Amazing Traces of a Babylonian Origin in Greek MathematicsWorld Scientific, 2007 - 496 էջ A sequel to Unexpected Links Between Egyptian and Babylonian Mathematics (World Scientific, 2005), this book is based on the authorOCOs intensive and ground breaking studies of the long history of Mesopotamian mathematics, from the late 4th to the late 1st millennium BC. It is argued in the book that several of the most famous Greek mathematicians appear to have been familiar with various aspects of Babylonian OC metric algebra, OCO a convenient name for an elaborate combination of geometry, metrology, and quadratic equations that is known from both Babylonian and pre-Babylonian mathematical clay tablets. The bookOCOs use of OC metric algebra diagramsOCO in the Babylonian style, where the side lengths and areas of geometric figures are explicitly indicated, instead of wholly abstract OC lettered diagramsOCO in the Greek style, is essential for an improved understanding of many interesting propositions and constructions in Greek mathematical works. The authorOCOs comparisons with Babylonian mathematics also lead to new answers to some important open questions in the history of Greek mathematics." |
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1 Elements II and Babylonian Metric Algebra | 1 |
2 El I47 and the Old Babylonian Diagonal Rule | 73 |
3 Lemma El X2829 1a Plimpton 322 and Babylonian igiigibi Problems | 83 |
4 Lemma El X3233 and an Old Babylonian Geometric Progression | 95 |
5 Elements X and Babylonian Metric Algebra | 101 |
6 Elements IV and Old Babylonian Figures Within Figures | 123 |
7 El VI30 XIII112 and Regular Polygons in Babylonian Mathematics | 141 |
8 El XIII1318 and Regular Polyhedrons in Babylonian Mathematics | 171 |
14 Herons Ptolemys and Brahmaguptas Area and Diagonal Rules | 361 |
15 Theon of Smyrnas Side and Diagonal Numbers and Ascending Infinite Chains of Birectangles | 373 |
16 Greek and Babylonian Square Side Approximations | 385 |
17 Theodorus of Cyrenes Irrationality Proof and Descending Infinite Chains of Birectangles | 405 |
18 The PseudoHeronic Geometrica | 415 |
Appendix 1 A Chain of Trapezoids with Fixed Diagonals | 431 |
Appendix 2 A Catalog of Babylonian Geometric Figures | 443 |
| 447 | |
9 Elements XII and Pyramids and Cones in Babylonian Mathematics | 189 |
10 El I4344 El VI2429 Data 5759 8486 and Metric Algebra | 211 |
11 Euclids Lost Book On Divisions and Babylonian Striped Figures | 235 |
12 Hippocrates Lunes and Babylonian Figures with Curved Boundaries | 309 |
13 Traces of Babylonian Metric Algebra in the Arithmetica of Diophantus | 327 |
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| 463 | |
Comparative Mesopotamian Egyptian and Babylonian Timelines | 476 |
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Common terms and phrases
angle appears application appr approximation Babylonian Babylonian mathematics base basic birectangle called Chapter circle computed Consequently constant construction cubits Data diagonal diagonal rule diagram diameter difference discussion divided Elements equal equalside equations of type example exercise explanation expressible feet field figure follows four Friberg front geometric given half hand height inscribed Inside instance interesting interpreted kind known length lower mathematical mathematicians means measure mentioned method metric algebra ninda Note pair parallel partial pentagon problem proof propositions pyramid quadratic ratio rectangle regular remaining respectively result right triangle rule says seed segments shown shows similar solution procedure square side step straight line system of equations tablet third translation transversal trapezoid triple upper values volume