[ 44 ] 



nnmber ; and the fine of n a = n s — "j-H — ? s , A-p 



I. 2. 3 + 



X v'l — J-* when n is any even number. 



In the former cafe the general term is 



2 2 2 l) + I 



n. n — 1. n — 3 - - to — — terms ^ 



+ ■ x-f 



~i. 2. 3 - - - toi) terms 



V being always odd, + when — -- — is odd and — 



when even. In the latter cafe the general term is + 



22 22 V ■\- \ 

 n. n — 2 . n — 3 . to — -— terms v , 



- J. X v/i— j% + when - is 



I. 2. 3 - - to t^ terms 

 odd and — when even. 



This Cor. may be deduced from the theorem in the fame 

 manner as the Cor. Art. III. was deduced from its theorem. 



Theorems for the Powers of the Sines and Cq/tnes. 



VI. Theorem. If c be the cofine of the arc a and rad. unity 

 then n being any whole pofitive number. 



« — »— « « -J- I 



e = ^ -x: cs ti a •\- n. cs n — 2 a -[- &c. cont. to terms 



when n is odd and when n Is even to ^ n ■\- i taking only -\ the 



laft 



