[26] 
follows } that, if P, C, £), E, &c. be given; the fum 
of thofe roots (P) ; the fum of their fquares 
and the fum of their cubes (P) &c. will alfo be 
given from the foregoing equations : whence will be 
had 
*P=P 
g=*+?B-iC 
S^+TD—gC+AB—tE 
7=— TE+QD— PC+d’P-b jF 
where the law of continuation is obvious. 
Thefe values are the fame with thofe given (with- 
out demonftration) by Sir Ifaac Newton, in his Uni- 
verfal Arithmetic, for finding when fome of the roots 
of an equation are impofiible. 
Problem II. 
?n 
m) 
To find a feries exprefling the value of i+ -I 
a 
» _ P . ? 
. jc 2 | . x 13 
X I +-7- X I+ — 
b c 
1 <*4 > 
m 
n 
PC' X 2 j 9 
By putting //=i + -| ,^=1+— | > &c. ; and 
proceeding as in the laft problem ; there will be had 
u mx x , x z x l , 
- = — X I—- — 7 &c. 
u a a a a 3 
w zitxx x z , iv* x 6 j 
LL X I — &C, 
b bb z fo 
" &c. 
Whence, 
