A Treatise ef Algebra. 83

ference you will have 7, the greater Number. In thesame Manher, if the Difference of the two Numbers hadbeen given 6, and the Difference of their Squares 60,the Numbers themselves would have come out 2 and L.

PROBLEM X.

Having given the Sum os two Numberequal to z o, andthe Difference of their Squares , equal to 120 ; to findthe Numbers.

Put a — 30 and b-=. 120, and let x be the lefferNum-ber sought, and then the greater will be a — x, whoseSquare is aa — 2 ax -j- x z ; from which the Square of theleffer being subtracted, we have a 2 — 2 ax — b ; this re-~ <t b

duced gives the lesser Number, —-— 1; ;

2 2a

a

therefore the greater (a — x) will be — a — — +h a b

— — — -j- — = 17. But if the greater Number had

2a z 2 a

been first made the Subject of our Inquiry or been put —x,the lesser would have been a — x, and it’s Square a 2 —-2 ax -J- at 2 , which subtracted from x 2 leaves 2 ax — a 2 —

b a

i ; whence 2a* = b a 2 , and therefore Ar — — -j- —

2a 2

— 17, the same as before.

PROBLEM XI.

If one Agent A, alone , can produce an EffeSl e in the Timea, and another Agent B, alone, in the Time b, in how longTime will they both together produce the fame Effect ?

Let the Time sought be denoted by at, and it will be,ex

as a : x \ : e : —, the Part of the Effect produced by A: (vid,

a

Thtor.lV.p.j^.) Also, as t-7 the Part produced by

b