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.

Contenuti

Introduction I. Pangeometry 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 Historical Note

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