Spherical Geometry II

Using a known method of Cesàro, we prove the spherical cosine law, the spherical sine law, and Euler’s formula for the spherical excess. The spherical cosine law is applied to prove a triangle comparison theorem for spheres. Euler’s formula for spherical excess is applied to prove a theorem for the area of a spherical triangle with two fixed edges and one variable edge. We also derive an isoperimetric theorem for spherical quadrilaterals.