34. ^ Treatise os Algebra.

So likewise, if a S — at 5 be divided by a — *, the Quo-tient will be found a* -j- alx -j- a z x z -f- «jr 3 -j- x*± as bythe ensuing Work will appear.

a — x) — * S (a 4 -J- a 3 * + a z x z -\- ax 3 -f- x*a S — a*x

a*x — x sa 4 x — a3x z

a3x z — * sa3x z — a z x3

a z x 3 — x !a z x3 — ax*

ax *—ax* — x s

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Moreover, if it was required to divide ^bcx -f-15*3—10 bx z — 6cx 2 by 5 at—2 c, then having ranged the Terms,according to the Dimensions of *, the Process will standthus:

5*— ic) I 5 * 3 Z ^Ixz+tfcx ( 3^—2 bx

1 5 * 3 — 6cx z

— lobx z -{-^.bcx- lobx z -\~^bcX

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But it is to be observed, that it is not always that theDividend can be thus exactly divided by the given Di-visor, without leaving a Remainder; and then this Me-thod is of little Use j and therefore, in all such Cases,it will he most commodious to express the Quotient, inthe Manner of a Fraction, by writing the Divisor underthe Dividend, with a Line between them, as has beenshewn in the Method of Notation.

It would be needless to offer any thing by way of De-monstration to the two last Rules, the Reasons thereofbeing already sufficiently clear from what has been deli-1 vered