A treatise on spherical trigonometry, and its application to geodesy and astronomy, with numerous examples. By John Casey.

Circumcircles. 79
Cor. 1.-If in equation (319) we substitute for B, C, 7r - B,
r - C, respectively, we get the circumradius of the colunar
triangle BCA'. Hence, denoting it by RA, we have
cot R =) (320)
sin (A - E)' (320)
Similarly, cot RB = (B E) (321)
and cot c= sinC (322)
Cor. 2.-From the equations (318), (319), we get the following formulae for the solution of spherical triangles, when
the angles are given. ThusIcot R = sin(A - E) + sin (B -E) + lsin ( C - E ) - sinE).
(323)
i cot - a = 1 cot R - i sin (A - E), &c. (324)
EXERCISES.-XXIII.
sin ~ a
1. Prove tanR =. 2 a. (325)
sin A cos 2 b cos 2 c
2 sin 1 a sin l b sin 1 c
2., tan R =. 2 (326)
3.t =- ^^-~ sin a(327)
3.,, tan RA (327)
sin A. sin ~b. sin(2c
2 sin 1 a cos ~ b cos ~ c
4.,, tan Rz =- (328)
n
5.,, tan R - tan R, = {sin s - sin (s - a)}. (329)
6.,, tan R. tan RA.tau R.tan c = N,. (330)
7.,, tan R + tan RA = cot rb + cot rc. (331)
8.,, tan RB + tan Rc = cot r + cot ra. (332)
9.,, tan R+ cot r = {tan + tan Rl + tan RB +tan Rc}. (333)