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

36 Connecting Sides and Angles of a Spherical Triangle.
are called the acdacent parts, and the remaining parts the opposites. Thus, if a be selected as the middle part - B, and
b are the adjacents, and, and - A the opposites; then
2 2
Napier's rules are sin middle part = product of tangents of adjacents = product of cosines of opposites. These rules will be
evident from equation (138)-(113). Though given in most
treatises on Spherical Trigonometry, they are disapproved of
by some of the ablest writers-Delambre, De Morgan, Serret,
Baltzer, and others. We have found by experience that the
formulae are easily remembered by the method of ~ 37, which
we recommend to the student.
EXERCISES.-VII.
On the right-angled triangle, Ex. 1-20.
1. Prove that sin2A + sin2 b - sin2 c = sin2 a sin2 b. (114)
2.,, sin2a cos2b = sin (c b) sin(c - b). (115)
3.,, tan2 a: tan2 b: sin2 c - sin2 b sin2 - sin2a. (116)
4.,, cos24. sin2c = sin2e - sin2 a. (117)
5.,, sin2A cos2C = sin2A - sin2 a. (118)
6.,, sin2A cos2 b sinc = sin2c- sin2b. (119)
7.,, os2a cos2B = sin2A - sin2a. (120)
8.,, os2A + cos2 - cos2. COS2 C = Cos2a. (121)
9.,, sin2A - cosB = sin2a sin2B. (122)
10. s 'A si (-b (123)
10.,, sin A= 2cosb sin (13)
11. 2 cos sine (124),, cos A =2 cos b sin '
12.,, sin(a+b) tan (A + B)=sin (a-b)cot (A - B). (125)
cos a + cos b
13.,, sin( +) = os cos(126)
1 + cos a cos b
cos b - cos a
14.,, sin(A-B ) (127)
16.,, cos (A + B)=-1 s b (128)
sin a sin b
16.,, cos(A/- D) = 1 cos a cos b' (129)