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

x Contents.
PAGE.
SECTION II.-Oblique-angled triangles,...... 54
Three pairs of cases of oblique-angled triangles,.. 54
First pair of cases,.... 55
Being given the three sides a, b, c, to calculate the angles,. 55
Type of the calculation,....55
Exercises XVI.,.... 56
Method of calculation when only one angle is required,.. 56
Being given the three angles A, B, C to calculate the sides,. 56
Exercises XVII.,........ 57
Method of calculation when only one side is required,.. 57
Second pair of cases,..58
Being given two sides a, b, and the angle opposite to one of them,
to calculate the remaining parts,...... 58
The ambiguous case,..58
Reidt's analogies, advantages of, in calculation,..59
This case solved by dividing the triangle into two right-angled
triangles,..... 60
Exercises XVIII.,... 60
Given two angles, A, B, and the side opposite to one of them to
solve the triangle,...61
Third pair of cases,......... 61
Being given the sides a, b and the contained angle C to calculate
A,,.......... 61
Type of the calculation,....... 61
Exercises XIX.,........ 62
Being given two angles A, B and the adjacent side c to find a, b, C, 63
Cauchy's method of solving the various cases of oblique-angled
triangles,.... 63
Exercises XX.,. 65
Brùnnow's series,. 65
CHAPTER IV.
VARIOUS APPLICATIONS.
SECTION I.-Theory of transversals,... 67
Ratio of section of an arc,........ 67
Anharmonic ratio of four point on an arc of a great circle,. 68
Ratio of section of an angle,.... 68
Anharmonic ratio of four great circles passing through the same
point,. 69
Properties of a great circle intersecting the sides of a triangle,. 69
Medians of a spherical triangle,.. 70
The altitudes,........... 70
The common orthocentre of two supplemental triangles,.. 70