A Remarkable Collection of Babylonian Mathematical Texts: Manuscripts in the Schøyen Collection: Cuneiform Texts I

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