| QUADRATURE of the CONIC SECTIONS, &c. 337 — 
here m is put for any integer power of 2. Let the product of 
the correiponding fides of thefe equations be now taken, and 
the common factors rejected, and the refult will be 
I 
r—I=m(« — 1) Ser we uN 
and hence 
ro 2 2 2 2 
m (x" — 1) = (% —1) 
I 
watir wer xt ty men B 
This equation holds true, m being any power of 2 whatever. 
Let us, however, conceive it indefinitely great. Then the 
number of factors will become infinite, and m ere 1) will 
become Nap. log x (Art. 57.). Therefore, 
2 2 2 2 
atay gee ee aie ate b y 
Nap. log « = (# — 1) » &e. 
ad infinitum. 
Tue product of any finite number of thefe factors being al- 
ways a function of this form m (a”—1) will of courfe be great- 
I ze 
er than log 2, (Art. 54.). However, the function — m (vc —r) 
m 
x 
I 
or m (: — — }, being in like manner expanded into an infi- 
nite 
