oe 
QUADRATURE of the CONIC SECTIONS, &c. 295 
sigh LET us OW; however, fuppofe » name re great, then 
A 
oa ta 3+ 4tant 2 
the quantity ety Ori ares be- 
us (2 (wand) 
A : A 
caufe tan S, and confequently 4 tan’—, vanifhes, and 2” tan — 
", becomes fimply -3 a 
becomes A, as we have already had occafion to obferve (Art. 6. 
and 7.).Alfo the geometrical feries 
I I I 
76° 16) 363.1? 
having the number.of its terms indefinitely great, and their 
common ratio oi. igi be + rch Therefore, by fubftitution and. 
eranfpofition we have 
Ata tAheer frahe A+ Fi A+— FEA t, &e.? 
or, fubficuting. for fA, and, F4)A, &c.: the: Acorns: ‘which. 
thefe fymbols exprefs, 
[3+4tamA , 14 
| tan? A 15 
cele ent 
5 7 ’ ji3 I 8 ‘ . : : ; 
i= { — 7g (4tan’s A +3 tant 4A) + (4 tans A4-gtan*1A) 
* | 8 a ABEHAY 3t0"4 A), BP 
2 and this j is s one form of eee feries which we Saran to alien 
tigate. 
- ya se 28, THis. 
