Amazing Traces of a Babylonian Origin in Greek MathematicsA sequel to Unexpected Links Between Egyptian and Babylonian Mathematics (World Scientific, 2005), this book is based on the author's 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 ?metric algebra,? 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 book's use of ?metric algebra diagrams? in the Babylonian style, where the side lengths and areas of geometric figures are explicitly indicated, instead of wholly abstract ?lettered diagrams? in the Greek style, is essential for an improved understanding of many interesting propositions and constructions in Greek mathematical works. The author's comparisons with Babylonian mathematics also lead to new answers to some important open questions in the history of Greek mathematics. |
Contents
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 |
453 | |
463 | |
Comparative Mesopotamian Egyptian and Babylonian Timelines | 476 |
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Common terms and phrases
2-striped triangle angle apotome appr area rule Babylonian mathematicians Babylonian mathematics barig base binomial birectangle bisected trapezoid clay tablet construction cubits cyclic quadrilaterals Data diagonal rule diagonal triple diagram in Fig diameter Diophantus divided equal equalside equation sq equations of type equilateral triangle Euclid’s example exercise expressible straight line extreme and mean field figure follows Friberg Geom geometric given straight line Heron’s Høyrup icosahedron inscribed interpreted known Late Babylonian lemma literal translation explanation lower front lunes metric algebra problems nigin ninda notations Old Babylonian pair parallel parallelogram parameters partial lengths pentagon Plimpton 322 proof propositions Ptolemy’s quadratic equation quadratic-rectangular system quadrilateral recombination text rectangle rectangular-linear system ridge pyramid right triangle seed measure semicircle sexagesimal numbers similar solution procedure square band step system of equations theme text transversal trapezoid upper front values volume