قراءة كتاب The Foundations of Science: Science and Hypothesis, The Value of Science, Science and Method
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اللغة: English
The Foundations of Science: Science and Hypothesis, The Value of Science, Science and Method
الصفحة رقم: 1
THE FOUNDATIONS
OF SCIENCE
SCIENCE AND HYPOTHESIS
THE VALUE OF SCIENCE
SCIENCE AND METHOD
BY
H. POINCARÉ
AUTHORIZED TRANSLATION BY
GEORGE BRUCE HALSTED
WITH A SPECIAL PREFACE BY POINCARÉ, AND AN INTRODUCTION
BY JOSIAH ROYCE, HARVARD UNIVERSITY
THE SCIENCE PRESS
NEW YORK AND GARRISON, N. Y.
1913
Copyright, 1913
BY The Science Press
PRESS OF
THE NEW ERA PRINTING COMPANY
LANCASTER, PA.
CONTENTS
| 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 | |