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

Astronomy. 149
6. If B be the circumradius of a spherical triangle, Ai, Bi, Ci the angles
of its chordal triangle; prove
sin A = sin a cosec, sin = sin cosec sin Bi = R s in C i c cosec 2.
(467)
7. Prove sin Ai: sin (B - C):: sin A: sin (B - C). (468)
8. Prove the proposition of ~ 132 from equation (351).
9. Prove E = (tan ~ a tan b) sin C - ~ (tan ~ a tan 2 b)2 sin 2C. (469)
[Make use of the value of tan E drawn from equations (351), (356).]
10. Show that in every case of the solution of spherical triangles, except
where the three angles are given, that Legendre's theorem may be used for
an approximate solution.
SECTION II. —ASTRONOMY.
135. Astronomical Definitions.
If PHNR represent the meridian of any place, produced to
meet the celestial sphere, P the north pole, O the south pole of
z
H /
Fig. 60.
the heavens, HR the horizon, EQ the equator, Z the zenith;
then, for a place whose zenith is Z, QZ is the latitude; and