QUADRATURE of the CONIC SECTIONS, &c. — 3:25 
which 2 re 1) approaches, when z is conceived to be inde- 
finitely increafed, will be variable, as it depends upon the par- 
ticular value of the number x. 
Ler us therefore denote the limit of m (3 a 1), or that of 
I 
m 1) 
————,, (for they are evidently the fame), by B, and then 
rp 
in the fyftem whofe bafis is 4, the logarithm of «x will be the li- 
mit of either of thefe two expreflions 
I I 
I n (x" —1) a(x" — T) 
ay B : B : 
n 
x 
when z is conceived to increafe indefinitely, or to {peak brief- 
I 
ly, log « ad when 2 is indefinitely great. 
= 
B 
logarithms have denominated the modulus of the fyftem. As in 
TuE conftant multiplier — is what writers on the fubjeé of 
NapieEr’s fyftem it is unity, we have, ~ being indefinitely great, 
Nap. logx = 2 fiek 1), and fince in any fyftem whatever 
B=m oe 1), or Boa (o" —1), for we may put m or x 
Ss 2 indifcriminately : 
