"The "rule of four quanitites" marked a stage in the transition from a calculus dealing with arcs of a spherical quadrilateral to spherical trigonometry proper, involving the sides and angles of a spherical triangle. This theorem states that in a pair of right spherical triangles having an acute angle (A and A') in common or equal...\sin a/a' = \sin c/\sin c'...[A]lthough it utilizes triangles, angles are not dealt with. ...[A] proof by means of ... [is] straightforward. ...The Menelaus equation... can be stated in terms of sines by use of the identity \sin \theta \equiv \frac{1}{2} \mathrm{Crd} 2 \theta."