[ '57 ] 



n — u 



and affixing to c the coefficient 



■ ;z.n 1. « — — — 2 X &c. to — terms n— «— i ^ 



^ ^ 2, + when — isevehand 



u 



2. 3 - - - 



when odd. Hence becaufe unity is the cofine of o, P (Peri 



n— 5 »— 2 



phery), 2 P, 3 P, &c. it follows that if 2 c — n. 2 c -{- Sec. 

 — I the different values of c will be a, a; a-\ &c, the cofines of o, 



p 9 P 



-, *^:^—, &c. or that the roots of the equation 



n n , 



n— 4 



" nc ^ 71. n — 3 c I 



'2' "^ I. 2. 2^ 



2 



'^ — ~~ T" "- r - ^ " ^_, = o will be a, a\ a'. Sec. 



Therefore by the nature of equations 



a -{■ a + a" + &c. = o 



a a + aa" + See. = — ~ 



- 2* ' 



a (f a" + aa a" + &c. = o 



n. n — X 



I /I III 1 0^^ J 



aaa a +&c. =+ iTZ^ 



&c. &c. 



or generally the fum of the produds of u values /?, a, a', &c. 



u u u 

 n.n — - — I. n — — 2. - (to — terms 

 u being even = + i 5 ! + when 



U a 



I. 2. 3 - - ^; 2 _ 



