Jl Treatise of Algebra. iiMoreover the Sum of

_ x z -

2 a-\-2'/ax — ~ -f 2/a 2 -J- x 2 ,

L

3 a— 3 V^«a , - 4 -~ + 5 ^*+

7«+ v'slAf— — 2/aT+ij

' ' . 3 -

is 120+ 7v/«* + — 2 y/a* -j- * J .

Lastly, the Sum of2a*— 3 ab-\-ib l — a'

3 b l — 2a 2 -j- a'—5r 3— 2^3 -j- ^ab -f- 100

20cti*j- 16a 2 — be — 80 _

will be 1 ja 1 z2.ab■$b’S-\-al —f3-J-20— be.

SECT. III.

Os Subtraftion.

QUbtr action of algebraic Quantities is performed by chang-O i n g a ll the Signs of the Subtrahend , and then connect-ing all the Quantities , as in Addition.

Thus ^b subtracted from 8 b leaves 8 b — 5 b or 3 b ; and5<2+3i subtracted from 8 a leaves 8a—5a—3 b or za—3 b.Also 5a— 3 b from 7a-f- ^b leaves 2a -j- 8b.

Moreover 12 ax — 3 be —5a 2 from 20a x -j- $bc — 7a*leaves loax-^-^bc — 7a 2 — l2a-r-s- 3if-j- 5° 2 or 8a*-f*8 be — 2a 2 ,

The Reason of these Operations will appear evident;for if, in the last Example, the Quantity 12a* (which isthe leading Term) had been to be subtracted, the Re-mainder would, it is manifest, have been 20 ax -f- 5 be7—7a 2 — 12.ax • but as the Quantity there proposed isless than 12 ax by both 3 be and 5a 2 , it is obvious that the{rue Remainder must be greater than ao ax -f- $bc —