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

Contents. xiii
CHAPTER VII.
INVERSIONS.
PAGE.
SECTION I.-Inversions in space,...... 119
Inversions in space defined,......119
The inverse of a plane is a sphere,..... 119
The inverse of a sphere is a sphere,. 120
The inverse of a circle in space is another circle,.. 120
Exercises XXXI.,. 120
SECTION II.-Stereographic projection,.... 121
Stereographic projection defined,...121
Stereographic projection of a circle is a circle,....121
Chasles' theorem,.........121
The projection of the poles of a great circle will be inverse points
with respect to its projection,..123
Projection of a system of circles whose planes are parallel,. 123
Circles whose projections are right lines,.... 123
The angle made by any two circles is equal to the angle made by
their projections,. 123
Circles 'whose projections are orthogonal to the primitive,..123
The projections of coaxal circles,......123
Application of stereographic projection to spherical trigonometry, 124
Exercises XXXII.,.. 125
Spherical excess of a spherical quadrilateral in terms of its sides
and diagonals,.... 126
Spherical excess of a cyclic quadrilateral,. 126
CHAPTER VIII.
POLYHEDRA.
SECTION I.-Regular polyhedra,.......128
Euler's theorem,..... 128
Proof that there can be but five regular polyhedra,.. 128
Inclination of two adjacent faces of a regular polyhedron,. 129
Polyhedra which are reciprocals,......130
Exercises XXXIII.,.... 131
SECTION II.-Parallelopipeds and tetrahedra,..131
Volume of a parallelopiped,.......131