Proof of Napier's Rules

Abstract

As the following graphical construction is easily executed, representing to the eye the figure usually employed for the proof of Napier's rules of the parts of right-angled triangles in spherical geometry, it will perhaps remove difficulties from their proof for beginners, like those which Mr. W. D. Cooley's work on “Elementary Geometry” must, from his description of some interesting parts of its contents in NATURE of the 19th of October, have proposed to itself to meet, and to render at least as easily accessible as possible to the inquiring student in mathematics.