QUADRATURE of the CONIC SECTIONS, &c. 279 
AOMELIIIS as I 5 i 
the equation == — "= ee 5 fan > - A, which, by ta- 
q tan A 2tantA.).2 y 
king the fquare of each fide, is transformed to 
I ogg I 21 I 
—— = ——____ + - tan -A— =. 
tan* A Ee ee 2 2 
In this formula, let each term of the feries of arches 
ee Se a 
G2 By ss Gye aleve,« 9 : 
2 4 8 Piast 
“sof which the number of terms is 2, be fubftituted fucceflively 
for a, and let the refults be multiplied by the cc has 
terms of the feries of fractions, 
' 
of? pease Sey 
coe ee aA oar van 
thus there will be formed the feries of equations 
I 
I I I 
=, Slleteee amity tiaqr ~tan'- 4 —i 
tan’ a 2*tan’ ia 4 2 2? 
I ey are I I 
“7 2 = ar] aang ‘ + = = (tan = a eee Pa 
2° tan’+a 4 tan’ >a 4 2A 
: i 
= ees = ea 8 = tan* = g)°2 Heat 
4 tan’ +a tan +4 43 8 2.42 
I I re I I I 
RSIS PEE ae eee 8 ne Stan —* zea) ee ee 
3* tan’? +a 16° tan’ =, 4 44 16 2.43” 
tod } oti I I , @ I 
_ = : ot jot tan’ a 
227—4 tan 22n—2 tan 
~ Qn—2 x _Qimt 
DB af I a 
> = x + = tan? = 4 ited 
4” an 2.4°—1 
27—2 tan —~ 22n tan’ 4 
gn—I Qn 
