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 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.