266 ALGEBRA. 



namely, the -first power of a ; aXa^ the same as aX(^^ or 

 «" + % that is, a'y and a'Xd is the same as a'Xn, or^?*'*^^ 

 or fl^ 



12. In expressing powers of compouiKl quantities,, we 

 -usually draw a line over the given quantity, and at the end 

 of the line place the exponent of the power. Thus, 



a J^h\ denotes the square or second power of a'\-h^ consid- 



ered as one quantity ; a'\'}\ the third power \ a-j-I^l ths 

 fourth power, &c. 



And it may be observed, that the quantity a-\-h, called 

 the first power of /3-j~^> ^^ ^^^ ^°^^ ^^ ^^^ these powers. 

 Let <3iZ4 and ^r:2, then will ^-f-3 become 4+2, or 6 .5 



and «+^[ zz:4-j-2| zz6*rz6X6zz36, the square of 6; 

 also fl+^l =:4+2| i=6^i=6X6X6zr2i6, the cube of 6. 



1 3. The divi-slon of algebraic quantities is very frequent- 

 ly expressed by writing down the divisor under the divi- 

 dend with a line between them, in the manner of a vulgar 



a 

 fraction : thus, — represents the quantity arising by • di- 

 viding a by r ; so that if a be 144 and c 4, then will 



_- be , or 36. And ■ — - — denotes the quantity ans* 



■V 4 * a — c 



ing by dividing ^z^-^ by a — c ; suppose ^^12, ^rz:6 and 



.1, -n ^+^ u ^^ + ^ '^^< 

 czzg, then will become or — rro. 



a — c 12 — 9. 3 



J ^ •4- ^ 



14. These literal expressions, namely, — and -, arc 



called algebraic fractions ; whereof the upper parts are call- 

 ed 



