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

CHAPTER III.
SOLUTION OF SPHERICAL TRIANGLES.
49. Preliminary Observations.
1~. The logarithms of trigonometrical functions are obtained
from their "Tabular Logarithms " by subtracting 10 from the
characteristics. For example,
log tan 37~ 40' 16" = 1. 8876649.
The ablest recent continental writers, such as SERRET, BRIOT, et BOUQUET,
and others, employ the logarithms thus reduced, instead of the Tabular
Logarithms. We may add that the late PROF. BOOLE was strongly in
favour of this alteration.
2~. It is necessary to avoid the calculation of very small
angles by their cosines, or of angles near 90~ by their sines, for
their tabular differences vary too slowly. It is better to determine such angles, for example, by means of their tangents.
3~. When angles greater than 90~ occur in calculation, we
replace them by their supplements, and if the functions of
such angles be either cos, sec, tan or cot, we take account of the
change of sign.
4~. Formulae not adapted to logarithmic computation can be
rendered so by means of an auxiliary angle. Thus:(a) For A cos a + B sin a we put A = B tan E,
which gives B sin (+ a) (216)
cos 4
(b) For A cos a + B we put B = A sin a tan 4,
whic -is.A cos(a-<)
which gives cos - (217)
cos 9