6 A Treatise of Algebra.

same as or ^/b, The Number or Fraction by whichthe Power or Root of any Quantity is thus design’d,is call’d it’s Index or Exponent.

The Sign — stgnijies that the Quantities on each Sideof it are equal. Thus x~a (hews that the Quantity

x is equal to the Quantity a and z = —signifiesthat z is equal to — ; so that, if a was 6, b 4, c 3

and d 2, then would z be equal to or 21.

The Note:: signifies that the Quantities between whichit stands are proportional: As a :b :: c:d denotes that ais in the fame Proportion to b, as c is to d ; or that ifa be twice, thrice or four times, £sV. as great as b ythen accordingly is c twice, thrice or four times, &c.as great as d.

To what has been hitherto laid down we may addwhat follows.

When any Quantity is to be taken more than once,the Number is to be prcfix’d, which (hews how manytimes it is to be taken: Thus 5 a denotes that the Quan-tity a is to be taken five times ; and 3 be stands for threetimes be, or the Quantity which arises by multiplying beby 3 : Also y^/a z -j-b z signifies that a z -^b z is to be takenseven times. And so in other Cases.

The Numbers thus prefixt are call’d Coefficients;and that Quantity which stands without a Coefficient isalways understood to have an Unit prefixt, or to be takenonce and no more.

Those Quantities are said to be like that are express’dby the fame Letters under the fame Powers, or whichdiffer only in their Coefficients. Thus $bc, $bc and 8 beare like Quantities; and the fame is to be understood of

the surd Quantities and T \/ - ° ■ But

a a

unlike Quantities are those which are express’d by dif-ferent Letters, or by the (ame Letters under different

Powers;