The elements of non-Euclidean plane geometry and trigonometry, by H. S. Carslaw.

102

Therefore
Further,

NON-EUCLIDEAN GEOMETRY [cH. Iv.
cosh c = cosh a cosh b......................IV.
(Hypothenuse and two sides.)
cosh a = sinh I snh a(by III.)
sinh b

Therefore
Applying (IV.)
we have
and this gives

= sinh cosh (by I.).
cosh
cosh a = tanh 1 cosh m....................V.
(Side and two angles.)
to the triangle
c, m', a, (, -,3)\
cosh a' = cosh c' cosh m',
tanh a = tanh m tanh c..................VI.
(Hypothenuse, a side, and included angle.)

C
FIG. 74.
These six formulae are all given by a rule similar to Napier's
Rules in Spherical Trigonometry:
(i) Let the letters a', 1, c, m, b' be written one at each of the sides
of a pentagon taken in order. Then
cosh of the middle part = the product of the hyperbolic sines of the
adjacent parts
and
cosh of the middle part = the product of the hyperbolic cotangents
of the opposite parts.