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