and Infinite Series. 423 
90. Let us now confider the cafes in which, c 2 is 
greater than b z , which include all the cafes not compre- 
hended by the former* or in which c 1 is not greater than 
b z . And this, it is evident, will happen both when a is 
pofitive and when negative ; namely when a is any pofi- 
tive quantity whatever, or when it is any negative quan- 
tity, and a 1 greater than a b 2 . And in thefe two clafles, 
c~ will be pofitive or negative, according as a is pofitive 
or negative. 
91. Now the feries in this clafs will be found the 
fame way as in the laft, by only writing here the letter 
c before the letter b; for then we fiiall have s — fic + 
and d zz \/~ c + b = - V c - b. 
Then j ■ =.\/c + b = ■l/c x :'i + 
h 
2.5 P 
4. J 
3 C 3 • 6 c z 3,6.9c 3 
2 .$b* 
2 b* 
and d = %/ c - b-Z/cx : - 1 + — + 
3 c 3 • 6c 
« h -r a -W 
Hence j * d - 
+ 
8cc. 
See. 
2 b . I . . 2 .$b z 2.5.8. lib 4 
5/ a X • ~ 4 “ > 
v'c 3 3 ■ 6 • 9 
+ 
3.6.9. 12. 15c 
3.6. 9 f 3 
Sec. =• 
the 1 ft root, and was given by clairaut. And 
s_+d 
2 . 
s — d 
2 
rb -3 
— b I 2 . Kb 71 2 . 5 . 8 . I lb 4 c 
-A,: -•* 77^ ! * -T— — - Sec. 
?< 3 3.6. 9? 
± J/c . y/ — z x : I 
3,6.9 .®2. 15c 
'it*' 2.5.8 b 4 
3 . 6c 2 3.6.9. izc 
for the other two roots, which, I believe, are new. 
9 a. Here it again appears, that when c l is pofitive, 
the two latter roots are imaginary ; becaufe then 
a * &c 
