« 
[ 574 ] 
IX. 
By taking the fquare root of a + w — 2 x a-f- w 
n 7.n 
x a — co + a — w , and of its two values juft now found, 
we have, when« is an even number, a-j-co — a — w 
= 2 a n a x V co z + c % x V -j- &c. 2 a taking 
place inftead of V -j- fq. of the tang, of 5)0°. 
And, when n is an odd number, a + &> — a — 
— 2 co x V u z c z x V u z -'r d 2 -, &c. Whence the 
following conftrudtion is inferr’d. 
X. 
Defcribe about the centre C ( Plate XX. Jig. 1. and 
2.), with the radius <7, the circle P A A' A ", &c. 5 
draw the diameter P C and the tangent B " P P 5 ; 
divide the femicircumference P A into as many 
equal parts P A , A A 1 , A" A ", &c. as there are 
units in the integer n ; draw the fecants C A B y 
C A" P", &c. and, taking on Ci^any point 0 , draw 
A'" 0 K s parallel to P P iP ; likewife draw P' A', 
P" A", P'" A", &c. parallel to P^ ; and call CO, 
Then will y be the cofine of twice the angle 
P C A , r the cofine of twice P C yP, j the cofine of 
twice P C A"\ &c. if the radius be 1. 
Therefore *P B' = O A' will be = c, P P" = O 
= < 7 , &c. and C K — V oo x ~\ - c 2 ,C K" = V «* + 
6cc. Confequently OP" — 0 JP being 
= a -f- co 
