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Book Categories |
1 | The problem in the world of Archimedes | 11 |
1.1 | The problem obtained | 11 |
1.2 | The problem solved by Archimedes | 16 |
1.3 | The geometrical nature of Archimedes' problem | 19 |
1.4 | The problem solved by Dionysodorus | 29 |
1.5 | The problem solved by Diocles | 39 |
1.6 | The world of geometrical problems | 54 |
2 | From Archimedes to Eutocius | 64 |
2.1 | The limits of solubility : Archimedes' text | 66 |
2.2 | The limits of solubility : distinguishing Archimedes from Eutocius | 71 |
2.3 | The limits of solubility : the geometrical character of Archimedes' approach | 85 |
2.4 | The limits of solubility : Eutocius' transformation | 91 |
2.5 | The multiplication of areas by lines | 97 |
2.6 | The problem in the world of Eutocius | 121 |
3 | From Archimedes to Khayyam | 128 |
3.1 | Archimedes' problem in the Arab word | 129 |
3.2 | A note on Al-Khwarizmi's algebra | 137 |
3.3 | Khayyam's solution within Khayyam's algebra | 144 |
3.4 | The problem solved by Khayyam | 155 |
3.5 | Khayyam's equation and Archimedes' problem | 160 |
3.6 | Khayyam's polemic : the world of Khayyam and the world of Archimedes | 171 |
3.7 | How did the problem become an equation? | 181 |
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