ioo Dr. Waring on 
&C.).V-5. . . . + («»“> -f />— +y”~ 1 + See. — ?)x~ m + (*’» + $ M + y 
+ See. = Q.) x-”‘— + («»+* + jQH-» + y -+ ■ ■ + &c. = R) *-— * + 
&c. ; then will ^or \/Q. be the greateft root nearly. 
Ex. 2 
CL 
R — « 2Qx -f 3 Pa z ~&c. 
n — i 
. nx — ( 1 1 I L n ^ L 
S — R^ + Q^ 21 — P^r 3 . y x n \ a @ ^ y ' 
(i 4 k + v z + T* + &c -) * + Gj + £ + 7 + &c -) + (i + ^4 + 
± +&c .)^+ +(^ + ^ + _i_ + &C. = P) *~ + 
T“ + - + - + &c. = Q)a: w - I + /'-i- +-ir + -i- + &c.)x a -h 
\x m { 3 m y m J \a w+I /S ’”* 1 J 
? w rr 
&c. ; then will — or > the leaft root nearly* 
Ex. 3- =*- + (« + fl + y + J+ &c.)*-— ‘ 
x — px -f- qx — &c. 
r + («* + /3 2 + / + &c.( + a/3 + *y + (2y + «S + &C.)) *— * + (« 3 + 
/3 3 + y 3 + &C.( + a 2 /3 + « 2 y + /3'y + + y'j 3 + &C.) + a/3^ + cc(2$-’r 
g 
«5/5+/3>^+ &c.")) 3 + &c. ; and = i 4 - 
JJ S — Rx + Qx 2 — 8cc. . . x ' 
(T + 7H +&c 0 B +(? + r + 7 +&c -( + 5 + i+s- | -<-..)) 
# 2 + &c. in each of which all the numeral co-efficients are x. 
The approximate values to the greateft and leaft root may be 
found in the fame manner as before. 
From the preceding examples it appears, that the fame ob- 
fervations which have been applied to Sir Isaac Newton’s. 
method are equally applicable to M. Bernoulli’s. 
13. In the Meditatlones this rule is further extended, viz. 
let the given equation involve irrational and other functions of 
the unknown quantity; reduce it fo that no fundlion of the 
unknown quantity (,v) may be contained in the denominator, 
and let the refulting equation be A = o. A flume a fraction 
B 
A* 
