CONTENTS
| PAGE | |
| Henri Poincaré | xi |
| Author’s Preface to the Translation | 3 |
| SCIENCE AND HYPOTHESIS | |
| Introduction by Royce | 9 |
| Introduction | 27 |
| Part I. Number and Magnitude | |
| CHAPTER I.—On the Nature of Mathematical Reasoning | 31 |
| Syllogistie Deduction | 31 |
| Verification and Proof | 32 |
| Elements of Arithmetic | 33 |
| Reasoning by Recurrence | 37 |
| Induction | 40 |
| Mathematical Construction | 41 |
| CHAPTER II.—Mathematical Magnitude and Experience | 43 |
| Definition of Incommensurables | 44 |
| The Physical Continuum | 46 |
| Creation of the Mathematical Continuum | 46 |
| Measurable Magnitude | 49 |
| Various Remarks (Curves without Tangents) | 50 |
| The Physical Continuum of Several Dimensions | 52 |
| The Mathematical Continuum of Several Dimensions | 58 |
| Part II. Space | |
| CHAPTER III.—The Non-Euclidean Geometries | 55 |
| The Bolyai-Lobachevski Geometry | 56 |
| Riemann’s Geometry | 57 |
| The Surfaces of Constant Curvature | 58 |
| Interpretation of Non-Euclidean Geometries | 59 |
| The Implicit Axioms | 60 |
| The Fourth Geometry | 62 |
| Lie’s Theorem | 62 |
| Riemann’s Geometries | 63 |
| On the Nature-of Axioms | 63 |
| CHAPTER IV.—Space and Geometry | 66 |
| Geometric Space and Perceptual Space | 66 |
| Visual Space | 67 |
| Tactile Space and Motor Space | 68 |
| Characteristics of Perceptual Space | 69 |
| Change of State and Change of Position | 70 |
| Conditions of Compensation | 72 |
