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

xii Contents.
CIAPTER VI.
SMALL CIRCLES ON THE SPHERE.
PAGE.
SECTION I.-Coaxal circles,... 99
Spherical power of a point with respect to a small circle,. 100
Fundamental property of small circles cutting orthogonally,.100
Coaxal circles defined,........101
Radical circle of the system,...... 101
Limiting points of system,..... 101
Exercise XXVII.,....... 102
SECTION II.-Centres of similitude,. 103
Homothetic points on two circle..... 103
Inverse points on two circles,.......103
Property of centres of similitude of three circles,...104
Homothetic lines on sphere,.......105
Inverse circles....... 105
Exercises XXVIII.,. 105
SECTION III.-Poles and polars,.......106
Harmonic pole and polar defined,......107
Properties of harmonic pole and polar,..108
Exercises XXIX.,.... 110
Anharmonic properties of pole and polar,.. 110
Pascal's theorem,........ 111
Salmon's theorem,.........111
Brianchon's theorem,........111
SECTION IV.-Mutual power of two circles,. 112
Relation between arcs of connection of a point to the vertices of a
trirectangular triangle,....112
Distance between two points in terms of the distance from the
vertices of a trirectangular triangle,. 112
Mutual power of two circles defined,...113
Frobenius's theorem,....113
Relation between the angles of intersection of any five circles on
the sphere,.....114
Condition that four circles should be cut orthogonally by a fifth, 115
Condition that four circles should be tangential to a fifth in terms
of their angles of intersection,. 115
The same in terms of their common tangents,. 116
Relation between a system of four great circles and four other
circles (great or small),.. 116
Relation between six arcs joining four points on a sphere,. 117
Exercises XXX.,.... 117