Leibniz on Binary

Table Of Contents

List of Figures ix
Abbreviations x
Preface xi
Acknowledgments xiii
Introduction 1
1 Notes on Algebra, Arithmetic, and Geometric Series (October 1674) 27
2 The Series of All Numbers, and on Binary Progression (before 15/25 March 1679) 31
3 Binary Progression (before 15/25 March 1679) 35
4 Geometric Progressions and Positional Notation (before 15/25 March 1679) 41
5 Binary Arithmetic Machine (before 15/25 March 1679) 45
6 On the Binary Progression (15/25 March 1679) 47
7 Attempted Expression of the Circle in Binary Progression (c. 1679) 61
8 Sedecimal Progression (1679) 63
9 Binary Progression Is for Theory, Sedecimal for Practice (c. 1679) 69
10 On the Organon or the Great Art of Thinking (first half [?] of 1679) 71
11 Binary Ancestral Calculations (early 1680s [?]) 71
12 Sedecimal on an Envelope (c. 1682-1685) 77
13 Remarks on Weigel (1694- mid-March 1695) 79
14 Leibniz to Duke Rudolph August (7/17-8/18 May 1696) 87
15 A Wonderful Expression of All Numbers by 1 and 0 Representing the Origin of Things from God and Nothing, or the Mystery of Creation (7/17 May 1696) 89
16 Wonderful Origin of All Numbers from 1 and 0, Which Serves as a Beautiful Representation of the Myster of Creation, since Everything Arises from God and Nothing Else (8/18 May 1696) 93
17 Leibniz to Duke Rudolph August (2/12 January 1697) 99
18 Duke Rudolph August to Johann Urban Müller (5/15 January 1697) 105
19 Leibniz to Claudio Filippo Grimaldi (mid-January-early-February 1697) 107
20 Periods (May 1698-first half of January 1701) 121
21 Leibniz to Philippe Naudé (15 January 1701) 121
22 Leibniz to Joachim Bouvet (15 February 1701) 125
23 Essays on a New Science of Numbers (26 February 1701) 135
24 Binary Addition (spring-fall 1701 [?]) 145
25 Periods in Binary (spring-fall 1701) 149
26 Periods and Powers (mid-to-late June 1701 [?]) 151
27 Demonstration That Columns of Sequences Exhibiting Powers of Arithmetic Progressions, or Numbers Composed from These, Are Periodic (November 1701) 157
28 Joachim Bouvet to Leibniz (4 November 1701) 161
29 Leibniz to Bouvet (early April [?] 1703) 177
30 Explanation of Binary Arithmetic, Which Uses Only the Digits 0 and 1, with Some Remarks on Its Usefulness, and on the Light It Throws on the Ancient Chinese Figures of Fuxi (7 April 1703) 189
31 Leibniz to César Caze (23 June 1705) 199
32 On Binary (late June 1705) 205
Bibliography 213
Index 225