Z2 A 'Treatise os Algebra.

I i i

tient of x 1 by will be.Ar+ (because \ — + — i) and

lastly that of ~c y XI by c -}-y) 3 will beT^y 1 * (because

■_ > — 41

a — 3 — <>)•

The Reason of the preceding Rule, and the Opera-tions depending thereon, will appear evident from theDemonstration of Rule 5, in the last Section.

6°. A compound Quantity is divided by a simple Quan-tity, by dividing each os its Terms by the given Divisor.

Thus 3 abc -J- 12 abx — $a z b divided by ^ab gives c -j-4* — Za, and 15 ab z c — lzacy z -f- jad 1 divided by —$ac12 y z d z

gives — 3 b z -\-

and so in other Cafes.

5 . . c

7°. But if the Divisor, as well as the Dividend, be atompound Quantity, let the Terms of both Quantities bedisposed in Order, according to the Dimensions ofsome Letterin them both, as shall be judsd most expedient, so that thoseTerms may sand firs wherein the highes Power os thatLetter is involved, and those next where the next highestPower is involved, and so on: This being done, seek howmany times the firs Term os the Divisor is contained inthe firs Term of the Dividend, which, when found, placein the Quotient (as in Division in vulgar Arithmetick) andthen multiply the whole Divisor thereby, subtracting theProduct from the respective Terms of the Dividend • tothe Remainder bring down, with their proper Signs, asmany of the next following Terms of the Dividend as are re-quisite for the next Operation 3 seeking again how often thesirs Term os the Divisor is contained in the firs Term ofthe Remainder, which also write down in your Quotient andproceed as before, repeating the Operation till all the Termsef the Dividend are txhaused, and you have nothing re-maining.

Thus, if it were required to divide alfi- 5 a z x -s- 5 ax z—J- a -3 by a -j- x (where the several Terms are disposedaccording to the Dimensions of the Letter a) I first writedown the Divisor and Dividend, in the Manner below,with a crooked Line between them fas in the Divisionof whole Numbers,) then I fay, how often is a containedin at, or what is the Quotient of at by a ; the An-i swer