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

CHAPTER IX.
APPLICATIONS OF SPHERICAL TRIGONOMETRY TO GEODESY
AND ASTRONOMY.
SECTION I.-GEODESY.
131. To reduce an angle to the horizon1~. General Solution.-Let OZ be the vertical of the observer
at O; then, if the angle MOON= a, NOZ = b, MOZ = c, it
is required to find the projection of MON on a horizontal plane
passing through 0.
2
N A
M
Fig. 57.
Sol.-From 0 as centre, with a unit radius, de scribe a sphere,
cutting OZ, OM1, ON in A, B, C, respectively; then the
sought angle is the measure of the dihedral angle BOA C, or of
the angle A of the spherical triangle BA C, which is given by
the formula
tan- - A_ sin(s - b) sin(s - c)
a sin s. sin (s - a)