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

¶The thirde parte treateth of certaine brief rules, called rules of practise, with di∣uerse necessarie questi∣ons, profitable for Marchauntes. (Book 3)

¶The first Chapiter.

SOme there be, which doe cal these rules of practise br〈…〉〈…〉 rules, for that by thē many questions maie be doen with quicker ex∣peditiō, then by the rule of thre. There bée others, whiche call them the small multiplication, for because that the producte, is alwaies lesse in quantitie, then the nomber whiche is to be mul∣tiplied. This practise commeth not in vse, but onely emong small kindes of nombers, whiche haue ouer theim, o∣ther nombers that are greater. And this beyng well considered, is no o∣ther thyng, but to conuerte lesser and perticuler kindes of nōber, into grea∣ter, the whiche maie bee dooen by the

meanes of diuision, in taking the half, the third, the fowerth, the fift, or suche other partes of the somme, whiche is to bee multiplied, as the multiplier is part of his greater kinde, & that which commeth thereof is worthe as muche (not in quantitie, but in his owne forme) as if you did multiplie simplie the twoo sommes, the one by thother, and for the better vnderstandyng of suche conuersions, you must haue re∣specte to one of these twoo considerati∣ons. The first is, when one would de∣maunde this question. At 6. pence the yarde of Cotton, what are. 18. yardes worth by the price? It is manifest that thei are worthe. 18. peeces of. 6. pence the pece, or. 18. halfe shillynges, which must be tourned into shillynges, in ta∣kyng the halfe of. 18. shillynges, and thei make. 9. shillinges. Or otherwise you muste consider, that at. 1 shillyng the yarde, the. 18. yardes are worth. 18. shillynges, wherefore at. 6. pence thei shalbe but halfe so muche, for. 6. pence

is but the ½ of. 1. shiliyng. Therefore you must take ½ of. 18. and thei make 9 shillinges, whiche are worth as much as. 108. pence, that is to saie, as. 18. ti∣mes. 6. pence.

2. Firste, if you will multiplie any nomber, after this maner by pence, whereof the nomber of thesame pence doe not extende vnto. 12. and therof to bryng shillinges into the product: you must knowe the certaine partes of. 12 whiche are these: that is to saie, 6, 4. 3. 2. and. 1. For. 6. is the ½ of. 12. and. 4. is the 〈◊〉〈◊〉. of. 12: 3. is the ¼: 2 is the ⅙: and 1. is the. ••/12. Then for. 6. pence, whiche is the halfe of. 1. shillyng, you must take the ½ of all the nomber, whiche is to be multiplied. And that which commeth thereof, shalbe shillynges, if there do remaine. 1. it is. 6. pence.

For fower pence you must take the ••/4 of all the nomber, that is to bée mul∣tiplied: and if any vnities doe remaine thei shalbe thirdes of a shillyng, eue∣ry one beyng in value. 4. pence.

For. 3. pence you muste take the, ¼. of all the somme: if any vnities dooe remaine, thei shall bee fowerthes of a shillyng, euery one beyng worthe three pence.

For 2 pēce you must take the ⅙ of all the the somme, and if any vnities doe remaine, thei shall bee sixe partes of a shillyng, beyng euery one of theim worthe twoo pence.

For. 1. penie, take the 1/12 of the whole somme, if any vnities remaine, thei are. 12. partes of a shillyng, eche of them beyng in value. 1. penie, as by these examples folowing doeth plain∣ly appeare. 〈 math 〉〈 math 〉

Here you maie se in the first exāple, that. 59. yardes, at. 6. pence the yarde is worthe. 29. shillynges. 6. in taking the ½ of. 59. And in the seconde exam∣ple, the. 82. yardes at. 4. pēce the yarde is worthe. 27. shillynges. 4. pence, in takyng the ⅓ of. 82.

Likewise, in the third example. 97 yardes, at three pence the yarde, brin∣geeh. 24. shillynges. 3. pence, in ta∣kyng the ¼ of. 97. Also in the ••owerth example. 346. yardes, a••. 2. pence the yarde, maketh. 57. shillynges eighte pēce, in taking the 1/•• of. 346. And final-

in the fyft example. 343. yardes, at I. d. the yarde, amount to 28. shill. 7. d. in taking the 1/12 of 343. And so is to be done of all suche lyke, when the nom∣ber of the pence, is any of the certaine partes of 12.

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

the productes. The totall summe of those two nombers shall be the solu∣tion to the question. And in like ma∣ner is to be done of all other. As by these former folowyng may appeare. 〈 math 〉〈 math 〉

Here in this same example where it is demaunded (at 5 pence y^e yard) howe much are nine and fourty yardes worth? Firste for four pence,

I take y^e ••/3 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. shill. 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 yarde.

For 7. d. take the ⅓ and the ¼ of the whole summe whiche is to be multi∣plied, and adde them togither, that is to say, for 4. d. the 〈◊〉〈◊〉 and for 3. d. the ¼: bycause 4. d. is the 〈◊〉〈◊〉 of 12. d. and 3. d. is the ¼ as in the second example before doth appeare: Where the question is thus, at 7. d. the yarde what are 54. yardes worth? Firste for 4. d. I take y^e 〈◊〉〈◊〉 of 54: and they make 18. s. Likewise for 3. 〈◊〉〈◊〉. I take the 〈◊〉〈◊〉 of 54. and they are 13. s. 6. d. Then I adde 18. s. and 13. s. 6 d. togither, so both amount to ••1. s. 6. 〈◊〉〈◊〉 and so muche are the 54 yardes worth at 5. d. the yarde.

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

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

For eight pence you must first take ••/3 of the whole sūme for 4. pence, and another ••/•• for other 4. d. and adde thē togither as in the. 3. example doth eui∣dently appeare. Where the question is thus, at 8. d. the yarde, what are 40 yardes worth? Firste 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 which is also 13. shillings & 4. pence. These twoo summes being added to∣gither, do make 26. shillings 8. pence, and so muche are the 40. yards worth at 8. pence the yard, as in the third ex∣ample abouesayd doth appeare.

Otherwayes, for eyght pence you may take first the ½ of the whole sūme for 6. d. Then for 2. d. you shal take the ••/3 of the product, which did come of the said ½, and adde them togither, so shall 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 ••/3 of the saide pro∣duct, that is to say of 20. s. which brin∣geth 6. 〈◊〉〈◊〉. 8. d. these two summes (20. s and 6. s. 8. d.) I adde togither and they make 26. s. 8. d. as before.

For 9. d. you must take the ••/2 & the ¼ of the whole sūme, and adde them togither: or els for 6. d. take fyrst ½ of the whole summe, then for 3. d. take y^e ••/2 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 twoo summes doe I adde togither, & they make 54. shil. 9. d. as in y^e said fourth example is euident.

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

For 11. ••••take fyrst ⅓ for 4. pence, se∣condely,

another ⅓ for other 4. d. and thirdly ¼ for 3. d. of all the whole sūme. and adde them togither.

Or els for 11. d take first the ½ then then ⅓ of the whole summe, and final∣lye the ¼ of the laste producte, addinge them togither.

3. Lykewise by the same reason, when you wil multiply (by shillings) anye nomber 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 ½. 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 ••/2 of the nomber, whiche is to bee multiplied, and you shal haue poundes in the pro∣duct. If there doe remaine 1, it shalbe worth ten shillings.

For 5. shillinges you muste take the ¼ of the nomber 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. 〈◊〉〈◊〉. you must take the ••/5 of the number whiche is to bee multiplyed. And if there do remaine any vnities, they shall be fift parts of a pound, eue∣ry one being worth foure shillings. 〈 math 〉〈 math 〉

For 2. shillings you must take the 1/10 of the nōber that is to be multiplied. Wherefore, if you wyll take the 1/10 of any nomber, you muste separate the last figure of the same number whiche is nerest your righte hande, from all

the other fygures. For all the other figures whiche doe remaine towarde your lefte hande, from the same fy∣gure, which is separated, shall bee the sayde 1/1•• of a pounde: and that separa∣ted fygure, towarde your right hand shall be so many peeces of 2. shillings the peece: the whiche fygure must be doubled, to make therof shillings, as by these examples appeareth. 〈 math 〉〈 math 〉

Herevpō doth depend an other exact way for to multiply by shillings (if y^e nomber of shillings be euen) which is thus: you shall take 〈◊〉〈◊〉 the nōber of the same shillings, and conuert them in∣to peeces of 2. shillings. Then by the

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

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

At 8. shillings the grosse, what are ••7. grosse worth after the rate?

Firste in this example I take halfe the nomber 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 dooeth appeare by diuers examples. 〈 math 〉〈 math 〉

Nowe in the first example, where it is demaunded, at 8. 〈◊〉〈◊〉. the grosse, what are 97 grosse? First the ½ of 8. s. whiche is 4. s. being set apart behind the croo∣ked line, as before is said: 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 shillings & I kepe y^• 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, whiche be∣fore I reserued, and they make 38. Therfore I put 38, vnder the lyne in the place of poundes, and the whole summe will 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∣tipliyng by 6. Likewise of 6. shillings if you multiply by 3. also of 14. if you multiply by 7. And so of all euen nom¦bers after the same maner.

For 1. Shilling you must take the ½ of the 1/10 parte of any nomber that is to be multiplied. And if any thyng 〈 math 〉〈 math 〉 do remaine, they are shil. Thus by thys maner shil.

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

First I separate the laste fygure of 359. nexte to my ryght hand, which is the 0 with a line betwene it and the figure 5. Then I make a line vnder the 3 |0, and I take the ½ of 35, after this maner: saiyng the ½ of 3. is I. and I remaineth, whiche remaine signifieth 10. in that secōd place. Then I put I. vnder the line against 3, & I proceede to the rest, saiyng: the halfe of 15. is 7. (which 15. came of the I. that remay∣ned, and of the 5. in y^• first place) I put 7. vnder the line right against 5, and they make 17 li. The I. which did last remaine, is 10. s. Therfore I put 10. s aparte vnder the line, and the whole summe is 17 .li. 19. s. so much are 350. worth at I. s. the peece.

But when the nomber of shillings

is not some certaine parte of 20. shil. you must then conuert the same nom∣ber of shillings, into the certain parts of 20. and make twoo or thrée products, as nede shall require, the whiche must bee added togither after this maner following.

For 3. shillings you must firste take for 2. shil. the 1/10 of the nomber that is to be multiplied, thē for 1. shilling you must take the ½ of the producte whiche 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. First, for 2 shillings I take the 1/10 of 684, which is 68: in separating the last 〈 math 〉〈 math 〉 figure 4, whiche 4 I must double, & they be 8. I set eight 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. whiche 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, that is to saie, 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 the peece, as may appere in the margent.

For 6. shll. take 3/•••• of the nomber whiche is to be multiplied: that is to say, first 1/10, then double the product of the same 1/10 and adde them together. Or otherwise for 4. s. take first y^e ⅕ of y^e nōber that is to be multiplied, then take the ½ of the product which is for two. s. and adde them togither.

Or els take for 5. shill. the ¼ of the whole summe, then for 1. shil. the 1/•••• of the product and adde them togither.

Likewise for 7. shil. take firste for 5. shil. the ¼ then for 2. shillings take the 1/10 of the nomber whiche is to be mul∣tiplied, and adde them togither.

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

For 9. shil. take first the ¼ and lyke∣wise the ⅓ of the nomber 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 ⅖ part of the pro∣duct, and adde them togither,

For 13. shil. take the ¼ then the ⅕, and againe another ⅕ of the nomber which is to be multiplied. And adde the pro∣ductes togither, that is to saye: fyrste for 5. shil. take the ¼, then for 4. shil. take the ⅕. And againe, another ⅕ for the other 4 shil. and assemble the three productes, the like is to be done of all others, when the price of the thynge which is valued, is onely of shillings. And as by these examples followyng doth plainly appeare.

〈 math 〉〈 math 〉

4. Likewise in multipliyng by pēce you shall haue (at the firste instaunte) poundes in the producte, in case you knowe the certaine partes of the 1/10 of a pounde, or of. 24. pence, whiche are these, 12. pence. 6. 4. 3. and. 2. For. 12. is the ½ of. 24:8. is the ⅕:6. is the ¼. 4. is the ⅙:3. is the ⅛:2. the 1/12: but for. 12. pence, whiche is 1. shillyng: wee haue before made mention thereof.

For 8 pence you muste take the ⅓ of the 1/10, and the reste whiche are the pe∣ces of 8 pence, muste bee doubled to make of them peeces of. 4. pence. And of the same nomber beyng doubled, you muste take the ⅓, whiche will bee

shillynges, and if there doe yet remain any thing, thei are thirds of a shilling being in value 4 pence the pece.

For 6 pence take the ¼ of the 1/12, and of that whiche remaineth, you muste take the ½, whiche shall be shillynges, if there doe yet remaine. 1. it shall bee in value. 6. pence.

For 4 pence you must take the ¼ of the 1/10, and of that whiche resteth, take the ⅓ to make therof shillynges, if any thyng dooe yet remaine, thei are thir∣des of a shillyng, beyng in value. 4. pence the pece.

For 3 pence take the ⅕ of the 1/10, and of that whiche remaineth, take the ¼, to make of theim shillynges: if any thyng doe yet remaine, thei are foure∣thes of a shillyng, euery one of theim beyng worthe 3. pence.

For 2 pence take the 1/12 of the 1/10: and of that whiche resteth take the ⅙, the whiche are shi. if there do still remain any thing, thei shalbe sixte partes of a shilling, euery one being in value 2 d.

For 1, penie it is impossible with ease, to bryng of pence, poundes (into the producte) vpon the totall somme: But firste you must bryng them into shillinges by the order of the seconde rule of this chapiter, and then after∣warde you shall conuerte them into pounds, if nede so require. As by these examples followyng may appere. 〈 math 〉〈 math 〉

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

For. 5. pence you shall first take for 3. pence, then for. 2. pence, and adde thē together, accordyng to the instruction of the laste rule. Or els firste take for 4. pence, and then for. 1. penie.

For. 7. pence, first take for. 4. pence then for. 3. d, and adde them together.

For 9 pence, firste take for 6 pence, then for 3 pence adoyng thē together.

For. 10. pence, firste take for 6. d. then for. 4. d, and adde them together.

For. 11. pence take firste for. 8. pence then for. 3. pence, and adde them toge∣ther: as by these examples followyng doeth appeare.

〈 math 〉〈 math 〉

5. If you will multiplie any nōber by shillynges and pence, beyng bothe

together, you must take first for the. s. accordyng to the instructiō of the third rule of this chapiter, then take for the pence, after the order of the ••owerth rule before mentioned: but if there be any certaine partes of. 1. pounde, con∣tainyng bothe shillynges and pence, then for suche partes you shal take the like parte of the nomber that is to bee multiplied, as the nomber is part of 1 .li. the whiche certain partes are these, 6. s. 8. d: 3. s. 4. d: 2. s. 6. d: and. 1. s. 8. d: For 6. s. 8. d. is the ⅓ of a li. 3. s. 4. d. is the ⅙ of a li. 2. s. 6. d. is the ⅛: and 1. s. 8. d. is the 1/12: then for 6. s. 8. d. you muste take the ⅓ of the nomber that is to bee multiplied: and if any thyng dooe re∣main, thei are thirdes of a pound, eue∣ry one being worthe 6 s. 8. pence. For 3. s. 4 d. you must take y^e ⅙ if any thing doe remain, thei are 6 partes of a li. e∣uery one beyng in valor 3. s. 4. d. For 2. s. 6. pēce, you must take the ⅛▪ if any thing be remainyng, the•• are 8 partes of a li. euery one being worth 2. 〈◊〉〈◊〉. 6. d.

For. 1. shillyng. 8. pence, you shall take the ••/12, if there dooe any thyng re∣maine, thei are twelfth partes of a .li. euery one beyng valued at. 1. s. 8. d. 〈 math 〉〈 math 〉

6. Here shall you accustome your self, to multiplie by all sortes of som∣mes, beyng compounde of shillynges, and pence, whiche maie come to prac∣tise. As thus, for. 1. shillyng. 1. penie: for. 1. shillyng. 2. pence: for. 1. shillyng 3. pence: for. 1. shillyng 4. pence. Like∣wise for 2. shillynges 1. penie: 2. shilly. 2. pence: 2. shillynges. 3. pence. 2. s. 4. d And so of all other: consideryng more∣ouer,

many subtile abreuiations, whi∣che happen oftentymes, that are easie to bee conceiued. As thus: at 11. s. 3. d. after that I haue taken firste the ½ for 10. shillynges. Then for 1. shillyng. 3. pence. I take the ⅛ of the product, be∣cause 1. shillyng. 3. pence is the ⅛ of 10 shillynges, in takyng thesaied ⅛ of the producte. And by this meanes, when ye haue taken one producte, ye maie oftentymes vpon the same, take an o∣ther more briefly, then vpon the sōme that is to be multiplied, whiche thyng you must foresée. 〈 math 〉〈 math 〉

7. But if you will multiplie, by poun∣des, shillinges & pence being together. Firste you muste wholly multiplie by poundes. Then take for the shillyngs & pēce, as in the. 5. rule of this chapiter is plainly declared. And as by these examples folowyng maie appeare. 〈 math 〉〈 math 〉

8. So these rules do serue, both to buy & sel, at suche a price the ell, the yard, y^• pece, the li. waight or any other thing: how much such a thing. Likewise thei are very necessary to conuert all peces of gold & siluer into li. for I may aswel saie, at. 4. s. 8. d. the Frenche croune, what are 135 crounes worth? As to say at. 4. s. 8. d. the yarde of clothe, what are 135. yardes worthe?

9. When any 1 of the sōmes (which is to be multiplied) is cōpounde of many denominations: & thother is of one fi∣gure alone: then shall ye multiplie al the denominations of thother somme, by the same one figure, beginning first with y^• somme, which is least in value towards your right hand, & bryng the product of those pence into shi. and the product of the shillinges into poundes as by this example doeth appeare. 〈 math 〉〈 math 〉

10. But (〈…〉〈…〉 of the nombers whiche are to be multiplied) there bee with it a broken nomber, you muste (accordyng to his denominator) take one or many partes of the nomber, as nede doeth require: and sette the nom∣ber whiche commeth thereof, vnder the productes, addyng the same toge∣ther. As thus: At 5. pounde 7. shillyn∣ges 8. pence the grosse, what shall. 34. grosse ½ cost? First you shall multi∣plie 〈 math 〉〈 math 〉 5. pound. 7. s. 8. pence by. 34. grosse, saiyng. 5. tymes. 34. dooe make 170. pound then for. 6. shilly. 8. pence, take the ••/3 of. 34. whiche is. 11. pounde. 6. shil∣lynges, 8. pence. Thirdly, for. 1. shil∣lyng, take. 34. shillynges, whiche is 1 pounde 14. shillynges. 0.

Lastly, for the ½ grosse, you muste take ½ of the. 5. pounde 7. shillynges 8

pence, whiche is. 2. pounde. 13. s. 10. d. And then adde thē all together, so you shall finde that the. 34. grosse ½ at. 5 .li. 7. shillynges. 8 pence is worthe. 185. pounde. 14. shillynges. 6. pence, as ap∣peareth in the margent.

And as in this last example, you did take the halfe of the money, (whiche one grosse was worthe) for the ½ grosse Because that one grosse beyng worth 5. pounde. 7. shillynges. 8, pence, the ½ grosse must be worthe halfe so muche So likewise, if you haue ⅓ of a grosse or of any other thyng, you muste take the. ⅓. of the price, that one grosse is worthe. Semblable, for the. ¼. of any thyng you shall take the ¼ of the price, that one is worth, and of all other fra∣ctions, as by these examples folowing doth appeare. 〈 math 〉〈 math 〉

11. If you will make the proofe of these rules aforsaid, you must first abate the somme of money (which the fractiō of the multiplicand doeth importe) from the total somme. And diuide the rest of the poundes of the said totall sōme, by the whole multiplicande, the fraction onely accepted. And if any thing dooe remain after the diuision is made, that remain shalbe multiplied by 20 & vn∣to

the producte of that multiplication, you shal adde the shi. which remained of the rest of the totall sōme. Again, if anything do remain after the same di∣uision, you must multiply the same by 12 & vnto y^e product adde the pence of y^e total sōme that remained if any be left And thus if ye haue truely wrought, you shall finde again the higher sōme of your questiō, that is to saie, the price that one grosse, or any other thyng is worthe, whereof you demaunde.

Or otherwise, reduce the remaine of the totall somme (the value of the money that the fraction is worthe, be∣yng firste deducted) all into pence, in multipliyng the poundes by. 20. and the shillynges by. 12. addyng thereun∣to the shillynges and pence, which are i••igned with the remaine of the saied totall somme, if any suche be, then di∣uide those pence by the foresaied nom∣ber that is to be multiplied, the fracti∣on of the same nomber being also aba∣ted. So shall you finde the price that

one pece, I grosse, or any other thyng is valued at. As in the firste example goyng before, where the totall sōme is. 201. pounde. 10. shillynges, from the whiche I dooe first abate the price of the halfe grosse, whiche is. 2. pound 3. shillynges. 4. pence, the reste is 199 .li. 6. shillynges 8. pence, whiche being reduced into pence, bringeth 47840. d. I diuide thesame by 46. and thereof commeth 1040. d. Then I diuide that 1040. d. by 12, and thei bryng 86. s. 8. d. that is to saie 4 .li. 6. s. 8. pēce, which is the price that one grosse, or any o∣ther thyng did coste, as in that firste example doeth eppeare.

12. The like is to bee doen of any maner of thyng, that is solde by the hundred, or by Kintall. As thus: at 12. pounde seuen shillynges six pence the hundreth pounde waight: what shall. 374. pounde waight coste. You shall first multiplie twelue pound se∣uen shillinges, sixe pence by thre: that is to saie, by three hundreth. Then for

50 .li. waight, you 〈 math 〉〈 math 〉 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 .l. 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, whiche will make the summe of 64 .li. 5. s. 7. d. ⅘, as by this exāply aboue writ∣ten doth appeare.

The proofe is made by reducinge the totall summe into pence. And to diuide the product by the nomber y^• is to be multiplyed, that is to saie by 374 likewise diuide the quotient produced of that first diuision by 12. so shall you finde againe the higher summe 12 .li. 7 shil. 6. d. whiche is the price of 100 .li. wayght, as before.

13. Also the like maye be done of

our vsuall waight here in Englande (whiche 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, whiche 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 ra••e?

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

which is 8, li. for 〈 math 〉〈 math 〉 24. nobles ma∣keth 8, li. after∣warde, for the 3. quarters of the C. you shall first for the 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. (whiche is the quar. of a C.) you shall take the ¼ of 3 .li. 6. s. 8. d. or els the ½ of the product, whiche came of 56 .li. which is 16, s. 8, d likewise for 14 .li. take the ⅛ of 3 .li. 6, s. 8. d. whiche is 8, d. 4, d. or els the ½ of the producte of 28 .li. which is all one: lastly for 7 .li. take the 1/16 of 3, li. 6. s. 8, d. or els 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^• 24 .c. 3. quar. 21 .l. waight worth after 3, li. 6. s. 8. d. y^• C. as appereth in

the margent.

The proofe hereof is made, lyke to to the other proofes aforesaide, saning that where in those proofes, you aba••e the price of the money, that the frac∣tion was worthe, from the totall summe: here in this example (and in suche 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 con∣uert into pence, diuidinge the product of y^e multiplication by the iuste nūber of the hundrethes, so shall you finde the pence y^e one hundreth is worthe, whiche you shall bringe into poundes by the order of diuision, & so all other.

¶The second Chapter treateth of the rule of three compounde, which are foure in nomber.

THere belongeth to the fyrst & seconde partes of the rule of thre compound alwaies fyue numbers: whereof (in the first

part of the rule of three compo••nde the seconde nomber and the 〈◊〉〈◊〉, are alwayes of one semblaunce, and ••ke denomination: whose rule is thus, multiply y^e first nōber by the seconde, & that shalbe your diuisor: then mul∣tiplie the other three nōbers the oneby the other to be your diuidende. Exā∣ple, of this first part: if 100. crowns in 12. monthes, do gaue 15 .li. what will 60. crownes gaine. in 8. monthes? Answere, first multiplie 100. crownes by 12. monthes, & therof cōmeth 1200. for your diuisor: then multiply 15 .li. by 60. crownes, & by 8. monthes & you shal haue 7200. diuide 7200. by 1200, & therof cōmeth 6 .li. so many li. wyl 6. crownes gaine in 8. mōthes: this que∣stiō may be done by y^e double rule of 3. y^t is to say by y^e rule of 3. at 2. times, but yet this rule of 3 cōpoūd is more brief. 〈 math 〉〈 math 〉

2. In the seconde part of the rule of third compound, the 3. nomber is like vnto the fift, wherof the rule is thus: multiplie the 3. nomber by the 4. the product shalbe your diuisor: then mul∣tiply the first nomber by y^e seconde, & the product therof by the fift, y^t whiche nomber shalbe your diuidend, or nō∣ber y^t is to be diuided: as by example,

When 60. crownes in 8 monthes do gaine 6 .li. in howe many monthes wil: 100. crownes gain. 15 .li. Aunswer Multiply the thirde nomber 6. by the fourth nōber 100, & ther of cōmeth 600 then multiplye the first nōber 60. by the secōd nōber 8. & by the fift nōber 15 thereof will come 7200. then diuide 7200. by 600. & y^e quotiēt wilbe 12: in so many monthes will 100. crownes gaine 15 .li. This question may like∣wise be done by the double rule of 3. 〈 math 〉〈 math 〉

3. In the thirde part of the rule of 3. compound, there may be 5. nombers or more: & in this rule the first nōber & the last alwayes dissemblaunt the one to thother: & the questiō is from the last nōber vnto the first, wherof y^e rule is thus: multiply that nomber which you woulde know by those nō∣bers which do giue the value, & diuide the product of the same, by y^e multipli∣cation of the nōbers which are alrea∣dy valued, as by exāple. If 4. deniers Parisis, be worth 5. deniers arnols, & 10. deniers tournois, be world 12. de∣niers of Sauoy, I demaūd how many deniers Parisis are 8. deniers of Sa∣uoy worth▪ Aunswere: Multiply 8. de∣niers of Sauoy (which is the nomber y^t you would know) by 4. deniers pa∣risis, & by 10 deniers t〈…〉〈…〉is whiche are y^e nōbers that giue y^e value, & they make 320: then multiplie 5. denters tournois, by 12 deniers of sauoy (which are the nombers alredye valued) and they make 60: lastly diuide 320. by 60

and you shall finde 5. deniers ⅓ parisis, so muche are the denies of Sauoye worth. 〈 math 〉〈 math 〉

4. In the fourthe parte of the rule of three compounde: the first nomber and the last are always semblant and of one denomination, and the questiō of this rule, is alwayes from the last nōber to the last sauing one. Where∣of there is a rule which is thus. You must multiplye that nomber whiche you woulde knowe, by the nombers that are alreadye valued, and diuide the product of the same, by the multi∣plication which commeth of the nom∣bers that giue the value, as by exāple

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

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

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

IF 31. Deuonsh. dosēs do cost me 100 .li. 15. shil. What shal 4. do∣sens cost? Aunswere: first 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 queti∣etit wilbe 260. s. The which diuide a∣againe by 20. & therof commeth 13 .li. 〈 math 〉〈 math 〉

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

100 .li. ¾, which ¾ are 15. s. and so much are 31. Dosens worth as before. 〈 math 〉〈 math 〉

If 49 elles be worth 2, li. 4, s. 11, d. what are 18 elles worthe by the price? First you must bring 2 .li. 4, s. 11, d. all into pence, in multipliyng 2 .li. by 20. maketh 40. adde thereto 4, shil. they make 44. s. y^• which multiply by 12. d. & they make 528, d. wherūto adde 11. d all is 539, d. the whiche 539, d. muste be your second nōber in y^• rule of 3. then multiply 539 by 18, & therof commeth 9792. diuide y^• same by 49, & you shall haue in your quotient 198, d. y^• whiche diuide by 12. & you shall finde 16 s. 6 d. so much are the 18. elles worth.

〈 math 〉〈 math 〉

IF 18. elles be worth 16 s. 6. d. what are 49. elles worth by the price? Auns. bring 19. s. 6. d. into pence, in multi∣plying 19. by 12. and thereof commeth 198. d. with the 6. d. adde dto it, then multiplye 198 by 49. the product will be 2702. 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 muche are the 49. elles worth. 〈 math 〉〈 math 〉

If a yarde of Ueluet cost 19. s. what shalt ¾ of a yarde cost? Aunswere: sette down your nombers thue. If 1/1 | 19/1 | 3/••, Then multiplye 1. times 16. by 3. and therof cōmeth 57, for your diuidēde, or nomber to be diuided. The whiche 57. you shall diuide by 1, times 1, foure times; which are 4, and your quotient wil be 14 s. ¼, which ¼ is worth 3. d. so

muche are the ¼ of a yarde worth after 19. shil. the yarde, as by practise follo∣weth. 〈 math 〉〈 math 〉

Or otherwise by the rules of prac∣tise first for 2/4 of a yarde whiche 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 nōbers togither, & 〈 math 〉〈 math 〉 you shall haue 14, s. 3, d. as aboue is sayd, and as appeareth here in the margent.

IF ¾ of a yarde of Ueluet do cost 14. shil. 3. d. What shall 1. yarde coste, set your nombers downe thus: if ¾ | 14 ¼ | 1/1. Reduce 14, ¼ into a traction, 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 will be 19. shil. so much is the yarde of veluet worth. 〈 math 〉〈 math 〉

Or otherwise by y^• rule of practise: you shall take the ⅓ parte of 14, sh. 3. d. and adde it with the same 14, sh. 3, d. and you shall haue 19, shill. as before. 〈 math 〉〈 math 〉

If one elle of Hollonde 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 three times 1 one time, they make 3, for your diui∣sor, then diuide 10, by 3. & thereof com∣meth 30. s. ⅓ which ••/3 is worth 4. pēce, &

so much are the 〈◊〉〈◊〉 of an ell worth. 〈 math 〉〈 math 〉

Or otherwise, by the rule of prac∣tise: take first the ⅔ of 5. s. for the ⅔ of an ell, which is 1. s. 8. d. Likewise, for the other ⅔ of an ell take againe ano∣ther ⅔ 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. 〈 math 〉〈 math 〉

If 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 〈◊〉〈◊〉|3〈◊〉〈◊〉|〈◊〉〈◊〉. Firste reduce 31/•• all into thirds, and it will be 10/3. Then mul∣tiply 1. times 10. 3, times, and thereof cōmeth 30. for your diuidēde. Likewi∣se multiplie 1. times 3. 2 times, your quotiēt wil be 6. then diuide 30, by 6. & you shall haue 5, s. so much is the ell

of Hollande clothe worthe. 〈 math 〉〈 math 〉

Or otherwise by practise, take the ½ of. 3. s. 4. whiche is. 1. s. 8. d. and adde it to the same 3. s. 4. d. and thereof will come. 5. as before. For the ⅓ of. 5. s. is as muche as the ½ of 3. s. 4. pēce, whiche was the 〈 math 〉〈 math 〉 price that the ⅔ of an elle did coste, as appereth.

If one elle coste me. 17. s. what shal 15. elles ⅔ part cost? Whiche ⅛ is halfe a quarter of an elle. Aunswere: safe of 〈◊〉〈◊〉|〈◊〉〈◊〉|15. ½. First reduce 15. 1/•• into. 8. par∣tes, and thei make 121/8, then multiplie 121. by. 17. 1. tyme, and thereof cōmeth 2057. for your diuidende. Likewise multiplie. 8. times. 1. 1. time, and your quotiente will bee. 8. for your diuisor, then diuide. 2057. by. 8. and you shall find. 257. shillynges ⅛, which is. 12. 〈◊〉〈◊〉. 17. shillynges. 1. penie ½, and so muche are the. 15. elles ⅛ worthe, as by prac∣tise doeth appere.

〈 math 〉〈 math 〉

Or otherwise, for 10. s. take the ½ of 15, which is 7 li. 10. s. then for 5 s. take the ½ of 7 li. 10s: which is 3 li. 15 s: third¦ly, for 2: s: take ⅕ of 7 li: 10: s: because the ½ of 10. s: is 2: s: Fourthly, for the ⅛ of 〈 math 〉〈 math 〉 the ell, you shal take the 〈◊〉〈◊〉 of 17: s: whiche is 2: s: 1: d: ½: Lastlie, adde all these sōmes together, and then shall you finde 12 .li. 17: s: 1: d: ½ as before, and as appereth more plainly in the margent.

If 25 elles bee worthe 2, li: 3: s: 4: d: what are 18 elles ¾ worth by the price? Answer: first put 3. s. 4. d. into the part of a li. and you shall haue ⅙, then saie, if 25/1 geue me 2 li. ⅙ what shall 18¾ geue: put the whole nomber into his brokē, and then multiplie 1 tymes 13 by 75: the product will be 975 the which you shall diuide by 25 tymes 6: 4 tymes,

which maketh 600. Then diuide 975 by 600, and your quotient will be 1 li. and 375. remaineth, the which 375. you shal multiply by 20. thereof commeth 7500. diuide the same by 600. youre quotient wil be 12. s. & 300. remaineth y^t which abreuiated bringeth ½ whiche is 6. d. thus the 18. elles ¾ are worth 1 .li. 12. s. 6. d. as by practise appeareth. 〈 math 〉〈 math 〉

Or otherwise by the rules of prac∣tise: for because that 12. elles ½ is the ½ of 25. elles, therefore take the ½ of 2 .li. 3. s. 4. d. which is. 1 .li. 1. s. 8. d. then for 9. elles ¼ take the ¼ of 2 .li. 3. s. 4. d. or else the ½ of the last product (that is to safe of 1 .li. 1. s. 8. d.) whiche is all one, and adde them together, so shall you haue 1 .li. 12. s. 6. d: as before. 〈 math 〉〈 math 〉

If. 15. yardes be worthe. 32. s. what are half a yard, or half a quarter, or els 〈◊〉〈◊〉 of a yarde worthe. Aunswere: saie, if 〈◊〉〈◊〉 geue 32/•• what will ⅝ geue? Multiplie 〈◊〉〈◊〉 times 32. by 5, and diuide the product by. 15. tymes. 〈◊〉〈◊〉. s. and 4, remaineth, whiche is ⅓ of a shi. that is to saie 4. d and so muche are 5/2 of a yarde worthe. 〈 math 〉〈 math 〉

Otherwise, see what the yarde is worthe, after the maner aforesaied in the other examples, and you shall find that the yarde is worthe, 2. s. 1. d. ⅗ of the whiche nomber take first the ½ for 4/6, whiche is 1. s. 0. d. ⅘, of the whiche nomber, take the ¼ for the other 〈◊〉〈◊〉, whiche is 3. d. ⅕, adde these. 2. nombers together, and you shall finde the ⅝ to be worthe 1. s. 4. d. as before is saied. 〈 math 〉〈 math 〉

If 13 els 〈◊〉〈◊〉, be worthe 27. s. what are 10 elles ⅔ worthe by the price? Aun∣swere:

saie if 13⅚ geue 27/〈…〉〈…〉 which shal 10 ⅔ geue: putte the whole nombers into their broken, and you shall finde 83/6, 27/1, end 32/3. Then multiplie 6 tymes 27 by 32 and thereof cōmeth 5184 the which nomber you shall diuide by 83 times 〈◊〉〈◊〉 thre times, and you shall finde 20. s. 〈◊〉〈◊〉 whiche is worth 9. d. 〈◊〉〈◊〉/85 part of a peny. 〈 math 〉〈 math 〉

If two yardes ½ be worthe 4. s. 8. d. what are 8 yardes ¼ worthe? Aunswer put the 8. d. into the part of a shillyng, which wilbe ⅔, then reduce the whole nombers into their broken, and thei will stand thus, 5/2, 14/3, 33/4, then multiplie twoo tymes 14 by 33, and diuide the producte by. 5. tymes 3. 4. tymes, and you shall finde 15. s. 4. d. ⅘, so muche are the eight yardes ¼ worthe. 〈 math 〉〈 math 〉

If one Kersey bee worthe 2 .li. 6. s. 8. d. how many Kerseis shal I buy for

36 .li. 3. s. 4 d. after y^e rate: Answere: put 6. s. 8. d. into the parte of a li. and you shall haue 2 li. ⅓ for the first nomber in the rule of 3. and 1 elle for the seconde nomber: then put 3 s. 4 d: into the part of a li. and you shal finde 36 li. 3/6 for the 3 nomber, then will your 3 nombers in the rule of 3 stand thus. 2⅓ | 1/1 | 36⅙. Therefore reduce the whole nombers into their broken, and you shall haue 7/3|1/1|217/6. Then multiplie 1 by 217, and thereof will come 651 for your diui∣dende. Likewise, multiplie 7 tymes 1 by 6, and the producte thereof will be 42. Then diuide 651 by 42. and you shall finde 15 ½. So many Kerseis of 2 pounde, 6 shillinges 8 pence the pece shall you haue for. 36. pounde, 3. shil∣lynges 4 pence. 〈 math 〉〈 math 〉

¶The fowerth Chapiter treateth of losses and gaines, in the trade of marchaundise.

IF 13 yardes ⅓ be worth 22 li. 10 shillynges, how shall I sell the yard to gaine ⅓, or to make of 3. 4? whiche is all one? An∣swere: saie by the rule of 3, if 3 be come of 4. or if 3. yelde 4. what will 22. ½: multiplie and diuide, and you shal find 30 .li. Then saie again by the rule of 3. if 13 yardes 1/〈…〉〈…〉 doe geue 30 .li. aswell of principall as of gain: what will 1 yard be worthe by the price? Multiplie and diuide, and you shall finde 2. pounde 5 shil. and for that price must the yard be sold to gaine the ⅓, or to make of 3. 4. 〈 math 〉〈 math 〉

Or otherwise, take the ⅓ part of 22. ••i. 10. s. which is 7 .l. 10. s. that shal you adde with 22 pounde 10 shillynges, & you shall haue 30 pound as before. Then diuide 〈 math 〉〈 math 〉 30. by 13. ⅓. and you shall finde 2 pounde 5 shillyn∣ges, as aboue is saied.

If one yarde bee worthe 27. s. 6. d. for how muche shall 16 yardes ⅔ bee solde, to gaine 2. s vpon the pounde of money, that is to saie: open 20. s. An∣swere: adde 2 vnto 20 & you shall haue 22, then saie: if 20. s. of principall, doe geue 22. s. aswel of principal as gain: howe muche will 27. s. 6. d. principall yeld. Multiplie and diuide & you shall find 30. s. ¼: then saie again by the rule of 3, if 1. yard do geue me 30. s ¼ (which is aswell the principall as the gaine) what shal 16 yardes ⅔ geue me? Mul∣tiplie 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 mo∣ney, or in 20. s. whiche is all one. 〈 math 〉〈 math 〉

If 10 yardes ⅔ be worthe 25 .li. 10. s For how muche shall 2 yards ¼ be sold to gaine after 10 .li. vpon the 100 .li. of money? Answere: saie if 100 of princi∣pall

yeld 110 aswell principall as gain how muche will 25 .li. 10. s. yelde me? Multiplie and diuide, and you shall finde 28 .li. 1. s. Then saie if 10 yardes ⅔ doe yeld me 28 .li. 1. s. aswell of prin∣cipall as of gaine, how muche shall. 2. yardes ¼ yelde me? Multiplie and di∣uide, and you shall finde 5 .li. 18. s. 4. d. 1/••2, for so muche shall the twoo yardes be solde, to gaine after 10 .li. vpon the 100 .li. of money. 〈 math 〉〈 math 〉

And although that in these questi∣ons of gaine and losse, sometymes the firste nōbers is not like vnto the third nomber, that is to saie, of the same de∣nomination: as one would saie: if 20. shillynges gaine. 2. shillynges, what shall. 50 .li. gaine? Or 25 .li. &c. Or if 20 .li. doe gaine 2 .li. What shall 25. s. gaine me, or what shall. 27. s. gaine? Yet neuerthelesse, the rule is not ther¦fore false. For if 20. s. dooe gaine 2. s:

20 .li. shall gaine 2 .li. and 20. d. shall gaine 2. d. likewise 20 crounes shall gaine 2 crounes, and so of all other: therefore it is to bee vnderstande, that the first nōber in these reasons, is pre∣supposed to be semblable to the thirde.

When one marchaunt selleth wa∣res to an other, and he geueth to the buyer 2 vpon 15: how muche shall the buyer gain vpō the 100 after the rate? Answere: saie if 15 geue 17, what shall 100 geue? Multiplie and diuide, and you shall finde 113⅓, so the buyer get∣teth after the rate of 13⅓ vpon the 100. 〈 math 〉〈 math 〉

If 1. Northe dosen cost me 3 li. 5 s. & I sel y^e same again for 3 .li. 12. s. 6 d. how muche do I gain vpō the li. of money after the rate. Answere saie if 3 .li. ¼ do geue 3. li ⅝, what shall 20/8 geue, put the whole nōber into their broken, & you shall haue 13/4, 29/8, 20/1, then multiplie 4 ty∣mes 29, by 20, & therof commeth 2320 for your nomber that is to be diuided, likewise multiplie 13 times 8. 1 time, &

therof cōmeth 104. Then diuide 2320 by 104, and you shall finde 22 shillin∣ges 4/13. So I shall get 2 shillynges 4/13 v∣pon 20 shill. or vpon the li. of money. 〈 math 〉〈 math 〉

If a yarde of clothe coste me 7 shil∣lynges 8 pence, and afterward I deli∣uer out 13 yardes ¼, for 4 pounde 13. s. 4 pence. I would know whether I do winne or lose, and how muche vpon the 100 pounde of money? Answere: se first at 7 shillynges 8 pence the yarde, what the 13 yardes ¼ shall cost, and you shall finde 5 pound 1 shil. 7 pence. And I solde them but for 4 pounde 13 shil. 4 pence, so that I doe lose vpon the 13 yardes ¼ the somme of 8 shilly. 3 pence. Then for to knowe how muche is lost vpon the 100: saie by the rule of 3, •••• 5. pound 1 shil. 7. pence doe lose 8 shil. 3. d What will 100 lose? First put 1 shill. 7 pence into the part of a pounde, and it will be 19/240. Likewise put 8 shill. 3. d. into the part of a li. and it is 33/80. Then

will your nomber stande thus 5. 19/240, 33/80, 100/••••, put the whole into his broken, and then multiplie and diuide, so you shall finde 8 .li. 1184/9752, whiche is worthe 2. shil∣lynges. 5. d. 169/1219 and so muche is lost v∣pon the 100 .li. of money. 〈 math 〉〈 math 〉

More, if 12 yardes ½ of Scarlet bes solde for 30 pounde 15 shillynges, vpō the whiche is gained after the rate of 〈◊〉〈◊〉 1/9 vpon the 100. I demaunde what the yarde did coste at the firste. Aun∣swere: from 30 pounde 15 shillynges, substracte his 1/10 part, whiche is 3 .li. 1. s 6. d. and there resteth 27 .li. 13. s. 6. d. the whiche number multiplied by. 2. bryngeth 55 .li. 7. s. of the which is 2 pounde, one shillyng and ••ower pēce. Then take againe the ⅕ of thesaied 〈◊〉〈◊〉 pounde 1 shillyng 4 pence, whiche is 2 pounde ••ower shillynges three pence, 9/25. And so muche did the elle cost at the firste penie.

〈 math 〉〈 math 〉

More, if 15 yardes ¾ of Scarlette doe cost me 32 pound 13. s. 4. pence. And I sell the yarde again for 2 pound, whe∣ther dooe I winne or lose, and howe muche vpon the pounde of money.

Answere: loke what the 15 yards ¾ are worthe at 2 .li. the yarde, and you shall find that thei are worth 31 .l. 10. s. But thei did cost 32 .li. 13. s. 4. d. so that there is lost vpō the whole 1 .li. 3, s 4. d. Thē to knowe how muche is lost vpon the li. saie by the rule of 3, if 32 li. ⅛ doe lose 1 li. ⅙: what will ⅓ lose? That is to saie: what will 1 li. lose? Reduce the whole nombers into their broken, and then multiplie and diuide, so shal you finde 21/••8•• parte of a li. Then multiplie 21 by

240. because so many pence are in a li. and deuide the producte by 588. so shall you finde 8. d. ⅗ ⅜ ⅝ which beyng abreuiated doe make 4/7, and thus you se that 8. d. 4/7 is lost vpō the li. of money. 〈 math 〉〈 math 〉

If 1. yarde of cloth of tissue be solde for 3 .li. 15. s. whervpon is lost after the rate of 10. s. vpon the 100. I demaund what 12. yardes ½ of the same tissue did cost? Aunswere: adde vnto 3 .li. 15. hys owne 1/10 part, whiche is 7. s. 6. d. and al amounteth to 4 .li. 2. s. 6. d. then looke what the 12. yardes ½ wil amount vn∣to, after 4 .li. 2. s. 6. d. & you shall finde that thei will come to 51 .li. 11. s. 3. d. so muche did the 12. yardes ½ coste. 〈 math 〉〈 math 〉

More, if I sell 1 Wilshire white for 6 li. 12 s. whereupon I doe gain after the rate of 2 shil. vpon the li. of money, that is to saie, vpon 20 s. I demaunde what 11 peeces of the same whites did cost me? Answere: abate from 6 pound 12 s. (whiche is 132 s) his 1/•••• parte, and thereof cōmeth 12 s. and there remai∣neth 120 s. or. 6 li. Then se at 6 .li. the clothe, what the 11 clothes are worthe and you shall finde them to be worthe 66 li. so muche did the 11 clothes coste. 〈 math 〉〈 math 〉

If I sel 10 elles ½ of Hollād for 12 s. 6 d. wherupon I doe lose after the rate of 2 s. vpon the li. of money. I demaūd what the ell did cost me? Answere: saie by the rule of: 3, if 18 geue 20: s. what will 20 s: 6: d: geue? Multiplie and di∣uide, and you shall find 25 s: Then di∣nide 25 s. by 10 ½, and thereof commeth 2 shil. 4. d. 4/7. So muche did the ell cost 〈 math 〉〈 math 〉

If I sell 1 clothe for 5 li. wherupon I do lose 10 vpō the 100, I demaunde how muche I should lose or gaine vp∣pon the 100, in case I had sold the same for 5 li. 10. s. Answere: saie, if 90 yelde 100, how muche will 5 li. geue. Mul∣tiplie and diuide, and you shall finde 5 li. 5/9: then saie again by the rule of 3, if 5/9 come to 5 ½, what will 100 come vn∣to? Multiplie and diuide, and you shal finde 99 li. whiche beyng abated from 100. there will remain 1 pounde, and so muche is loste vpon the 100. 〈 math 〉〈 math 〉

¶The fifte Chapiter treateth of leng∣thes & breadthes of tapistrie, and other clothes.

IF a peece of Tapistri••e bee 5 elles ¾ longe, and 4 elles ⅔ in bredth, how many ells square doeth the same pece containe? Answere: multiplie the length by the breadth, that is to saie 5 ¾ by 4 ⅔, and therof cōmeth 26 elles ⅚, so many elles

square doth the same peece conteine.

More, if a peece of Tapistrie doe conteine 32. elles square, and the same being in length 6 elles ¼. I demaūde howe many elles in breadth the same peece doth conteine. Auns. diuide 32. elles by 6 ¼ and thereof commeth 5. 3/28: So manye elles dothe the same péece conteine in breadth.

More, a péece of clothe beynge 13. yardes ⅓ in length, and 5, quarters ½ in breadth, how many yardes of ⅔ and ½ broade will the same peece make? Aunswere: see what parte of a yarde, the 5/4 and ½ be, and you shall finde that they make 1 yarde ⅜. Then multiplye 13 yardes 〈◊〉〈◊〉 by 1 yarde ⅜ and you shall haue 18. yardes ⅓ in square the whiche you must diuide by ⅔ & ½ that is to saye by 〈◊〉〈◊〉, (bicause the ⅔, ½ beinge brought into 1 fraction maketh 5/〈…〉〈…〉) and you shall finde 22. yardes: So many yardes of 〈◊〉〈◊〉 & 〈◊〉〈◊〉 large doth the same peece conteine.

More, a marchant hath bought 4. yardes ⅔ of cloth beinge syre quarters 〈◊〉〈◊〉 broade to make hym a gowne the whiche he will line thoro••out, wyth black Say of three quarters of a yarde broad, I demaund how much Say he must bye? Aunswere: Multiplye the length of the cloth, by the breadth, that is to say 4 ⅔ by 1 ⅝, (which is the syx quarters ½) and thereof commeth 7. yardes 7/12, the which diuide by ¾ and you shal finde ten yardes 1/9. So many yardes of Say must he haue to line the same 4 yardes ⅔ of clothe of 6. quart. 〈◊〉〈◊〉 broad.

More, at 6, s. 8, d. the elle square, what shall a peece of tapistrie cost me, which is fiue elles ½ lōg and 4, elles ¼ broade? Aunswere, multiply 5, ½ by 4, 〈◊〉〈◊〉 and therof cōmeth 23 elles ⅜ square: then say by the rule of three, if one elle square cost me 6, s. 8, d. what shal 23 ⅜ cost? Multiplye and diuide, and you shall finde 7 li. 15. s. 10 d. so muche the said peece of tapistrie did cost.

Or otherwise, by the rules of prac∣tise, take the ⅓ of 23. ⅜: and you shall finde 7 .li. 15. s. 10. d. as aboue is sayde.

More, a peece of Hollande clothe conteining 42. elles ⅔ Flemish, howe many elles Englishe doe they make? Here must you fyrst note that 100. els Flemish, do make but 60. elles Eng∣lishe, and so consequentlye fiue elles Flemishe do make but 3. els English. Therfore say by the rule of 3. if 5. elles flemish doe make three elles English, how many elles English will 42, els ⅔ Flemish make. Multiply and diuide so shall you finde 25. elles ⅗ Englishe, and so many elles Englishe doth 42. ⅔ Flemish conteine, the lyke is to bee done of all others.

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

First, forasmuch as three elles english are worth 5 elles flemishe, therefore put 3 elles english into hys square, in multipliyng 3. by himself whiche ma∣keth 9: likewise multiplye 5. in hym∣selfe squarely, and it wilbe 25. Then multiplye 5¾ whiche is the length of the peece, by 4⅔ which is the breadth, & therof cōmeth 26 elles ⅚ square, then say by y^• rule of thrée, if 25 elles square of flemishe measure, be worth 9 elles square of englishe measure, what are 26 elles flemish ⅚ worth? multiply and diuide, and you shall finde that they are worthe nine elles 33/50 square of en∣glish measure.

More at 3. s. 6. d: the ell flemish what is the englishe ell worth after y^• rate. Answere: saye if 5. elles flemishe bee worth three ells english, what is 1 ell flemishe worth? multiply and diuide, & you sh••ll fiynde 3/•• of an englishe ell. Then saye by the rule of 3, if 〈◊〉〈◊〉 of an englishe ell, be worth 3 s. 6 d. what is 1. englishe ell worth? multiplye and

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

More at 6 s. 8 d. the flemishe elle square, what is the english ell worth. Aunswere: 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 elle: Then saye, if 9/25 of an englishe elle be worth 6 s. 8. d. what is one square elle englishe worth? mul∣tiplie and diuide, and you shall fynde 18. s. 6. d. ••/9, so muche shal one englishe elle square be worth.

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

I Haue bought 97. paumes 〈◊〉〈◊〉 of Genes veluet, & I would know howe manye yardes they will

make? Aunswere, Diuide 97. 〈◊〉〈◊〉 by 4. and you shall haue 24. yardes 〈◊〉〈◊〉. So manye yardes doe the 97. paumes ••/2 conteine.

Or otherwise, take some other nō∣ber at your pleasure, as 20, paumes, which doe make fiue yardes, and then 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 ⅜ as before.

More, at two shillings 7, d. y^• pau〈…〉〈…〉 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 〈◊〉〈◊〉 yarde worth? Multiplie & diuide, and you shall finde ten shil∣lings 4. d. So muche is the Englishe yarde worth.

Or otherwise, multiply 4. paumes (which is one yarde) by two shillings 7, pence, and you shal 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? Annswere, saye: by the rule of 3, if 257, ½ paumes be worthe 20. 5/••, what are 4/•• paumes worth. Mul∣tiply and diuide, and you shall fynde 100/309 part of a pounde, which is worthe 6 s. 5. pence, 〈◊〉〈◊〉: so much is one yarde worthe.

¶ The vii. Chapter treateth of mar∣chaundise solde by waight.

AT 9. d. ½ the ounce, what is the li. waight worth? Answere, say if 3/•• giue 9. ½ what will 〈◊〉〈◊〉 gyue 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 syre pence, take the ½ of 16. which is 8. s. then for 3. d. take the ½ of 16. s. whiche is 4. s. Finally, for the halpenye, take 16. ob. which are 8. d. adde all these nombers togither and you shal 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 ounces: in multipliyng. 112 .li. by 16. ounces & you shall haue 1792. ounces, then say by the rule of 3. if 1/••|10½|1722/1: Mul∣tiplie and diuide, and you shall finde 18816 d. whiche do make 78 .li. 8. s. and so much are the 112 .li. worth after 10. d. ½ the ounce.

At 12. s. 8. d. the li. waight, what is the ounce worth: Aunswere: put 12. s. 8 d. into pence, and you shall haue 152. pence: then say by the rule of 3. if 16. ounces cost 152. d. what shall 1. ounce coste, multiplye and diuide, and you shall finde 9. d. 1/1, so much is the ounce 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. 2 d. 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. 12. s. al into shil∣lings and you shal haue 650. s.

Then say, by the rule of three, if 〈…〉〈…〉 650 〈…〉〈…〉. multiply and diuide, and you shall finde, 6 s. 6. d. so muche is the 11. worthe.

If one pound waight of saffron do cost me 18. s. 8 d. what shall 355 .li. 10. ounces cost me by the same price? Aunswere, saye by the rule of 3. if ½|18 ⅔|355⅝. Multiply and diuide, and you shall finde 331 .li. 18. s. 4. d. so much are the 355 .li. ten ounces worth.

Brief rules of waight.

WHo that multiplieth the pēce that 1 .li. waight is worth by 〈◊〉〈◊〉, & diuideth the product ther∣of by. 12. hee shall finde howe manye pounds in mony the quintal is worth that is to saye, howe 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 deuide the product by 5. and you shall fynde howe many pēce the poūd waight is worth.

¶ Example.

AT seuentene pence the pounde waight, what is the 100 pounde waight worth? Aunswere, Multiplie 17. by 5, and thereof cōmeth 85. diuide the same by 12. and you shall finde 7. pound 1/12, whiche 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 worth? Aunswere, Multiplie 13. by 12. amoun∣teth to 156. the whiche diuide by 5. and you shal finde 31. d. ••/5 which is 2. s. 7 d. 1/•• and so muche 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 worthe, by 6. And diui∣deth the product by 12. he shall fynde how many poundes in money y^e 120. elles are worth, which 120 elles wee count but for a C.

And contrariwise, be that multi∣plieth the poundes in money that the 120 elles are worth by 12, and diuideth the multiplicotion 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 elle worthe? Aunswere, Multiplie nine pound by twelue, and therof commeth 108, the which diuide by 6. and you shal finde 18. d. so much is one elle worth.

The like is to be done of alll ma∣ner

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

¶ Briefe Rules for ••ure hundreth waight here at London, whiche 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 howe many pounds in mo∣ney the 112 .li. waight is worth.

ANd contrariwise, he that multi∣plied y^• poundes in money that the 112, li. is worth by 6••, and diuideth the product by 28. shal finde howe manye pence one li. waight is worth.

Example.

AT nine pence the pounde waight, what is the 112 li. waight worth•• Aunswere: multiplie 6. 〈◊〉〈◊〉. by 28, and thereof cōmeth 2, 2, the whiche diuide by 60, and you shal finde 4 .li. 12/60 which beinge abbreuiated is 〈◊〉〈◊〉 of a pounde, whiche is worthe 4, s. And thus the 〈◊〉〈◊〉 .li. 2. is worth 4. pound 4, shil.

At 8 li. the 112, li. waight, what is 1 .li. waight worth? Aunswere, Multi∣plie 8 li. by 60, and thereof commeth 480, the whiche diuide by 28. and you shall finde 17. d. 〈◊〉〈◊〉: so muche 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 vppon 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 1•• .li. what are 987 li. waight worthe? multiply & diuide, & you shal finde 113, li. 〈◊〉〈◊〉 which is worthe 17. s. 8, d. 4/••••. So much shal y^e 987 .li. waight be worth. 〈 math 〉〈 math 〉

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

what the 100 pound is worth saying, if 〈◊〉〈◊〉|6⅓|100/1 Multiplie and diuide, and you shall finde 33 .li. ⅓ then adde 4 .li. vnto 100, & they are 104. then say a∣gain by the rule of 3. if a 104 .li. be sold for 33, li. ⅓ for how muche shall 345 .li. ½ be sole? multiply & diuide, and you shal finde 110 .l. 14. s. 8. d. 12/13 So much shal the 345 .li. ••/2 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 & Close? Answere, Multiply 780. by 4. and therof commeth 3120. The which diuide by 100. and you shal haue 31, li. ⅕ abate 31. ⅕ from 780. and there wyll remaine 748⅘. 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. ••8/25, and so much shall the 780 .li. cost, in rebatinge 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. vpō the 100. for care and cloffe? Answere. First, note that hee which giueth 5 .li. vpō the 100. giueth 105. for 100: and he which rebateth 5 .li. vpon the 100. giueth the 100. for 95. Therefore saye by the rule of 3. if 105. be giuen for 100: for how much shal y^• 100. be giuen? Multiply and diuide & you shal finde 65. 5/2••: and be whiche re∣bateth 5. vpō the 100. maketh but 95. of 100: so that he loseth 5. vpon the 100 & the other which giueth 5. vpon y^• 100 loseth but 4. 16/21 vpon the 100. Thus he that rabateth 5. vpon the 100. loseth more by 5/21 vppon the 100. than the o∣ther whiche gaue 5. vppon the 100. for tare and clo••fe.

If 100. of Allam do〈…〉〈…〉 me. 26. s. 8. d. how shall I sell the li. waight to gaine after the rate of 10. vpon y^• 100. Answere, put 26. s. 8. d. al into pence. & you shal haue 320. d. Thē say by y^• rule at 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 〈◊〉〈◊〉, li. multiplye & diuide, and you shall haue 3, d. 26/50 whiche 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 howe 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. 2/6 what will 105/1 yelde? Put the whole nombers into theyr broken, the 〈…〉〈…〉ul••iplie and diuide, & you shall finde 10436/41 from the whiche substract 100, and there resteth 4 .li. 36/41 so muche 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 geue? Putte the whole nom∣ber into their broken. Then multi∣plie and diuide, and you shall finde 89 1/10. the whiche you must substract from 100. and there will remain. 10. pound 15/••6, so muche is lost vpō the. 100. pound of money.

More, if the pounde waight doe cost me. 3. shillynges. 2. pence: and I sell it againe for. 3. shillynges. 4. pence, how muche shall I gaine vpon. 20. shillin. Aunswere: saie if 3⅙ geue 4⅓, what shall 20/1 geue. Multiplie and diuide and you shall finde 27. shillinges 7/19: out of the whiche abate. 20. shillynges, and there will remaine. 7. shillynges 7/19, whiche is. 4. pence 4/19: and so muche is gained vpon the pound of money, that is to saie vpon 20. shillinges.

If the pounde waight doe coste me 4. shillinges. 4. pēce, and sell it again for. 3. shillinges. 2. pence. I demaunde how muche I shall lose vpō the pound of money? That is to saie, vpon. 20. shillynges. Answere: saie, if, 4. ⅓ geue

but 3⅙, what will 20/1 geue, multiplie and diuide, and you shall finde. 14. s. 〈◊〉〈◊〉, the whiche you must abate from. 20 shillynges, and there will remaine. 5. shillinges 5/13, whiche 〈◊〉〈◊〉, is worthe. 4. d. 〈◊〉〈◊〉 of a penie, and so muche is lost vpon the pounde of money.

¶ The ninth Chapter treateth of cer∣tain questions, doen by the dou∣ble rule, and also by the rule of three compounde.

WHen the quarter of Wheate doeth cost 6. s. 8. d the loafe of breade waiyng. 20. ounces is solde for a ob. I demaunde that if the quarter of Wheate did cost 10 shillin∣ges, for how muche shall the loafe of bread be sold, that waieth. 16. ounces? Answere: by the first part of the rule of 3. compounde, whiche is mentioned in the third parte of this boke, and in the seconde Chaptier of the same. There∣fore saie by thesame firste parte of the rule of. 3. compounde, if 6⅔|20/1|½|10/1|16/1.

Then multiplie the firste nomber by the seconde, and the producte there∣of shalbe your diuisor. Likewise mul∣tiplie the other three nombers, the one by the other, and the producte thereof shalbe your diuidende: As thus, firste multiplie. 6⅔ by. 20. and thereof com∣meth 400/〈…〉〈…〉 for your diuisor, then multi∣plie ½ by 10/1, and the producte thereof by 16/1, so you shall haue 〈◊〉〈◊〉 for youre nomber that is to bee diuided, then diuide 150/•• by 400/••••, and thereof commeth 480/800. the whiche beeyng abbreuiated, bryngeth 〈◊〉〈◊〉. of a penie: and for that price muste the loafe of breade bee solde, whiche waieth sixtene ounces, and the quarter of Wheate beeyng worthe tenne shillynges.

Or otherwise by the rule of three, at twoo tymes. Firste saie if ••0/1 oun∣ces geue ½, what will 16/1 ounces geue? Multiplie and diuide, and you shall finde 2/••, of a pennie. Then saie a∣gaine, if. 6. 〈◊〉〈◊〉 dooe geue me ⅖, what will 10/2 geue? Multiplie and diuide,

and you shall finde ⅗ of a penie, as a∣fore is saied.

When the cariage of one hundreth waighte of Marchaundise. 50. miles doeth cost. 5. shillinges, what shall the cariage of. 500. waight cost me for. 16. mile? Aunswere. By the firste parte of the rule of. 3. compounde, saiyng, if 100|50|5|500|16 Multiplie. 100. by 50. the produ••••e will be. 5000. whiche shalbee your diuisor. Then multiplie 5. tymes. 500. by. 16. and thereof com∣meth. 40000. for your diuidende. Therefore diuide. 40000. by. 5000. and you shall finde. 8. shillynges, so muche shall coste the cariage of. 500. waight. 16. miles.

Or otherwise by the double rule of three, that is to saie, by the rule of three at twoo tymes: firste safe if. 50. miles dooe paie. 5. shillinges, what shall. 16. miles paie? Multiplie and diuide, and you shall finde. 1. shilling ⅗. Then saie againe, if. 100. waight doe coste me. 1: shilling 3/••, what shall. 500. waighte

coste? Multiplie and diuide, and you shall finde. 8. shillinges, as before.

When the cariage of. 800. pounde waight of Marchaundise. 84. miles, doeth cost me. 6. shillinges, how many miles maie I haue. 64. pound waight carted for. 3. shillinges. 4 pence. Aun∣swere, by the second part of the rule of 3. compounde: saie if 〈◊〉〈◊〉 | 84/1 | 6/1 | 64/1 | 3 ⅓.

Then multiplie the fowerth nom∣ber 64/1 by the third nomber ⅙, and ther∣of commeth 〈…〉〈…〉 for your diuisor. Like∣wise multiplie. 3⅓ by 100/1, and by 14/1, and you shal haue in the product 24000/••. then diuide ••••000/3 by 384/1 and you shall find. 72. miles 11/12 of a mile. So many miles shal the. 64. pounde waight be caried, for three shillinges. 4. pence.

Otherwise by the rule of. 3. at twoo tymes: first saie, if. 100. waight do cost me. 6. shillinges, what shall. 64. p••ūd waight cost? Multiplie and diuide. and you shall finde. 3. shillinges 21/25. Then saie, if 3 21/25. hee paied for. 84. miles car∣riage: for how many miles shal 〈◊〉〈◊〉. shil∣lynges

⅓ bee paied? Multiplie and di∣uide, and you shall finde 72 miles 1••/12.

If 100 horses in 100. daies do spend 180. quarters of otes: how many quar∣ters of Otes will. 300. horses spende in. 150. daies? Aunswere: by the firste parte of the rule of three compounde: multiplie. 180. tymes. 350. by. 150. and diuide the product by. 100. tymes. 100 and you shall finde. 945. quarters. So many quarters of Otes will 350. hor∣ses spende in. 150. daies.

Or otherwise by the rule of three at twoo tymes: first saie, if 100. daies doe yelde me. 180. quarters of Otes: what shall. 150. daies yelde: multiplie and diuide, and you shall finde. 270. quar∣ters: then saie againe, if. 100. horses doe spende. 270. quarters of otes, how many quarters of otes wil. 350. horses spende? Multiplie and diuide, as you shall finde. 945. quarters as before.

¶ The tenth Chapiter treateth of the rule of fellowship, with out any time limited.

THE rule of Fellowship is thus: you must sette doune eche mannes somme of mo∣ney that he laieth into com∣panie, euery one directly vnder the o∣ther, the whiche you shall adde altoge∣ther, and the totall somme of all their whole stocke beyng thus assembled, shalbe your commō diuisor, to the fin∣dyng out of euery mannes part of the gaine. Then shall you multiplie the gaine, or els the losse, by eche mannes portion of money that be laied in, and diuide the productes by the saied diui∣sor: so shall you haue in your quotient euery mannes parte of the gaine, or els of the losse, if any thyng be lost.

¶ Example.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Aunswere.

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

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

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

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

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

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

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

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

¶ The rule of Felowship with time.

THe money that euery mā lay∣eth in, muste be multiplied by the time that it remaineth in company: and of that whiche cōmeth thereof you shall make their newe layings in for eche of them: and then multiplye the gaines by euery one of them seuerally, the whiche you shall diuide by all their new layings in ad∣ding togither, and you shall haue pro∣portionally eche mannes parte of the gaine according to his laying in.

¶ Example.

1. Two Marchauntes 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 did put 450 .li. the fyrste of January: his 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 7, 0 li. but at the first daye of Maye: so that his money remained in companye but 8 mone∣thes. Therefore multiplye his 750 li. by 8. and therof commeth 6000 for his new laying in: Thē ••dde 5400. with 6000. and they make 11400 for your 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 and so muche 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 gaines? Aunswere, Mul¦tiply 640 li. by 12. monethes that his money abideth in the companye, and therof cōmeth 7680 li. for his layinge in. And so muche oughte the seconde mannes layinge in to be, for because he taketh ½ of the gaine: But for that, that be putteth in nothinge 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 oughte the seconde marchaunt to laye in the first of Aprill, to the ende that he maye take the one moy••y of the gaynes.

3. Three Marchayntes 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 muche money, that of the gaine, he muste haue the ⅓ parte: and the thirde laide in y^e first of Nouember so muche mo∣ney, that of the gaines he muste haue likewise ⅓ and thei continued in com∣pany, vntil y^e next Marche folowing. I demaunde howe muche the seconde and the thirde Marchauntes 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 his laying in: and so muche ought the se∣conde and the thirde marchaunt eche of them to lay in: Bicause they parte the gaynes by thirdes. But for that, that the seconde Marchaunt putteth in nothinge tyll the first of Iune, hys money can bee in companye but nine monethes. Therefore diuide 1200. by nine monethes, and therof commeth 133. ⅓. And so muche ought the seconde Marchaunt to laye in: Then, foras∣much as the thirde Marchaunt, dyd

laye in nothing vntil the first 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 thirde 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 fyftye pounde, the fyrste of Marche: And the thirde putte in a Iewell the fyrste of Iulye: And at the yeares ende, they had gained foure hundred crownes: of the whiche, the fyrste marchaunt must haue fifty crownes, and the seconde muste haue 80. I de∣maunde what the Duc••et was worth and at what price the Iewell was va∣lued, whiche the thirde Marchaunte layde in?

Aunswere: the firste mannes money is 1200 as afore is sayde, and he ta∣keth 50 crownes of the gayne: there∣fore say, if fifty crownes of gayne be come of 1200, whice was his stock, of how much shall 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 be 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 fynde 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. (whiche is the third mannes layinge in) by 6. mone∣thes that his Iewel remained in com∣panye, and you shall finde 1080 Duc∣kets: and for that price was y^e Iewell put in company.

5. Three Marchauntes haue com∣panied togither: the first layed in the first of Ianuary 100 li. and the firste of April 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 againe 50 li. And at the yeres end, they found that they had gained 160 li. I demaunde how muche euery man shall haue? Aunswere, Multiply 100 li. which the first man layed, by 12 monethes, and therof commeth 1200. li from that nomber 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 hun∣dred, which are 500. so all amounteth to 1100. for the second mans laying in Afterwardes, multiplie 150. pounde, which the thyrde man hath layed in, by 6. monethes, and therof commeth 900. from the which nōber abate three times 50. and they are 150: so there resteth 750. for the thyrde mans lay∣ing in. Then procede wyth the reste, as in the firste Question of the rule of felowship with tyme, in adding 1020, 1100. and 750. altogither, whiche shall be your Diuisor: Then multiplie 160 by 1020. by 1100. and by 750. & diuide at euery time by your Diuisor, which is by all theyr layinges in added togi∣ther, and they make 2870, so you shal fynde 56. 241/287: for the fyrste man, 61. 93/••87 for the seconde, and 41. 233/287 for the thirde man.

6. Two Marchaunts haue compa∣nied

togither, the fyrste hath put in 960. pounde, for the space of 12. mon∣thes, and he ought to haue 8. pounde vpon the hundred pound of the gaine. The second hath layed in 1120 .li. for the space of eight monthes, & he ought to haue after 12. pounde vpon the 100. pound of the gaine.

And at the yeares ende, they haue gained eyght hundred pounde. I de∣maunde how much eche of them shall 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 62160. for the fyrst mans laying in: then multiplye the 1120. that the seconde hath layed in by eyght mone∣thes, and that whiche commeth thereof you shall multiplie againe by 12. and you shal finde 10••520. for the seconde mans layinge 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 3993/13 for the first man: and 430 .li. 10/13 for the second man.

¶ The rule of company, betwene Marchauntes and their Factours.

7. The estimation of the bodye or persone of a Factour, is in suche pro∣portion to the stocke, whiche the Mar∣chaunt layeth in: as the gaine 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 profise, the persone of the sayd Factour shal be esteemed 200 li. And if the Factour do take but the ••/3 of the gaine, he shoulde 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 Marchaunt layeth in, that is to say 100 li.

And if the Factour did take the ⅖ of

the gaine, then the Marchaunt shall take the residue, which are ⅗ of y^e gaine 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? Multiply 200 by 2 and diuide be 3 so you shall finde 133 ••/3 Otherwise, consider that the Factour taketh the ⅗ of that whiche the Mar∣chaunte taketh. And therfore take the ⅔ of 200, and you shall fynde 133. ⅓ as before: and so muche is the persone of the Factoure esteemed to bee worthe.

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 gaine: I demaund for how much shall his person be esteemed 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 esteemed twise as muche as the stock that the marchant layeth in, which shoulde haue but ⅔ of the gaine: for ⅔ vnto ⅓, is in double proportion. Therefore double twoo 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 the gaine, that shall bee but the ½ of ⅔ whiche the marchaunt taketh: then the estima∣••ion of his person, with his layinge in should be esteemed but the halfe of the whiche the marchaunt layeth in: take therfore the ••/2 of 200 .li. whiche is 100 .li. from the which abate fourty pound and the rest whiche is 60 .li. is the esti∣mation of his person.

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

haue but the ¼ of the gaine, and yet he would haue the ⅔, I demaunde howe much he shoulde put in of readye mo∣ney, besides his person? Aunswere, seing that his person gaineth the ¼, all the whole layinge in, shall gaine the rest that is to saye the ¾: nowe for by∣cause ¼ is the ⅓ of ¾ therfore his person shalbe estemed the ⅓ of all the layinge in. Take then the ⅓ of 240. and you shall haue 80. for the estimation of his person, and for that, that he wyll 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 muste lay in the ouerplus, whiche amounteth to 160 .li.

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

shall 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 gaine, hys persone ought to bee estee∣med as muche as ½ of the stock whiche the Marchaunte layeth in, that is to say y^e ½ of 1200 li. which is 900 l. The reason is, bycause the ⅓ of the gayne that the Factoure taketh, is the ••/2 of the ⅔ of the gaine that the Marchaunt taketh.

11. A Marchaunt that deliuereth 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 be shal take the ⅖ of y^• gain: I demaūde for how much his persone was estee∣med? Aunswere, Forasmuche as the Factour taketh the ⅖ of the gaine, he saketh the ⅔ of that which y^• March••ūt taketh, for ⅖ are the ⅔ of ⅗: and there∣fore

the Factours laiyng in ought to be 800. pound, which is the ⅔ of 1200. pounde, that the marchaunt laied in: Then abate 500. pounde, whiche the Factour did lay in, from 800. pounde, whiche should be his whole stock and there remaineth thrée hundred pound for the estimation of his persone.

12. More, a marchaunt hath deli∣uered vnto hys factoure a thousande pounde vpon suche condition, that the factour for his paines and seruice, shal haue the gaines of 2. hundred pound, as though he had laide so muche in of redy money: I demand what the por∣tion of the gaine, the saide Factour shall take? Aunswere: Sée what parte the two hundreth pounde (whiche the Factour layed in) is of one thousande twoo hundreth whiche is the whole stocke of their companie, and you shal finde that it is the ⅙, and such parte of the gaine shall the Factour take.

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

Factour should haue the gaine of two boundred pounde of the stocke, whiche the marchaunte layeth in, that is to saie of the thousande pounde. Then shoulde the Factour take the ⅕ part of the gaine. For twoo hundred pounde is the ⅕ of a thousande pounde.

¶ The 11 Chapiter treatteth of the Rules of barter.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

¶ The 12 Chapter treateth exchaun∣ging of money from one place to another.

FIrste, you muste note, that at An∣dwerpe they vse to make their ac∣comptes by Deniers de gros, that is to saye by pence Flemishe, whereof 12 doe make 1 shill. Flemishe, and 20 shil. Flemish do make 1 li. de gros.

1. If I deliuer in Flaunders, 500 li. Flemishe, at 19 shil. 6. de gros that is to saye, at 19s. wil. 6. d. Flemish, to receiue 20 shil at London: I demaund howe much I shall receyue sterlynge at London for the sayde 500 li. Fle∣mishe? Aunswere: Saye, yf 19 ½ geue 20/1•• what wyll 50••/1 geue? Multiplie and diuide, and you shal finde 512 li. 16. sh. 4. d. 12/13 of pennye. And so muche ster∣ling shall I receyue in London for my 500 li. Flemishe.

2. If I deliuer in London 375 li. sterlyng, to receyue in Andwerpe 21 shill. 9. d. de gros, that is to saye Fle∣mishe, for euery pounde sterlinge. I demaunde howe many poundes Fle∣mishe I shall receiue in Andwerpe, for the sayd 375 pound sterling?

Answere, say if 23/•• giue 21 ¾: what will 375/•• giue? Multiplie and diuide, and you shall finde 407 .li. So many poundes Flemishe shall I receyue for the sayde 375 .li. sterlinge in Andwerpe.

3. If I take vp monie at Andwerpe after 19 sh. 6 d. Flemishe to pay for y^e same at London 20 s. ster. & when the daye of paiment is come, I am forced to rechaunge the same, and to take vp money againe here in London to re∣pay the same, so that for 20 shillings, which I take vp here, I must repaye, 19 shill. 9. at Andwerpe. I demaunde whether I do winne or lose, and how muche vpon the 100 pound of money? Aunswere, Saye, if 19 ••/4 giue 19 ••/••, what wyll 100/•• giue?

Multiplie and diuide, and you shall finde 9858/79, the whiche beinge abated from 100 there will remayne 121/79. And so muche doe I lose vpon the 100 li. of money.

4. If I take vp at London 20. shill. ster. to paye at Andwerpe 21. shill. 8. d. Flemishe, and when the day of payment is come. I am con∣strained to take vp money againe at Andwerpe wherewith to repay the foresayde summe: and there I doe re∣ceyue 22. shill. Flemishe to paye 20. shill. at London. Nowe I demaund whether I do winne or losse and howe much vpon the 100 pounde of money after the rate.

Answere: say, if 212/2 giue 22/1. What wil 100/1 giue•• Multiplie and diuide, and you shall finde 1017/13, from the whiche abate 100, and there will remaine 1〈…〉〈…〉 and so muche shall I gaine vpon the 100 li. of money.

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

Flaunders but is deliuered by the Frenche crowne, whiche is worth 50 souse Tournois the pece.

And here muste you note that in Fraunce they make theyr accompte by Deniers Tournoys, whereof 12 maketh one souse Tournois, and 20. souse. Tournois maketh 1. pound Tournois, whiche thei call a Liure, and the Frenche Crowne is currant amonge Marchauntes for 51 souse Tournois, but by excaunge it is o∣therwyse, for they wyll deliuer but 50 souse. Tournois, whiche is 2 li. 10 souse. Tournois for a crowne, or at suche price as the takers vp of money can agree with the deliuerer. As by Example.

5. If I deliuer 340 pound ster. here in London after 6. shill. 4. d. ster. the crowne, to receyue at Roan or at Paris 50 souse Tournois for euerye crowne, I woulde knowe howe ma∣nye

liures Tournoys I shall receiue there for my 340 li. ster. Aunswere, say if 6 sh. ⅓ do giue me 2 li. Tournois what will 6100/1 sh. giue (whiche is the 340 li. reduced into shillings) multi∣plie and diuide, & you shall finde 2684 Liores 4/19 whiche is worthe 4. shill. 4/19 Tournois, and so much shal I receiue in Roan or Paris for my 340 li. sterl.

6. If I deliuer in Paris or Roan, or els where in Fraunce 1250 liures Tournyis, at 50 souse tournois the crowne, to recyue for euerye suche crowne 6 shillings 3. d. sterling at Lon¦don. I demaunde howe much sterling money I shall receyue at London for my 1250 .li. Tournois. Aunswere: saye, if twoo li. ½ doe giue me 6 shil∣linges ¼, what wyll 1250/1 giue? Mul∣tiplie and diuide, and you shal finde 3125 shyllynges sterlynge, whiche maketh 156, pounde, fyue shillyngs sterlynge. And so many poundes shal I receyue at London, for the sayde

1250 pounde Tournois, after 6 shil∣linges 3 pence for euery crowne.

¶ The 13 Chapter treateth of the Rule of Alli∣gation.

THe Rule of Alligation is so na∣med, for that it teacheth to alli∣gate or binde togither diuers percelles of sundrie prices, and to knowe howe muche you muste take of euerye percell, accordynge to the nombers of the Question.

Example.

1 A Goldsmythe hath three sortes of Golde. The fyrste is worth thir∣tye Crownes the pounde weyghte: The secende is worthe 36 Crownes. And the thyrde is worthe 45. crow∣nes, and of these three sortes he will make a Scepter of sixe pound weight, whiche shalbe worthe 40, Crow∣nes the pounde. I demaunde howe muche he muste take of euery sorte?

Answere: first you must set downe the nōbers whereof you wyl make the Al¦ligation (which are 30. 36. 38, and 45) orderly the one vnder the other, as if you shoulde make of them an addiciō: and the common nomber whereunto you will reduce them, shall you set on the left hand, which common nomber in this example is 40. Then marke what summes bee lesser, then that common nomber, and whiche bee greater, and wyth a draught of your penne, euermore lynke two nombers togither, so that the one be lesser then that common nomber, and the other greater then he. For 2 greater nor twoo smaller nombers maye not bee linked together, for they wyll eyther be lesser, or els greater then the com∣mon nomber: but one greater nom∣ber, and one smaller maye be so mi∣xed, that they will make the common nomber. And two greater or twoo smaller nombers, can neuer make the common nomber in dewe order,

as here after shall appeare.

After that you haue thus lynked them, then make howe muche eche of the lesser nombers is smaller then the common nomber, and that difference shall you set against the greater nom∣bers, whiche bee linked with those smaller, eche of them with his matche styll on the righte hande. And lyke∣wise you muste set the excesse of the greater nombers againste the lesser which be combyned with them. Then shall you adde all those differences in∣to one summe, whiche shalbe the first nomber in the rule of three, and the second nomber shalbe the whole mas∣sye pece that you will haue of all the perticulers, the thirde summe shalbe eche difference by it selfe, and by them shall you finde out the fourth nomber declarynge the luste portion of euerye perticuler in that mixture, as nowe by the former example, I wyll make it plaine.

〈 math 〉〈 math 〉

Here in this former example, you see that I haue set downe the seuerall prices, whiche be 30, 36. 42. 45, and haue linked together 30, with 45. & 36. with 42. The cōmon price 40, I haue set on the lefte syde, and the difference of it from euerye seuerall price, I haue set on the ryght hande, agaynste that summe wyth the whiche it is lynked. So the difference of 30 from

40 is 10, whiche I set against 45, that he is lynked wythall, and the diffe∣rence of 45, aboue 40 is 5. whiche I haue set against 30.

So lykewayes, the differences of 42 aboue 40, is 2, that I haue sette a∣gainste 36. And the difference betwen 36 and 40 (whiche is 4) I haue sette againste 42. Then I adde all those differences togither and they make 21, whiche I make the fyrste nom∣ber in the Rule of three, and 6 the seconde nomber, which is the weyght of the Scepter of Golde, and the thyrde nomber shall bee euerye per∣ticuler difference. Then I worke by the Rule of three: sayinge yf 21. (whiche is the differences added to∣gether) doe geue me 6 pounde, whi∣che is the weyghte of the Scepter, what shall 5 gyue, whiche is the first difference?

Multiplie and diuide, and you shall fynde one pounde 1/7: so muche muste I haue of the fyrste price.

Then doe likewise with the reste and you shall finde 4/7 of the seconde price, 1 li. 1/7 of the thirde price, and 2 .li. 6/7 of the fourth, the whiche 4 summes beinge added together, do make 6 li. whiche is the totall that I would haue. And now to proue if the prices do agre, you shall do thus: Firste multiplie this totall summe 6 by the common price 40 and it will make 240 Crownes, whiche you shall kepe be it selfe. And afterward multiplie euery seue∣rall summe of weight by the price be∣longynge to the same weyght, and if that sume do agree with the first that you kepte by it selfe, then is youre worke well done, as here 1 li. 3/7 is the weyght of that sorte of golde whiche is of 30 Crownes price. Then mul∣tiplie 30. by 1 li. 3/••, and it maketh 42. crownes, 6/7, which you shall set downe. Then multiplie 4/7 (whiche is the weyght of the seconde sorte of golde) by 36, which is the price of the same, & therof cōmeth 20 crownes 4/2: so again

1 .li. ⅓ multiplyed by 42, doth make 48 crownes. And laste of all 2 pounde. 〈◊〉〈◊〉 multiplied by 45. maketh 128 crow∣nes 4/7. Al these added together dothe make 240 crownes, agreable to the former summe of 40 multiplied by 6: And thus I maye affirme that this worke is well done.

2. A Tauerner hathe foure sortes of wine, of foure seuerall prices, the firste of 8 pence the Gallonde, the se∣conde of tenne pence the Gallonde, the third of 15 pence, and the fourht of 18 pence. And he will mingle one pū∣chen with all these sortes, so that the Gallonde shalbe worthe but twelfe pence. I demaunde howe many Gal∣londes he muste take of euery sorte? Aunswere: Firste suppose the pun∣chen to holde some certayne mea∣sure, as to conteyne 84 Gallondes and then the (forme wyll bee after this sorte, as you see here after folo∣wynge.

〈 math 〉〈 math 〉

¶ The 14 chapter treateth of the rule of falshode, or false positions.

THe Rule of falsehod is so named not for that it teacheth any de∣ceyte of falsehode, but that by fayned nombers taken at all aduen∣tures, it teacheth to finde out the true nōber that is demaunded. And this (of all the vulgare Rules whiche are in practise) is the most excellent: this rule hath two parts, the one is of one false position alone: the other is of two po∣sitions as here after shall appeare.

Those questions whiche are done by false positions, haue theyr opera∣tions, in a maner like vnto that of the rule of three, but onely that in the rule of three, we haue three nombers knowen, and here in this rule wee haue but one (I meane that commeth in operation) vnto the likenes where∣of we muste diuise two other, the one multiplying, and the other diuidyng, as by example.

1. I haue deliuered to a banker a certein summe of pounds in money, to haue of him by the yeare 6 li. vpon the 100 li. And at the ende of 10 yeres he payed me 500 pounde for all bothe principall an gaine. I demaund howe muche was the principall summe that I deliuered at the fyrste. Here you see that there are diuers termes: but the chiefe to worke with all is 500 li. whiche commeth of the other nom∣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 nomber at pleasure, and with the same let vs make oure discourse, euen as though it were the principalll summe that we seke for. As by Example. Suppose that I de∣liuered hym at the firste 200 pounde, the whiche were worthe to me in 10 yeares 120 pounde after the rate of 6 vpon the hundred pound. Then 120 pounde added with 200 pounde. Do make but 320 li. and I must haue 500 li. Thus you see that I haue three termes for the rule of three: the one which shall conteine the Question the other two, which I haue 200, & 320: in such sorte, that 320, ought ta haue su∣the proporcion to 200, as 500 hat vnto the nomber that I seeke: that is to say, vnto the true principal summe, then must I haue recourse vnto the rule of three, after this sorte, saying.

If 320. pound become of 200. pounde of howe muche shall come 500. pound Multiply 500: by 200. and thei are 100000. the whiche you shall diuide by 320. pounde and thereof commeth 312. pounde. ½ whiche is the summe that I deliuered at the firste, 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 bée opened, the water will auoyde cleane in one houre, at the seconde yt will anoyde in twoo houres, and at the thirde it will require three houres. Nowe I demande in what space wil it auoide, all the cocks beyng set open. Suppose that it wyll auoide in halfe an houre, that is to saie, in 30. minutes. Then muste there auoide at the firste cocke, the ½, whiche is thirtie 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 whiche

summes beeyng added together doeo make fiftie fiue pipes, but it shoulde be sixtie pipes. Therefore I saie by the rule of thrée, if fiftie fiue pipes doe voide in thirtie minutes: in how ma∣nye minutes will sixtie pipes voide? Multiplie and diuide, and you shall finde thirtie twoo minutes 40/55. And in that space will the water auoide if all the cockes be set open.

¶ Of the rule of two false positions.

THe summe of this rule of two false positions is thus, when any question is proponed ap∣pertaining to this rule. First imagine any nūber at your pleasure, which you shal name the first position, and with the same shall you worke in stede of the true number, as the questi¦on doth import, and if you sée that you haue missed. Then is the last number of y^e worke either to great or to litle, y^t shal you note for to be the first errour,

in the which you haue missed with the signe of more, or lesse, whiche signes shalbe noted with these figures, 4••:—This figure 4: betokeneth more, and this plaine line—signifieth lesse, that is to saie the one signifieth to muche & the other to little: then begin again, & take an other number, whiche shal be the second position, and worke by the question as before, if you haue missed againe, note the excesse or want, for that is the seconde errour. Then shall you multiplie the first position by the second errour crossewise, and againe the seconde position by the first errour (and this must alwaies be obserued) & keepe the two productes: then if the si∣gnes be both like, that is to saie, either both to muche, or both to little, abate the lesser producte frō the greater and likewise, you shall substract the lesser error from y^e greater, & by the remaine of those errours, you shal diuide the re∣sidue of the products: the quotient shal be the true number that you séeke for.

But if the twoo signes be vnlyke, that is to say, the one to muche and the o∣ther to lyttle, then shall you adde those productes together so shall you also adde bothe the errours together, and by the summe of those errours, diuide the totall summe of both the products: the quotient shall be likewise the true number that the question seketh, and this is the wholerule, as by example. ••3. A manlying at the point of death, saied that he had in a certain Coffer a hundred duckets, the which he bequea ched to 3. of his frends by him named, after this sorte. The first must haue a certain portion, the 2. must haue twise so manie as the first abatyng 8. Duc∣kets & the third muste haue 3. times so many as the first, lesse by 15 Duckets. Nowe, I demaunde howe many eue∣rie of them must haue. Answere: First I doe imagine that the firste man had thirtie Duckets, then by the order of the question, the seconde shoulde haue fiftie twoo: and the third seuentie fiue.

These three summes beyng added to∣gether doe make 157: and I shoulde haue but a hundred soe that this fiirste errour is to much by fiftie seuen, then I note a parte the first position thirtie, with hys errour fiftie seuen, to muche after this sorte thirtie. 457.

Therefore I prosecute my worke and I suppose that the firste hadde twentie foure, then by the orderder of the que∣stion, the seconde should haue 40. and the third, fiftie seuen, these three sum∣mes beyng added together, doe ma•••• 121. and I must haue but a hundred, so the seconde errour, is to muche by 21. Therefore I note 24. 421. vnder the thirtie. 457. as you maye see in the margent of the nexte side following. Then I multiplie crossewaies, thirty (which is the firste position) by twelue which is the seconde errour, and ther∣of commeth 630. likewise I multiplie twentie and four (which is the second position) by fiftie seuen, whiche is the firste errour, and I finde 1368: then

because the signes of the errours are 〈 math 〉〈 math 〉 bothe like: that is to saye muche, I must therfore sub¦stracte 630. from 1368. and ther wil remain 731 which is the diuidende: again I must sub∣stract the lesser er∣ror from the grea∣ter, that is to wit, 21. out of 57. and there will remain 36. whiche shalbee my diuisor. Thys done I diuide 738 by 36 and the quotient will bee 20. 〈◊〉〈◊〉. The which 20. ½ is the iust number of the duckets that the first man had for his parte, so consequently the seconde manne had thirtie three Duckets, and the thirde fourty six ½, as by proofe in the margent maie appeare.

The like number wil also appeare. in case the errours wer both to little, as in makyng the twoo positions by 18. and 20. where you shal finde the 〈 math 〉〈 math 〉 two errours both to little, the firste will bée to lyttle by 15. and the se∣conde to little by 3. as by perusing this worke in the margent you shal well perceiue.

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 finde that the firste errour will be 21. to muche, and the seconde wil be three to little: Therfore I multiplie twentie foure by thirtie, crossewaies, thereof commeth 72.

Likewise I multi∣plie twentie by 21. 〈 math 〉〈 math 〉 the product will be 420: These twoo summes 72. and 420, I adde both together because y^e signes of the er∣rours bee vnlyke, and thei mak. 492. the whiche shalbee my diuidende, and againe, I addde the lesser errour three, with the greater errour 21. and they mak 24. for my diuisor, then diuiding foure hundred ninetie two by twenty foure, the quotiet wilbe twentie ½: as in the margent doth plainlie appeare.

And now because you shall not for∣get this parte of the rule, learne thys briefe remembraunce followyng.

The signes both like substraction doe require And vnlike signes addition will desire

The meanyng whereof is thus yf both the errours haue lyke sygnes, then muste the diuidende and the di∣uisor bee 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, hauynge to them bothe, but one couer, the waight whereof is fiue ounces, if the couer be putte to the lesser cuppe, it wyll bee in double proportion vnto the waight of the greater, and the couer béeyng put to the greater cuppe, will bee in tri∣ple proportion, vnto the waight of the lesser. I demaunde what was the waight of euery cuppe.

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

the greater muste waigh six ounces 〈 math 〉〈 math 〉 adde vnto it 5 oun¦ces for y^e couer, all wil be 11. ounces, but it should be 21 for to haue it in triple proportion, vnto 7. which re∣presēteth y^e weght of the lesser cuppe So that this first errour is to little by 10. which you shall note after seuen in this sorte. 7.-10.

After you shall suppose some other number, as 9. and make the like work as before, so shal you finde 15. to little, for the second errour, which you shall put behind nine, and then worke with the reste as aboue is sayed, and you shall finde that the lesser cuppe wayed three ounces, and consequentlye the greater foure ounces.

5. One man demaunded of ano∣ther

in a mornynge what a clocke it was, the other made hym thys aun∣swere, if you doe 〈◊〉〈◊〉 (saieth hee) the ½ of the houres whiche he passte synce mindnight, with the ⅓ of the houres whiche are to come vntill noone, you shall haue the iuste houre, that is to saie, you shall knowe what a clocke it was: Suppose that it was 4•• clocke in the mornynge, so shoulde there re∣maine 8. vntill none: then I take the ••/4 of 4. whiche is 1. and the ⅔ of 8. whiche is 5. ⅓, and I adde them together, so I finde 6. ⅓ and I supposed but 4. ther∣fore thys first errour is to muche by 2. 〈◊〉〈◊〉, which I note after my position thus 4. † 2. ••/3: then againe I suppose an o∣ther number, that is to saye nine, soe shoulde remaine but 3. houres vntill noone., I take the ¼ of 9. and the ⅔ of 3. whiche is 2. ¼ and 2. these I adde to∣gether and they make 4. ¼: but I sup∣posed that it was 9. therfore the second errour is 4. ¾ to little whiche I note behinde my position thus. 9. † 4. 2/4.

And then I multiplie crossewyse, as before 〈 math 〉〈 math 〉 is taught, and bicause th•• sygnes of the er∣rours are vnlike, that is to saye, the one to muche, and the other to lyttle, therefore in thys woorke I muste adde the products, and they will bee fourtie. Likewise I adde the errours, and thei be seuen, 〈◊〉〈◊〉. Then I diuide fourtie by seuen 1/12, and thereof commeth fiue houres 11/17, and that houre it was in the mornyng.

¶ The fiueth Chapiter treateth of sportes, and pastime, done by number.

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

Bydde hym triple the same number, then of the product let hym take the 〈◊〉〈◊〉

if the number be euen, or els the grea∣ter halfe, if the same bee odde, then bid him triple againe the saied ½: after say to him that he put awaie, if he can 36. 27. 18. or. 9. from the laste number be∣yng tripled: that is to saie, cause hym subtellye to put awaie nine as many times as is possible and kepe the num¦ber secretly: and when ye can no more take away 9. then to know if that yet there remaine anye nomber, bid hym abate three and twoo or one, if he can: this doone, see how manie tymes nine you haue caused hym to abate, for the which keepe you in mind so manie ty∣mes 2. and if that you knowe that hee had any thing remaining beside the ni¦nes, y^e same shall also note vnto you 〈◊〉〈◊〉.

Suppose that he thought 6. whiche beyng tripled is 18. wherof the ••/2 is 9. the triple of that is 27: now cause hym to abate 18, or 9. or 27. and againe 9: but then he will saie vnto you that he cannot, bid hym then abate 3. or 2. or 1. ••e wyl saie also that he can not: wher∣fore

consideryng that you haue made hym to abate 3. tymes nine iustly, you shall tell him that he thought 6. for 3. tymes 2. maketh 6. If he had thought 5. the triple therof is fiftene, wherfore the greater ½ is 8. the triple of that ma∣keth 24. which conteineth 2. times 9. thei ar worth 4. and the remain signi∣fieth 1. the which added togither make 5. which is the nōber that he thought.

2. If in any companie, one of them hath a ringe vpon his finger, and you woulde know by maner of deuining, who hath the same and vpon what fin¦ger and what ioint: cause the persons to sit doune in order, & keepe likewise an order of their fingers: then separate your self from them in some certaine place, and saie vnto one of the lookers on, that hee double the number (mar∣kyng the order) of hym that hath the ring: and vnto the double bid hym ad 5. and then cause him to multiply this addition by 5 and vnto the product bid hym adde the number of the finger of

the person whiche hath the ring: bee if that the same last sum did amounte to 89. then afterward say to him y^t he put after the same laste number towarde his right hand a figure signifiyng vp∣pon whiche of the iointes hee hath the ring. As if it be vpon the third iointe, lette hym put 3. after 89. and it will bee 893: this doen, you shal aske him what number hee keepeth, from the whiche you shal abate 250. and you shal haue thrée figures remainyng at the least. The fyrste towarde youre lefte hande shall signifie the number of the per∣son whiche hath the ring. The second or middle figure shall represente the number of the finger. And the last fi∣gure towarde your right hande, shall be token the number of the ioynte. As if the number whiche hée dyd keepe were 893. from that you shall abate 250. and there will remaine 64•• Which do note vnto you, that the sixt person hath the ringe vpon the fourth finger, and vpon his thirde iointe.

But note that when you haue made your substraction, if there do remaine a cipher in the place of tennes, that is to saie in the seconde place, you muste then abate from that figure whiche is in the place of hundreds, that is to saie from the figure which is next your left hand, & that shalbe worth ten tenthes, signifiyng the tenth finger: as if there should remain 703. you must saye that the sixte person) vpon his tenth finger and vpon his third ioint) hath the ring

3. And after the same maner, if a man do cast thrée dice, you maie know the poincts of euery one of them, for if you do cause him to doube the poincts of one die, & vnto that double to ad 5. and the same sum to multiplye by 5. & vnto the product ad the poincts of one of the other dice, and behind the num∣ber towarde the right hand, to put the figure which signifieth the poinctes of y^e last die, & then shal you aske him what nūber he kepeth 〈◊〉〈◊〉 y^e which abat 250 〈◊〉〈◊〉 ther wil rema〈…〉〈…〉 figures, which do

note vnto you the pointes of euery die.

4. Likewise if 3. of your compani∣ons, to saie Peter, Iames, and Ihon, that would (in your absence) giue them selfe euerie one a contrarie name: as for example: Peter woulde be called a king, Iames a duke, and Ihon a coun∣tie: And I woulde deuine whiche of them is called the kinge, whiche the duke, and which the county. Take 24. stones, or other peces whatsoeuer, and geue vnto Peter. 1. vnto Iames 2. and vnto Ihon. 3. or otherwise. But marke well vnto whiche of them you haue 1. vnto which 2. and vnto whom 3. Then leuing the 18. stones (before them) that are ramainyng, you shall absent your selfe from their sighte, or elles tourne your face from them, saiyng thus vn∣to them, whosoeuer nameth himselfe a kinge: for euerie stone that I gaue him lette hym take one of the residue, and he that nameth hymselfe a duke fore∣uerie stone that I gaue hym lette hym take twoo of them that remain, and he

that calleth hym selfe a countie, for euerie stone that I gaue hym let, hym take foure, this beyng done approache nere them, and marke towe man••e stones are remainyng: and know this that there can not remaine any other, but one of these sire, 1, 2, 3, 5, 6, 7, for the whiche sire numbers we haue cho∣sen to euerie of them a seuerall name, whiche are these: Angeli, Beati, quali∣ter, Messias, Israel, p••etas: eche of them containyng three ••oweiles, a, e, i, whiche doe shewe the names by or∣der: that is to say, a, sheweth whiche is the king, e, telleth which is the duke, i, shewe∣eth which is the coū 〈◊〉〈◊〉 fo∣lewynge the order how, and to whom you haue geuen 1. 〈 math 〉〈 math 〉

stone, to which 〈◊〉〈◊〉. and to which 〈◊〉〈◊〉. Then there doe remaine but 1 stone, the first name Augeli•• by these three vowels a, e. i, sheweth that Peter is the kinge, Iames the doke, and Ihon the county. And if there doe remaine 2 stones, the second name Bea••, shall shewe you by these three vowels, e, a, i, that Peter is the duke. Iames the king, and Ihon the countie. And so of the other as by this Ta∣ble dooeth plainly appeare.

FINIS.