4 r 1 
and Infinite Series . 
■ W i i : i it • ! i 
fubftituted in the above value of the two roots, they 
+4 .jhf t . ..t, .Ah . :• . 
become — f r 
P 
it 
. v • r ■ t ? * 
VU y it' /,(.-! f - ' ij : : 
53. And again, if -p be expelled from this laft form 
< : ' 1 ’ ■ : mj * < : ! • ; x k3 > 
by means of its value r 2 - 1 , the fame two roots will be 
" 1 ; ' : ' ■ - r " ■' 1 o 1 i' - ■ ; t 1 
exprdfed hy • -r ■•ft W f •+• — '= — 
V x I 
54. And farther, if r 3 be' expelled from this laft form 
by means of its value 'q '^ pr, rheftame two roots will alfo 
become -Ir x i±vi 
4? _ 
if X I ± ,/pa 
2 >. Spr-_q 
55, We might have, derived the above forms in yet 
" • • ; 4 
another manner thus, fhe firft root being r, let the 
other two roots, be <y and w: then we fhall have thefe 
v va 
two equations, namely, v + w - - f 5 and == 
or y.w — t; from the fquare of the firft of thefe fubtradt 
•- , r- - f 
i •/ 
four times the laft, fo fhall v z ^'2 vw + w 7 = r* *■’ — ; the 
r 
root of this is v — * w = \ 4 - 2 - — , which being added to, 
1 ' - " - ^ ' 1 " ■ - j ■■ ■ ■*. ‘ r \ f 
and taken fronts ■* - w - - r, and dividing by 2 5 tve have 
1 _ ' 
V? - -ir^^s/r 1 X 1 ± \/i -Jf, the farpe 
with one of the formulae above given ; and thenbyfub- 
ftitution the others will be deduced. 
56. To illuftrate now the rules x — s +.d, or 
~ s -~- ± s ~ = -i \/- 3, by fome examples; fuppofe a the 
Vol. LXX, lii given 
