Synopses & Reviews
This fine and versatile introduction to non-Euclidean geometry is appropriate for both high-school and college classes. Its first two-thirds requires just a familiarity with plane and solid geometry and trigonometry, and calculus is employed only in the final part. It begins with the theorems common to Euclidean and non-Euclidean geometry, and then it addresses the specific differences that constitute elliptic and hyperbolic geometry. Major topics include hyperbolic geometry, single elliptic geometry, and analytic non-Euclidean geometry. 1901 edition.
An elementary introduction to the two most important non-Euclidean geometries, hyperbolic and elliptic, this undergraduate-level text presents an extremely simple and direct account of a tremendously important branch of mathematics.
This fine and versatile introduction begins with the theorems common to Euclidean and non-Euclidean geometry, and then it addresses the specific differences that constitute elliptic and hyperbolic geometry. 1901 edition.
Table of Contents
I. Propositions Depending Only on the Principle of Superposition
II. Propositions Which Are True for Restricted Figures
III. The Three Hypotheses
II. The Hyperbolic Geometry
I. Parallel Lines
II. Boundary-curves and Surfaces, and Equidistant-curves and Surfaces
III. Trigonometrical Formulae
III. The Elliptic Geometry
IV. Analytic Non-Euclidean Geometry
I. Hyperbolic Analytic Geometry
II. Elliptic Analytic Geometry
III. Elliptic Solid Analytic Geometry