, y^t is to say: vpō 20.s. Answere, adde 2. vnto 20. and you shal haue 22, thē say: if 20.s. of principall, doe giue 22.s. as wel of principal as gaine: how much wil 27.s. 6.d. principall yelde. Multi∣plie and diuide & you shall finde 30.s. ¼: then saye againe by the rule of 3. if one yarde do giue me 30.s.¼ (which is aswel the principal as y^e gaine) what shall .16. yardes ⅔ giue me? Multiplie and diuide, and you shall finde 25. li. 4.s. 2.d. For the same price shall the 16. yardes ⅔ be solde to gaine after the rate of 2.s. vpon the pound of money, or in 20.s. which is all one.

		55.		121	50
20/1	22/1	27 ½.	1/1	30 2/4	16 ⅔

If 10. yardes ⅔ be worthe 25. li. 10.s. For how much shal 2 yardes ¼ be sold to gaine after 10. li. vpon the 100. li. of money? Aunswere: say if 100. of princi∣pall

yelde 110. as well principall as gaine, how muche will 25. 10.s. yelde me? Multiply & diuide, and you shall finde 28. li. 1.s. Then saye if 10. yardes ⅔ do yelde me 28. li. 1. sh. aswel of prin∣cipal as of gaine, how much shal two yardes ¼ yelde me? multiply & diuide & you shall finde 5. li. 18.s. 4.d. 1/12, for so much shall the 2. yardes ¼ be solde to gaine after 10. li. vpō y^e 100. li. of mony.

		51
100/1	110/1	25 ½	10 ⅔	28 1/20	2 ¼

And although that in these questi∣ons of gaine and losse, sometimes the fyrst number is not like vnto y^e thirde number, that is to saye, of the same denomination: as one woulde saye: if 20.s. gaine 2. shil. what shall 50. li. gaine? or 25. li. &c. Or if 20. li. do gain 2. li. What shall 25.s. gaine mee, or what shall 27. sh. ½ gaine? Yet neuer∣thelesse, the rule is not therfore false. For if 20.s. doe gaine 2.s: 20. li. shall gaine 2. li. & 20.d. shall gaine 2.d. like∣wise

20. crownes shall gaine 2. crow∣nes, and so of all other: therefore it is to be vnderstand, that the first nūber in these reasons is presupposed to bee semblable to the thirde.

When one Marchant selleth wa∣res to another, and hee giueth to the byer 2. vpon 15: howe much shall the byer gaine vpō the 100. after the rate? Aunswere: say if 15. giue 17. what shall 100. giue? Multiplie and diuide, and you shall finde 113 ⅓, so the byer get∣teth after the rate of 13 ⅓ vpon the 100.

15

17

100.

If one northen dosen cost me 3. li. 5. s. & I sel the same againe for 3. li. 12.s. 6.d. how much doe I gaine vpon the pounde of money after y^t rate? Auns. say if 3. li. ¼ doe giue 3. li. ⅝ what shal 20/8 giue, put the whole nūber into their broken & you shal haue 13/4, 29/8, 20/1, then multiply 4. times 29. by 20. & thereof commeth 2320. for your number that is to be diuided, likewise multiply 13. times 8. 1 time, & therof cōmeth 104.

Then diuide 2320. by 104. & you shall finde 22.s. 4/13. So I shal get 2.s. 4/13 vp∣on 20.s. or vpon the li. of money.

13	29
3 ¼	3 ⅝	20/1

If a yarde of cloth cost me 7.s. 8.d. & afterwarde I deliuer out 13. yardes ¼, for 4. li. 13.s. 4.d. I woulde knowe whether I doe winne or lose, & how much vpon the 100. li. of money?

Aunswere: see first at 7.s. 8.d. the yard, what the 13. yardes ¼ shall coste, and you shal finde 5. li. 1.s. 7.d. And I sold them but for 4. li. 13.s. 4.d. so y^t I doe lose vpon the 13. yardes ¼ the summe of 8.s. 3.d. Then for to knowe howe much is lost vpon the 100: saye by the rule of three, if 5. li. 1.s. 7.d. doe lose 8.s. 3.d. What will 100. lose? Fyrst, put 1. shil. 7.d. into the part of a li. and it will be 19/240. Likewise put 8.s. 3.d. into the part of a li. and it is 33/80. Then will your nūbers stand thus 5 19/240, 33/80, 100/1, put the whole into his brokē, and

then multiply and diuide, so you shal finde 8. li. 1184/9752 which is worth .2. sh. 5. d. 169/1219 and so muche is loste vpon the 100. li. of money.

	1219.
5	19/240.	38/80	100/1.

More, if 12. yardes ½ of scarlet bee solde for 30. li. 15.s. vpon the which is gained after the rate of 11 1/9 vpon the 100. I demaunde what the yarde dyd cost at the first. Aunswere: from 30. li. 15.s. substract his 1/10 part which is 3. li. 1.s.6.d. and there resteth 27. li. 13.s.6.d the which number multiplied by 2. bringeth 55. li. 7.s. of the which is 11. li one shilling and foure pence.

Then take againe the ⅕ of the saide 11 pounde 1. shil. 4. pence, which is 2. pounde 4. shillinges thre pence. 9/25. And so muche did the Elle cost at the fyrst pennye.

30. li.	15. sh.
3.	1. sh.	6.d.
27.	13.	6.
2.
55.	7.	0.
11.	1.	4.	⅘.
2.	4.	3.	9/25.

More, if 15. yardes ¾ of scarlet doe cost me 32. li. 13.s. 4.d. And I sell the yarde againe for 2. li. whether doe I winne or lose, and howe much vpon the pounde of money.

Aunswere: Loke what the 15. yardes ¾ are worth at 2. li. the yarde, and you shall finde y^t they are worth 31. li.10.s. But they did cost 32. li. 13.s. 4.d. so y^t there is lost vpō y^e whole 1. li.3.s.4.d. Then, to know how much is lost vpō the li. say by the rule of thre, if 32. li. ⅔ doe lose 1. li. ⅙: what will ⅛ lose? that is to say, what will 1. li. lose? reduce the whole nūbers into their brokē, & then multiplie & diuide, so shall you

finde 21/588. part of a li. Then multiplye 21. by 240. bicause so many pence are in a li. & diuide the product by 588. so shall you finde 8.d. 336/588 which being abbreuiated doe make 7/4, & thus you se y^t 8.d. 4/7 is lost vpon the li. of money.

98	7
32 ⅔.	1 ⅙	1/1

If 1. yarde of cloth of tissue be solde for 3. li. 15.s. whereupon is lost after y^e rate of 10.s. vpon the 100. I demaunde what 12. yardes ½ of y^e same tissue did cost? Aunswere: adde vnto 3. li. 15. hys owne 1/10 part, which is 7.s.6.d. and al amounteth to 4. li. 2.s. 6.d. then loke what the 12. yardes ½ wil amount vn∣to, after 4. li. 2.s. 6.d. & you shal finde that they will come to 51. li. 11.s. 3.d. so much did the 12. yardes ½ cost.

3. li. 15.s.	12.		½
7.s. 6.d.	4. li. 2.s. 6.d.
4. li. 2s. 6d.	48.	.00.	.0.
	1.	.10.	.0.
	2.	.01.	.3.
	51. li.	11.s.	3.d.

More, if I sell one wilshire white for 6. li. 12.s. whereupon I doe gaine after the rate of 2.s. vpon the li. of money, that is to saye, vpon 20.s. I demaunde what 11. peeces of the same whites did cost mee? Aunswere: abate from 6. li. 12.s. (which is 132.s.) hys 1/11 part, & thereof cōmeth 12.s. and there remaineth 120.s. or 6. li. Thē see at 6. li y^e cloth, what the 11. clothes are worth 66. li. so much did the 11. clothes coste.

132. sh.	11
12. sh.	6
120. sh.	66. li.

If I sell 10. elles ½ of Hollād for 22 s.6.d. whereupon I do lose after the rate of 2.s. vpon the li. of money. I demaunde what the ell did cost mee? Aunswere: say by y^e rule of 3. if 18. giue 20.s. what will 22.s.6.d. giue? Mul∣tiplie & diuide, & you shall fynde 25.s. Then diuide 25.s. by 10. ½, & therof cō∣meth 2s.4 d. 4/7: So much did y^e el cost.

11/1

20/1

22 ½

If I sell one clothe for 5 li. wher vp∣on I do lose after 10 vpon y^e 100, I de∣maunde how muche I should lose or gayne vpon the 100, in case I had solde the same for 5 li.10 shil. Aunswere: saye, if 90 yelde 100, howe muche wyl 5. li. giue? Multiplie & diuide, & you shall finde 5. li. 5/9: then say againe by y^e rule of thre, if 5.5/9 come to 5. ½, what wyll 100. come vnto? Multiplie & diuide, & you shal finde 99. li. which being aba∣ted from 100. there wyll remaine 1. li. and so much is lost vpon the 100.

90.

100.

5.

5 5/9

5 ½

100/1

¶The 5. Chap. treateth of leng∣thes & breadthes of tapistry, and other clothes.

IF a peece of tapistry be 5 elles ¾ longe, and 4 elles ⅔ in breadth, how mani elles square doth the same pece conteine? Aunswere: Mul∣tiplie the length by the breadth, that is to saye 5. ¾ by 4. ⅔, and thereof commeth 26. elles ⅚ so many elles

square doth y^e same peece conteine.

More, if a peece of Tapistrie doe conteine 32. ells square, and y^e same being in lēgth 6. elles ¼. I demaūde how many elles in breadth y^e same peece doth conteine. Ans. diuide 32. elles by 6 ¼ and thereof commeth 5. 3/25: So many elles dothe the same peece conteine in breadth.

More, a peece of clothe beyng 13. yardes ⅓ in length, and 5 quarters 1/2 in breadth, how many yardes of ⅔ & ½ broade will the same peece make? Answere: see what parte of a yarde, the 5/4 and ½ be, and you shall finde y^t they make 1 yarde ⅜. Thē multiply 13. yardes ⅓ by 1 yarde ⅜ and you shall haue 18. yardes ⅓ in square y^e which you must diuide by ⅔ & ½ y^t is to saye by ⅚, (bicause y^t ⅔, ½ being brought into 1 fraction maketh ⅚) & you shall finde 22. yards: So many yardes of ⅔ & ½ large doth y^e same peece conteine.

More, a marchant hath bought 4. yardes ⅔ of cloth being syxe quarters ½ broade to make him a gowne the which he will line thorowout, wyth black Say of three quarters of a yarde broad, I demaund how much Say he must bye? Answere: Multiply y^e lēgth of the cloth, by the breadth, that is to say 4 ⅔ by 1. ⅝, (which is the syx quar∣ters ½) and therof commeth 7. yardes 7/12, the which diuide by ¾ & you shall finde ten yardes 1/9. So many yardes of Say must he haue to line the same 4. yards ⅔ of cloth of 6. quart. ½ broad.

More, at 6.s. 8.d. the ell square, what shall a peece of tapistre cost me, which is fiue ells ½ long and 4. ells ¼ broade? Aunswere, multiply 5. ½ by 4. ¼ and therof cōmeth 23. ells ⅜ square: then say by the rule of three, if one ell square cost me 6.s. 8.d. what shal 23. ⅜ cost? Multiplie and diuide, and you shall finde 7. li. 15.s. 10.d. so much the saide peece of tapistrie did cost.

Or otherwise, by the rules of prac∣tise, take the ⅓ of 23. 3/8: and you shall finde 7. li. 15.s. 10.d. as aboue is saide.

More, a peece of Hollande clothe conteining 42. elles ⅔ flemishe, how many elles englishe doe they make? Here must you fyrst note that 100. els flemishe, doe make but 60. elles eng∣lishe, and so consequentlye fiue elles flemishe doe make but 3. els english. Therefore say by the rule of 3. if 5. els flemishe doe make three ells english, how many elles englishe will 42. els ⅔ flemishe make. Multiplye & diuide, so shall you finde 25. elles ⅗ englishe, and so many elles englishe doth 42. 2/3 flemishe conteine, the like is to bee done of all others.

More, I haue bought a peece of Tapistrie, being 5. elles ¾ longe, and 4. elles ⅔ broade measure of Flaun∣ders, I demaunde howe many elles square it maketh Englishe measure?

Aunswere.

First, forasmuch as three ells english are worth 5 elles flemishe, therefore put 3 elles english into hys square, in multiplying 3. by him self which ma∣keth 9: likewise multiplye 5. in hym selfe squarely, and it wilbe 25. Then multiplye 5 ¾ which is the length of the peece, by 4 2/3 which is the breadth, & therof cōmeth 26 elles ⅚ square: thē say by y^e rule of three, if 25 elles square of flemishe measure, be worth 9 elles square of englishe measure, what are 26 elles flemish ⅚ worth? multiplie & diuide, and you shall finde y^t they are worth nine elles 33/80 square of english measure.

More at 3 s. 6 d. y^e ell flemish what is the englishe ell worth after y^t rate. Answere,: saye if 5. elles flemishe bee worth three ells english, what is 1 ell flemishe worth? multiply and diuide, & you shall fynde ⅗ of an englishe ell. Then saye by the rule of 3, if ⅗ of an englishe ell, be worth 3 s. 6 d. what is 1. englishe ell worth? multiplie and

diuide, and you shall finde 5 s. 10d. so much shall the englishe ell be worth.

More at 6 s. 8d. the flemishe ell square, what is y^e englishe ell worth. Answere, say by the aforesaid reasō, if 25 elles flemishe square, be worth 9. elles square englishe, what is one ell square flemishe worth? multiply and diuide, & you shall finde 9/25 of a square englishe ell: Then saye, if 9/25 of an englishe ell be worth 6 s. 8 d. what is one square ell englishe worth? mul∣tiplie and diuide, and you shall fynde 18 s. 6d. 2/9, so much shal one englishe ell square be worth.

¶The sixt Chapter treateth of y^e reducing of the paumes of Ge∣nes into english yardes, wher∣of foure Paumes maketh one englishe yarde.

I Haue bought 97. paumes ½ of Genes veluet, & I would know howe many yardes they wyll

make? Aunswere, Diuide 97. ½ by 4. and you shall haue 24. yardes ⅜. So many yards doe the 97. paumes ½ cō∣teine.

Or otherwise, take some other nū∣ber at your pleasure, as 20. paumes, which doe make fiue yardes, and thē say by the rule of three, if 20/1 paumes, giue 5/1 yardes, what will 97. ½ giue? Multiplye and diuide, and you shall finde 24. yardes 3/2 as before.

More, at two shillings 7.d. y^e paume of Genes, what wil the english yarde be worth after the rate? Aunswere, say by the rule of three, if ¼ of an english yarde bee worthe twoo shillings 7/12. What is 1/1 yarde worth? Multiplie & diuide, and you shall finde ten shil∣lings 4.d. So much is the englishe yarde worthe.

Or otherwise, multiply 4. paumes (which is one yarde) by two shillings 7. pence, and you shall finde 10.s. 4.d. as before.

If 257. Paumes ½ bee worth 20. li. 16.s. 8.d. What is one yarde worthe after the rate? Aunswere, saye: by the rule of 3. if 257. ½ paumes be worth 20. ⅚, what are 4/1 paumes worth. Mul∣tiply and diuide, and you shall fynde 100/309 part of a pounde, which is worth 6.s. 5. pence, 5••/103: so much is one yard worthe.

¶The. vij. Chapter treateth of marchaundise solde by waight.

AT 9.d. ½ the ounce, what is y^e li. waight worth? Answere, say if 3/2 giue 9. ½ what will 16/1 giue multiply and diuide, & you shal finde 12.s. 8.d. so much is the yarde worth?

Or otherwise, by the rules of prac∣tise for syxe pence, take the ½ of 16. which is 8.s. then for 3.d. take the ¼ of 16.s. which is 4.s. Finally, for the halpenye, take 16. ob. which are 8.d. adde all these numbers togither and you shall finde 12.s. 8.d. as before.

More, at 10 d. ½ the ounce, what are 112. li. waight worth after the rate? Aunswere: reduce. 112. li. into oūces, in multiplying. 112. li. by 16. ounces & you shall haue 1792. ounces, thē say by the rule of 3. if

1/1

10 ½

1792/1

: Mul∣tiplie and diuide, and you shall finde 18816 d. which do make 78. li. 8 s. and so much are the 112. li. worth after 10.d ¼ the ounce.

At 12.s. 8d. the li. waight, what is the ounce worth? Answere: put 12.s. 8d. into pence, and you shall haue 152. pence: then say by the rule of 3. if 16. ounces cost 152d. what shall 1. ounce coste, multiplie and diuide, and you shall finde 9.d. ½, so much is the oūce worth.

Or otherwise, take the ¼ of 12 s. 8.d for 4 ounces, and thereof commeth 3.s. 2.d. then for one ounce, take the ¼ of 3.s. 2d. and you shall haue 9.d. ½ as before.

At 32. li. 10.s. the quintall, that is to

saye, the 100. li. waight: what is 1. li. waight worthe after the same rate? Aunswere, Put 32. li. 10.s. all into shil∣lings and you shall haue 650.s.

Then say, by the rule of three, if

100

650

1.

multiply and diuide, and you shal finde, 6.s. 6.d. so much is the li. worthe.

If one pound waight of saffron do cost me 18.s. 8.d. what shal 355. li. 10. oū¦ces cost me by y^e. same price? Aunswere saye by the rule of 3. if

1/1

18 ⅔

355 ⅝

. Multiply and diuide, & you shal finde 331. li. 18.s. 4.d. so much are the 355. li. ten ounces worth.

Briefe rules of vvaight.

WHo that multiplieth the pence that 1. li. waight is worth by 5. and diuideth y^e product therof by. 12. hee shal finde how many poūds in money the quintall is worth, that is to say, how much the 100. li. waight is worth.

And contrariwise he that multipli∣eth

the pounds of money that the 100. waight is worth by 12. and deuideth the product by 5. shall fynde how ma∣ny pence the poūde waight is worth.

¶Example.

AT seuentene pence the pounde waight, what is the 100. pounde waight worth? Aunswere, Multiplye 17. by 5. and thereof cōmeth 85. diuide the same by 12. and you shall finde 7. pound 1/12, which 1/12 is worth one shil∣ling and eight pence. So much is the 100. pounde waight worth.

More, at 13. li. the 100. li. waight, what is one pounde waight worthe? Aunswere, Multiplie 13. by 12. amoun∣teth to 156. the which diuide by 5. and you shal finde 31.d. ⅕ which is 2.s. 7.d. ⅕ and so much is one pounde waight worth.

The lyke is to be done of yardes, elles, or of any other measure, when we recken but fyue score to the hun∣dred.

Briefe Rules for measure.

Who that multiplieth the pence that one ell is worth, by 6. And diui∣deth the product by 12. hee shall fynde how many poundes in money y^e 120. elles are worth, which 120. elles wee count but for a C.

And contrariwise, hee that multi∣plieth the poundes in money that the 120. elles are worth by 12. and diuideth the multiplication by 6. shall fynde howe many pence the ell is worthe.

¶Example.

At ten pence the ell, what are 120. elles worth? Answere, Multiplie 10.d. by 6. and thereof commeth 60: The which diuide by 12. and you shall find fyue pounde, so many pounds in mo∣ney are 120. ells worth at 10.d. the ell.

More, at 9. pounde, the 120. elles, what is one ell worthe? Aunswere, Multiplie nine pound by twelue, and therof commeth 108. the which diuide by 6. and you shall finde 18.d. so much is one ell worth.

The like is to be done of all ma∣ner

of wares, which are sold after 120. for the hundred.

¶Briefe Rules for our hundreth waight here at London, which is after 112. li. for the C.

WHo that multiplieth y^e pence that one pounde waight is worthe by 28. and diuideth the product by 60. shall finde how many pounds in mo∣ney the 112. li. waight is worth.

ANd contrariwise, hee that multi∣plieth the poundes in money that 112. li. is worth by 60. and diuideth the product by 28. shall finde how many pence one li. waight is worth.

¶Example.

AT nine pence the pound waight, what is the 112. li. waight worth? Aunswere: multiplie 9.d. by 28, and thereof cōmeth 252, the which diuide by 60. & you shall finde 4. li. 12/60 which being abbreuiated is 1/5 of a pounde, which is worthe 4.s. And thus the 112. li. is worth 4. pound 4. shil.

At 8. li. y^e 112. li. waight, what is 1. li. waight worth? Answere, Multiplie 8. li. by 60. and thereof commeth 480, y^e which diuide by 28. & you shall finde 17.d. 1/7: so much is 1. li. waight worth.

¶The. viij. Chapter treateth of tares and allowances of mar∣chaundise solde by waight.

AT 12. li. the 100. suttell, what shall 987. li. suttell be worth? in giuing 4. li. waight vpon euery 100 for tret? Answere, adde 4. li. vnto 100. & you shall haue 104. Then say by the rule of thre, if 104 be worth 12. li. what are 987. li. waight worth? multiply & diuide, & you shal finde 113. li. 23/26 which is worth 17.s. 8.d. 4/13. So much shal y^e 987. li. waight be worth.

104.

12.

987.

At 6.s. 8.d. y^e pound waight what shall 345. li. ½ be worth in giuing 4. li. waight vpon euery 100. for the tret. Answere, see first by the rule of three,

what the 100. pound is worth saying, if

1/1

6 ⅔

100/1

Multiplie and diuide, & you shal finde 33. li. ⅓ then adde 4. li. vnto 100. & they are 104. thē say againe by the rule of 3. if a 104. li. be solde for 33. li. ⅓ for how much shall 345. li. ½ be solde? multiply & diuide, and you shal finde 110. li. 14.s. 8.d. 12/13 So much shal the 345. li. ½ be worth, at 6.s. 8.d. the pound, in giuing 4. vpon the 100.

More, if 100. bee worth 36.s. 8.d. what shall 780. li. bee worth in reba∣ting 4. li. vpon euery 100. for Tare & Cloffe? Answere, Multiply 780. by 4. and therof commeth 3120. The which diuide by 100. and you shall haue 31. li. ⅕ abate 31. ⅓ from 780. and there wyll remaine 748 ⅘. Then say by the rule of three, if 100/1 do cost 36. ⅔, what will 748. ⅘ cost after the rate? Multiplie & diuide so shall you finde 274.s. 6.d. 18/25, and so much shall the 780. li. cost, in rebating 4. li. vpon euery 100. for Tare and Cloffe.

More, whether doth he lose more that giueth 5. li. vpō the 100. or he that rebateth 5. li. vpon the 100. for tare and cloffe? Answere. Fyrst, note that hee which giueth 5. li. vpon the 100. giueth 105. for 100: and he which rebateth 5. li. vpon the 100. giueth the 100. for. 95. Therefore say by the rule of 3. if 105. be giuen for 100. for how much shall y^e 100. be giuen? Multiply and diuide & you shal finde 95. 5/21: and he which re∣bateth 5. vpon the 100. maketh but 95. of 100: so that he loseth 5. vpon the 100. & the other which giueth 5. vpon y^e 100 loseth but 4. 16/21 vpon the 100. Thus he y^t rebateth 5. vpon the 100. loseth more by 5/21 vppon the 100. than the other which gaue 5. vpō the 100. for tare and cloffe.

If 100. of Allam doo cost mee. 26.s. 8.d. how shall I sell the li. waight to gaine after the rate of 10. vpon y^e 100. Answere, put 26.s. 8.d. al into pence, & you shal haue 320.d. Thē say by y^e rule of 3. if 100. giue 110. what shal 320. giue,

multiplie and diuide, and you shall finde 352.d. Thē say, if 100. li. be worth 352.d. what is 1. li. multiplye & diuide, and you shall haue 3.d. 26/50 which 26/50 is worth ½, and 1/25 of ½. That is to saye, the pounde waight shalbe worth 3.d. ½. 1/25 of a halfe pennye, in gaining 10. vpon the 100.

If one pound waight doe cost me, 6.s. 10.d. and I sell the same for 7.s. 2.d. I demaund how much I should gaine vpon the 100. li. of money after the rate? Answere, say by the rule of 3. if 6. ⅚ yelde 7. ⅙ what will 100/1 yelde? Put the whole numbers into theyr broken, then multiplie and diuide, & you shal finde 104. 36/41 from the which substract 100. and there resteth 4. li. 36/41 so much is gained vpon the hundred pounde of money after the rate.

More, if one pound do cost me 5.s. 4.d. and I sell the same againe for 4. s. 9.d. I demaunde how much I shal lose vpon the 100. pounde of money? saye, if 5. ⅓ doe giue but 4. ¾, what

shall 100/1 giue? Put the whole num∣ber into their broken. Then multi∣plie and diuide & you shall finde 89. 1/16 the which you must substract frō 100. and there wyll remaine 10. li. 15/16, so much is loste vpon y^e 100. li. of money.

More if the li. waight doe cost mee 3.s. 2.d. & I sell it againe for 4.s. 4.d. how muche shall I gaine vpon 20.s. Answere: say if 3. ⅙ giue 4. ⅓ what shal 20/1 giue, Multiplie and diuide & you shall fynde 27.s. 7/19: out of the which abate 20.s. and there will remaine 7. shillings. 7/19, which is 4.d. 4/19: and so muche is gained vpon the pounde of money that is to say vpon 20.s.

If the pounde waight doe coste me 4.s. 4.d. and I sell it againe for 3.s. 2.d. I demaunde howe muche I shall lose vpon the pounde of money? that is to saye vpon twenty shillings.

Answere: say, if 4. ⅓ giue but 3. ⅙ what wil 20/1 giue, multiply & diuide & you

shal finde 14.s. 8/13 the which you must abate from 20.s. & there wil remaine 5.s. 5/13 which 5/13, is worth 4.d. 8/13 of a pennye and so much is loste vpon the pounde of money.

¶The. ix. Chapter treateth of certeine questions, done by the double rule, and also by y^e rule of three compounde.

WHen the quarter of wheate, doth cost 6.s. 8.d. the loafe of breade waying 20. ounces is solde for a ob. I demaund y^t if y^e quar∣ter of wheat did cost ten shillings, for how much shall the loafe of breade be solde, that wayeth 16. ounces?

Aunswere: by the fyrst part of y^e rule, of 3. compound which is mentioned in the thirde part of thys booke, and in the seconde Chapter of the same. Therfore say by the same first part of y^e rule of 3. cōpound, if

6. ⅔

20/1

½

10/1

16/1.

Then multiplye the fyrst number

by the seconde, and the product therof shalbe your diuisor. Likewise multi∣plie the other three numbers the one by the other, and the product thereof shalbe your diuidende: as thus, first multiply 6. ⅔ by 20/1, and thereof com∣meth 400/3 for your diuisor, then mul∣tiply ½ by 10/1 and the product therof by 16/1, so you shall haue 160/2 for your nū∣ber that is to be diuided, then diuide 160/2 by 400/3, and thereof commeth 480/800 y^e which being abbreuiated bringeth ⅗ of a peny: and for y^t price must the loafe of bread be solde, which wayeth 16. ounces, and the quarter of wheate being worth ten shillings.

Or otherwise by the rule of 3. at two times. First saye if 20/1 ounces giue, ½ what wyll 16/1 ounces gyue? Multiplie and diuide, and you shall fynde ⅖ of a pennye. Then saye a∣gaine, if 6. 2/7 doe giue mee ⅖, what will 10/1 giue? Multiplye and diuide, and you shall fynde ⅗ of a pennye, as afore is sayde.

When the cariage of one hundreth wayghte of marchaundise 50. miles doth cost 5s. what shall the cariage of 500 waight coste me for 16 miles?

Answere, By the fyrst part of the rule of 3 compound, saying if

100

50

5

500

16.

Multiply 100 by 50 the product wyl be 5000, which shal bee your diuisor. Then multiply 5 tymes 500 by 16 and therof commeth 40000 for your diui∣dend. Therfore diuide 40000 by 5000 and you shall finde 8 s. so muche shall coste the carriage of 500 wayghte 16 miles.

Or otherwise by the double rule of three, that is to saye by the rule of thre at two times: first say if 50 miles do paye 5 s. what shall 16 miles paye? Multiply and diuide, & you shall find 1 s. ⅗. Then say, agayne, if 100 waight do cost me 1 s. ⅗ what shal 500 wayght cost? Multiply and diuide, and you shall finde 8 s. as before.

When the cariage of 100. pounde waight of Marchaundise 84. miles, doth cost me six shillings, how many miles may I haue 64. pound waight caried for three. s. 4.d. Aunswere, by y^e second part of the rule of three com∣pounde: saye if

100/1

14/1

6/1

64/1

3 ⅓.

Then multiplie the fourth num∣ber 64/1 by the thyrde number 6/1, and thereof commeth 304/1 for your diuisor. Likewise multiplie 3 ⅓ by 100/1, and by 14/1 and you shall haue in the product 14000/3: then diuide 14000/3 by 384/1 and you shall fynde 72. miles 11/12 of a mile. So many miles shall y^e 64. li. waight be caried, for three shillings 4.d.

Otherwise by the rule of three, at two times: Fyrst say, if 100. waight doe cost me 6.s. what shall 64. pound waight cost? Multiplye and diuide, and you shall finde three shillings .21/25. Then saye, if 3. 21/25 bee payed for 84. miles cariage: for howe many miles shall 3.s. ⅓ be payed? Multiplye & di∣uide and you shall finde 72. miles. 11/12.

If 100. horses in 100. dayes do spende 180. quarters of otes: howe manye quarters of otes wil 350. horses spend in 150. dayes? Answere: by the fyrste part of the rule of three compounde: multiply 180. times 350. by 150. and di∣uide the product by 100. times 100: and you shall finde 945. quarters. So ma∣ny quarters of Otes will 350. horses spende in 150. dayes.

Or otherwise by the rule of 3. at two times: fyrst say, if 100. dayes doe yelde mee 180. quarters of otes: what shall 150. dayes yelde: multiplye and diuide, and you shall finde 270. quar∣ters: then say againe, if 100. horses do spende 270. quarters of Otes, howe many quarters of otes wyl 350. horses spend? Multiply and diuide, and you shall finde 945. quarters as before.

¶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.

¶The xj. Chapter treateth of the Rules of barter.

[unspec I] TWoo Marchants wil chaūge their marchandise, the one w^t the other. The one of them hath cloth of 7.s. 1.d. y^e yarde to sell for ready money, but in barter he will sell it for 8.s. 4.d. The other hath Sinamon of 4.s. 7.d. y^e li. to sell for ready money. I demaund how he shall sell it in barter to the ende he be no loser? Answere, say, if 7. 1/12 (which is y^e price y^t the yard of cloth is worth in redy 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 y^t the li. of Synamon is worth in ready money, reduce the whole numbers into their

brokē, and then multiply and diuide, and you shall finde 5.s. 4.d. 12/17 parts, of a peny, and for so much shall he sell the pounde of Synamon in barter.

2. Two Marchaunts wil chaunge their marchaundise the one with the other, the one of them hath Chaum∣lets of two pounde 18.s. 4.d. the peece to sell for ready money, and in barter he wyll sell the peece for 4. li. 3.s. 4.d. the other hath fine capps of 35.s. 10.d. y^e dossen to sell in barter. I demaund what y^e dossen of caps did cost in redy money? Answere, say if 4. li. 3.s. 4.d. which is the ouerprice of the peece of Chamlet, become of 2. li. 18.s. 4.d. which was the iust price of the same, of what shall come 35.s. 10.d. which is the ouerprice of the dossen of cappes? Multiply and diuide, & you shall finde 25.s. 1.d. and so much are the dossen of capps worth in redy money.

3. Two Marchaunts wil chaunge their marchaundise the one with the other: y^e one of them hath Fustians

of 18.s. 4.d. the pece to sell for readye money, and in barter hee will sell the peece for 26.s. 8.d. The other hath tapistry of 15.d. the ell to sell for readie money, and in barter hee wyll sell it for 20.d. the ell: I demaunde which of them gaineth, and how much vpō the hundred pounde of money?

Aunswere: saye if 18.s. ⅓ (which is the iust price of the peece of Fustian) bee solde in barter for 26.s. ⅔: for howe much shall 1.s. ¼ (which is the iuste price of the ell of tapistry) bee solde in barter? Multiplie and diuide, & you shal finde 21.d. 9/11. And he doth ouer∣sel it but for 20.d. so that of 21.d. 9/11: he maketh but 20.d. And therefore saye by the rule of three, if the seconde marchaunt, of 21 9/11, do make but 20/1 how much shall he lose vpon the 100/1? Multiplie and diuide, and you shall finde 91. ⅔, y^e which being abated frō a hūdred there wil remaine 8. ⅓. And after y^e rate of 8. ⅓. doth y^e secōde mar∣chāt lose vpō y^e 100. And consequētly,

the first marchaunt, of 20.d. maketh 21.d. 9/11: and therefore saye againe by y^e rule of three, if the first marchaunt of 20/11, do make 21.9/11 how much shall he gaine vpon 100/1? Multiplie and di∣uide, and you shall finde 109. li. 1/11.

Thus the fyrst gaineth after the rate of 9. li. 1/11: vpon the hundred pounde of money.

For your better vnderstanding of these Questions, you must note that when one marchaunt gaineth of an other after the rate of ten pound vpō y^e hundred pound he gaineth the 1/10 of his owne principall, and the other which loseth after the rate of 9. 1/11 vp∣on the hundred he loseth the 1/11 of his principal. And it may be proued thus: When one marchaunt will sell hys wares vnto another, which wares stande him but in 100. li. & hee will sell them for 110. li. he, of his 100. li. maketh 110. li. wherfore hee gaineth after 10. li. vpon the 100. which is the 1/10 of hys principall, and the other which byeth

wares for 110. li. that cost but 110. poūd of the 110. pound he maketh but 100. li. And therefore say by the rule of thre, if 110. become of 100. of howe much shall come 100? Multiplie and diuide, and you shall finde 90.10/11, the which abate from 100: and there resteth 9.1/11 is the 1/11 of hys principal that the se∣conde loseth vpon the 100. as afore is saide. And therefore, who so that wil know what one Marchāt gaineth of another, either after the rate of tenne vpon the hundred, which is the 1/10 of of hys principall, or else after the rate of twenty vpon the hundred which is the ⅕, or of any other parte, and that he would likewise knowe what part the other loseth of hys principall: hee must take for the numeratour of the broken number of hym that loseth, as much as for him that gaineth, thē adde the numerator and the denomi∣nator (of the broken number of hym that gaineth) both togither, & make thereof the denominator of the brokē

number of him y^t loseth, & then shall you haue the part of him that loseth, as by exaumple, of him that gayneth after ten. li. vpon the 100. li. which is the 1/10 of hys principall: take the nu∣meratour which is 1. and make that the numerator of the broken number of him that loseth, then adde 1. which is y^e numerator of the fraction of him that gaineth with ten, whych is hys denominator, & you shall haue 11. for the denominatour of the fraction of him that loseth. Then put one ouer the 11. and so you shal haue 1/11. Thus it appereth when one marchant gai∣neth of another after ten vppon the hūdred, he gaineth the 1/10 of his prin∣cipall, and the other loseth 9. 1/11 which is the 1/11 of his principall. And yf hee would gaine after 20. vpon the hun∣dred which is the ⅕ of hys principall, the other shoulde lose 16. ⅖ which is the ⅙ of hys principall, and so is to bee vnderstande of all 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 sell for readye money, and in barter he will sell the peece for 23.s. 4.d. & yet hee will gaine moreouer after ten pounde vpon the hundred pound. The other hath woll of 50.s. the hundred to sell for readye money. I demaund how hee shall sell the C. of woll in barter? Aunswere, say if 20.s. 10.d. which is the iust price of the peece of Sey, be solde in barter for 23.s. 4.d. for how much shall 50.s. (which is y^e iust price of y^e C. of woll) be solde in barter? Multiplie & diuide, & you shal finde 56.s. Thē for bicause the first marchant gaineth after 10. li. vpon the C. li. he maketh of his C. li. 10. li. & consequently the seconde mar∣chaunt maketh of 110. li. but 100. li. And therfore say, if the seconde mar∣chaunt of 110. doe make but 100. how much shall he make of 56: Multiplie & diuide, & you shal find 50.s. 10.d. 10/11 of

a peny, and for so much shall he sell y^e hundred of woll in barter.

5. More, twoo Marchauntes wyll chaunge their marchaundise, the one with the other, the one of them hath Taffeta, of 16. crownes the peece to sell for redie money, and in barter he will sell the peece for twēty crownes, and yet he wyl gaine moreouer after ten pounde, vpon the hundred poūd. The other hath ginger of 3.s. 9.d. the pounde waight, to sel in barter. I de∣maunde what the pounde dyd coste in readye money? Aunswere: saye if twēty crownes which is the surprice of the peece of Taffata, become of 16. crownes the iuste price, of how much shall come. 3.s. 9.d. which is the price of the ouerselling the pound of Gin∣ger? Multiply & diuide, and you shall finde 3.s. Then, for bicause that the Marchaunt of Taffeta wil gayne af∣ter the rate of ten vpon the hundred: say if 100. doe giue 110. what shall 3.s. giue? Multiplye and diuide, and you

shall finde 3.s. 3.d. ⅗ and so much dyd the pounde of Gynger cost in readye money.

6. More, two marchaunts wyll chaunge their marchaundise the one with the other, the one of them hath Worsteds of 25.s. the peece to sell for ready money, and in barter, hee wyll sell the peece for 33.s. 4.d. and yet hee loseth after ten vpon the hundred: the other hath waxe of 3. li. 6.s. 8.d. the hundred to sell for readye money. I would know howe he should sell hys waxe in barter? Aunswere: say if 25.s. which is the iuste price of the peece of Worsted bee solde in barter for 33.s. 4.d. for how much shall three pounde 6.s. 8.d. be solde, which is the iuste price of the hundred of waxe. Multi∣plie and diuide, and you shall fynde 4. li. 4/9 which is 8.s. ten pence, ⅔ then for bycause that the Marchaunt of Worsteds, loseth after ten vpon the hundred: Of a hundred hee maketh

but 90. And therefore, saye: If 90. giue 100. what giueth 4. pounde. 4/9? Multiplie and diuide, and you shall fynde 4. 76/81 which is worthe 18.s. 9.d. 5/27, and for so much shall he sell y^e 100. of Ware in barter.

7. More, two Marchaunts wyll chaunge their marchaundise the one wyth the other, the one of them hath Worsteds of 5. pounde 6. shillinges, eight pence the peece to sell for ready money, and in barter he will sell the peece for 6. pounde, 13. shillings. 4.d. and yet he loseth after ten vppon the hundred, and the other hath Muske of two shillings, nine pence ⅓, the poūd waight, to sell in barter? I demaūde what the pound did cost in ready mo∣ney? Answere: say if 6. pound. ⅔ which is the ouerprice of the peece of Wor∣sted, become of 5. pound, ⅓ which is y^e iuste price of the same, of how much shall come two shillings 9. pence. ⅓.

Multiplie and diuide, & you shal finde 2. 2/9 which is 2.d. ⅔ then for bicause y^t the marchaunt of Worsteds loseth after ten vpon the hundred, of a hun∣dred he maketh but 90. and therefore say if 100. giue but 90. how much shal 2.s. 2/9 giue? Multiplie and diuide and you shall fynde 2.s. and so much cost the pound of Muske in ready money.

Other Rules of Barter, vvherein is giuen some part in ready money.

WHen a Marchaunt ouer sel∣leth hys marchaundise & he wyll giue also some part of hys ouerprice in ready mo∣ney as the ½ the ⅓ or the ¼ &c. He must substract the same parte of money frō the iuste price, and also from the ouer price of hys marchaundise: and the two numbers that remaine after the substraction is made, shalbe that two first numbers in the rule of three and the iuste pryce of the seconde mar∣chaunt

shalbe the third, to know how much he shall ouersell the part of his marchaundise.

8. Two Marchaunts wyll chaūge theyre marchaundise the one wyth the other, the one of them hath fyne woll at fiue pound the hundred, to sel for ready money, and in barter he wil sell it for six pounde, and yet hee wyll haue y^e ⅓ in ready money. The other hath cloth of 13.s. 4.d. to sel for ready money. I would know how hee shall sell y^e same in barter? Aunswere: take the ⅓ of 6. li. which is the ouerprice of the 100. of wolle, & you shall haue 2. li. the which abate frō 5. li. which is the iust price of y^e 100. of wolle & from 6. li. which is the ouerprice, and there shal rest 3. li. and 4. li. for the two first nū∣bers in the rule of three, thē take 13.s. 4.d. which is the iust price of a yarde of cloth for the thirde number: Then multiply and diuide & you shal finde 17.s. 9.d. ⅓: for so muche shall the se∣conde sell his cloth in barter.

9. More, twoo Marchauntes wyll chaunge their marchaundise the one with the other, the one of them hath waxe of thre pound 6.s. 8.d. the C. to sel for readie money, and in barter he will sell the same for 4. li. 3.s. 4.d. & yet he will haue the ¼ in redy money: and the other hath fine Crimson sat∣tine of 15.s. the yarde to sel in barter. I demaund what it is worth in redy money. Answere, Take the ¼ of 4. li. 3.s. 4.d. and abate it frō 4. li. 3.s.4.d. and from three pounde 6.s. 8. pence, and there resteth 3. li. 2.s.6.d. & 2. li. 5.s. 10.d. for the two first numbers in the rule of three, and 15.s. for y^e thirde number which is the ouerprice of the yarde of sattine. Then multiply and diuide, and you shall fynde 11.s. And so much did the yarde of Sattine cost in ready money.

10. Twoo Marchaunts will chaūge their marchaundise the one wyth the other, y^e 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 hee wyll gaine after ten vpō the hundred, and yet he will haue y^e one halfe in ready money: and the other hath leade of 3. halfepence the li. to sel for redy mo∣ney. I demaund how hee shal sell the pounde in barter? Answere: See first at ten vppon the hundred, what the three pound ⅓ wil 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 whych he demaundeth in ready money, is 36. shillings and 8. pence, the whych being abated from fyftye shillings, and also from three pounds 13. shillings 4. pence, there shall reste 13. shillings 4. pence, and one pound 16.s. 8.d. for the twoo firste numbers in the rule of three, which you muste put al into halfepence, and thre halfe∣pence for the thirde number, and thē multiply and diuide, & you shall finde 4.d. ⅛, and for so much shall he sell y^e pounde of leade in barter.

11. More, twoo marchauntes wyll chaunge their marchaundise the one with the other, the one of them hath steele of 16.s.8.d. the hundred waight to sell for ready money, & in barter he will sell it for 25.s. and yet hee loseth after ten vpon the hundred, but hee wyll haue the ½ in readye money, the other hath yron of 6.s. 8.d. the hun∣dred to sell in barter, I demaunde what it did coste in readye money? Aunswere: say if a hundred come but to 90. how much shall 25.s. come to? Multiplie and diuide, and you shall fynde 22.s.6.d. of the which number, take the ½ which is 11.s. 3.d. & substract it from 22.s.6.d. and from 16.s.8. pēce and there shall rest 11.s.3.d. and 5.s.5. pence, for the two fyrst numbers in y^e rule of thre, and 6.s. 8.d. which is the ouerprice of a hundred of yron for the thyrde number, then multiplie and diuide, and you shal finde 3.s. 2. pēce, 14/27: & so much did the hundred of yron cost in ready money.

12. More, twoo marchaunts wyll chaunge their marchaundise, the one with the other, the one of them hath seyes of 20.s. 10.d. y^e peece to sel for re∣dy money, & in barter he wyll sell the peece for 21.s. & hee wyll haue the ¼ in ready money: The other hath capps of 35. shillings the dossen to sell for re∣dy money: but hee wyll gaine after ten vpon the hundred. I demaunde how he shall sell y^e same caps in bar∣ter? Aunswere: saye if a hundred bee worth 110. What shal 35.s. be worth, which is the iust price of the dossen of cappes? Multiplie and diuide, and you shall fynde 38. shillings 6. pence. Then take the ¼ of 25. which is 6.s. 3.d. and substract it from 20.s. 10.d. & from 25.s. and there shall rest 14.s. 7.d. and 18.s. 9.d. for the twoo fyrste numbers in the rule of three, and 38.s 6.d. which is the iust pryce wyth hys gaine of the dossen of cappes, for the thirde number: then multiplie and diuide, and you shall finde 49.s. 6.d.

and for so much hee shall sell the dos∣sen of caps in barter.

¶The 12. Chapter treateth of the exchaunging of money from one place to another.

FIrst, you must note, that at Andwerpe they vse to make their accomptes by Deniers de gros, that is to saye by pence Fle∣mishe, whereof 12. doe make 1.s. Fle∣mishe, and 20, shillings Flemishe doe make 1. li. de gros.

1. If I deliuer in Flaunders, 500. li. Flemishe, at 19.s.6. de gros that is to say at 19.s. 6.d. Flemishe, to receaue 20.s. at London, I demaunde how much I shal receaue sterling at Lon∣don for the sayde 5. hundred pounde Flemishe? Answere,: Say, if 19 ½ giue 20/1, what will 500/1 giue? Multiplie & diuide, and you shal fynde 512. li.16.s. 4. pence 12/13 of a pennye. And so much sterling shal I receaue in London for

my 500. li. Flemishe.

2. If I deliuer in Londō 375. li.ster∣ling, to receaue in Andwerp 21.s.9.d. de gros, that is to say Flemishe, for euery pounde sterling. I demaunde how many poundes Flemish I shall receaue in Andwerpe, for the sayde 375. li. sterling? Answere, say if 20/1 giue 21. ¾: what will 375/1 giue? Multiplie & diuide, and you shall finde 407. li. So many poūds Flemish shal I receaue for the said 375. li. ster. in Andwerpe.

3. If I take vp money at Andwerp after 19.s. 6.d. flemishe to pay for the same at London 20.s. ster. and when the day of paiment is come, I am for∣ced to rechaūge the same, and to take vp money againe here in London to repaye the same, so that for twentye shillings, which I take vp here, I must repay, 19. shillings 9 d. at And∣werpe. I demaunde whether I doe winne or lose, and how much vpon y^e 100. li. of money? Answere, Say. if 19. 3/4 giue 19. ½, what will 100/1 giue?

Multiplie and diuide, and you shall finde 98. 58/79, the which beyng abated frō a hundred there wil remaine 1. 21/79. And so much doe I lose vpon the 100. pounde of money.

4. If I take vp at London 20. shill. sterling to pay at. Andwerpe 21. s. 8. d. Flemishe, and when the day of pay∣ment is come. I am constrained to take vp money againe at Andwerpe wherwith to repay the foresaide sum: and there I doe receaue 22. shillings. Flemishe to pay 20. shill. at London. Nowe I demaunde whether I doe winne or lose and howe much vpon the 100. li. of money after the rate? Answere, say if 21. ⅔ giue 22/1. What wil 1000/1 giue? Multiply & diuide, and you shall finde 101. 7/13, frō the which abate 100. and there wyll remaine 1. 7/13, and so much shal I gaine vpon the 100. li. of money.

The exchaunge from London in∣to Fraunce, is not lyke as it is

into Flaunders but is deliuered by the French crowne, which is worth 50. souse Tournois the peece.

And here muste you note that in Fraunce they make theyr accompte by Deniers Tournois, wherof 12. ma¦keth one souse Tournois, and 20. sou. Tournois maketh 1. li. Tournois, which they cal a Liuer, and y^e Frēche Crowne is currant amonge Mar∣chaunts for 51. souse Tournois, but by exchaunge it is otherwise, for thei wyll deliuer but 50. sou. Tourneys, which is. 2. li. 10. sou. Tournois for a crowne, or at such price as the takers vp of money can agree wyth the deli∣uerer. As by Example.

5. If I deliuer 340. li. ster. here in London after 6. s. 4. d. sterling the crowne, to receaue at Roan, or at Parris 50. sou. Tournois for euery crowne, I would knowe how many Liures Tournois I shall receaue

there for my 340. li. ster. Answere: say if 6. s. ⅓ doe giue mee 2. li. ½. Tour. what will 6800/1 shil. giue (which is the 340. li. reduced into shillings) multi∣plye and diuide, and you shall fynde 2684. Liures 4/19 which is worth 4. s. 4/19 Tournois, and so much shall I re∣ceaue in Roan or Parris for my 340. li. sterling.

6. If I deliuer in Parris or Roan, or elsewhere in Fraunce 1250. Liures Tournois, at 50. sou. Tournois the crowne to receaue for euerye suche crowne, 6. s. 3. d. sterling at London. I demaunde how much sterling mo∣ney I shal receaue at London for my 1250. pound Tournois. Answere: say, if two pounde, ½ doe giue mee 6. shil. ¼, what will 1250/1 giue? Multiplye & diuide, and you shall fynde 3125. shil. sterling, which maketh 156. pounde, 5. shillings sterling. And so manye poundes shall I receaue at London, for the sayde 1250. pounde Tour∣nois,

after 6. shillings three pence for euery crowne.

¶The 13. Chapter treateth of the Rule of Alligation.

THe Rule of Alligation is so named, for that it tea∣cheth to alligate or bynde togither diuers percelles of sundrie prices, and to knowe how much you must take of euery percell, according to the numbers of the Question.

¶Example.

1. A Goldsmith hath three sortes of Golde. The fyrste is worth thirtye Crownes the pounde waight: The seconde is worth 36. Crownes. And the thyrde is worth 45. crownes, and of these three sortes hee wyll make a Scepter of syxe pound waight, which shall be worth fourtye Crownes the pounde. I demaunde how much hee must take of euery sorte?

Aunswere: fyrst you must set downe the numbers wherof you shall make y^e Alligation (which are 30.36.38. & 45. orderly the one vnder the other, as yf you should make of them an additiō: and the common number wherunto you will reduce them, shall you set on the left hand, which common nū∣ber in this exāple is 40. Then marke what summes bee lesser than that commō number, and which be grea∣ter, and with a draught of your pen, euermore lynke two numbers togi∣ther, so that the one be lesser thā that commō number, and the other grea∣ter than he. For two greater nor two smaller numbers may not be lynked togither, for they wil either be lesser, or else greater than the common nū∣ber: but one greater number, and one smaller may bee so mixed, y^t they wyl make the common number. And two greater or twoo smaller nūbers, can neuer make the common num∣ber in due order, as hereafter shall

appeare.

After that you haue thus lynked them, then marke howe much eche of the lesser numbers is smaller than the common number, and that diffe∣rence shal you set against the greater numbers, which be linked with those smaller, eche of them with his match still on the right hande. And likewise you must set the excesse of the greater numbers against the lesser which bee combined with them. Then shal you adde all those differences into one summe, which shalbe the fyrst num∣ber in the rule of three, and the second number shalbe y^e whole massye peece that you wyll haue of all the perticu∣lers, the thirde summe shall be eche difference by it selfe, and by thē shall you finde out the fourth number, de∣claring the iust portion of euery par∣ticuler in that mixture, as nowe by the former exaumple, I wyll make it playne.

The prices seuerall.	The diffe∣rences.
The common price or nūber.	40	30	5.	A
36	2.	B
42	4.	C
45	10	D
			21.

21.	.6.	.5.
21.	.6.	.2.
21.	.6.	.4.
21.	.6.	.10.

Here in this former example, you see that I haue set downe the seueral prices, whych bee 30.36.42.45. and haue linked togither 30. with 45. and 36. with 42. The common price 40. I haue set on y^e left syde, & the diffe∣rence of it from euery seuerall price, I haue sette on the righte hande, a∣gainst that summe with the which it is lynked. So the difference of 30. frō

fourtie is ten, which I set against 45. that hee is lynked with all, and the difference of 45. about 40 is 5. which I haue set againste. 30. So likewyse, the difference of 42. aboue 40. is 2. that I haue set against 36. And the differēce betweene 36. and 40. (which is 4.) I haue set againste 42. Then I adde all those differences togither & they make 21. which I make the fyrst number in the Rule of thre, and syxe the seconde number, which is the waight of the Scepter of Golde, and the thyrde number shall bee euerye particulers differēce. Then I worke by the Rule of three: saying if twenty and one (which is the differences ad∣ded togither) do giue mee syx pound, which ts the waight of the Scepter, what shall fyue giue, which is the fyrste difference?

Multiplye and diuide, and you shall fynde one pounde 3/7: so much muste I haue of the fyrste price.

Then doe likewyse with the rest and you shall finde 4/7 of the seconde price, one pound, 1/7 of the thirde price, and 2. li. 6/7 of the fourth, the which foure summes being added togither, doe make 6. li. which is the totall that I would haue. And now to proue if the pryces doe agree, you shall doe thus: Fyrst multiply this totall summe 6. by the common price 40. and it wyll make 240. crownes, which you shall keepe by it selfe. And afterward mul∣tiply euery seueral summe of waight by the price belonging to the same waight, and if that summe doe agre with the fyrst that you kept by it self, then is your work well done, as here one pound, 3/7 is the waight of y^e sorte of golde which is of 30. crownes price. Then multiplye 30. by 1. li. 3/7, & it ma∣keth 42. crownes 6/7, which you shall set downe. Then multiplye 4/7 (which is the wayght of the seconde sorte of gold) by 36. which is y^e price of y^e same & thereof commeth 20. crownes 4/7: so

againe 1. li. 1/7 multiplied by 42. doth make 48. crownes. And last of al 2. li. 6/7 multiplied by 45. maketh 128. crow∣nes 4/7. All these added togither doth make 240. crownes, agreable to the former summe of 40. multiplied by 6 And thus I maye affirme that thys worke is well done.

2. A Tauerner hath foure sortes of wyne, of foure seuerall prices, the fyrst of eight pence the Gallonde, the second of ten pence the gallonde, the thirde of 15. pence and the fourthe of 18. pēce. And he wil mingle one pun∣chen with all these sortes, so that the Gallonde shall bee worth but twelue pence. I demaunde how many Gal∣londes he muste take of euery sorte? Aunswere: First suppose the punchen to holde some certaine measure, as to conteine 84. gallonds and then the forme wyll be after thys sort, as you see hereafter folowing.

12	8	3
10	6
15	4
18	2
		15

If 15. doe giue 18.

What will. 3.	They make	16 ⅘ of the first.
What will. 6.	33 ⅗ of the secōde
What will. 4.	22 ⅖ of the third.
What will. 2.	11 ⅕ of the fourth
		84

¶The 14. chapter treateth of the Rule of falsehode, or false po∣sitions.

THe rule of falsehode is so na∣med, not for that it teacheth any deceit or falsehode, but y^t by fained numbers taken at al aduētures, it teacheth to finde out the true nūber y^t is demaunded. And this (of all the vulgare Rules which are in practise) is the most excellent: this rule hath two partes y^e one is of one false position alone: y^e other is of two positiōs as hereafter shal appere

Those questions which are done by false positions, haue theyr opera∣tions, in a maner like vnto that of the rule of three, but only that in the rule of three, we haue thre numbers kno∣wen, and here in thys rule wee haue but one (I meane that commeth in operation) vnto the likenes whereof wee muste diuise two other, the one multiplying, and the other diuiding, as by example.

1. I haue deliuered to a banker a certeine summe of poundes in mo∣ney, to haue of hym by the yeare 6. li. vpon the 100. li. And at the ende of 10. yeares, he paide mee 500. li. for al both principal and gaine. I demaund how much was the principall summe that I deliuered at the fyrst. Here you see that there are diuers termes: but the chiefe to worke with all is 500. pound which commeth of the other num∣bers, that is to saye, of 10. and 100. for of them is compounde the tenour

of the question, the practise whereof is thus.

Let vs faine a number at pleasure, and wyth the same let vs make oure discourse, euen as though it were the principall summe that wee seeke for. As by Example. Suppose that I de∣liuered him at y^e first 200. li. the which were worth to me in ten yeres. 120. li. after the rate of 6. li. vpō the hundred poūde. Thē 120. li. added with 200. li. Do make but 320. li. and I must haue 500. pound. Thus you see that I haue three termes for the rule of three: the one which shall conteine the Questiō the other two, which I haue formed artificially, which are 200. and 320: in such sort, that 320. ought to haue such proportion to 200, as 500. hath vnto y^e number that I seeke: that is to saye, vnto the true principall summe, then must I haue recourse vnto the rule of thre, after this sorte, saying.

If 320. li. become of 200. li. of howe much shall come 500. li. Multiply 500. by 200. and thei are 100000. the which you shall diuide by 320. li. and thereof commeth 312. li. ½ which is y^e summe that I deliuer at the first. And thus, this rule hath some congruence with the double rule of three.

2. I haue a Cesterne with 3. vnegal cockes conteining 60. pipes of water: And if the greatest cocke bee opened, the water wyll auoide cleane in one houre, at the seconde it wyll auoide in twoo houres, and at the thyrde it will require three houres. Nowe I demaūde in what space wil it auoide, all the cocks being set open. Suppose that it will auoide in halfe an houre, that is to say, in 30. minutes. Then must there auoide at the fyrste cocke the ½, which is thirtye pipes, and by the seconde cocke the ¼ whiche is 15, pipes, and by the thirde cocke the ⅙, that is tenne pypes, all the whych

summes being added togither dooe make 55. pipes, but it shoulde bee 60. pipes. Therefore I say by the rule of three, if 55. pipes doe voide in 30. mi∣nutes: in how many minuts wil 60. pipes voide? Multiplie and diuide, & you shall finde 32. minutes 40/55. And in that space will the water auoide if all the cockes be set open.

¶Of the Rule of twoo false po∣sitions.

* 1.2THe sūme of this Rule of two false positions is thus, when any questiō is proponed ap∣pertaining to this rule. First imagine any nūber at your pleasure, which you shal name the first positiō, and with the same shall you work in stede of the true number, as y^e questiō doth import, and if you see y^t you haue missed. Then is the last number of y^e work either to great or to little, that shal you note for to be y^e fyrst errour,

in the which you haue missed with y^e signe of more, or lesse, which signes shalbe noted with these figures, 4:—. This figure 4: betokeneth more, & this plaine line — signifieth lesse, that is to say the one signifieth to much, & the other to little: thē begin againe, & take another number, which shall be the second position, and worke by the questiō as before, if you haue missed againe, note the excesse or want, for that is the seconde errour. Thē shall you multiplie the first position by the second errour crossewise, and againe the seconde positiō by the first errour (& this must alwayes be obserued) & keepe the twoo products: then if the signes be both like, y^t is to say, either both to much, or both to little, abate the lesser product frō the greater, and likewise, you shall substract the lesser errour frō y^e greater, & by y^e remaine of those errours, you shall diuide the residue of y^e products: the quotiēt shal be the true nūber that you seeke for.

But if the twoo signes be vnlyke, y^t is to saye the one to much and the o∣ther to lyttle, thē shall you adde those productes togither so shall you also adde both the errours togither, and by y^e summe of those errours, diuide the totall sūme of both the products: the quotient shall bee lykewise the true number that the questiō seketh, and thys is the whole rule, as by exaumple.

3. A mā lying at the point of death, sayde that hee had in a certaine Cof∣fer a hundred Duckets, the whych he bequeathed to three of his frendes by hym named, after this sort. The first must haue a certeine portion, the se∣conde must haue twise so many as y^e fyrst abating eyght Duckets: and y^e thyrde must haue thre times so many as the fyrst, lesse by 15. Duckets. Now I demaunde howe many euerye of them must haue. Aunswere: Fyrst I doe imagine that the fyrst mā had 30.

Duckets, then by the order of y^e que∣stion the seconde should haue 52: & the third 75. These thre sūmes being ad∣ded togither do make 157: & I should haue but 100: so that this fyrst errour is to much by 57. then I note a parte the fyrst position 30. wyth his errour 57. to much after this sort 30.457. Therfore I prosecute my worke and I suppose that the fyrste had 24. then by the order of the questiō, the second should haue 40. and y^e thyrd 57: these three summes being added togither, do make 121. & I must haue but 100. so the seconde errour is to much by 21. Therfore I note 24.421. vnder the 30.457. as you may se in the margēt of the next syde following.

Then I multiplye crossewayes, 30. (whych is y^e fyrst position) by twelue whych is the seconde errour, and thereof commeth 630. lykewyse I multiplye twenty & 4. (whych is the seconde position) by 57. which is the fyrst errour, and I fynde 1368: then

bicause the signes of the errours are both lyke: that is to saye to much, I must therfore sub∣stract 630. from 1368. & there will remain 738 which is the diuidende: again I must sub∣stract the lesser er∣rour from y^e grea∣ter, that is to wit, 21. out of 57. and there wil remaine 36. which shall bee my diuisor. Thys done I diuide 738. by 36. and the quotient wyll be 20. ½. The which 20. ½ is the iust number of the Duckets that the first mā had for his parte, so consequently the seconde man had 33. Duckets, and the thyrde 46. ½, as by proofe in the margent, may appere. 〈 math 〉〈 math 〉

	11.
	738.
20 ½	366. (20. ½
33	3
46. ½
100.

The like number will also appere, in case the errours were both to litle, as in making the twoo positions by 18. and 20. where you shal fynde the two errours both to lyttle, the fyrst wyll bee to lyttle by 15. and the se∣conde to little by 3. as by perusing this worke in the margent you shal well perceiue. 〈 math 〉〈 math 〉

Againe if one of the errours were to muche, and the other to little, yet shall I haue the true number, as be∣fore: As if the twoo positions were 24. and 20. I shall fynde that the first errour will be 21. to muche, and the seconde wyll be three to little: Ther∣fore I multiply 24. by 3. crossewaies, therof commeth 72.

Lykewise I multi∣plye twentye by 21. the product will be 420: These twoo summes 72. and 420, I adde both togither bycause y^e signes of the er∣rours bee vnlyke, & they make 492. the which shall bee my diuidende, and againe, I adde the the lesser errour 3. wyth the greater errour 21. and they make 24. for my diuisor, thē diuiding 492 by 24. the quotient wilbe 20 ½: as in the margent doth plainly appeare. 〈 math 〉〈 math 〉

And now bicause you shall not for∣get thys part of the rule, learne thys briefe remembraunce folowing.

The signes both like substractiō do require. And vnlike signes addition will desire.

The meaning whereof is thus yf both the errours haue lyke sygnes, thē must the diuidende and the diui∣sor be made by substraction, as is taught before, and if those sygnes bee vnlike, then muste I by addition ga∣ther the diuidende, and the diuisor, as I haue done in this laste example.

4. A man hath twoo siluer cups of vnegall waight, hauinge to them bothe, but one couer, the weyght whereof is 5. ounces, if the couer bee put to the lesser cuppe, it wyll bee in double proportion vnto the waight of the greater, and the couer being put to the greater cuppe, wyll bee in tri∣ple proportion, vnto the waight of the lesser. I demaunde what was the waight of euerye cuppe?

Suppose that the lesser cuppe dyd wayghe seauen ounces, then wyth the couer it must waigh twelue, and thys waight should be in double pro∣portion vnto the greater, therefore

the greater muste waygh sixe ounces adde vnto it 5. oun∣ces for y^e couer, all will be 11. ounces, but it should be 21. for to haue it in tri∣ple proportion, vn∣to 7. which repre∣senteth the waight of the lesser cuppe: So that this fyrste errour is to little by 10. which you shal note after 7. in this sorte 7.— 10. 〈 math 〉〈 math 〉

After you shall suppose some other number, as 9. & make the lyke worke as before, so shal you find 15. to little, for y^e seconde errour, which you shall put behinde 9. and then worke with the reste as aboue is sayde, and you shall fynde that the lesser cup wayed three ounces, and consequentlye the greater foure ounces.

5. One man demaunded of ano∣ther

in a morning what a clocke it was, the other made hym this aun∣swere, if you doe adde (saith hee) the ¼ of the houres which be paste synce midnight, with the ⅔ of the houres which are to come vntyll noone, you shall haue the iuste houre, that is to say, you shall knowe what a clocke it was: Suppose y^t it was 4. a clocke in y^e morning, so shoulde there remaine 8. vntill none: then I take the ¼ of 4. which is 1. and the ⅔ of eight which is 5. ⅓, and I adde them togither, so I finde 6. ⅓ and supposed but 4. there∣fore this fyrst error is to much by 2. ⅓, which I note after my position thus, 4.42. ⅓: then againe I suppose ano∣thee nūber, y^t is to saye 9. so shoulde remaine but 3. houres vntill none, I take the ¼ of 9. and the ⅔ of 3. which is 2. ¼ & 2. these I adde togither and they make 4. ¼: but I supposed y^t it was 9. therefore the seconde errour is 4. ¾ to little which I note behinde my posi∣tion thus 9.44. ¾.

And then I multiplie crossewyse, as before is taught, and bicause the sygnes of the er∣rours are vnlike, that is to saye, the one to much, and the other to lyttle, therefore in thys worke I muste adde the productes, and they wyll bee 40. Lykewyse I adde the errours, and they be 7.1/12. Then I diuide 40. by 7.1/12, and thereof commeth 5. houres 11/17, and that houre it was in the mor∣nyng. 〈 math 〉〈 math 〉

¶The 15. Chapter treateth of sportes, and pastime, done by number.

IF you would know the num∣ber that anye man doth thinke or imagine in hys minde, as though you coulde deuine.

Bydde him triple the same number, then of the product let him take the, ½

if the number bee euen, or else the greater halfe, if y^e same be odde, then bid hym triple againe the saide ½: af∣ter say to him that put away, if he cā 36.27.18. or 9. from the last number being tripled: y^t is to saye, cause hym subtellye to put awaye 9. as many times as is possible & keepe the nūber secretly: & when he can no more take away 9. thē to know if y^t yet there re∣maine any nūber, bid him abate 3.2. or one, if he can: this done, see howe many times 9. you haue caused hym to abate, for the which keepe you in minde so many times 2. & if that you know y^t he had any thing remaining besyde the nines, the same shall also note vnto you 1.

Suppose that he thought 6. which being tripled is 18. wherof the ½ is 9. the triple of y^t is 27: nowe cause him to abate 18, or 9. or 27. and againe 9: but then he will say vnto you that he cannot, bid him then abate 3. or 2. or 1. he will say also that he can not: wher∣fore

considering that you haue made him to abate three times 9. iustly, you shal tell him that he thought 6. for 3. times 2. maketh 6. If he had thought 5. the triple thereof is 15. whereof the greater ½ is 8. the triple of y^t maketh 24. which cōteineth two times 9. thei are worth 4. & the remaine signifieth 1. the which added togither make 5. which is y^e number that he thought.

2. If in any company, one of them hath a ringe vpō his finger, and you would know by maner of deuining, who hath the same & vpon what fin∣ger & what ioint: cause the persons to sit down in order, & kepe likewise an order of their fingers: then seperate your self from them in some certeine place, and say vnto one of the lookers on, that he double the number (mar∣king the order) of him y^t hath y^e ring: and vnto the double bid hym adde 5. and then cause him to multiplye this addition by 5. & vnto the product byd him adde the number of the finger of

the person which hath the ring: be it y^t the same laste sum did amoūt to 89. then afterwarde saye to him y^t he put after the same last nūber toward hys right hande a figure signifiyng vpon which of the ioints he hath the ring. As if it bee vpon the thirde ioint, let him put 3. after 89. and it wil be 893: this done, you shall aske him what number hee kepeth, from the which you shall abate 250. & you shall haue three fygures remaining at the least. The fyrste towarde your lefte hande shall signifye the number of the per∣son which hath the ring. The second or middle fygure shall represent the number of the finger. And the last fy∣gure towarde your right hande, shal betoken the number of the ioint. As if the number which hee did keepe were 893. from that you shall abate 250. and there wyll remaine 643: Which do note vnto you, that y^e syxt person hath the ring vpon the fourth finger, and vpon his thirde iointe.

But note y^t when you haue made your substraction, if there do remain a cipher in the place of tennes, y^t is to say in y^e seconde place, you must then abate from that figure which is in y^e place of hundreds, y^t is to say from the figure which is next your left hand, & y^t shalbe worth ten tenths, signifiyng the tenth finger: as if there should re∣maine 703. you must say that the syxt person (vpon his tenth finger & vpon hys thirde ioint) hath the ring.

3. And after the same maner, if a mā do cast three dice, you may know the poinctes of euery one of thē, for if you do cause him to double y^e poincts of one die, & vnto y^e double to adde 5. & the same sum to multiply by 5. & vnto y^e product adde the poincts of one of y^e other dice, and behinde the number toward y^e right hand, to put y^e figure which signifieth y^e poincts of the last die, & thē shal you aske him what nū∣ber he kepeth frō y^e which abate 250. & there wil remaine 3. figures, which do

note vnto you y^e poincts of euery dye.

4. Likewise if 3. of your compani∣ons, to say, Peter, Iames, and Iohn that woulde (in your absence) giue themself euery one a contrary name: as for example: Peter would be cal∣led a king, Iames a duke, and Iohn a coūtie: And I would deuine which of them is called a king, which the duke, and which the countie. Take 24. stones, or other peeces whatsoe∣uer, & giue vnto Peter 1. vnto Iames 2. and vnto Iohn 3. or otherwise. But marke well vnto which of them you haue giuen 1, vnto which 2, and vnto whom 3. Then leauing the 18. stones (before thē) that are remaining, you shall absent your selfe from theire syght, or else tourne your face from them, saying thus vnto them, who∣soeuer nameth hymselfe a king: for euery stone that I gaue him let hym take one of the residue, and hee that nameth himselfe a duke for euerye stone that I gaue him let him take 2

of them that remain, and he that cal∣leth himself a countie, for euery stone that I gaue him let him take 4: this being done approche nere them, and marke how many stones are remai∣ning: and know this, that there can not remaine any other number, but one of these sixe, 1, 2, 3, 5, 6, 7, for the which sixe numbers we haue chosen to euery of them a seuerall name, which are these: Angeli, Beati, Quali∣ter, Messias, Israel, Pietas: eche of them containing three Vowelles, a, e, i, which doe shew the names by order: That is to say, A,

1	2	1	2	3	3
2	1	3	3	1	2
3	3	2	1	2	1
a	e	a	e	i	i
e	a	i	i	a	e
i	i	e	a	e	a
1	2	3	5	6	7
A	B	Q	M	I	P

sheweth which is the kinge, E, tel∣leth which is the duke and, I, she∣weth which is y^e county: in follo∣winge the order how, & to whom you haue giuen one stone, to which 2, and to which 3.

Then if there doe remaine but one stone, the first name Angeli, (by these thre vowels a, e, i,) sheweth that Pe∣ter is the king, Iames the duke, and Iohn the countie. And if there doe remaine 2 stones, the seconde name Beati, shal shew you by these three vowels, e, a, i, that Peter is y^e Duke, Iames the King, and Iohn the countie. And so of the other as by this Table doth plainely ap∣pere.

Notes

• * 1.1

  A Rule.
• * 1.2

  A Rule.