The Trigonometry of the Tetrahedron

Extract

So far as I know the properties of a tetrahedron are not given in any mathematical text-book. In the late Dr. Wolstenholme’s Examples for Practice in the use of Seven-figure Logarithms, the formulae which are necessary to determine the plane and dihedral angles and the volume of the tetrahedron, having given the six edges, are stated, but nothing beyond this. Dr. Wolstenholme worked at the subject for some years, and several of his results were sent as problems to the Educational Times, where they appeared for the most part after his death. In one set of questions he remarks that they are “the equations I have been looking for for years,” and so I think we may fairly infer that these questions represent the more advanced results of his investigations. The solutions of these questions, so far as I have been able to find them, are practically all given in this paper. “With regard to the rest of the matter, I hardly dare claim any originality. Wolstenholme must have known all or nearly all the results, and any one seriously attacking the subject must come upon them. All I can say is that I have never seen them in print, and that under any circumstances the bringing of them together must be helpful to students in many branches of mathematics.