'i7' 2 -d Treatise of Algebra.

Number y by the Question, it is manifest that - ^ ^

21

must also be a whole Number : Now the least Value ofy, in whole Numbers, that will bring out the Value ofthat Expression as required, will, by the precedingLemma, appear to be equal to 4; the Expression itselfcoming out — 3 ; and consequently the correspondingor greatest Value of xz=. 92 ; which being divided by17, the Coefficient of y (according to the precedingNote) the Quotient comes out — 5, and the Remainder= 7 Therefore the least Value of x is equal to 7, andthe Number of Answers (—5 -j- 1) = 6 : And these arcas follow, viz.

* = yr I 75 I 58 I 41 I 24.1 7.

•' 4 I 25 j 4.6 I 67 J 88 J 109.

Q_U E S T I O N 4.

To determine whether it ^possible to pay tool. in Guineas(indMoidorts only f the former being reckoned at 21Shillings each , and the latter at 27.

Here, by proceeding as in the last Question, we have

2000 — 2 7y

2 ix -j- 277 — 2000, and consequently * = ---;

21

where the Fraction being in its lowest Terms, and theNumbers 27 and 21 not prime to each, the Solution, byNote the second to the preceding Lemma, is thereforeimpossible.

Q_U ESTION

A Butcher bought a certain Number of Sheep and Oxen,for which he paid tool j for the Sheep he paid 17 Shil-lings a-piece, and for the Oxen , one with another , hepaid 7 Pounds a-piece j ’tis required to find how many hsbought of each firt.

Let x be the Number of Sheep, and y that of theOxen ; then, the Conditions of the Question being ex-pressed in algebraic Terms, we lhall have this Equation,

viz.