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

First Class. 35
Plane Triangle. Spherical Triangle.
a sin a
sin A -, sin =,
c sin c
b tan b
cosA = -, cos A =t
Ce tan l
a tan a
tan A = - tan =
b >sin b'
cos b
If in these formulae we interchange the letters A, B, and at
the same time the small letters a, b, we get four others, which,
however, may be regarded as not essentially different. The
formula (113) has a remarkable analogy to Euc. I. xLvI. The
formula (112) has no analogue in Plane Trigonometry.
38. Napier's Mnemonic Rules. - If as in the annexed
diagram we trace in a plane a pentagon, whose sides have
respectively the same numerical measures as the quantities
a, 7r A7r 7r
a, b, i —,, -B,
we obtain a closed figure representing the system of five quanti- -
Fig. 16.
ties called Napier's Circular Parts. Any one of the five may
be selected, and called the middle part, then the two next to it
D2