PROPERTIES of the CIRCLE, 49 



A is the cofine of , B is the cofine of \ X , C is the 



180 

 cofine of 5 X , and fo on ; and when n — 1 is a multiple of 



Tm 



2 by an even number, the laft of the terms A, B, C, &c. is the 



n — 2 1 8 ° 



cofine of - X , and a, the firft of the terms a, b, c, 8cc. 



2 n • 



is the cofine of X ; b t the fecond, is the cofine of 



2 n ' ' 



»-f-c 180 ..... ,, r n + Q r 8o° , 

 X ; c. the third, is the coime of - X ; and 



the laft of the terms #, 3, ^ &c. is the cofine of ^ x — ~+ 



180 



or of n — 2 X — - — . But when n — 1 is a multiple of 2 by 



an odd number, the laft of the terms A, B, C, &c. is the cofine 



of — - — X : the firft of the terms a y b, &c. is the cofine 



2 n ' 



of - X and the laft of the terms a, b, &c is the co- 



2 n 



180 



fine of n — 2 X . Univerfally, if m be any odd number 



lefs than n, we have A M -f B™ -f C m -f &c. to ■■ * terms, 



4 



n — 1 r m 



— a m — b m — c m — &c to terms, =r — , when n — 1 is 



4 2- 



a multiple of 2 by an even number ; and A'" -j- B'" -f- O -f &c., 



n -f- 1 n — 3 f m 



to terms, — a n — b m — &c. to terms, = — , when 



4 4 2 



Vol. VI— P.I. 



n — 1 



