CONTENTS
Project Gutenberg EPUB3 edition
Poincaré, Henri and Halsted, George Bruce
PAGE
Henri Poincaré
ix
Author's Preface to the Translation
SCIENCE AND HYPOTHESIS
Introduction by Royce
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