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

xiv Contents.
PAGE.
Volume of a tetrahedron in terms of three conterminous edges and
their inclinations,....132
Volume of a tetrahedron in terms of its six edges,...132
The second Staudtians of the solid angles of a tetrahedron are
proportional to the areas of the opposite faces,...133
Volume of a tetrahedron in terms of two faces and their included
angle,........... 133
Relation between the areas of the four faces of a tetrahedron,.133
Relation between the six dihedral angles of a tetrahedron,. 134
The diagonal of a parallopiped in terms of three conterminous
edges,. 134
To find the radius of the circumscribed sphere,..135
First method (Staudt's),..... 135
Second method (Dostor's),.. 136
The isosceles tetrahedron,. 138
Definition of,,....... 138
Properties of,,.... 139
The inscribed sphere touches the faces at the centres of their
circumcircles,.........139
Volume of isosceles tetrahedron,.... 140
Radius of circumscribed sphere,.... 140
Radius of inscribed sphere,.... 140
Exercises XXXIV.,. 141
CHAPTER IX.
APPLICATIONS OF SPHERICAL TRIGONOMETRY.
SECTION I.-Geodesy,....... 143
To reduce an angle to the horizon,. 143
General solution,.... 143
Legendre's solution,. 144
Property of chordal triangle,.... 144
Legendre's theorem,....146
Area of spherical triangle,... 147
Roy's rule,......148
Exercises XXXV.,. 148
SECTION II.-Astronomy,. 149
Astronomical definitions,. 149
To find the time of rising or setting of a known body,. 151