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

von: Jöran Friberg

Springer-Verlag, 2007

ISBN: 9780387489773 , 536 Seiten

Format: PDF

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


 

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