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 fifth Chapiter entreateth of Losse and Gaine vppon Time, wrought by the double Rule of three: or by the Rule of three composed, whiche is contained in foure speciall selected braunches or questi∣ons of diuers formes, eche one of them springing from the firste questi∣on, and eache one of them also beeing a proofe to other, &c.

IF one yeard cost me 2 s 8 d readie mo∣ny: and after I sell the same againe for 2 s 10 d to be paide for it at the ende of 3 moneths: the question is, what I gaine vpon the 100 lb in 12 moneths?

Answere. First saye, if 2 ⅔ gaine 1/•• what shal 100 lb gaine: Multiplie, and diuide, and you shal finde — 6 ¼ lb: Then saye againe

by the Rule of thrée: if 3 moneths gaine 6 ¼ lb what shall 12 moneths gaine: Worke, and you shall finde 25 lb: and so muche shall I gaine in 12 moneths after that rate.

Itē you may also work it at one working by y^e first part of the Rule of 3 composed: say∣ing, if 2 ⅔ s in 3 moneths do gaine ⅙ of a s, which is 2 d, what wil 100 lb gaine in 12 moneths: whiche for thy further encourage∣ment, the worke of this one Example I wil here putte downe, to verifie that I affyrmed when I deliuered in the firste parte of this Ground of Artes, that this Rule, and so all others more reioiceth in Broken than in Whole.

〈 math 〉〈 math 〉

If a yeard be deliuered for 2 s — 10 d: wherevpon was gained after the rate of 25 lb in the 100 for 12 moneths: The que∣stion is nowe, what the yeard coste at the first hande.

Answere. firste saye, if 12 moneths gaine 25 lb, what shal 3 moneths gaine: and you shall finde 6 ¼ lb: Then say againe the secōd time, if 106 ¼ lb giue but 100, what shall 2 ⅚ s giue? worke, and you shall finde 2 ⅔ s, which is the iust price that the yeard coste at the firste hand.

If one yeard of cloth cost me 2 s — 8 d ready mony, for what terme shal I sel the same again for 2 s 10 d: So that I might gaine after the rate of 25 lb vpō the 100 lb in 12 moneths.

Answere. First say, if 2 ⅔ gaine ⅙ what shall 100 lb gaine: Multiply and diuide, and you shall finde 6 1/•• lb. Then saye againe for the second worke, if 25 lb become of 12 mo∣neths, what shal come of 6 1/•• lb: Work, and you shall finde 3 moneths: the iuste terme of time that the cloth ought to bée deliuered at

2 s 10 d, to gaine 25 lb, vppon the 100 lb in 12 moneths.

If one yeard coste me 2 s 8 d readye mony for what price shal I sel the same a∣gaine to be paid at the end of 3 moneths: So that I may gaine after the rate of 25 lb in the 100 lb for 12 moneths?

Answere. Firste saye, if 12 gaine 25 lb what shal 3 moneths gaine? Multiplie, and diuide, and you shal finde 6 ¼ lb: then saye for the second worke: if 100 lb gaine 6 ¼ lb, what shall 2 ⅔ s gaine? worke, and you shall find 2 d, whiche muste be added to 2 s — 8 d: and then it maketh 2 s — 10 d: and for that price muste the yeard be solde to gaine after the rate of 25 in the 100 for 12 moneths, you may also worke it by the first part of the rule of three composed, saying if 100 lb in 12 mo∣nethes doe gaine me ••5 lb? what shall 2 ⅔ s gaine in •• moneths: work and you shall find ••/2•• of a lb, which in lesser termes is 1/1••, and is in known mony worth 2 d, as before.

Many other of these questions I might heere haue deliuered, but for feare the booke woulde rise to too thicke a vo∣lume, and so to make the price so much

the dearer, whereby it mighte not bee so partable to my Countrymen as I wish it. But these foure, I haue of purpose framed in this order, hauing relation one to an other: Assuring you, that what questions soeuer maye bee propo∣ned within the compasse of this rule, you shall finde by one of these foure to make a solution: And moreouer, diuers other are yet to be deliuered: where the Cre∣ditour giueth diuers dayes of payment, which can neuer bee well wrought, nor yet vnderstoode, vnlesse you can firste finde by Arte, the iust time that al those payments, how different soeuer they be, ought to be paide at once: wherevppon first I thinke good here to giue some in∣structions into such a Rule, for it is the onelie aide for the finishing of such que∣stions as hereafter shall follow.