QUADRATURE of the CONIC SECTIONS, &c. 32%. 
53. Purtine v and f to denote, as in laft article, it is mani- 
feft that the feries 
is greater than this other feries 
TFL et t-te ct a, (to pyterms) = A, 
but lefs than this feries 
v+u+u+u...+4 (topterms) = pv; 
but by a known formula, the fum of the firft of thefe three ie- 
ries is 
U—— F 
——, therefore, 
p 
U—tI 
U1 U—tI 
1 > p; I <pyu, 
p ry 
v—I UV —tI 
and hence it follows, that 
vp <r4 2S}, P(F—D pel 
(6). 
y—tI 
I 
w>t 
i Ft 
= i 
? B Gad ok) > a 
54. Ler us now recur to the fymbols r, x, b, y and m, whofe 
values are affigned in Art. 51. and let us aflume y = /, and 
r= v"; then, from the two expreflions () in Art. 52, we have 
I> 
i 
