A Treatise of Algebra.

which Value being substituted for y % t in the first Equa-tion, we shall have

iooa 4 — i2oa3*—- 224a 2 ** 4. t; 6 ax 3 4° 169.V+

4- 2 ax — 4« e , or 209^+ ijxaxl — 25 6a i x* — iroat^4- 100a 4 = o.

EXAMPLE V.

r>- 5«V + ^ +

G.ven i Av J, x .

}sX;:lZ~i^ oexteimiMte y'

Multiply the first Equation by /, and the second by0 and you will have

asxy 4 bfx 4. ify — dfof y 4 ogx 4 ahy — ok

subtract the latter of these from the former, and therewill come out bfx — ogx-\-cfy — 0by — df — ak ; whence,

df — ak-\-agx — bfx

by Transposition and Division, y — -—--;

cf — ah

let this Value be substituted in the first Equation, and

1 dfx — d l kx 4 o 1 gx l — abfx-

+ 4

cf — ah

there will arise -

cdf — ack 4 ac gx — befx

— d; which, multiply’d by

cf — ab

tf — ah, and contracted, gives ag — bf x x* 4*

df—ak cg — bhxx—ck — hd.

SECT. X.

Of PROPORTIONS,

Arithmetical and Geometrical.

O Uantities. of the fame Kind, may be compared with. each other two Ways, viz. either with regard tothcTxcess of one above the other, or to the Part or Partswhich one is of the other, called their Ratio: The

Comparison of Quantities according to their Excesses it

caU’4