Friberg A Remarkable Collection of Babylonian Mathematical Texts

Manuscripts in the Schøyen Collection: Cuneiform Texts I
1. Auflage 2007
ISBN: 978-0-387-48977-3
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 536 Seiten

Reihe: 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.

Autoren/Hrsg.

Friberg, Jöran

Inhaltsverzeichnis

1;Acknowledgements;6
2;Introduction;7
3;Statement of Provenance of Near Eastern Pictographic and Cuneiform Tablets in the Schøyen Collection;11
4;Abbreviations;13
5;Table of Contents;15
6;How to Get a Better Understanding of Mathematical Cuneiform Texts;21
6.1;0.1. On Avoiding Anachronisms in Translations of Mathematical Terms;21
6.2;0.2. Conform Transliterations, Translations, and Interpretations;22
6.3;0.3. Babylonian Sexagesimal Numbers;23
6.4;0.4. Counting with Sexagesimal Numbers in Relative Place Value Notation ;26
7;Old Babylonian Arithmetical Hand Tablets;32
7.1;1.1. Old Babylonian Multiplication Exercises;32
7.2;1.2. Old Babylonian Squaring Exercises;37
7.3;1.3. An Old Babylonian Division Exercise;41
7.4;1.4. Old Babylonian Operations with Many-Place Regular Sexagesimal Numbers;42
7.5;1.5. Old Babylonian Squares and Squares of Squares of Many-Place Sexagesimal Numbers ;56
8;Old Babylonian Arithmetical Table Texts;64
8.1;2.1. Old Babylonian Tables of Squares ;64
8.2;2.2. Old Babylonian Tables of Square Sides;68
8.3;2.3. Old Babylonian Tables of Cube Sides;71
8.4;2.4. Old Babylonian Tables of Quasi-Cube Sides ;75
8.5;2.5. The Old Babylonian Standard Table of Reciprocals;86
8.6;2.6. Old Babylonian Multiplication Tables ;90
8.7;2.7. Old and Late Babylonian Sexagesimal Representations of Decimal Numbers ;116
9;Old Babylonian Metrological Table Texts;119
9.1;3.1. Old Babylonian Capacity Measures. System C;119
9.2;3.2. Old Babylonian Weight Measures. System M;127
9.3;3.3. Old Babylonian Area Measures. System A;134
9.4;3.4. Old Babylonian Length Measures. Systems Ln and Lc;136
9.5;3.5. Old Babylonian Combined Metrological Tables;139
10;Mesopotamian Weight Stones;145
10.1;4.1. MS 4576. A Kassite Reused Talent Weight with an Inscription in Sumerian;145
10.2;4.2. MS 2481. A Barrel-Shaped 1 Mina Weight with an Inscription in 3 Lines;148
10.3;4.3. MS 2837. An Ellipsoid-Shaped 3 Shekels Weight with a Brief Inscription;148
10.4;4.4. MS 2836. A Small Duck Weight in Agate with the Inscription ‘1/3 Shekel’;148
10.5;4.5. MS 5088. 55 Assorted Weight Stones Found Together in a Damaged Bronze Pot;149
10.6;4.6. YBC 4652. Weight Stones in an Old Babylonian Mathematical Theme Text;151
10.7;4.7. YBC 4669 § 1. Measuring Vessels in an OB Mathematical Theme Text;152
11;Neo-Sumerian Field Plan Texts (Ur III);155
11.1;5.1. MS 1984. A Field Plan Text from Umma with a Summary on the Reverse;155
11.2;5.2. MS 1850. A Field Plan Text without a Summary on the Reverse;158
11.3;5.3. Four Ur III Field Plan Texts, Published in 1915, 1898, 1922, and 1962;160
12;An Old Sumerian Metro-Mathematical Table Text ( Early Dynastic IIIa);165
12.1;6.1. Three Previously Published Metro-Mathematical School Texts from Shuruppak;165
12.2;6.2. MS 3047. An Old Sumerian Metro-Mathematical Table Text;168
13;Old Babylonian Hand Tablets with Practical Mathematics;172
13.1;7.1. MS 2317. Division of a Funny Number by a Non-Regular Factor ;172
13.2;7.2. Combined Market Rate Exercises ;174
13.3;7.3. Old Babylonian Brick Types and Brick Constants;186
13.4;7.4. Inheritance Problems with the Shares Forming a Geometric Progression ;196
14;Old Babylonian Hand Tablets with Geometric Exercises;205
14.1;8.1. Triangles and Trapezoids ;205
14.2;8.2. Figures Within Figures;218
14.3;8.3. Labyrinths, Mazes, and Decorative Patterns ;235
15;The Beginning and the End of the Sumerian King List;246
15.1;9.1. The Sumerian King List;246
15.2;9.2. MS 1686. A New Version of the Ur-Isin King List;248
15.3;9.3. MS 2855. A New Version of the Antediluvian Part of the Sumerian King List;251
15.4;9.4. The Numbers in the Antediluvian King List;257
15.5;9.5. Mesopotamian Year Names;257
16;Three Old Babylonian Mathematical Problem Texts from Uruk;259
16.1;10.1. MS 3971. A Double-Column Mathematical Recombination Text;259
16.2;10.2. MS 3052. A Single-Column Mathematical Recombination Text;268
16.3;10.3. MS 2792. Two Exercises Dealing with a Divided Ramp ;292
17;Three Problem Texts Not Belonging to Any Known Group of Texts;309
17.1;11.1. MS 3049. A Fragment of a Mathematical Recombination Text ;309
17.2;11.2. MS 5112. A Text with Equations for Squares and Rectangles;322
17.3;11.3. MS 3876. Three Problems for 20 Equilateral Triangles and a ‘Horn-Figure’ ;356
17.4;11.4. On the Dating of the Texts in Chapter 11;366
18;Subtractive Notations for Numbers in Mathematical Cuneiform Texts;368
18.1;A1.1. Hilprecht’s List of Signs for ‘19’ in Multiplication Tables from Nippur;368
18.2;A1.2. Ist. T 7375. An Ur III Table of Reciprocals with Subtractive Number Notations;369
18.3;A1.3. A 681. A Table Text from ED IIIb Adab with Subtractive Number Notations;370
19;The Old Babylonian Combined Multiplication Table;374
20;An Old Babylonian Combined Arithmetical Algorithm;379
20.1;A3.1. CBS 10201. Hilprecht’s Misunderstood Algorithm Text from Nippur;379
20.2;A3.2. UM 29.13.21. A Fragment of a Multiple Algorithm Text from Nippur;380
20.3;A3.3. CBS 1215. An Algorithm Text with Explicit Computations;381
21;Cuneiform Systems of Notations for Numbers and Measures;384
21.1;A4.1. Proto-Literate/Traditional Sexagesimal Counting Numbers;384
21.2;A4.2. Proto-Literate Bisexagesimal Counting Numbers;386
21.3;A4.3. Proto-Elamite Decimal Counting Numbers;386
21.4;A4.4. Proto-Literate and Traditional Capacity Numbers;387
21.5;A4.5. Proto-Cuneiform and Traditional Weight Numbers;388
21.6;A4.6. Proto-Literate/Traditional Area Numbers;388
21.7;A4.7. Old Akkadian and Neo-Sumerian/Old Babylonian Length Numbers;389
21.8;A4.8. Proto-Cuneiform Time Numbers;390
21.9;A4.9. An Integrated Family of Numbers and Measures;390
21.10;A4.10. Pre-Literate Number Tokens;391
22;Old Babylonian Complete Metrological Tables;396
22.1;A5.1. The Complete Metrological Table for System C(NS/OB);396
22.2;A5.2. The Complete Metrological Table for System M(NS/OB);398
22.3;A5.3. The Complete Metrological Table for System A(NS/OB);400
22.4;A5.4. The Complete Metrological Tables for Systems Ln and Lc(NS/ OB);402
22.5;A5.5. Old Babylonian (and Other) Combined Metrological Lists;406
22.6;A5.6. Old Babylonian Combined Metrological Tables;409
22.7;A5.7. On Prisms, Cylinders, and a Family of Subscripts;409
23;Metro-Mathematical Cuneiform Texts from the Third Millennium BC;412
23.1;A6.1. Two Old Akkadian Applications of the Field Expansion Procedure;412
23.2;A6.2. Old Akkadian Square-Side-and-Area Exercises;414
23.3;A6.3. Old Akkadian Metric Division Exercises;418
23.4;A6.4. IM 58045. An Old Akkadian Trapezoid Partition Problem;420
23.5;A6.5. TM.75.G.1392 (Ebla). A Division Algorithm in Decimal Numbers;421
23.6;A6.6. TM.75.G.2346 (Ebla). Another Decimal Division Algorithm;423
23.7;A6.7. TSS 50, 671 (Shuruppak). Sexagesimal Metric Division Exercises (ED IIIa);425
23.8;A6.8. Examples of Complicated Designs;427
24;A Combined Metro-Mathematical Table Text with Areas of Large and Small Squares ( ED IIIb);430
24.1;A7.1. CUNES 50-08-001. An Early Dynastic Metro-Mathematical Table Text;430
24.2;A7.2. A Parallel Text from Adab (ED IIIb);436
24.3;A7.3. The Historical Importance of the Combined Table Text CUNES 50-08-001;436
24.4;A7.4. CUNES 47-12-176. An Old Akkadian Lexical Text with Fractions of the Mina2;437
24.5;A7.5. RA 35, Texts 1-2 and IM 96183. OB Table Texts Related to CUNES 50-08-001;439
25;Plimpton 322, a Table of Parameters for igi– igi. bi Problems;444
25.1;A8.1. Plimpton 322. A Description of the Preserved Part of the Table Text;445
25.2;A8.2. Related Texts: Texts with igi–igi.bi Problems;447
25.3;A8.3. A Suggested Reconstruction of the Lost Columns on Plimpton 322;451
25.4;A8.4. The OB Rectangle Parameter Equations. Restrictions on the Parameters;452
25.5;A8.5. The Purpose of the Tables on Plimpton 322;458
25.6;A8.6. The Diagonal Rule in the Corpus of Mathematical Cuneiform Texts;460
26;Many-Place Squares of Squares in Late Babylonian Mathematical Texts;463
26.1;A9.1. Squares of Squares of Many- Place Regular Sexagesimal Numbers;464
26.2;A9.2. An Explicit Late Babylonian Multiplication Algorithm;466
27;Color Photos of 70 Selected Texts;475
28;Vocabulary for the MS Texts;513
29;Index of Subjects;519
30;Index of Texts;524
31;References;530