Algebra in Cuneiform: Introduction to an Old Babylonian Geometrical Technique - Max PlanckResearch Library for the History and Development of Knowledge - Textbooks 2

Introduction to an Old Babylonian Geometrical Technique Preface......Page 15 “Useless mathematics”......Page 17 The First Algebra and the First Interpretation......Page 19 A New Reading......Page 26 Concerning the Texts and the Translations......Page 33 TMS XVI #1......Page 37 TMS VII #2......Page 44 BM 13901 #1......Page 49 BM 13901 #2......Page 53 YBC 6967......Page 55 BM 13901 #10......Page 58 BM 13901 #14......Page 59 TMS IX #1 and #2......Page 64 TMS IX #3......Page 67 AO 8862 #2......Page 70 VAT 7532......Page 75 TMS XIII......Page 80 BM 13901 #12......Page 83 BM 13901 #23......Page 85 TMS VIII #1......Page 87 YBC 6504 #4......Page 89 VAT 8512......Page 93 BM 85200 + VAT 6599 #6......Page 99 BM 15285 #24......Page 103 Drawings?......Page 105 Algebra?......Page 107 The Scribe School......Page 111 The First Purpose: Training Numerical Calculation......Page 112 The Second Purpose: Professional Pride......Page 113 The Origin: Surveyors’ Riddles......Page 115 The Heritage......Page 120 A Moral......Page 125 TMS XVI #2......Page 127 VAT 8389 #1......Page 128 VAT 8390 #1......Page 131 VAT 8520 #1......Page 132 Str 368......Page 133 YBC 6504 #1......Page 134 YBC 6504 #3......Page 135 Db2–146......Page 136 Key to Vocabulary and Standard Translations......Page 139 AO 8862 #2......Page 143 BM 13901 #1, #2, #10, #12, #14 and #23......Page 144 BM 85200+VAT 6599 #6 and #23......Page 146 Db2–146......Page 147 TMS VII #1 and #2......Page 148 TMS IX #1, #2 and #3......Page 149 TMS XVI #1......Page 151 VAT 8389 #1......Page 152 VAT 8390 #1......Page 154 VAT 8512......Page 155 YBC 6504......Page 156 YBC 6967......Page 158 Bibliographical Note......Page 159 Preface 15 Introduction: The Issue – and Some Necessary Tools 17 “Useless mathematics” 17 The First Algebra and the First Interpretation 19 A New Reading 26 Concerning the Texts and the Translations 33 Techniques for the First Degree 37 TMS XVI #1 37 TMS VII #2 44 The Fundamental Techniques for the Second Degree 49 BM 13901 #1 49 BM 13901 #2 53 YBC 6967 55 BM 13901 #10 58 BM 13901 #14 59 TMS IX #1 and #2 64 Complex Second-degree Problems 67 TMS IX #3 67 AO 8862 #2 70 VAT 7532 75 TMS XIII 80 BM 13901 #12 83 BM 13901 #23 85 TMS VIII #1 87 YBC 6504 #4 89 Application of Quasi-algebraic Techniques to Geometry 93 VAT 8512 93 BM 85200 + VAT 6599 #6 99 BM 15285 #24 103 General Characteristics 105 Drawings? 105 Algebra? 107 The Background 111 The Scribe School 111 The First Purpose: Training Numerical Calculation 112 The Second Purpose: Professional Pride 113 Origin and Heritage 115 The Origin: Surveyors’ Riddles 115 The Heritage 120 A Moral 125 Appendix A: Problems for the Reader 127 TMS XVI #2 127 TMS VII #1 128 VAT 8389 #1 128 VAT 8390 #1 131 VAT 8520 #1 132 Str 368 133 YBC 6504 #1 134 YBC 6504 #3 135 BM 85200+VAT 6599 #23 136 Db2–146 136 Appendix B: Transliterated Texts 139 Key to Vocabulary and Standard Translations 139 AO 8862 #2 143 BM 13901 #1, #2, #10, #12, #14 and #23 144 BM 15285 #24 146 BM 85200+VAT 6599 #6 and #23 146 Db2–146 147 TMS VII #1 and #2 148 TMS VIII #1 149 TMS IX #1, #2 and #3 149 TMS XIII 151 TMS XVI #1 151 VAT 7532 152 VAT 8389 #1 152 VAT 8390 #1 154 VAT 8512 155 YBC 6504 156 YBC 6967 158 Bibliographical Note 159 "This textbook analyzes a number of texts in "conformal translation," that is, a translation in which the same Babylonian term is always translated in the same way and, more importantly, in which different terms are always translated differently. Appendixes are provided for readers who are familiar with basic Assyriology but otherwise philological details are avoided. All of these texts are from the second half of the Old Babylonian period, that is, 1800-1600 BCE. It is indeed during this period that the "algebraic" discipline, and Babylonian mathematics in general, culminates. Even though a few texts from the late period show some similarities with what comes from the Old Babylonian period, they are but remnants. Beyond analyzing texts, the book gives a general characterization of the kind of mathematics involved, and locates it within the context of the Old Babylonian scribe school and its particular culture. Finally, it describes the origin of the discipline and its impact in later mathematics, not least Euclid's geometry and genuine algebra as created in medieval Islam and taken over in European medieval and Renaissance mathematics"--Provided by publisher