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

Contents. xi
PAGE.
The Gergonne point of a spherical triangle,.... 70
Anharmonic ratio of a pencil of four great circles,.. 71
Harmonic division of the diagonals of a spherical quadrilateral,. 71
Exercises XXI.,...72
Normal coordinates defined,...... 73
Triangular coordinates,........ 73
Isotomic conjugates,......... 73
Isogonal conjugates,..... 73
Isotomic transversal of a point,....... 73
Isogonal transversal of a point,....... 73
The Lemoine point,. 75
The Symmedian point,.... 75
Normal coordinates of Lemoine point,... 75
Normal coordinates of Symmedian point,..... 75
SECTION II.-Incircles,........ 75
Exercises XXII.,.... 77
SECTION III.-Circumcircles,.... 78
Exercises XXIII.,......... 79
Angles of intersection of the sides of a spherical triangle with its
circumcircle,......... 80
Distance between poles of incircle and circumcircle,. 80
Properties of the Lhuilierian,.... 80
SECTION IV.-Spherical mean centres,...... 81
Spherical mean centres defined,..81,, fundamental proposition,... 81
Hart's circle, property of,..82
Exercises XXIV.,.... 84
CHAPTER V.
SPHERICAL EXCESS.
SECTION I.-Formulas relative to E,..85
Rule of transformation,...85
Cagnoli's theorem,.... 86
Lhuilier's theorem,.... 89
Prouhet's proof of Lhuilier's theorem,.. 89
Exercises XXV.,... 92
SECTION II.-Lexell's theorem,... 92
Steiner's proof,,.... 92
Serret's proof,,....... 93
Steiner's theorem,.... 93
Keogh's theorem,........ 95
Triangle of maximum area, two sides being given,. 95
Exercises XXVI.,.... 97