A Treatise of Algebra^ 119

4*) 1

Denomination and contracted, will become — — —

a 2 - y-

= and from the latter, by proceeding in the s ame

4 X x 6 -f 7^4 f -f 7x 2 y 4 ■+■ y 6Manner, we have -

xx —yy\ 2

-» or

4 x x 2 -f- y*xx* -f + y*

— b : Let the last Equation

xx — yy 2

be divided by that which immediately precedes it, and

y4 fj

you will have-=====— — — j which, fubtract-

x x x 2 —y 2 a

el from ( VLZHl ) leave*

V A i — v 2 ) xxx z ~y z

—a — —; from which

x*—yZ 3* 4 — 2x*y 2 — y 4 \ 3V X X X 2 - V 2 '

Equation, if a — — be put — e, y 2 will come out — exa _

— 3X 2 : Also from the Equation 1 ^- X —— s, y 1

x z —y 2

will be, again, found, —

ax 2 —' 4 >3

Therefore, by

° + 4 * .

comparing these two Values of y z , with -each other, we

have ex — 3* 2 x a -)- q-x — ax 1 — 4.x 3 , or c—z^xa-j-4- 2 '

= ax — 4 2 ; whence 8 a 1 -j- 4<* x — 4cx =r ac, and con-

f — 9 + vV + c 2 , _

— —-!-; whence y ( —

4

fequently a :

\f ex — 3 a 2 ) is also given, and consequently x —y, A -s-y,tec. which are the Numbers that were to be found.

Lnui a.

If the Sum of the Squares of any odd Number of Termsin geometrical Progression be divided by the Sum of theNumbers, the Quotient added to the Divisor will be equalto twice the Sum of the firjl } third, tic. Terms of the Pro-gression, taken alternately ; and, if the Quotient be fub-Irachd from the Divisor , the Remainder will be eqtcal to

I 4 , twice