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

Astronomy. 151
latitude. The longitude is reckoned eastward, from 0 to 360~.
The latitude is positive when north, and negative when south.
136. If the small circle, M, M', passing through S, and parallel
to the equator, represent the apparent diurnal motion of the
sun or other heavenly body (the declination being supposed
constant), it is evident he will be rising or setting at A (according as the eastern or the western hemisphere is represented by
the diagram). He will be east or west at to, will be at B at
6 o'clock, morning or evening, will be at noon at M, and at
midnight at MI'.
137. The foregoing definitions and diagram will enable us to
solve several astronomical problems of an elementary character,
such as the following:1~..Tofind the time of rising or setting of a known body.
Consider the spherical triangle APR. We have
cos RPA = tan RP. cot AP.
Ience, denoting the hour angle APZ by t, the latitude by c,
and the declination by 8, we have
cos t = - tan q tan 8. (470)
And the hour angle being known, the time may be found. In
the case of the sun, the formula (470) gives the time from sunrise to noon, and hence the length of the day.
2~. Being given the declination and the latitude, to find the
azimuth from the north at rising.
Let A denote the required azimuth, then A = AR. Hence,
from the triangle ARP, we have
sin 8 = cos <j. cos A. (471)
3~. Being given the hour angle and declination of a star, tofind
the azimuth and altitude.