Geometry in Space

Abstract

THIS book is a sequel to “Euclid Revised” by the same author. It consists of one hundred pages, divided into three chapters and an appendix. The first chapter is devoted to the discussion of planes and solid angles, covering much the same ground as Euclid's eleventh book; it contains, besides, some very useful notes on elementary perspective and the drawing of solid figures. This is an excellent feature of the book, and the author might with advantage have given more than a couple of pages to it, for there is no doubt that, to most students, the representation of solid figures, other than the simplest, is a real and often a permanent stumbling-block to the development of the science in their own minds. The second chapter is concerned with polyhedra. It begins with Euler's theorem establishing a linear relation between the numbers of edges, corners, and faces, and Listing's extension of it. In giving the latter the author speaks of “facets,” “sheets,” and “interfaces,” without having previously defined them, thus leaving a student in some little difficulty as to their precise meaning. Considering the great analytical interest of the algebraical researches of Klein and Cayley in the polyhedral functions and the finite groups of linear substitutions, which represent geometrically the production of congruence of figure by the rotations of the corresponding polyhedra, we think it would add greatly to the interest of the book to show the elementary geometrical relations which interpret the algebraical operations. The mensuration and usual properties of the simple solids are worked out, the method of limits being freely employed. The third chapter is of “Solids of Revolution,” and includes Pappus's theorems of mensuration, the extension of the modern geometry of lines and circles to planes and spheres, and an elementary account of surface spherics.

Geometry in Space.

Edited by R. C. J. Nixon “Clarendon Press Series.” (London: Henry Frowde, 1888.)