| PAGE |
| Henri PoincarÉ | ix |
| 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 |
| Syllogistic 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 | 53 |
|
| 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 |
| Solid Bodies and Geometry | 72 |
| Law of Homogeneity | 74 |
| The Non-Euclidean World | 75 |
| The World of Four Dimensions | 78 |
| Conclusions | 79 |
| Chapter V.—Experience and GeometryChapter II.—Mathematical Definitions and Teaching | 430 |
| Chapter III.—Mathematics and Logic | 448 |
| Chapter IV.—The New Logics | 460 |
| Chapter V.—The Latest Efforts of the Logisticians | 472 |
|
| Book III. The New Mechanics |
| Chapter I.—Mechanics and Radium | 486 |
| Chapter II.—Mechanics and Optics | 496 |
| Chapter III.—The New Mechanics and Astronomy | 512 |
|
| Book IV. Astronomic Science |
| Chapter I.—The Milky Way and the Theory of Gases | 523 |
| Chapter II.—French Geodesy | 535 |
| General Conclusions | 544 |
| Index | 547 |
