QUADRATURE of the CONIG SECTIONS, &c. 323 
Now we have found, that one factor of this expreffion, viz. 
I 
a(x = 1) 
cannot exceed the logarithm of x; with re- 
ae 
m(b a) 
= -[4 
T I 
fpe&t to the other factor b" «”—1, fince it appears from the 
firft of the four formule (@), (Art. 53.), 
and « <1 ee = ot therefore, aoe x < eas 
( , and hence 
Z" eae eee | Se Cae 
UL Min . 
_ Now as we may conceive m and 7 to be as great as we pleate, 
it is evident that this quantity, which exceeds the factor 
I T 
3" Pg 1, may be {maller than any aflignable quantity ; there- 
fore the product of the two factors, or the difference between 
the limits to the value of log x, may, by taking m and 2 fuffi- 
ciently great, be lefs than any affignable quantity. 
Upon the whole, then, it appears, that the logarithm of w is 
a limit to which the two quantities 
n (x” — Ey nay (x" —1I) 
=. : int 
m(b" —1) m(b” — 
Vou VI.—P. II. Ss continually 
ols 
