268 ALGEBRA. 



3fAr 

 then will ax^rz6x*, nnd dyzr:4y. Again, -at, or — , de-^ 



notes the half of the quantity Xj and the coefficient of ^^ 



is -f- ; so likewise -^x, or — , signifies ^ of x, and the co^ 



efficient of -^x is -!-• 



4 4 



1 7. iii^^ quantities arc those, that are represented by the 

 same letters under the same powers, or which differ only 

 in their coefficients : thus, 3^2, 5^ and a are like quanti- 

 ties, and the same is to be understood of the radicals 



t^ x"" •{■ a^ and ']\/ x^ -^-a^ . But unlike quantities are 

 those, which are expressed by different letters, or by the 

 same letters under different powers: thus laby a^h^ lahcy 

 ^ah^ y ^^ , J, y^ and z^ are all unlike quantities. 



1 8. The douHe or amhiguous sign +_ signifies plus or mi-- 

 nus the quantity, which immediately follows it, and being 

 placed between two quantities, it denotes their sum, or dif-. 



ference. Thus, -j^ + V^ " ^ shews, that the quan- 



4 



^^ 

 tity \/^ — — ■ ^ is to be added to, or subtracted from, ^.7. 

 4 



19, A general exponent is one, that is denoted by a letter 

 instead of a figure : thus, the quantity x^ has a general 

 exponent, viz. w, which universally denotes the ?«th pow- 

 er of the root x. Suppose mzz2y then will x"':zzx^ ; if m 

 :rz3, then will x^^znx^ j if ni=:4y then will x'"zz:x^, &c. 



In like manner, a — 1?\ expresses the ///th power of n- — k 



2 J. This root, viz. a — A, is called a residual root, be- 

 cause its value is no more than the residue, remainder, or 

 difference,' of its terms a and k It is likewise call- 



. ed 



