QUADRATURE of the CONIC SECTIONS, &c. 275 
) : ; I I 
ie fec ; A <fec A, and confequently eee AS oe eee 
tan; A. tanzA tanzA 
therefore oN” al EAT , and tanjAs 7a Fay X tantA. 
In this expreffion, let +a, +a, $a, &c. be fubftituted for A, 
and let the refults be divided by 8,16, 32, &c.; then we get 
“tana t 1 
a ae ad 
3 tan; ss hear X ; tan 74, 
ytanta 
Seta > ~ tanta; 
Bey pe > Stanta * : ae 
&e. 
from which it appears, that in the feries, 1 — ; Pimp l tan Fg 
a ana! 3 
I I I r I rT" 
age q tan got = tan 7g 4 +, &e. 
each term after the third (that after + tan 4a), is greater 
than a third proportional to the two terms immediately before 
it, taken in their order; and this is, another limit to the rate of. 
convergency of the feries. 
10. Tue, limits which we have found to the rate of conver- 
gency of the feries, enable us alfo to affign limits to the fum 
of all the terms after any given term. Let the feries be put. 
under this form,, 
Ts vr I I I I 
== haa gn 7 Oia 4. ue t Tom) + T(m+1) 
+ P(m42) +, &e. 
Vou. VI.—P. IT. Mm. where: 
