QUADRATURE oj the CONIC SECTIONS, &c. 321 



53. Putting v and/> to denote, as in laft article, it is mani- 

 feft that the feries 



~ - 2 /■— t 



I -j- 1> + ^ + V ... + ^ 



is greater than this other feries 



3 + i-f-i+i...-fi(to/> terms) = p f 



but lefs than this feries 



v + v -\-v -f- v . . . -\-v (to p terms) zz p v ; 



but by a known formula, the fum of the firft of thefe three ie- 

 ries is 



v — 1 



-, therefore, 



p 

 v — 1 



v 



I V 



->p, - 



<pv, 



p 



V 1 



V 



and hence it follows, that 



V p <i-f-?L=JL, p(j—.j) <» — 1, 



<v 



vF > 1 + 



v — 1 

 p v 



, pQ-i)>i~\. 



V (ft- 



54. Let us now recur to the fymbols r, x, b,y and m, whofe 

 values are afligned in Art. 51. and let us afliime y == />, and 

 r=:v n ; then, from the two expreffions (a) in Art. 52, we have 



