Worlds Out of Nothing : A Course in the History of Geometry in the 19th Century (Paperback, 2 Revised edition)

Mathematics in the French Revolution.- Poncelet (and Pole and Polar).- Theorems in Projective Geometry.- Poncelet's Traite.- Duality and the Duality Controversy.- Poncelet, Chasles, and the Early Years of Projective Geometry.- Euclidean Geometry, the Parallel Postulate, and the Work of Lambert and Legendre.- Gauss (Schweikart and Taurinus) and Gauss's Differential Geometry.- Janos Bolyai.- Lobachevskii.- Publication and Non-Reception up to 1855.- On Writing the History of Geometry - 1.- Across the Rhine - Mobius's Algebraic Version of Projective Geometry.- Plucker, Hesse, Higher Plane Curves, and the Resolution of the Duality Paradox.- The Plucker Formulae.- The Mathematical Theory of Plane Curves.- Complex Curves.- Riemann: Geometry and Physics.- Differential Geometry of Surfaces.- Beltrami, Klein, and the Acceptance of Non-Euclidean Geometry.- On Writing the History of Geometry - 2.- Projective Geometry as the Fundamental Geometry.- Hilbert and his Grundlagen der Geometrie.- The Foundations of Projective Geometry in Italy.- Henri Poincare and the Disc Model of non-Euclidean Geometry.- Is the Geometry of Space Euclidean or Non-Euclidean?.- Summary: Geometry to 1900.- What is Geometry? The Formal Side.- What is Geometry? The Physical Side.- What is Geometry? Is it True? Why is it Important?.- On Writing the History of Geometry - 3.