Beyond Geometry : Classic Papers from Riemann to Einstein

Introduction 1 Bernhard Riemann: On the Hypotheses That Lie at the Foundations of Geometry (1854) 23 Bernhard Riemann: Two Excerpts from Riemann's Nachlass (1853) 41 Hermann von Helmholtz: On the Factual Foundations of Geometry (1866) 47 Hermann von Helmholtz: The Origin and Meaning of Geometrical Axioms (1870) 53 William Kingdon Clifford: On the Space-Theory of Matter (1870) 71 William Kingdon Clifford: The Postulates of the Science of Space (1873) 73 Simon Newcomb: Elementary Theorems Relating to the Geometry of a Space of Three Dimensions and of Uniform Positive Curvature in the Fourth Dimension (1877) 89 Henri Poincare: Non-Euclidean Geometries (1891) 97 Felix Klein: The Most Recent Researches in Non-Euclidean Geometry (1893) 109 Henri Poincare: On the Foundations of Geometry (1898) 117 Albert Einstein: Geometry and Experience (1921) 147 Albert Einstein: Non-Euclidean Geometry and Physics (1925) 159 Albert Einstein: Space-Time (1926) 163 Albert Einstein: Space, Ether, and Field in Physics (1930) 173 Elie Cartan: Euclidean Geometry and Riemannian Geometry (1931) 179 Albert Einstein: The Problem of Space, Ether, and the Field in Physics (1934) 187 References 195 Index 208