z8 A Treatise of Algebra.

, 2/3 x b-\- x' 1 x s+ yl } .... , _

lastly, - - — . 1 — involv d to the fifth Power

3^x xy J

-, i -.i

Z2<r^ Xs 4- X ^ x r-j-yN

k'ves -- ^- - — ii —•

243i J xr-(-jsl* xy 1

The Reason of this Rule will appear manifest fromthe Demonstration of Rule 3 in Multiplication.

Note. When the Quantity to be involv’d has the Sign— prefix’d to it, the Power itself, if the Index is anodd Number, must be expressed with the fame negativeSign, but if an even Number, with the contrary Sign, or +•Thus the second Power of—s, or — ax — a, is-J- a 2 * (because — into — produces Also the Cubeof —■ a, or -)- <2* x — a is — al (because -J* into — pro-duces —) so, likewise the fourth Power of — a, or — alx — a is -(- sl+ > and the fifth Power, or -j- a 4 x — a,is —a s &c. &c.

5°. Quantities compounded of several Terms, are in-volved, by an actual Multiplication of all their Parts.

Thus, if « -f- b was proposed to be involved to thesixth Power; by multiplying a -f- b into it’s self, we shallfirst have a 2 -\- zab b z , which is the second Power ofa + b ; and this, again, multiply’d by a-\-b, gives aZ-j-j,a 2 b-\-%ab 2 -\-bl, or the third Power of afb : Whence,by proceeding on, in this Manner, the sixth Powerof <3 -f- b will be sound to come out, a b -f- 6 a f b st-1 $a 4 b z

-f- 20aibl 4. 1 s a 2 b* 4 - 6 ab s 4- b b . See the Operation.a 4 - b, the Root or single Power

a 4- b

aa 4- ab4- ab 4- b z

a 1 4 - zab 4 - b *, the Square or second Power of <3 4- *

a 4~ b _

<33 4 * 2 a 2 b 4 " °b*

4- a 2 b 4- 4* hi

ai 4- 3 a 2 b 4. za^ 4 - bi, the Cube, or third Power

a b