C 558 ] 
Hyp. log. of - — 1 — x + L 
and confequently X = — 1 — a: — - 
1 — x)* 
3 
1 - 
, 8 c. 
, 8 c. 
3 
Moreover the fluent of - x hyp. log. of is = 
x 4 - — 4- ", 8 c. which vanishes when x vanishes ; 
1 2* 1 3 1 
and the fluent of — x X is = 1 — x-f- — 
1 - .*• 2 1 3 
8 c. — P, being corredted fo as to vanifh when x 
vanishes. 
But the fluent of ~ x hyp. log. of — - f fluent 
JC 1 A* 
of _jL_ x X is = X x hyp. log. of , which 
I X 1 * 
alio vanishes when x vaniflies. 
Therefore X x hyp. log. of -j— ; is = x -f- *— -j- 
&C. + I — * 4- ^=p- + 
II 
p. 
2‘ _ 3 
From whence, by taking a: equal to we find 
— fquare of hyp. log. of 2 = 2 x ~ 
X • j 
— — 4-d-. 
2*. 2 2 ‘ 3 Z .2 3 ' 
2 a 1 
8 c. 
— P : hence, P being before found = — , it appears 
x x ^ * 3 
that, when x is = ■£, the feries x + — + — > 8 c. is 
2 3 
= 1 — 1 x hyp. log. of 2I 2 * 
Furthermore, x -f - 3 -f ^- 3 , the value of F in 
2 3 
art. 2. muft be equal to 2 P X 4- ^X 2 — — -f x~* 
^ 3 
