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Evolution of the Concept of a Geometric Space
This book is an investigation of the mathematical and philosophical factors underlying the discovery of the concept of noneuclidean geometries, and the subsequent extension of the concept of space. Chapters one through five are devoted to the evolution of the concept of space, leading up to chapter six which describes the discovery of noneuclidean geometry, and the corresponding broadening of the concept of space. The author goes on to discuss concepts such as multidimensional spaces and curvature, and transformation groups. The book ends with a chapter describing the applications of nonassociative algebras to geometry.
Spherical Geometry -- The Theory of Parallels -- Geometric Transformations -- Geometric Algebra and the Prehistory of Multidimensional Geometry -- Philosophy of Space -- Lobacevskian Geometry -- Multidimensional Spaces -- The Curvature of Space -- Groups of Transformations -- Application of Algebras -- References -- Index.
Studies in the history of mathematics and physical sciences ; 12