Table of Contents

PART I: Early geometry; Euclidean geometry and the parallel postulate; Investigations by Islamic mathematicians. PART II: Saccheri and his Western Predecessors; J H Lambert's work; Legendre's work; Gauss' contribution; Trigonometry; the first new geometries; the discoveries of Lobachevskii and Bolyai; Curves and surfaces; Riemann on the foundations of geometry; Beltrami's ideas; New models and old arguments; Resume. PART III: Non-Euclidean mechanics; The
question of absolute space; Space, time and space-time; Paradoxes of special relativity; Gravitation and non-Euclidean geometry; Speculations; Some last thoughts.

Reviews

Reviews of this edition

'a very readable book that is stimulating and thought provoking.' New Scientist
From reviews of the first edition

`Jeremy Gray has provided a superb exposition which tells a good story.' Mathematics Teaching
'This promises to become a classic text for those interested in considering changing mathematical perceptions of space. Gray's book is a pleasure to read.' Historia Mathematica
`An admirable exposition for well-educated laymen of the evolution of geometrical thought from before Euclid to black holes.' American Mathematical Monthly