Contents 5
Preface 8
Chapter 1 Arithmetic and the beginnings of algebra 10
1.1 In the beginning. . . 10
1.2 Classical Greece 21
1.3 The Greek written heritage 24
1.4 Numbers in Classical Greece 25
1.5 All is number 33
Chapter 2 Alexandria ad Aegyptum 36
2.1 The capital of memory 36
2.2 Diophantos\u2019 Alexandria 41
2.3 Education and the culture of paideia 44
2.4 Heron of Alexandria: a Diophantine precursor? 46
Chapter 3 Diophantos and the Arithmetika 51
3.1 The manuscripts 51
3.2 Diophantos 54
3.3 The book On Polygonal Numbers and the lost books 57
3.4 Symbolism in the Arithmetika 60
3.5 The structure of a Diophantine problem 65
3.6 The Arithmetika 67
3.7 The algebra of the Arithmetika 86
3.8 Interpretations of algebra in the Arithmetika 96
3.9 Negative numbers? 105
3.10 Conclusion 109
Chapter 4 Sleeping beauty in the Dark Ages 111
4.1 The sins of the Fathers. . . 111
4.2 From Alexandria to Baghdad 115
4.3 The Byzantine connection 121
4.4 Diophantos reinvented: Fibonacci 125
Chapter 5 New vistas 131
5.1 Printed by . . . 131
5.2 Wherefore art thou number? 133
5.3 From the rule of coss to algebra 136
Chapter 6 Humanism 141
6.1 Trait d\u2019union: Bessarion and the humanists 141
6.2 Diophantos goes north: Regiomontanus 143
Chapter 7 Renaissance or the rebirth of Diophantos 147
7.1 Xylander: A sphinx to solve a riddle 147
7.2 Coincidence of traditions: Rafael Bombelli 150
7.3 The great art: Guillaume Gosselin 154
7.4 The marvel is no marvel: Simon Stevin 158
Chapter 8 Fair stood the wind for France 162
8.1 Diophantos\u2019 triangles: Fran莽ois Vi猫te and the New Algebra 162
8.2 Emulating the Ancients: Claude-Gaspar Bachet de M茅ziriac 168
8.3 This margin is too small. . . 173
Chapter 9 Coda: Hilbert\u2019s tenth problem 177
Chapter 10 Stemma 179
Bibliography 182
Index 206