Henry Parker Manning (1859–1956)

Builds on what is taught in most geometry texts. Begins with "Foundations" of the Four Dimensional figures -- points and lines, triangles, planes, convex polygons, tetrahedrons, hyperplanes, convex pyramids and pentahedroids, space of four dimensions, hyperpyramids, and hypercones. Then a chapter on perpendicularity, followed by angles of two planes and higher orders. The fourth chapter is on symmetry, order, and motion, in rectangular systems and isocline planes. The work then explodes hyperpyramids, hypercones, and the hypersphere. The next chapter connects this to Euclidean geometry with the axiom of parallels. The penultimate chapter shows how to measure volumes and hypervolumes. Finally, Chapter VIII describes the Regular Polyhedroids. The work does not develop or trespass upon further dimensions.

This is an unabridged reproduction of the 1914 first edition. It introduces this branch of modern mathematics as part of applied physics.… (mehr)