[ zz 3 



From thefe obfervations it immediately follows, if a, a. 



" ' 72. n. — in — 2 



rt", &c. are all equal, that the fine oi na = nc s— ^ ' ^' ^ 



c J + &C. andthatthecofuieof«a = c — n c s + &c. and 



I • s 



alfo that the general terms are as ftated in the theorem. Q; E. D. 



„ — 1 n n — 3 n— 2 



II. Theorem, i. The cofine of n a = i c — n. 2 c + 

 "• "—3 /"V""^ &c. to be continued by fucceflively diminifhing the 



I. 2 



« — u 



index of c by 2 till it becomes i or o, and affixing to c the coefF. 



u 



„—u—i n. n — u + 1. « — u + 2. - "to — terms 

 -f 2 • ■ — ■ of which the fign is 



I. 2. 3 ^ 



+ when — is even, and — when odd. 

 ' 2 



n — I n — I n — j n — 3 _^_ __ 



2. The fine of «a = 2 c — n — 2. 2 f + &c. 'Wi — c- 



continued by diminifhing the index of r by 2 till it becomes 



n — u 



I or o, and affixing to c the coefficient 



u — I 



„_„ n — «+ I. « — u + 2. - - ( terms) 



+ 2 X of which the fign 



r. 2. - - u — I ^ 



2 



is + when « + i is odd and — when even. 



2 



Vol. VII. E DemonStr. 



•0 



