A Remarkable Collection of Babylonian Mathematical Texts: Manuscripts in the Schøyen Collection: Cuneiform Texts I (Sources and Studies in the History of Mathematics and Physical Sciences)

The sub-collection of mathematical cuneiform texts in the Schøyen Collection makes a substantial addition to the known corpus of such texts. It contains 121 texts, not counting 151 multiplication tables and 53 small weight stones. According to the catalog at the end of the Index of Subjects below, where those 121 mathematical texts are ordered by content, nearly all known kinds, and some new kinds, of mathematical cun- form texts are represented in the collection. Therefore it has been possible to organize the present work as a broad general account of Mesopotamian mathematics, illustrated mainly by texts from the Schøyen Collection, but occasionally also by previously published texts. The general disposition of the book is borrowed from my own concise but comprehensive survey of Mesopotamian mathematics in the article on “Mathematics” in Reallexikon der Assyriologie, vol. 7 (1990). My ambition has been to make the account easily accessible to all kinds of readers, yet still as detailed and exhaustive as possible. For that purpose, there is, for instance, an introductory Chapter 0 on “how to get a b- ter understanding of mathematical cuneiform texts”. The chapter begins with a discussion of the danger of unintentional anachronisms in translations of pre-Greek mathematical texts, and continues with a presentation of the kind of “conform” transliterations, translations, and interpretations, true to the original, that will be used throughout the book in discussions of individual texts. Cover......Page 1 Series: Sources and Studies in the History of Mathematics and Physical Sciences......Page 2 A Remarkable Collection of Babylonian Mathematical Texts: Manuscripts in the Schøyen Collection: Cuneiform Texts I......Page 4 Copyright......Page 5 Acknowledgements......Page 6 Introduction......Page 8 Statement of Provenance of Near Eastern Pictographic and Cuneiform Tablets in the Schøyen Collection......Page 12 Abbreviations......Page 14 Table of Contents......Page 16 0.1. On Avoiding Anachronisms in Translations of Mathematical Terms......Page 22 0.2. Conform Transliterations, Translations, and Interpretations......Page 23 0.3. Babylonian Sexagesimal Numbers......Page 24 0.4. Counting with Sexagesimal Numbers in Relative Place Value Notation......Page 27 1.1. Old Babylonian Multiplication Exercises......Page 34 1.2. Old Babylonian Squaring Exercises......Page 39 1.3. An Old Babylonian Division Exercise......Page 43 1.4. Old Babylonian Operations with Many-Place Regular Sexagesimal Numbers......Page 44 1.5. Old Babylonian Squares and Squares of Squares of Many-Place Sexagesimal Numbers......Page 58 2.1. Old Babylonian Tables of Squares......Page 66 2.2. Old Babylonian Tables of Square Sides......Page 70 2.3. Old Babylonian Tables of Cube Sides......Page 73 2.4. Old Babylonian Tables of Quasi-Cube Sides......Page 77 2.5. The Old Babylonian Standard Table of Reciprocals......Page 88 2.6. Old Babylonian Multiplication Tables......Page 92 2.7. Old and Late Babylonian Sexagesimal Representations of Decimal Numbers......Page 118 3.1. Old Babylonian Capacity Measures. System C......Page 122 3.2. Old Babylonian Weight Measures. System M......Page 130 3.3. Old Babylonian Area Measures. System A......Page 137 3.4. Old Babylonian Length Measures. Systems Ln and Lc......Page 139 3.5. Old Babylonian Combined Metrological Tables......Page 142 4.1. MS 4576. A Kassite Reused Talent Weight with an Inscription in Sumerian......Page 148 4.4. MS 2836. A Small Duck Weight in Agate with the Inscription ‘1/3 Shekel’......Page 151 4.5. MS 5088. 55 Assorted Weight Stones Found Together in a Damaged Bronze Pot......Page 152 4.6. YBC 4652. Weight Stones in an Old Babylonian Mathematical Theme Text......Page 154 4.7. YBC 4669 § 1. Measuring Vessels in an Old Babylonian Mathematical Theme Text......Page 155 5.1. MS 1984. A Field Plan Text from Umma with a Summary on the Reverse......Page 158 5.2. MS 1850. A Field Plan Text without a Summary on the Reverse......Page 161 5.3. Four Ur III Field Plan Texts, Published in 1915, 1898, 1922, and 1962......Page 163 6.1. Three Previously Published Metro-Mathematical School Texts from Shuruppak......Page 168 6.2. MS 3047. An Old Sumerian Metro-Mathematical Table Text......Page 171 7.1. MS 2317. Division of a Funny Number by a Non-Regular Factor......Page 176 7.2. Combined Market Rate Exercises......Page 178 7.3. Old Babylonian Brick Types and Brick Constants......Page 190 7.4. Inheritance Problems with the Shares Forming a Geometric Progression......Page 200 8.1. Triangles and Trapezoids......Page 210 8.2. Figures Within Figures......Page 223 8.3. Labyrinths, Mazes, and Decorative Patterns......Page 240 9.1. The Sumerian King List......Page 252 9.2. MS 1686. A New Version of the Ur-Isin King List......Page 254 9.3. MS 2855. A New Version of the Antediluvian Part of the Sumerian King List......Page 257 9.5. Mesopotamian Year Names......Page 263 10.1. MS 3971. A Double-Column Mathematical Recombination Text......Page 266 10.2. MS 3052. A Single-Column Mathematical Recombination Text......Page 275 10.3. MS 2792. Two Exercises Dealing with a Divided Ramp......Page 299 11.1. MS 3049. A Fragment of a Mathematical Recombination Text......Page 316 11.2. MS 5112. A Text with Equations for Squares and Rectangles......Page 329 11.3. MS 3876. Three Problems for 20 Equilateral Triangles and a ‘Horn-Figure’......Page 363 11.4. On the Dating of the Texts in Chapter 11......Page 373 A1.1. Hilprecht’s List of Signs for ’19’ in Multiplication Tables from Nippur......Page 376 A1.2. Ist. T 7375. An Ur III Table of Reciprocals with Subtractive Number Notations......Page 377 A1.3. A 681. A Table Text from ED IIIb Adab with Subtractive Number Notations......Page 378 Appendix 2. The Old Babylonian Combined Multiplication Table......Page 382 A3.1. CBS 10201. Hilprecht’s Misunderstood Algorithm Text from Nippur......Page 388 A3.2. UM 29.13.21. A Fragment of a Multiple Algorithm Text from Nippur......Page 389 A3.3. CBS 1215. An Algorithm Text with Explicit Computations......Page 390 A4.1. Proto-Literate/Traditional Sexagesimal Counting Numbers......Page 394 A4.3. Proto-Elamite Decimal Counting Numbers......Page 396 A4.4. Proto-Literate and Traditional Capacity Numbers......Page 397 A4.6. Proto-Literate/Traditional Area Numbers......Page 398 A4.7. Old Akkadian and Neo-Sumerian/Old Babylonian Length Numbers......Page 399 A4.9. An Integrated Family of Numbers and Measures......Page 400 A4.10. Pre-Literate Number Tokens......Page 401 A5.1. The Complete Metrological Table for System C(NS/OB)......Page 406 A5.2. The Complete Metrological Table for System M(NS/OB)......Page 408 A5.3. The Complete Metrological table for System A(NS/OB)......Page 410 A5.4. The Complete Metrological tables for Systems Ln(NS/OB) and Lc(NS/OB)......Page 412 A5.5. Old Babylonian (and Other) Combined Metrological Lists......Page 416 A5.7. On Prisms, Cylinders, and a Family of Subscripts......Page 419 A6.1. Two Old Akkadian Applications of the Field Expansion Procedure......Page 422 A6.2. Old Akkadian Square-Side-and-Area Exercises......Page 424 A6.3. Old Akkadian Metric Division Exercises......Page 428 A6.4. IM 58045. An Old Akkadian Trapezoid Partition Problem......Page 430 A6.5. TM.75.G.1392 (Ebla). A Division Algorithm in Decimal Numbers......Page 431 A6.6. TM.75.G.2346 (Ebla). Another Decimal Division Algorithm......Page 433 A6.7. TSS 50, 671 (Shuruppak). Sexagesimal Metric Division Exercises (ED IIIa)......Page 435 A6.8. Examples of Complicated Designs......Page 437 A7.1. CUNES 50-08-001. An Early Dynastic Metro-Mathematical Table Text......Page 440 A7.3. The Historical Importance of the Combined Table Text CUNES 50-08-001......Page 446 A7.4. CUNES 47-12-176. An Old Akkadian Lexical Text with Fractions of the Mina......Page 447 A7.5. RA 35, Texts 1-2 and IM 96183. Old Babylonian Table Texts Related to CUNES 50-08-001......Page 449 Appendix 8. Plimpton 322, a Table of Parameters for igi–igi.bi Problems......Page 454 A8.1. Plimpton 322. A Description of the Preserved Part of the Table Text......Page 455 A8.2. Related Texts: Texts with igi–igi.bi Problems......Page 457 A8.3. A Suggested Reconstruction of the Lost Columns on Plimpton 322......Page 461 A8.4. The Old Babylonian Rectangle Parameter Equations. Restrictions on the Parameters......Page 462 A8.5. The Purpose of the Tables on Plimpton 322......Page 468 A8.6. The Diagonal Rule in the Corpus of Mathematical Cuneiform Texts......Page 470 Appendix 9. Many-Place Squares of Squares in Late Babylonian Mathematical Texts......Page 474 A9.1. Squares of Squares of Many-Place Regular Sexagesimal Numbers......Page 475 A9.2. An Explicit Late Babylonian Multiplication Algorithm......Page 477 Appendix 10. Color Photos of 70 Selected Texts......Page 486 Vocabulary for the MS Texts......Page 524 Index of Subjects......Page 530 Index of Texts......Page 536 References......Page 542 This new text from Jöran Friberg, the leading expert on Babylonian mathematics, presents 130 previously unpublished mathematical clay tablets from the Norwegian Schøyen collection, and provides a synthesis of the author's most important work. Through a close study of these tablets, Friberg has made numerous amazing discoveries, including the first known examples of pre-Classical labyrinths and mazes, a new understanding of the famous table text Plimpton 322, and new evidence of Babylonian familiarity with sophisticated mathematical ideas and objects, such as the three-dimensional Pythagorean equation and the icosahedron. In order to make the text accessible to the largest possible audience, the author has included an introductory chapter entitled, "How to get a better understanding of mathematical cuneiform texts." Throughout the text he avoids anachronisms and makes every effort to teach the reader to do the same. The approach in this book is inherently pedagogical, as Friberg illustrates all the steps of the process of interpretation and clearly explains the mathematical ideas, including terminology, metrological systems, and methods of calculation. Drawings and color photos of a large selection of tablets are also included. Particularly beautiful hand copies of the most complicated texts were made by Farouk Al-Rawi, professor of Ancient Languages and Archaeology at Baghdad University. While the book is reader-friendly, it remains as detailed and exhaustive as possible. It is the most comprehensive treatment of a set of Babylonian mathematical texts ever published and will open up this subject to a new generation of students, mathematicians, and historians of science. Jöran Friberg is Professor Emeritus of Mathematics at Chalmers University of Technology, Sweden. He has recently published the book Unexpected Links Between Egyptian and Babylonian Mathematics (World Scientific 2005), and its sequel Amazing Traces of a Babylonian Origin in Greek Mathematics (World Scientific 2007) "This new text from Joran Friberg, the leading expert on Babylonian mathematics, presents 120 previously unpublished mathematical clay tablets from the Norwegian Schoyen collection, and provides a synthesis of the author's most important work. Through a close study of the many new texts, Friberg has made numerous amazing discoveries, including the first known examples of pre-Classical labyrinths and mazes, new texts explaining the famous table text Plimpton 322, and new evidence of Babylonian familiarity with sophisticated mathematical ideas and objects, such as the three-dimensional "Pythagorean equation" and the icosahedron." "While the book is reader-friendly, it remains as detailed and exhaustive as possible. It is the most comprehensive treatment of a set of Babylonian mathematical texts ever published and will open up this subject to a new generation of students, mathematicians, and historians of science."--BOOK JACKET The book analyzes the mathematical tablets from the private collection of Martin Schoyen. It includes analyses of tablets which have never been studied before. This provides new insight into Babylonian understanding of sophisticated mathematical objects. The book is carefully written and organized. The tablets are classified according to mathematical content and purpose, while drawings and pictures are provided for the most interesting tablets.