QUADRATURE of the CONIC SECTIONS, &c. 287 
That is, putting S for Tom+2) + T(m+3) + T(m+4) +, &ee 
iy I 
S< ~ § Ton+1) + Bit and hence S < re T(m+1): 
Thus it appears, that the fum of all the terms following any 
: I 
term, is lefs than = of that term. 
20. As to the other limit, it muft be the fame:as the like li- 
mit of our firft feries, on account of their having the fame li- 
mit to their correfponding rates of convergency. That is, 
putting S to denote as above, then ; 
—_ Tm4+n) T 
S Pe nL A m 4 
T(m) — T(m+1) Weipa 
Tm) — 16 T(m41) 
or S > me T m ae 7 + m e 
5 6s eae CE (ue) aT (ea) OED 
21. Ir yet remains for us to confider how the feries of quan- 
heh — cof — cof + ! : 
tities Pareare eet ee &c. are to be found. Now this 
may be done, either by computing the cofines of the feries of 
4 ! T 
3% &c. one from another by means of the 
arches 4, z a, ze a, 
ark 
formula cof 7A= NA a and thence computing the fe- 
I—cofta 1—cofta . 
——.2-, ——_-+,, &c. Or we ma 
1+cofta’ 1+ cofia’ y 
compute each fraction at once from that which precedes it, by 
a formula which may be thus inveftigated.: 
ries of fractions 
Put 
