QUADRATURE of the CONIC SECTIONS, &c. 279 



T T T T 



the equation — rr — ; tan - A, which, by ta- 



^ tan A 2 tan 7 A 2 2 J 



king the fquare of each fide, is transformed to 



nr = rrr + - tan2 -A . 



tan A 4 tan 4 7 A 422 



In this formula, let each term of the feries of arches 



ill a 



a, - a, - a, - a . . . . , 



2 4 8 2"— 1 



of which the number of terms is », be fubftituted fucceffively 

 for a, and let the refults be multiplied by the correfponding 

 terms of the feries of fractions, 



ill 1 1 . 



4 4 4 3 4«— 2' 4«— 1 



thus there will be formed the feries of equations 



-r -tan - a — i 



42 2 ' 



+ -tan** a — _L_ 

 4 4 2.4* 



+ 4 tan i« — -, 



4 3 8 2.4*' 



-f- — tan* — a i_, 



8 2 tan 2 ia i6*tan a T V" 4 4 16 2.43' 





tan 1 



a 







1 







2 2 



tan 2 



1 



2 



d 



4 2 



tan 2 



1 



1 



a 



2' 



tan 2 

 1 



i'H 



4* 



tan' 



i* 





1 





8 2 



tan 2 



1 



i* 



+ -L_tan*-^ * 



22 «-4tan-A_ a »«utf-f- 4"- 1 2—* 2.4— a' 



2« — 2 2" — 1 



I 



■ 1 2 a x 



+ — tan — * — . 



4 » 2 « 2 . 4 «-i 



Let 



2 2 «— 2 tan 2 2n tan 



2 «— 1 2" 



