Page:Spherical Trigonometry (1914).djvu/26



15. Spherical Trigonometry investigates the relations which subsist between the angles of the plane faces which form a solid angle and the angles at which the plane faces are inclined to each other.

16. Spherical Triangle. Suppose that the angular point of a solid angle is made the centre of a sphere; then the planes which form the solid angle will cut the sphere in arcs of great circles. Thus a figure will be formed on the surface of the sphere which is called a spherical triangle if it is bounded by three arcs of great circles; this will be the case when the solid angle is formed by the meeting of three plane angles. If the solid angle be formed by the meeting of more than three plane angles, the corresponding figure on the surface of the sphere is bounded by more than three arcs of great circles, and is called a spherical polygon.

17. Definitions. The three arcs of great circles which form a spherical triangle are called the sides of the spherical triangle; the angles formed by the arcs at the points where they meet are called the angles of the spherical triangle. (See Art. 9.)

18. Thus, let $$O$$ be the centre of a sphere, and suppose a solid angle formed at $$O$$ by the meeting of three plane angles.