DEFINITIONS AND NOTATION. 2^ 



ed the numerators, and the lower the denominators : thus, a 

 is the numerator of the fraction — , and c is its denomi- 



c 



nator j a^c? is the numerator of , and a — c is its 



a — c 



denominator. 



15. Quantities, to which the radical sign is applied, arc 

 called radical quantikesy or surds ; whereof those consisting 



of one term only, as ^^ and y/ ^ a', are called simple 



surds ; and those consisting of several terms, as ^ ab 4- cd 



and ^rt"* — b^-{-bcy compound surds. 



i6. When any quantity is to be taken more than once, 

 the number is to be prefixed, which shews how many 

 times it is to be taken, and the number so prefixed Is called 

 the numeral coejjicient : thus, 2a signifies twice a, or a tak- 

 en twice, and the numeral coefficient is 2 ; 3a,'* signifies, 

 that the quantity ^^ is multiplied by 3, and the numeral 



coeiiicient is 3 ; also Sv^A^^-j-^" denotes, that the quan- 



tity ^>^^-{-a^ is multiplied by 5, or taken 5 times. 



When no number is prefixed, an unit or 1 is always un- 

 derstood to be the coefficient : thus, i is the coefficient of 

 n or of .V ; for a signifies the same as la, and x the same 

 as iXi since any quantity, multiplied by unity, is still the 

 same. 



Moreover, if a and d be given quantities, and a;^ and v 

 required ones *, then ax"" denotes, that x" is to be taken a 

 rimes, or as many times as theje are units, in a ; and dy 

 shews, that y is to be taken d times ; so that the coefficient 

 of <7.v' is ay and that of dy is d : suppose jZZfS and dzz^, 



then 



