A ‘Treatise of Algebra. 35

vered in the last Section, and the Rules themselves, no-thing more than the Converse of those there demon-strated—I shall here (hew the Reason why, in Division(as well as Multiplication) like Signs produce -(- and un-like —. In order thereto, it is to be observed that (ac-cording to the Nature of Division) every Quotient what-ever, multiplied by the Divisor, ought to produce thegiven Dividend. Hence it follows, that if the Sign,of the Divisor and Dividend are both -J-, and thereforelike, the Sign of the Quotient must also be -(-, because-j- into -j- (the Sign of the Divisor) gives -j- (as has beenalready proved in the last Section) which is the givenSign of the Dividend : Secondly, if the Signs of the Di-visor and Dividend are both —, and therefore still like,that of the Quotient must be -j-, because -(- into— (theSign of the Divisor) produces —, the given Sign of theDividend : Thirdly, if the Sign of the Divisor be -f- andthat of the Dividend —, and therefore unlike, that of theQuotient must be —, because — into -}- sthe Sign ofthe Divisor,) produces —, the given Sign of the Divi-dend. Lajlly, if the Sign of the Divisor be— and thatof the Dividend -f-, and therefore unlike, that of theQuotient must be still —, because — into— ('which isalso the Sign of the Divisor) produces the given Signof the Dividend.

SECT. VI.

Of Involution .

I Nvolution is the raising of Powers from any pro-posed Root, and may be performed by the follow-ing Rules.

i°. If the Quantity or Root proposed to le involved hatno Index, that is, if it be not itself a Power or Surd, thePower thereof ivill be represented by the same Quantity withthe given Index placed just above it.

D L

Thus