The grounde of artes teaching the perfect vvorke and practise of arithmetike, both in whole nu[m]bers and fractions, after a more easie ane exact sort, than hitherto hath bene set forth. Made by M. Robert Recorde, D. in Physick, and afterwards augmented by M. Iohn Dee. And now lately diligently corrected, [and] beautified with some new rules and necessarie additions: and further endowed with a thirde part, of rules of practize, abridged into a briefer methode than hitherto hath bene published: with diverse such necessary rules, as are incident to the trade of merchandize. Whereunto are also added diuers tables [and] instructions ... By Iohn Mellis of Southwark, scholemaster.

The tvvelfth Chapter treateth of the making of Factors which is ta∣ken in twoo sortes.

THe first is when the estimation of the Factor, is taken vppon the sending of the Merchant: as if the estimation of his per∣son be 1/••, it is vnderstoode, that he shall haue ¼ of the gaine, and the Merchaunte the o∣ther ¼.

The other sorte is when the estimation of his making is out of the sending of the Merchaunt: as if the order and agréement betwéen them were such, that the Merchant shall putte in 800 lb: and the Factor for hys making shall haue ¼: neuerthelesse he shall haue but ⅕ of gaine or profit: for the ¼ of 800 is 200 (for the estimation of his making) which with the 800 lb make 1000 lb; wher∣of the 200 lb is ⅕.

A Merchaunt dothe putte in 800 lb

into the handes of hys Factor: vnder suche condition, that the saide Factor shall haue ¼: And after certayne time, they finde in profite 124 lb—6 s— 8 d I demaunde howe muche the Merchant shall haue hereof, and howe muche oughte the Factor to haue?

Answere. When the estimation of the Factor is out of the sending of the Mer∣chaunt, it maketh 〈 math 〉〈 math 〉 for the Merchant 〈 math 〉〈 math 〉 for the Factor

But if that his estimation be at the sen∣ding of the Merchaunt, then it maketh but 〈 math 〉〈 math 〉 for the Merchant 〈 math 〉〈 math 〉 for the Factor.

For the Merchaunt is then to haue ¾ and the Factor ¼.

A Merchant doth putte into the handes of his Factor 800 lb, & the Factor 400 lb to haue the ⅕ of the profite: I demaunde nowe, for howe much his person is estée∣med: when the same is counted vpon the sending of the Merchant.

Answere. According to the tenor and order before prescribed in the firste Rule: That is, if his estimate be ¼, he shall haue the ••/4 of the gaine. Therefore saye by the Rule of 3 direct: If ¼ taken putte in 400 lb what is y^e estimate, or putting in of ⅕ taking? Multiplie, and diuide, and you shal find 320 lb: and so much is the person of the Factor e∣stimated.

Otherwise.

To finde the estimation of the person of the Factor, you shall consider, that séeyng it was agréede betwéene them, that the Fa∣ctor shoulde take the ⅕: then the Merchaunt shall haue the residue, which are ⅘: where∣fore the gaine of the Merchant, vnto that of the Factor is in such proportion as 5 vnto 4: Then if you will know the estimation of the person of the Factor: Say, if 5 giue 4, what

will 400 giue? multiply and diuide, and you shal find 320 lb: And so much is the person of the Factor estéemed to be worth.

Other conditions then these aforesaid, may also be betwéene Merchauntes and Factors without respect, either of sending or not sen∣ding of the Merchaunt: where most commō∣ly the estimation of the bodie of the Factor is in suche proportion to the stocke whiche the Merchaunt layeth in, as the gaine of the saide Factor is vnto the gaine of the Merchaunte. As thus: if a Merchant do deliuer into y^e hāds of his Factor 400 lb & he to haue half the pro∣fit: The person of the said Factor shal be estée∣med to bée worth 400 lb And if the Factor do take but ⅓ of the gaine: he shoulde haue but ½ so much of the gaine as the Merchant taketh: which muste haue ⅔: wherefore the person of the Factor is estéemed but the ½ of that which the Merchaunte layeth in. That is to saye 200 lb.

And if the Factor did take the ⅖ of the gain, then the Merchant shal take the residue whi∣che are ⅖: wherefore the gaine of the Mer∣chaunt vnto the Factor is then in suche pro∣portion as 3 vnto 2: wherevpon if you wyll

then know the estimation of the person of the Factor. Say if 3 giue 2: what shal 400 giue? work and you shal find 266 ⅔ pounds: And so much is the person of the Factor estéemed to be worth.

And if the Merchaunte shoulde deliuer vnto his Factor 400 pounde and the Fa∣ctor woulde lay in 80: and his person to the ende he might haue the ½ of the gaine I demaunde howe muche shall his person be estéemed?

Answer. Abate 80 from 400: and there wil remaine 320. And at so muche shall hys person be estéemed.

A Merchaunt hath deliuered vnto his Factor 900 lb to gouerne in the trade of merchandise, vpon condition that he shall haue the 1/•• of the gain, if any thing be gai∣ned: and also to beare the ⅓ of the losse if any thing be lost: Now I demaunde howe much his person was estéemed at?

Answer. Séeing that the Factor taketh the ••/3 of the gaine, his person ought to be estéemed

as muche as ½ of the stocke, whiche the Mer∣chant layeth in. That is to saye the ½ of 900 pound which is 450: The reason is, because ⅓ of the gaine that the Factor taketh: is the ½ of the 2/•• of the gain that the Merchant taketh, and so the Factor his person is esteemed to be worth 450 pound.

A Merchaunte hathe deliuered vnto hys Factor 600 pound. And the Factor layeth in 250 pound and his persō. Now bicause he layeth in 250 pound, and his person: it is agréed betwéene them, that he shal take the ⅖ of the gaine. I demaunde for howe much his person was estéemed?

Answer. For as muche as the Factor ta∣keth ⅖ of the gaine, he taketh ⅔ of that which the Merchant taketh: for ⅖ are the ⅔ of ⅗. And therefore the Factors laying in, ought to bée 400 pounde, which is ⅔ of 600 pounde that the Merchant laid in: Then Subtract 250, whiche the Factour did laye in from 400 pounde whiche shoulde haue bene his whole stocke: And there remaineth 150 pound: For the estimation of his person.

More, a Merchaunt hathe deliuered vn∣to hys Factour 840 lb vpon condition that the Factor shal haue the gaines of 160 lb as though he laide in so muche readie mo∣ney: I demaunde what portion of the gain the said Factor shal take?

Answer Sée what parte the 160 lb (which the Factor layde in) is of 950 whiche is the whole stocke of theyr company: And you shal find 3/19: And such part of the gaine shall the Factor take.

But in case, that in making theyr co∣uenauntes, it were so agréede betwéene them: that the Factour shoulde haue the gaine of 160 lb of the whole stocke whiche the Merchaunt layeth in: That is to saye of the 800 lb: then shoulde the Fa∣ctor take ⅕ of the gaine: for 160 is ⅕ of 800 pounde.