I 



p 



glJADRATURE of the CONIC SECTIONS, &c. 281 

 the adjacent tangents until they meet, (Art. 6.) \ therefore 

 2 2n tan* — will be the fquare of that perimeter. Let the pe- 



2" 



rimeter itfelf be denoted by P, then, fubftituting P* in the 

 equation inftead of 2 2n tan tL, and - (1 — -^) inftead of the 



feries to which it is equivalent, and bringing ^ to one fide, 

 we get 



— L- + ?(i-I) 



tan 2 a '3 ^ 4»' 



= <j — (- x tan 4 la+Lt9xi % La+ - tan 2 ! «+ *W -La. .. 

 v 4 2 4* 4 '43 8 44 16 



-+- — tan — J. 



4» 2 n/ 



15. This is true, whatever be the value of n, the number of 

 terms of the feries in the parenthefis. Let us now conceive 

 the feries to be continued indefinitely, then, as upon this hypo- 



thefis, n may be considered as indefinitely great, — will become 

 lefs than any aflignable quantity, and therefore - (1 — L\ 



will become fimply - ; moreover, P will in this cafe become a, 



(Art. 7.), and P* will become a\ Thus, upon the whole, we 



mail 



