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

viii Contents.
PAGE.
Antipodal triangles,....... 10
Any two sides of a spherical triangle are greater than the third,
and the sum of the three sides is less than a great circle,.. 10
Positive and negative poles distinguished,.. 11
Polar triangles defined,...... 11
Relation between polar triangles,.... 12
Sum of angles of a spherical triangle,... 12
Sum of external angles of a spherical polygon,.. 13
Spherical excess defined,..13
Antipodal triangles are equal in area,. 13
Cases in which two spherical triangles on the same sphere have
all their corresponding elements respectively equal,.. 14
Properties of isosceles spherical triangles,..15
Area of a lune,........ 15
Girard's theorem.-The area of a spherical triangle,. 16
Ratio of area of a spherical triangle to area of a great circle,. 17
Area of spherical polygon,....... 17
Exercises II.,. 17
Diametrical triangles defined,... 18
Spherical parallelograms defined,..... 18
CHAPTER II.
FORMULAE CONNECTING THE SIDES AND ANGLES OF A
SPHERICAL TRIANGLE.
Three classes of formulae,...19
SECTION I.-First class,. 19
Case I.-Three sides and an angle,.. 19
Exercises III.,... 22
First Staudtian of a spherical triangle,.... 22
Second Staudtian of a spherical triangle,... 22
Norms of the sides and angles of a spherical triangle,. 23
Case II.-Two sides and their opposite angles,. 24
The sines of the sides of a spherical triangle are proportional to
the sines of their opposite angles,... 24
Exercises IV.,... 26
Case III.-Two sides and two angles, one of which is contained
by the sides,. 27
Exercises V.,...... 28
Case IV.-Three angles and a side,...... 29
Exercises VI.,. 31
Substitutions made in order to pass from a spherical triangle to
its polar triangle,. 32