C 5 6 9 ] 
III. 
Ify be — — « i; then, A being = - ; p, r, s, &c. 
will be the cofines of 
C 3 C c / \ r cl 
— , — , — , &c. (») refped- 
2« 2 72 2 n 
ively: Therefore, if « be an odd number, one of 
C 
thofe arcs will be whofe cofine is — i. 
IV. 
If in the equations z , 271 — 2 y z n + i = o, and 
* a — 2 x z + I = o, we fubftitute v — i for z, they 
zn n s 
become v — i — 2 y xv — i + i = O, and v — i 
2 XXU 1 -j- I = V z 2 -j- 2 XX. V -|- 2 *-j- 2 X = O. 
Confequently 
171 1 ^ 
<U 2n 272V 2u ~ . . . + 27ZX V 2 2?2V-\-l 
2 
.... J^iynx — — -tf + zynv'+iy ( 
+ iJ 
■ , - - 
V 2 — 2 -\- 2 pXV-\- 2+ 2pXV 2 2 -j-2y XV + 2-f-2yx 
^2 — 2 -(- 2 r X'u-f 2 r x &c. («) i where, of 
the two figns prefix’d to the terms where y is a fa&or, 
the upper or lower takes place, according as n is an 
even or an ©dd number. Whence, by the n ature of 
equations, it follows, that 2 + 2 /> x 2 + 2 qx 2 -j- 2 r, 
&c. is = 2 +2 y. But this equation vanishing when 
y is = I and n an even number, or when y is = — 1 
4 C and 
