CONTENTS

Editorial Note XIII Preface 1 1 Infinite and Indefinite 7 2 The Contradiction of ‘Infinite Number’ 15 3 The Innumerable Multitude 19 4 The Measurement of the Continuous 25 5 Questions Raised by the Infinitesimal Method 31 6 ‘Well-Founded Fictions’ 35 7 ‘Degrees of Infinity’ 41 8 ‘Infinite Division’ or Indefinite Divisibility 47 9 Indefinitely Increasing; Indefinitely Decreasing 54 10 Infinite and Continuous 60 11 The ‘Law of Continuity’ 64 12 The Notion of the Limit 69 13 Continuity and Passage to the Limit 74 14 ‘Vanishing Quantities’ 78 15 Zero is not a Number 83 16 The Notation of Negative Numbers 89 17 Representation of the Equilibrium of Forces 95 18 Variable and Fixed Quantities 100 19 Successive Differentiations 103 20 Various Orders of Indefinitude 106

21 The Indefinite is Analytically Inexhaustible 111 22 The Synthetic Character of Integration 115 23 The Arguments of Zeno of Elea 120 24 The True Conception of ‘Passage to the Limit’ 124 25 Conclusion 128 Index 131