DEFINITIONS AND NOTATION. 2% 



ed a binomial, as well as a-^b^ because it is composed of 

 two parts, connected together by the sign —- w 



2f. A fraction, which expresses the root of a quantity, 

 is also called an ifidtXy or exponent ; the numerator shews 



the power, and th^ denomihiitor the root : thus ^r* signifies 



the same as -y/ ^ 5 itnd a-^-ab"^ the same as ^a-^-ab 9 

 likewise n\ denotes the square of the cube root of the 

 quantity a. Suppose ^11:64, then will a^'z=L6^z:zd^^ ziz 

 16 •, for the cube root of 64 is 4, anti the square of 4 

 is 16. 



Again, a + bf expresses the fifth power of the biquad- 

 ratic root of a^b» Suppose orzp and ^iry, then will 



<2 + /i'^ii:9+7i^zi:i6|'^~2^zz32 -, for the biquadratic 

 root of 16 is 2, and the fifth power of 2 is 32. 



Also, qH signifies the wth root of ^. If //IZ4, then will 

 ^Turr/'^ ; if /'/ = 5, then will aH'iz.di, &c. 



Moreover, a-\~hY denotes the /;7th power of the ;nh root 



of a-\-h, \i ^ = 3 and ;/=2, then will a^hY •::^a-\-b\ , 

 namely, the cube of the square root of the quantity a-\-b \ 



and as «" equals ^/^S or y/a^ so a-^-bY = Y/^^^^^, 

 namely, the «th root of the wth pov/er of a-{-b. So that 

 the wth power of the n'Oii root, or the «th root of the f;2th 

 power, of a quantity are the very same in 'effect, though 

 differently expressed. 



22. An exponential quantity is a power, whose exponent 

 is a variable quantity, as a;''. Suppose .v=2, then will 

 ^*=2*=4 5 if ^^'=3, then wilU^*' = 3^=27. 



ADDITION. 



