QUADRATURE of the CONIC SECTIONS, &c. 30% 
fent. Before leaving this part of our fubject, however, it may 
be proper to obferve, that the fecond feries may be deduced 
from the firft, and the third from the fecond, and fo on with 
refpect to innumerable others of the fame kind, by the fluxional 
or differential calculus. 
For refuming the firft feries 
I 
ot ead * tan 5 a jean | a tan 5 Ta &ce. 
Boe re 7 La +; a 
if we take the fluxion of si term, alain a as a variable 
quantity, we have 
—da _ —dafec’a 
aS hae css Bes 
a tan 4 
a ‘ da fec* > a+ = dafec’* yet pds fec*s a+, &c, 
and hence, changing the figns, and rejecting da from each 
: I 
term, and putting 1-++ tan =a for fec** a, we find 
n 
( ae ETE ) 
eta a ge pec teaaps cits Bete 
— OR RE net's . tan & 
L © 92 tag an oh c) 
In this expreffion, ar of the numeral feries 7 3 + et gb &c. 
(which is a geometrical progreffion having its common ratio *) 
fubftitute its value, viz. > and the refult is 
Life oii 2 I aI I I 
i = — Yotan? ca stan’ l a4 tant + . 
- : "3 F ri » &e ¢ 
a; tan’ a ait 
which is cae with the formula found at Art. 15. 
Pp2 FRom 
