DEt^lNITlONS AND NOTATION. 26^ 



lof the compound quantities a-{-b and c-^d multiplied to- 

 gether. 



7. When we would express, that one quantity, as a, is 

 greater than another, as b, we write ^C~^> or c; > 3 •, and 

 if we would express, that a is less than ^, we write a^h 



or ^ <3 ^. " 



8. When we would express the di|Ference between two 

 quantities, as a and ^, while it isunknown which is the 

 greater of the two, wc write them thus, t? £o ^, which de- 

 notes the difference of a and ^. 



9. Powers of the same quantities or factors are the prod- 

 ucts of their multiplication : thus oXt?, or af2y denotes the 

 ■square^ or second poiuer^'oi the quantity represented by ar \ 

 ^jX«X«, ox aaay expresses the cube, on third power ; 2^nd 

 >flX«X^X«> or aciaay denotes the biquadrate^ or fourth power 

 of ay Sec. 



And it is to be observed, that'the quantity a is the root 

 of all these powers. Suppose azzi^y then will aaz:zaXa:iZ 

 5X5^:25=1 the square of .5,^ ^1^^—^7X^^X^1=5X5X5 = 

 J25ZZ the cube of 5 5 and aaaazHaXaXaXaZZ^X ^X S 

 X5ZZ625ZI the fourth power of 5. 



I o. Powers are likewise represented by placing above the 

 root, to the right hand, a figure expressing the number of 

 fafctors, that produce them. Thus, instead of aa, we 

 writer* ; instead of aaa, we write a^ -, instead of aaaa^ 

 we write a"^, &:c. 



IT. These figures, which express the number of factors, 

 that produce powers, are called their indices, or exponents : 

 thus, 2 is the index or exponent oi a' \ 3 is that of x^ ; 4 

 is that of x"^, &c. 



But the exponent of the first power, though generally 

 omitted, is unity, or i ; thus a signifies the same as «, 



namely, 



K K 



