Remarkable Collection of Babylonian Mathematical Texts (eBook)

Acknowledgements 6
Introduction 7
Statement of Provenance of Near Eastern Pictographic and Cuneiform Tablets in the Schøyen Collection 11
Abbreviations 13
Table of Contents 15
How to Get a Better Understanding of Mathematical Cuneiform Texts 21
0.1. On Avoiding Anachronisms in Translations of Mathematical Terms 21
0.2. Conform Transliterations, Translations, and Interpretations 22
0.3. Babylonian Sexagesimal Numbers 23
0.4. Counting with Sexagesimal Numbers in Relative Place Value Notation 26
Old Babylonian Arithmetical Hand Tablets 32
1.1. Old Babylonian Multiplication Exercises 32
1.2. Old Babylonian Squaring Exercises 37
1.3. An Old Babylonian Division Exercise 41
1.4. Old Babylonian Operations with Many-Place Regular Sexagesimal Numbers 42
1.5. Old Babylonian Squares and Squares of Squares of Many-Place Sexagesimal Numbers 56
Old Babylonian Arithmetical Table Texts 64
2.1. Old Babylonian Tables of Squares 64
2.2. Old Babylonian Tables of Square Sides 68
2.3. Old Babylonian Tables of Cube Sides 71
2.4. Old Babylonian Tables of Quasi-Cube Sides 75
2.5. The Old Babylonian Standard Table of Reciprocals 86
2.6. Old Babylonian Multiplication Tables 90
2.7. Old and Late Babylonian Sexagesimal Representations of Decimal Numbers 116
Old Babylonian Metrological Table Texts 119
3.1. Old Babylonian Capacity Measures. System C 119
3.2. Old Babylonian Weight Measures. System M 127
3.3. Old Babylonian Area Measures. System A 134
3.4. Old Babylonian Length Measures. Systems Ln and Lc 136
3.5. Old Babylonian Combined Metrological Tables 139
Mesopotamian Weight Stones 145
4.1. MS 4576. A Kassite Reused Talent Weight with an Inscription in Sumerian 145
4.2. MS 2481. A Barrel-Shaped 1 Mina Weight with an Inscription in 3 Lines 148
4.3. MS 2837. An Ellipsoid-Shaped 3 Shekels Weight with a Brief Inscription 148
4.4. MS 2836. A Small Duck Weight in Agate with the Inscription ‘1/3 Shekel’ 148
4.5. MS 5088. 55 Assorted Weight Stones Found Together in a Damaged Bronze Pot 149
4.6. YBC 4652. Weight Stones in an Old Babylonian Mathematical Theme Text 151
4.7. YBC 4669 § 1. Measuring Vessels in an OB Mathematical Theme Text 152
Neo-Sumerian Field Plan Texts (Ur III) 155
5.1. MS 1984. A Field Plan Text from Umma with a Summary on the Reverse 155
5.2. MS 1850. A Field Plan Text without a Summary on the Reverse 158
5.3. Four Ur III Field Plan Texts, Published in 1915, 1898, 1922, and 1962 160
An Old Sumerian Metro-Mathematical Table Text ( Early Dynastic IIIa) 165
6.1. Three Previously Published Metro-Mathematical School Texts from Shuruppak 165
6.2. MS 3047. An Old Sumerian Metro-Mathematical Table Text 168
Old Babylonian Hand Tablets with Practical Mathematics 172
7.1. MS 2317. Division of a Funny Number by a Non-Regular Factor 172
7.2. Combined Market Rate Exercises 174
7.3. Old Babylonian Brick Types and Brick Constants 186
7.4. Inheritance Problems with the Shares Forming a Geometric Progression 196
Old Babylonian Hand Tablets with Geometric Exercises 205
8.1. Triangles and Trapezoids 205
8.2. Figures Within Figures 218
8.3. Labyrinths, Mazes, and Decorative Patterns 235
The Beginning and the End of the Sumerian King List 246
9.1. The Sumerian King List 246
9.2. MS 1686. A New Version of the Ur-Isin King List 248
9.3. MS 2855. A New Version of the Antediluvian Part of the Sumerian King List 251
9.4. The Numbers in the Antediluvian King List 257
9.5. Mesopotamian Year Names 257
Three Old Babylonian Mathematical Problem Texts from Uruk 259
10.1. MS 3971. A Double-Column Mathematical Recombination Text 259
10.2. MS 3052. A Single-Column Mathematical Recombination Text 268
10.3. MS 2792. Two Exercises Dealing with a Divided Ramp 292
Three Problem Texts Not Belonging to Any Known Group of Texts 309
11.1. MS 3049. A Fragment of a Mathematical Recombination Text 309
11.2. MS 5112. A Text with Equations for Squares and Rectangles 322
11.3. MS 3876. Three Problems for 20 Equilateral Triangles and a ‘Horn-Figure’ 356
11.4. On the Dating of the Texts in Chapter 11 366
Subtractive Notations for Numbers in Mathematical Cuneiform Texts 368
A1.1. Hilprecht’s List of Signs for ‘19’ in Multiplication Tables from Nippur 368
A1.2. Ist. T 7375. An Ur III Table of Reciprocals with Subtractive Number Notations 369
A1.3. A 681. A Table Text from ED IIIb Adab with Subtractive Number Notations 370
The Old Babylonian Combined Multiplication Table 374
An Old Babylonian Combined Arithmetical Algorithm 379
A3.1. CBS 10201. Hilprecht’s Misunderstood Algorithm Text from Nippur 379
A3.2. UM 29.13.21. A Fragment of a Multiple Algorithm Text from Nippur 380
A3.3. CBS 1215. An Algorithm Text with Explicit Computations 381
Cuneiform Systems of Notations for Numbers and Measures 384
A4.1. Proto-Literate/Traditional Sexagesimal Counting Numbers 384
A4.2. Proto-Literate Bisexagesimal Counting Numbers 386
A4.3. Proto-Elamite Decimal Counting Numbers 386
A4.4. Proto-Literate and Traditional Capacity Numbers 387
A4.5. Proto-Cuneiform and Traditional Weight Numbers 388
A4.6. Proto-Literate/Traditional Area Numbers 388
A4.7. Old Akkadian and Neo-Sumerian/Old Babylonian Length Numbers 389
A4.8. Proto-Cuneiform Time Numbers 390
A4.9. An Integrated Family of Numbers and Measures 390
A4.10. Pre-Literate Number Tokens 391
Old Babylonian Complete Metrological Tables 396
A5.1. The Complete Metrological Table for System C(NS/OB) 396
A5.2. The Complete Metrological Table for System M(NS/OB) 398
A5.3. The Complete Metrological Table for System A(NS/OB) 400
A5.4. The Complete Metrological Tables for Systems Ln and Lc(NS/ OB) 402
A5.5. Old Babylonian (and Other) Combined Metrological Lists 406
A5.6. Old Babylonian Combined Metrological Tables 409
A5.7. On Prisms, Cylinders, and a Family of Subscripts 409
Metro-Mathematical Cuneiform Texts from the Third Millennium BC 412
A6.1. Two Old Akkadian Applications of the Field Expansion Procedure 412
A6.2. Old Akkadian Square-Side-and-Area Exercises 414
A6.3. Old Akkadian Metric Division Exercises 418
A6.4. IM 58045. An Old Akkadian Trapezoid Partition Problem 420
A6.5. TM.75.G.1392 (Ebla). A Division Algorithm in Decimal Numbers 421
A6.6. TM.75.G.2346 (Ebla). Another Decimal Division Algorithm 423
A6.7. TSS 50, 671 (Shuruppak). Sexagesimal Metric Division Exercises (ED IIIa) 425
A6.8. Examples of Complicated Designs 427
A Combined Metro-Mathematical Table Text with Areas of Large and Small Squares ( ED IIIb) 430
A7.1. CUNES 50-08-001. An Early Dynastic Metro-Mathematical Table Text 430
A7.2. A Parallel Text from Adab (ED IIIb) 436
A7.3. The Historical Importance of the Combined Table Text CUNES 50-08-001 436
A7.4. CUNES 47-12-176. An Old Akkadian Lexical Text with Fractions of the Mina2 437
A7.5. RA 35, Texts 1-2 and IM 96183. OB Table Texts Related to CUNES 50-08-001 439
Plimpton 322, a Table of Parameters for igi– igi. bi Problems 444
A8.1. Plimpton 322. A Description of the Preserved Part of the Table Text 445
A8.2. Related Texts: Texts with igi–igi.bi Problems 447
A8.3. A Suggested Reconstruction of the Lost Columns on Plimpton 322 451
A8.4. The OB Rectangle Parameter Equations. Restrictions on the Parameters 452
A8.5. The Purpose of the Tables on Plimpton 322 458
A8.6. The Diagonal Rule in the Corpus of Mathematical Cuneiform Texts 460
Many-Place Squares of Squares in Late Babylonian Mathematical Texts 463
A9.1. Squares of Squares of Many- Place Regular Sexagesimal Numbers 464
A9.2. An Explicit Late Babylonian Multiplication Algorithm 466
Color Photos of 70 Selected Texts 475
Vocabulary for the MS Texts 513
Index of Subjects 519
Index of Texts 524
References 530