[ 572 ] 
prefix’d to y taking place according as n is an even or 
an odd number. 
zn 
Therefore — 2 yxa-j~a xa—w &, is= 
2 _p 2jy x co s + 
&c. 
— r “ x o) a + \rr a 2 x&, 2 + —j— 
J+P i+y i-f-r 
a' 
Now /> being the cofine of any number of degrees, 
radius being 1 , — < 3 * will be the fquare of the tan- 
gent of half fo many degrees, radius being a: There- 
fore, denoting that tangent by b ; and the tangents 
of half the arcs defcrib’d with the radius a , whofe 
cofines, when the radius is i, are y, r, s , Sec. 
being denoted by c y d y e y Sec. refpedtively ; we have 
m n n m _______ 
a~\~M — 2 y x a + &> x w -\- a — &> == 2 Ip 2 y x 
&> 2 -f- £ 2 x&, z -f“ x w a -j-fl 2 ,&c. But when y is = r, 
and n an even number j or y — — 1, and n an odd 
number ; 2 Ip 2 y being = o ; nothing can be deter- 
min’d from that equation: Wherefore, in thofe 
cafes, recourfe muft be had to what is done above. 
VIII. 
Let us fuppofe y — 1, and n an even number : 
2 n _ n n 
Then the equation a-j- w — 2 ^ x ^ + <y x a — M 
-j- a — cu = 2 -j- 2 p x 2 -f- 2 y x 2 -{- 2 r, Sec. 
x U ) 2 -j- - — r^-ei z x co 2 + ~-r~ a* X &) 2 + —r~ ^ 2 , &c. 
I -\-p i +q 1+r 
becomes 
