PROPERTIES of the CIRCLE. jt 



________ 77 — — • <? 



frp — b"' -f- c* — c"> + &c. to terms, is equal to n X 



4 



i.-s. C.7 . . . to p — i . ,_ 



p X I » which when r r_ I 



1.2.3.4. . . to £ _±* 22 



/>4-2 £ + 6 p-h 10 2/> — 2 

 . . - ... to - 



2 2 2 2 I 



IS = « X 7 X -J+T = » X 



... tO - 2 2 



7 2 



/>4-2./>-f6--.to 2 /> — 2 _ 



^ X~7x-i. Hence the fummation of 



2 . 4 .... to c 2 — 



__5 



an endlefs variety of ieries, of which the terms are powers of the 

 fines and cofines of angles ; and though they do not confift of an 

 infinite number of terms, they may confift of any number of 



n — — 1 

 terms whatever, fince may be equal to any given number 



11 n ~^ J i n — 3 •— -U /r w I'VI'l • • • to/> — I 

 as well as and ■ - The expreilion n X — ° ' 



4 4 P 



~ - 1.2.3.4. • ,to 



2 



/>+ 2 • p-\- 6 ... to 2 ^ — 2 



I 2 2 2 T 



X -7+7- is -: » X x -j+t , when 



2 2 2. 4. ..to- 2 2 



2 



- is equal to an even number, or p is a multiple of 2 by an even 



number. But when £ is an odd number, it is equal to n x 



p+A ' __L? ' ' to 2 ^ — 2 



22 2 ^ 



X -7+7 , which muft then be ufed. 



p — 2 

 4 . . to - 2 a 



* 2 



G 2 The 



