The transformation of mathematics from its ancient Greek practice to its development in the medieval Arab-speaking world is approached by focusing on a single problem proposed by Archimedes and the many solutions offered. From a practice of mathematics based on the localized solution (originating in the polemical practices of early Greek science), we see a transition to a practice of mathematics based on the systematic approach (grounded in the deuteronomic practices of Late Antiquity and the Middle Ages). A radically new interpretation is accordingly offered of the historical trajectory of pre-modern mathematics.
Author(s): Reviel Netz
Series: Cambridge Classical Studies
Edition: Reissue
Publisher: Cambridge University Press
Year: 2007
Language: English
Pages: 212
Cover......Page 1
The Transformation of Mathematics in the Early
Mediterranean World: From Problems to Equations......Page 4
Contents......Page 8
Acknowledgments......Page 9
Introduction......Page 12
1.1 The problem obtained......Page 22
1.2 The problem solved by Archimedes......Page 27
1.3 The geometrical nature of Archimedes’ problem......Page 30
1.4 The problem solved by Dionysodorus......Page 40
1.5 The problem solved by Diocles......Page 50
1.6 The world of geometrical problems......Page 65
2 From Archimedes to Eutocius......Page 75
2.1 The limits of solubility: Archimedes’ text......Page 77
2.2 The limits of solubility: distinguishing Archimedes from Eutocius......Page 82
2.3 The limits of solubility: the geometrical character of Archimedes’ approach......Page 96
2.4 The limits of solubility: Eutocius’ transformation......Page 102
2.5 The multiplication of areas by lines......Page 108
2.6 The problem in the world of Eutocius......Page 132
3 From Archimedes to Khayyam......Page 139
3.1 Archimedes’ problem in the Arab world......Page 140
3.2 A note on Al-Khwarizmi’s algebra......Page 148
3.3 Khayyam’s solution within Khayyam’s algebra......Page 155
3.4 The problem solved by Khayyam......Page 166
3.5 Khayyam’s equation and Archimedes’ problem......Page 171
3.6 Khayyam’s polemic: the world of Khayyam and the world of Archimedes......Page 182
3.7 How did the problem become an equation?......Page 192
Conclusion......Page 198
References......Page 204
Index......Page 207
