t o® Mr. waring on the General 
farther has this peculiar advantage over all other trans- 
formations yet invented, that it often eafily difcovers 
fome of the firft: terms of the equation required, from 
which many elegant Theorems may be derived. 
In the works above-mentioned, viz. Mifcell. Analyt. 
Medit. Algeb. Sec. are given fome problems ferving to 
this transformation.; the firft of which is a feries, which 
from the coefficients of a given algebraical equation 
{x n —px n ~ lj rqx n ~~ z —Scc, — o') finds the fum of any power 
of the roots {viz. a m +/3 m +y m +$ m + See. where a, (3, y, o', 
&c. denote the roots of the given equation), the law of 
which feries was publiffied by me many years before 
that it was given by Mr. euler. The third Problem 
•often mentioned in this paper is an elegant and ufeful 
feries for finding the fum of quantities of the follow- 
ing kind, viz. a'/SyJ*, Sec. + x r (3 m y s $‘, &c.+ a'/Sytf'&c. 
+ «$*/<?' Sec. + aTffft' Sec + . &c. 
Mr. euler gave the following refolution, x = J/z + 
\/§ +{ / tr+ l/r+Sec. where tt, ?, a, r, 8ec. denote the roots 
of an equation of n— I dimenfions v n ~ l -pv”~' lj rqv n ~ 5 - 
Sec. =o. It is evident, that in this cafe the equation 
whofe root is x will have n n ~ 1 dimenfions ; for let the 
roots of the equation z n - 1 =o be denoted by oc, ft , y, 
8tc. then will the quantity f/z have the n following va- 
lues 
