or; thus ab confifts of two terms, and is called a binomial; a+b+c confifts of three terms, and is called a trinomial. These are called compound quantities: a fimple quantity confifts of one term only, as a, or tab, or + abc.

The other fymbols and definitions neceffary in Agebra fhall be explained in their proper places.

$ 9. C

**********

CHA P. II.

Of ADDITION,

ASE I. To add quantities that are like and have like figns.

9:

Rule. Add together the coefficients, to their fum prefix the common fign, and fubjoin the common letter or letters.

Cafe II. To add quantities that are like but have unlike figns.

Rule. Subtract the leffer coefficient from the greater, prefix the fign of the greater to the remainder, and fubjoin the common letter or let

This rule is easily deduced from the nature of pofitive and negative quantities.

If there are more than two quantities to be added together, first add the pofitive together into one fum, and then the negative (by Case I.) Then add these two fums together (by Cafe II.)

Cafe III. To add quantities that are unlike.

1

Rule. Set them all down one after another, with their figns and coefficients prefixed.

§ 10.

CHA P. III.

Of SUBTRACTION.

G

"

Eneral rule. Change the figns of the quantity to be fubtracted into their contrary figns, and then add it fo changed to the quantity from which it was to be fubtracted (by the rules of the last chapter :) the fum arifing by this addition is the remainder. For, to subtract any quantity, either pofitive or negative, is the fame as to add the oppofite kind.

It is evident, that to fubtract or take away a decrement is the fame as adding an equal increment. If we take If we take away b from a

b,

there remains a; and if we add + b to ab, the fum is likewise a. In general, the fubtraction of a negative quantity is equivalent to add-ing its pofitive value.

CHA P.

CHA P. IV.

Of MULTIPLICATION.

Multiplication the General rule for the figns is, That when the signs of the factors are like (i. e. both +, or both -,) the fign of the product is +; but when the figns of the factors are unlike, the fign of the product

Cafe I. When any pofitive quantity, + a, is multiplied by any pofitive number, +n, the meaning is, That + a is to be taken as many times as there are units in ; and the product is evidently na.

Cafe II. When -a is multiplied by n, then →a is to be taken as often as there are

units in #, and the product must be

na.

Cafe III. Multiplication by a positive number implies a repeated addition: but multiplication by a negative implies a repeated fubtraction. And when + a is to be multiplied by , the meaning is, That + a is to be fubtracted as often as there are units in #: there

fore