A remarkable collection of Babylonian mathematical texts:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin, New York [u.a.]
Springer
2007
|
| Schriftenreihe: | Manuscripts in the Schøyen Collection
Cuneiform texts ; 1 |
| Schlagworte: | |
| Online-Zugang: | http://deposit.dnb.de/cgi-bin/dokserv?id=2798757&prov=M&dok_var=1&dok_ext=htm Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. 521 - 533 |
| Beschreibung: | XX, 533 S. zahlr. Ill., graph. Darst. |
| ISBN: | 9780387345437 |
Internformat
MARC
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| 100 | 1 | |a Friberg, Jöran |d 1934- |e Verfasser |0 (DE-588)1051628709 |4 aut | |
| 245 | 1 | 0 | |a A remarkable collection of Babylonian mathematical texts |c Jöran Friberg |
| 264 | 1 | |a Berlin, New York [u.a.] |b Springer |c 2007 | |
| 300 | |a XX, 533 S. |b zahlr. Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Manuscripts in the Schøyen Collection : Cuneiform texts |v 1 | |
| 490 | 0 | |a Sources and studies in the history of mathematics and physical series | |
| 500 | |a Literaturverz. S. 521 - 533 | ||
| 610 | 2 | 7 | |a Schøyen Collection |0 (DE-588)5222053-9 |2 gnd |9 rswk-swf |
| 648 | 7 | |a Geschichte 2600-500 v. Ch. |2 gnd |9 rswk-swf | |
| 650 | 0 | 7 | |a Mathematik |0 (DE-588)4037944-9 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Keilschrifttext |0 (DE-588)4130946-7 |2 gnd |9 rswk-swf |
| 651 | 7 | |a Babylonien |0 (DE-588)4004102-5 |2 gnd |9 rswk-swf | |
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Datensatz im Suchindex
| _version_ | 1804137048046567424 |
|---|---|
| adam_text | Table
of
Contents
Acknowledgements
.....................................................................
v
Introduction
.........................................................................
vii
Statement of Provenance of Near Eastern Pictographic and Cuneiform Tablets
in the Sch0yen Collection
...............................................................xi
Abbreviations
........................................................................xiii
0.
How to Get a Better Understanding of Mathematical Cuneiform Texts
....................... 1
0.1.
On Avoiding Anachronisms in Translations of Mathematical Terms
...........................................1
0.2.
Conform Transliterations, Translations, and Interpretations
..................................................2
0.3.
Babylonian Sexagesimal Numbers
......................................................................3
0.3
a. Sexagesimal Numbers
............................................................................3
0.3
b. Sexagesimal Numbers in Relative Place Value Notation
......... ........................................5
0.4.
Counting with Sexagesimal Numbers in Relative Place Value Notation
.........................................6
0.4
a. Addition of Sexagesimal Numbers
..................................................................6
0.4
b. Subtraction of Sexagesimal Numbers
................................................................7
0.4
с
Multiplication of Sexagesimal Numbers
..............................................................7
0.4
d. Division of Sexagesimal Numbers
..................................................................8
0.4
e. Computing Square Sides (Square Roots) of Sexagesimal Numbers
.........................................9
0.4
f. Number Signs for Sexagesimal Numbers With and Without Place Value Notation
............................10
1.
Old Babylonian Arithmetical Hand Tablets
............................................ 13
1.1.
Old Babylonian Multiplication Exercises
................................................................13
1.1
a. MS
2728
and
2729.
Two Linked Triples of Consecutive Multiplication Exercises
............................13
1.1
b. MS
3944.
Another Triple of Consecutive Multiplication Exercises
........................................15
1.1
c.MS
3955.
Four Multiplication Exercises with Funny Numbers
...........................................15
1.1
d. The Proto-Literate Field Expansion Procedure
........................................................17
1.2.
Old Babylonian Squaring Exercises
....................................................................18
1.3.
An Old Babylonian Division Exercise
..................................................................22
1.4.
Old Babylonian Operations with Many-Place
Regulai·
Sexagesimal Numbers
...................................23
1.4 a. Factorization by Use of the Trailing Part Algorithm
....................................................24
1.4
b. Reciprocals of Many-Place Regular Sexagesimal Numbers
..............................................27
1.5.
Old Babylonian Squares and Squares of Squares of Many-Place Sexagesimal Numbers
...........................37
1.5
a. Squares of Many-Place Regular or Semiregular Sexagesimal Numbers
.....................................37
1.5
b. Non-Square Semiregular Sexagesimal Numbers
......................................................41
1.5
с
Many-Place Squares of Squares of Regular or Semiregular Numbers
......................................42
2.
Old Babylonian Arithmetical Table Texts
..............................................45
2.1.
Old Babylonian Tables of Squares
.....................................................................45
2.1
a. Standard Tables of Squares
.......................................................................45
2.1
b. Special Tables of Squares
........................................................................47
2.2.
Old Babylonian Tables of Square Sides
.................................................................49
2.3.
Old Babylonian Tables of Cube Sides
..................................................................52
2.4.
Old Babylonian Tables of Quasi-Cube Sides
.............................................................56
xv
xvi
Table
of
Contents
2.4
a.
MS
3899.
A Table
of
η
■
η
·
(и
+ 1)
Sides
............................................................56
VAT
8492 § 3.
Another Table of
η
·
η
■
(η
+ 1)
Sides, for
η
from
[1]
to
[1 00]..............................57
2.4
b. For What Could a Table of
η
■
η
■
(η
+ 1)
Sides Possibly be Used?
........................................58
2.4
с
VAT
8521.
A Problem Text with References to a Table of
η
■
η
■
(η
- 1)
Sides
..............................61
2.4
d.
MS
3048.
A Table of
η
■
(η +
1) ·
(η
+ 2)
Sides
.......................................................62
2.4
e.
For What Could a Table of
η
■
(η +
1) ·
(и
+ 2)
Sides Possibly be Used?
....................................63
2.4
f. A Note on Excerpts from Old Babylonian Arithmetical Table Texts
.......................................66
2.5.
The Old Babylonian Standard Table of Reciprocals
.........................................................67
2.6.
Old Babylonian Multiplication Tables
...................................................................71
2.6
a. Single Multiplication Tables
......................................................................71
2.6
b. Double Multiplication Tables
.....................................................................77
2.6
с
Multiple Multiplication Tables
....................................................................80
2.6
d. The Old Babylonian Combined Multiplication Table
..................................................82
2.6
e
.
Tables of Reciprocals and Multiplication Tables in the Sch0yen Collection
.................................87
Nine Double Multiplication Tables
...............................................................88
Three Multiple Multiplication Tables
.............................................................88
2.6
f
.
An Explanation of the Head Numbers in the Combined Multiplication Table
................................91
2.7.
Old and Late Babylonian Sexagesimal Representations of Decimal Numbers
....................................97
2.7
a. MS
3970.
An Old Babylonian Unfinished Conversion Table
............................................97
2.7
b. BM
36841.
A Late Babylonian Parallel Text
.........................................................98
3.
Old Babylonian Metrological Table Texts
..............................................101
3.1.
Old Babylonian Capacity Measures. System
С
...........................................................101
3.2.
Old Babylonian Weight Measures. System
M
............................................................109
3.3.
Old Babylonian Area Measures. System
Л
..............................................................116
3.4.
Old Babylonian Length Measures. Systems Ln and Lc
.....................................................118
3.5.
Old Babylonian Combined Metrological Tables
..........................................................121
4.
Mesopotamian Weight Stones
........................................................127
4.1.
MS
4576.
A Kassite Reused Talent Weight with an Inscription in
Sumerian
.................................... 127
4.2.
MS
2481.
A Barrel-Shaped
1
Mina
Weight with an Inscription in
3
Lines
.......................................130
4.3.
MS
2837.
An Ellipsoid-Shaped
3
Shekels Weight with a Brief Inscription
......................................130
4.4.
MS
2836.
A Small Duck Weight in Agate with the Inscription
1/3
Shekel
.................................... 130
4.5.
MS
5088.55
Assorted Weight Stones Found Together in a Damaged Bronze Pot
................................ 131
4.6.
YBC
4652.
Weight Stones in an Old Babylonian Mathematical Theme Text
................................... 133
4.7.
YBC
4669 § 1.
Measuring Vessels in an Old Babylonian Mathematical Theme Text
............................ 134
5.
Neo-Sumerian Field Plans (Ur III)
....................................................137
5.1.
MS
1984.
A Field Plan Text from Umma with a Summary on the Reverse
.....................................137
5.2.
MS
1850.
A Field Plan Text without a Summary on the Reverse
............................................140
5.3.
Four
Urlii
Field Plan Texts, Published in
1915,1898,1922,
and
1962.......................................142
6.
An Old
Sumerian
Metro-Mathematical Table Text (Early Dynastic Ilia)
...................147
6.1.
Three Previously Published Metro-Mathematical School Texts from Shuruppak
................................147
6.2.
MS
3047.
An Old
Sumerian
Metro-Mathematical Table Text
..............................................150
6.2
a. MS
3047,
obv. The Sum of the Areas of a Series of Similar Large Rectangles
..............................151
6.2
b. MS
3047,
rev. A Geometric Progression of Areas(?)
..................................................152
7.
Old Babylonian Hand Tablets with Practical Mathematics
.............................. 155
7.1.
MS
2317.
Division of a Funny Number by a Non-Regular Factor
............................................155
7.1a. Interpretation of the Three Numbers in the Text
.....................................................155
7.1
b. A
Proposed Solution Algorithm for the Division Problem
..............................................156
7.1
cUETő,
121 § 2.
A Parallel Text from Early Old Babylonian Ur
.........................................157
7.2.
Combined Market Rate Exercises
.....................................................................157
7.2
a. Combined Market Rate Exercises with Regular Sexagesimal Market Rates
................................157
7.2
b. YBC
7234,7235,7354,7355,7358,
and
11127,
Six Parallel Texts in MCT
................................161
7.2
с
Combined Market Rate Exercises with One Non-Regular Factor in the Data
...............................162
7.2
d. N
3914,
a Parallel Text with
10
Given Numbers
.....................................................163
Table
of Contents
xvii
7.2
e.
Combined Market Rate Exercises with Several Non-Regular Factors in the Data
....................................................... 165
7.2
f. VAT
7530.
A Theme Text with Combined Market Rate Problems
............................................................................... 166
7.3.
Old Babylonian Brick Types and Brick Constants
................................................................................................................169
7.3
a. MS
2221,
obv. Walking Numbers, Loading Numbers, and Carrying Number
for Three Kinds of Bricks, and for Mud
....................................................................................................................... 169
7.3
b. On Carrying Numbers in Old Babylonian Metro-Mathematical Problem Texts
.......................................................... 174
7.3
с
MS
2221,
rev. A Combined Carrying Number Problem for Three Types of Bricks
..................................................... 175
7.3
d. Other Texts with Combined Work Norm Problems Involving Bricks and Mud
........................................................... 176
7.3
e. An Early Text with a Brick Problem and Sexagesimal Numbers in Place Value Notation
.......................................... 178
7.4.
Inheritance Problems with the Shares Forming a Geometric Progression
............................................................................179
7.4
a. MS
2830,
obv. A Theme Text with Five Inheritance Problems
.................................................................................... 179
7.4
b. MS
1844.
A Lentil with the Solution Algorithm for an Inheritance Problem
............................................................... 182
7.4
с
The Terms of a Geometric Progression
......................................................................................................................... 182
7.4
d. The Sum of the Geometric Progression
......................................................................................................................... 185
7.4
e. The Intended Application of the Algorithm
.................................................................................................................. 185
7.4
f. UET
5,121.
A Parallel Text from Early Old Babylonian Ur
......................................................................................... 187
8.
Old Babylonian Hand Tablets with Geometric Exercises
................................189
8.1.
Triangles and
Trapezoide
........................................................................................................................................................189
8.1
a. MS
3042.
The Area of a Triangle
.................................................................................................................................. 189
8.1
b. MS
2107.
The Area of
a Trapezoid.
An Almost Round Area Number
......................................................................... 189
8.1
с
Examples of Proto-Literate Field-Sides and Field-Area Texts
...................................................................................... 194
8.1
d. MS
3908.
A Trapezoid
Divided into Three Stripes
....................................................................................................... 195
8.1
e. Ash.
1922.168, IM 43996,
Two More Texts with Striped Trapezoids or Triangles
..................................................... 197
8.1
f. MS
1938/2.
An Arithmetical Progression of Stripes in
a Trapezoid
.............................................................................200
8.1
g.
MS
3853/2.
A Doodle on the Reverse of a Single Multiplication Table
.......................................................................201
8.2.
Figures Within Figures
..........................................................................................................................................................202
8.2
a. MS
2192.
A Triangular Band between two Concentric Equilateral Triangles
.............................................................. 202
8.2
b. An Assignment: To Compute the Area between the Two Equilateral Triangles
..........................................................203
8.2
с
MS
3051.
An Equilateral Triangle Inscribed in a Circle
...............................................................................................207
8.2
d. MS
3050.
A Square with Diagonals, Inscribed in a Circle
............................................................................................ 210
8.2
e. MS
2985
A Circle in the Middle of a Square
................................................................................................................ 212
8.2
f. MS
1938/2.
A Circle in the Middle of a 6-Front
............................................................................................................ 216
8.3.
Labyrinths, Mazes, and Decorative Patterns
.........................................................................................................................219
8.3
a. MS
4515.
A Babylonian Square Labyrinth
................................................................................................................... 219
8.3
b. The Greek Labyrinth
..................................................................................................................................................... 221
8.3
с
MS
3194.
A Babylonian Rectangular Labyrinth
........................................................................................................... 224
8.3
d. MS
4516.
A Geometric Theme text with
8
Assorted Mazes
......................................................................................... 227
8.3
e. MS
3940.
A Pattern Superimposed on a Dense Grid of Guide Lines
........................................................................... 229
8.3
f. MS
3031.
The Ground Plan of a Palace
......................................................................................................................... 229
9.
The Beginning and the End of the
Sumerian
King List
..................................231
9.1.
The
Sumerian
King List
.......................................................................................................................................................... 231
9.2.
MS
1686.
A New Version of the Ur-Isin King List
............................................................................................................... 233
9.3.
MS
2855.
A New Version of the Antediluvian Part of the
Sumerian
King List
................................................................... 236
9.4.
The Numbers in the Antediluvian King List
......................................................................................................................... 242
9.5.
Mesopotamian Year Names
...................................................................................................................................................242
10.
Three Old Babylonian Mathematical Problem Texts from
Uruk
.........................245
10.1.
MS
3971.
A Double-Column Mathematical Recombination Text
.......................................................................................245
10.1
a. MS
3971 § 1.
A Broken Reed Problem of a New Type
.............................................................................................. 245
10.1
b. Other Examples of Broken Reed Problems with Arithmetical Progressions
..............................................................247
10.1
с
Other Examples of Broken Reed Problems for Rectangles or Trapezoids
..................................................................250
10.1
d. MS
3971 § 2.
To Find a Rectangle with a Given Diagonal and a Given Area
...........................................................251
10.1
e. A Parallel Text:
IM 67118
(=Db2-146)
......................................................................................................................252
10.1
f.MS
3971 § 3.
Five Examples of igi-igi.bi Problems
....................................................................................................252
10.1
g. MS
3971 § 4.
A Scaling Problem for a Rectangle with its Diagonal
..........................................................................254
10.2.
MS
3052.
A Single-Column Mathematical Recombination Text
........................................................................................254
10.2
a. MS
3052 § 1.
Mud Walls Partitioned into Two or More Separate Layers
..................................................................258
xviii
Table
of Contents
MS
3052 § 1
a. Repairing a Breach in a Wall with Mud from the Top of the Wall
..................................................258
MS
3052 § 1
b. Measuring the Thickness of a Wall by Drilling a Hole through It
...................................................260
MS
3052 § 1
с
Another Example of a Wall with a Hole Drilled through It
.............................................................263
MS
3052 § 1
d. A Wall with a Hole Drilled through it and a Breach Repaired
.........................................................267
Earlier Published Parallel Texts: YBC
4673 § 12, Str. 364,
and VAT
8512.............................................................270
MS
3052 § 1
e. A Badly Preserved Exercise Dealing with a Mud Wall with a Breach
............................................ 274
10.2
b. MS
3052 § 2.
A Diagonal . The Basic igi-igi.bi Problem
.........................................................................................274
10.2
с
MS
3052 § 3.
An Excavation of the igi-igi.bi Type
.................................................................................................275
10.2
d. MS
3052 § 4.
A Square . Another Badly Damaged Exercise
...................................................................................275
10.2
e. MS
3052,
Subscript. A List of the Separate Topics in the Text
..................................................................................278
10.3.
MS
2792.
Two Exercises Dealing with a Divided Ramp
...................................................................................................278
10.3
a. MS
2792 # 1.
A Layer on Top of a Ramp Divided Equally along the Length
...........................................................278
10.3
b. MS
2792 # 2.
A Layer on Top of a Ramp Divided Unequally along the Length
.......................................................285
10.3
с
The Work Norm for Building a Ramp
........................................................................................................................ 290
10.3
d. The Construction of the Data for the Two Problems
..................................................................................................290
A Related Text:
Str. 362 # 6.
A Combined Work Norm for Carrying and Building
.................................................293
11.
Three Problem Texts Not Belonging to Any Known Group of Texts
...................... 295
11.1.
MS
3049.
A Fragment of a Mathematical Recombination Text
..........................................................................................295
11.1
a. MS
3049 § 1
a. Computing the Length of a Chord in a Circle
...................................................................................295
A Couple of Parallel Texts in the Mathematical Recombination Text BM
85194....................................................298
11.1
b. MS
3049,
Subscript. A List of the Separate Topics in the Text
.................................................................................299
11.1
с
MS
3049, § 4
с
A Small Fragment of a Problem for a Brick Mold
........................................................................299
11.1
d. MS
3049, § 5.
The Inner Diagonal of a Rectangular Gate in a Wall
..........................................................................301
Explanation of the Calculations in the Text of
§ 5.....................................................................................................301
The Diagonal Rule for a Rectangular Prism
..............................................................................................................303
BM
96957 +
VAT
649 §§ 5-7.
A Related Theme Text for the Dimensions of a Gate
..............................................304
11.2.
MS
5112.
A Text with Equations for Squares and Rectangles
...........................................................................................308
MS
5112,
obv. Metric Algebra Problems for One or More Squares
..........................................................................309
11.2
a. MS
5112 § 1.
Old Babylonian Metric Algebra: Completing the Square
.................................................................... 309
11.2
b. BM
13901 # 23.
A Related Text, with a Four Ways Extended Square Field
.............................................................311
11.2
с
MS
5112 §2
a. A trivial Problem for Two Squares
....................................................................................................312
11.2
d. MS
5112 § 2
b. A
Standard Quadratic-Linear System of Equations
..........................................................................314
A Parallel Text: BM
13901 # 8..................................................................................................................................315
11.2 e.
MS
5112 §2
с
A Quadratic-Rectangular System of Equations
.................................................................................316
11.2
f.MS
5112 § 3.
Three Squares With their Sides in an Arithmetical Progression
..........................................................318
11.2
g. MS
5112 §4.
A Quadratic-Linear System of Equations for Two Squares
.................................................................319
11.2
h. MS
5112 § 5.
Finding the Number of Terms in an Arithmetical Progression
............................................................321
11.2
i. MS
5112 § 6.
A Quadratic Equation with Incorrect Data
...........................................................................................323
MS
5112,
rev.: Metric Algebra Problems for the Length and Front of a Rectangle
..................................................326
11.2
j. MS
5112 § 7
а
-b.
Two Badly Preserved Rectangular-Linear Systems
.......................................................................326
11.2
k. MS
5112 § 8.
A Rectangle where the Area is Equal to the Length Plus the Front
.....................................................327
A Parallel Text:
АО
8862 § 1
d..................................................................................................................................
328
Another Related Text:
АО
6770 # 1..........................................................................................................................328
Other Texts Mentioning the Sum of the Length, the Front, and the Area
..................................................................329
11.21.
MS
5112 § 9.
Changing the Form of a Rectangle while Keeping the Area
................................................................332
11.2
m. MS
5112 § 10.
A System of Linear Equations for the Length and the Front
............................................................333
Other Old Babylonian Mathematical Texts with Systems of Linear Equations
........................................................334
11.2
n. MS
5112 § 11.
One of the Basic Rectangular-Linear Systems of Equations
.............................................................336
YBC
6967,
a Related Text With an igi-igi.bi Equation
..............................................................................................337
11.2
o.MS
5112 § 12.
A Rectangular-Linear System of Equations
.......................................................................................338
11.2
p. MS
5112 § 13.
Another Rectangular-Linear System of Equations
............................................................................340
Table
of
Contents
xix
11.3.
MS
3876.
Three Problems for
20
Equilateral Triangles and a Horn-Figure
.....................................................................342
11.3
a. Computation of the Weight of a Horn-Figure
...........................................................................................................342
11.3
b. Constants for Copper and Silver in Mathematical Cuneiform Texts
..........................................................................347
11.3
с
A Horn-Figure Consisting of
20
Equilateral Triangles
.............................................................................................349
11.4.
On the Dating of the Texts in Chapter
11............................................................................................................................352
Appendix
1.
Subtractive Notations for Numbers in Mathematical Cuneiform Texts
.............355
Al
.1.
Hilprecht s List of Signs for
19
in Multiplication Tables from Nippur
.............................................................................355
Al
.2. Ist.
Τ
7375.
An
Ur
III Table of Reciprocals with Subtractive Number Notations
................................................................356
Al
.3.
A
681.
A Table Text from ED
ШЬ
Adab with Subtractive Number Notations
....................................................................357
Appendix
2.
The Old Babylonian Combined Multiplication Table
...........................361
Appendix
3.
An Old Babylonian Combined Arithmetical Algorithm
..........................367
A3.1.
CBS
10201.
Hilprecht s Misunderstood Algorithm Text from Nippur
................................................................................367
A3.2. UM 29.13.21.
A Fragment of a Multiple Algorithm Text from Nippur
...............................................................................368
A3.3. CBS
1215.
An Algorithm Text with Explicit Computations
................................................................................................369
Appendix
4.
Cuneiform Systems of Notations for Numbers and Measures
.....................373
A4.1. Proto-Literate/Traditional Sexagesimal Counting Numbers
................................................................................................373
A4.2.
Proto-literate Bisexagesimal Counting Numbers
..................................................................................................................375
A4.3.Proto-Elamite
Decimal Counting Numbers
..........................................................................................................................375
A4.4.
Proto-Literate and Traditional Capacity Numbers
................................................................................................................376
A4.5.
Proto-Cuneiform and Traditional Weight Numbers
............................................................................................................377
A4.6.
Proto-Literate/Traditional Area Numbers
............................................................................................................................377
A4.7.
Old Akkadian and Neo-Sumerian/Old Babylonian Length Numbers
.................................................................................378
A4.8.
Proto-Cuneiform Time Numbers
..........................................................................................................................................379
A4.9.
An Integrated Family of Numbers and Measures
.................................................................................................................379
A4.10. Pre-Literate Number Tokens
..............................................................................................................................................380
Appendix
5.
Old Babylonian Complete Metrological Tables
................................385
A5.1
.
The Complete Metrological Table for System CCNS/OB)
...................................................................................................385
A5.2. The Complete Metrological Table for System
M(NS/OB)...................................................................................................387
A5.3. The Complete Metrological table for System A(NS/OB)
.....................................................................................................389
A5.4. The Complete Metrological tables for Systems
L«(NS/OB)
and LcCNS/OB)
.....................................................................391
A5.5. Old Babylonian (and Other) Combined Metrological Lists
.................................................................................................395
A5.6. Old Babylonian Combined Metrological Tables
..................................................................................................................398
. On Prisms, Cylinders, and a Family of Subscripts
...............................................................................................................398
Appendix
6.
Metro-Mathematical Cuneiform Texts from the Third Millennium
ВС
............401
A6.1
.
Two Old Akkadian Applications of the Field Expansion Procedure
...................................................................................401
A6.2. Old Akkadian Square-Side-and-Area Exercises
...................................................................................................................403
A6.3. Old Akkadian Metric Division Exercises
.............................................................................................................................407
A6.4.
IM 58045.
An Old Akkadian
Trapezoid
Partition Problem
..................................................................................................409
A6.5. TM.75.G.1392 (Ebla). A Division Algorithm in Decimal Numbers
....................................................................................410
A6.6. TM.75.G.2346 (Ebla). Another Decimal Division Algorithm
..............................................................................................412
A6.7. TSS
50,671
(Shuruppak). Sexagesimal Metric Division Exercises (ED
Ша)
......................................................................414
A6.8. Examples of Complicated Designs
.......................................................................................................................................416
xx
Table
of
Contents
Appendix
7.
A
Combined Metro-Mathematical Table Text
with Areas of Large and Small Squares (ED Illb)
..............................419
A7.1
.
CUNES
50-08-001.
An Early Dynastic Metro-Mathematical Table Text
............................................................................419
A7.2. A Parallel Text from Adab (ED
ШЬ)
...................................................................................................................................425
A7.3. The Historical Importance of the Combined Table Text
CUNES
50-08-001......................................................................425
A7.4.
CUNES
47-12-176.
An Old Akkadian Lexical Text with Fractions of the
Mina
................................................................426
A7.5.
RA
35,
Texts
1-2
and
IM 96183.
Old Babylonian Table Texts Related to
CUNES
50-08-001...........................................428
Appendix
8.
Plimpton
322,
a Table of Parameters for igi-igi.bi Problems
.................... 433
Ae.l. Plimpton
322.
A Description of the Preserved Part of the Table Text
........................................434
A8.2. Related Texts: Texts with igi-igi.bi Problems
..........................................................436
A8.3. A Suggested Reconstruction of the Lost Columns on Plimpton
322.........................................440
A8.4. The Old Babylonian Rectangle Parameter Equations. Restrictions on the Parameters
...........................441
A8.5. The Purpose of the Tables on Plimpton
322............................................................447
A8.6. The Diagonal Rule in the Corpus of Mathematical Cuneiform Texts
........................................449
Appendix
9.
Many-Place Squares of Squares in Late Babylonian Mathematical Texts
..........453
A9.1. Squares of Squares of Many-Place Regular Sexagesimal Numbers
..........................................454
A9.2. An Explicit Late Babylonian Multiplication Algorithm
...................................................456
Appendix
10.
Color Photos of
70
Selected Texts
..........................................465
Vocabulary for the MS Texts
.......................................................... 503
Index of Subjects
.................................................................... 509
Index of Texts
....................................................................... 515
References
.......................................................................... 521
Remark. The successive chapters of this book have been ordered into what initially seemed to be a logical succession of
increasingly sophisticated topics. After the work with the book had been finished, much too late to be considered,
С
Proust s
dissertation TMN
(2004)
became available, with its thorough statistical analysis of nearly the whole corpus of known mathe¬
matical cuneiform texts from Nippur. According to Proust, at the elementary level of the education in the Old Babylonian scribe
schools at Nippur, metrological and mathematical table texts were studied in the following order: a) metrological lists for
systems C, M. A, L, b) metrological tables for systems
С, М.
A, Ln, Lc, c) tables of reciprocals, multiplication tables, tables of
squares, d) tables of square sides and cube sides. All other mathematical cuneiform texts are relegated by Proust to the category
of exercises at an advanced level.
It is not clear to what extent the results of Proust s analysis are applicable to the mathematical cuneiform texts in the Sch0yen
Collection. The great majority of the mathematical texts used by Proust for her statistical analysis are (fragments of) clay tablets
of the so called type Ila/IIb
,
and very few belong to what she calls the advanced level
.
In contrast to this
,
of the Old
В
abylonian
mathematical tablets in the Sch0yen Collection very few, if any, are of type
Па/ПЬ,
and all the texts discussed in Chapters l(?),
7,8,10,
and
11
of this book belong to what Proust calls the advanced level.
|
| adam_txt |
Table
of
Contents
Acknowledgements
.
v
Introduction
.
vii
Statement of Provenance of Near Eastern Pictographic and Cuneiform Tablets
in the Sch0yen Collection
.xi
Abbreviations
.xiii
0.
How to Get a Better Understanding of Mathematical Cuneiform Texts
. 1
0.1.
On Avoiding Anachronisms in Translations of Mathematical Terms
.1
0.2.
Conform Transliterations, Translations, and Interpretations
.2
0.3.
Babylonian Sexagesimal Numbers
.3
0.3
a. Sexagesimal Numbers
.3
0.3
b. Sexagesimal Numbers in Relative Place Value Notation
.".5
0.4.
Counting with Sexagesimal Numbers in Relative Place Value Notation
.6
0.4
a. Addition of Sexagesimal Numbers
.6
0.4
b. Subtraction of Sexagesimal Numbers
.7
0.4
с
Multiplication of Sexagesimal Numbers
.7
0.4
d. Division of Sexagesimal Numbers
.8
0.4
e. Computing Square Sides (Square Roots) of Sexagesimal Numbers
.9
0.4
f. Number Signs for Sexagesimal Numbers With and Without Place Value Notation
.10
1.
Old Babylonian Arithmetical Hand Tablets
. 13
1.1.
Old Babylonian Multiplication Exercises
.13
1.1
a. MS
2728
and
2729.
Two Linked Triples of Consecutive Multiplication Exercises
.13
1.1
b. MS
3944.
Another Triple of Consecutive Multiplication Exercises
.15
1.1
c.MS
3955.
Four Multiplication Exercises with Funny Numbers
.15
1.1
d. The Proto-Literate Field Expansion Procedure
.17
1.2.
Old Babylonian Squaring Exercises
.18
1.3.
An Old Babylonian Division Exercise
.22
1.4.
Old Babylonian Operations with Many-Place
Regulai·
Sexagesimal Numbers
.23
1.4 a. Factorization by Use of the Trailing Part Algorithm
.24
1.4
b. Reciprocals of Many-Place Regular Sexagesimal Numbers
.27
1.5.
Old Babylonian Squares and Squares of Squares of Many-Place Sexagesimal Numbers
.37
1.5
a. Squares of Many-Place Regular or Semiregular Sexagesimal Numbers
.37
1.5
b. Non-Square Semiregular Sexagesimal Numbers
.41
1.5
с
Many-Place Squares of Squares of Regular or Semiregular Numbers
.42
2.
Old Babylonian Arithmetical Table Texts
.45
2.1.
Old Babylonian Tables of Squares
.45
2.1
a. Standard Tables of Squares
.45
2.1
b. Special Tables of Squares
.47
2.2.
Old Babylonian Tables of Square Sides
.49
2.3.
Old Babylonian Tables of Cube Sides
.52
2.4.
Old Babylonian Tables of Quasi-Cube Sides
.56
xv
xvi
Table
of
Contents
2.4
a.
MS
3899.
A Table
of
η
■
η
·
(и
+ 1)
Sides
.56
VAT
8492 § 3.
Another Table of
η
·
η
■
(η
+ 1)
Sides, for
η
from
[1]
to
[1 00].57
2.4
b. For What Could a Table of
η
■
η
■
(η
+ 1)
Sides Possibly be Used?
.58
2.4
с
VAT
8521.
A Problem Text with References to a Table of
η
■
η
■
(η
- 1)
Sides
.61
2.4
d.
MS
3048.
A Table of
η
■
(η +
1) ·
(η
+ 2)
Sides
.62
2.4
e.
For What Could a Table of
η
■
(η +
1) ·
(и
+ 2)
Sides Possibly be Used?
.63
2.4
f. A Note on Excerpts from Old Babylonian Arithmetical Table Texts
.66
2.5.
The Old Babylonian Standard Table of Reciprocals
.67
2.6.
Old Babylonian Multiplication Tables
.71
2.6
a. Single Multiplication Tables
.71
2.6
b. Double Multiplication Tables
.77
2.6
с
Multiple Multiplication Tables
.80
2.6
d. The Old Babylonian Combined Multiplication Table
.82
2.6
e
.
Tables of Reciprocals and Multiplication Tables in the Sch0yen Collection
.87
Nine Double Multiplication Tables
.88
Three Multiple Multiplication Tables
.88
2.6
f
.
An Explanation of the Head Numbers in the Combined Multiplication Table
.91
2.7.
Old and Late Babylonian Sexagesimal Representations of Decimal Numbers
.97
2.7
a. MS
3970.
An Old Babylonian Unfinished Conversion Table
.97
2.7
b. BM
36841.
A Late Babylonian Parallel Text
.98
3.
Old Babylonian Metrological Table Texts
.101
3.1.
Old Babylonian Capacity Measures. System
С
.101
3.2.
Old Babylonian Weight Measures. System
M
.109
3.3.
Old Babylonian Area Measures. System
Л
.116
3.4.
Old Babylonian Length Measures. Systems Ln and Lc
.118
3.5.
Old Babylonian Combined Metrological Tables
.121
4.
Mesopotamian Weight Stones
.127
4.1.
MS
4576.
A Kassite Reused Talent Weight with an Inscription in
Sumerian
. 127
4.2.
MS
2481.
A Barrel-Shaped
1
Mina
Weight with an Inscription in
3
Lines
.130
4.3.
MS
2837.
An Ellipsoid-Shaped
3
Shekels Weight with a Brief Inscription
.130
4.4.
MS
2836.
A Small Duck Weight in Agate with the Inscription
'1/3
Shekel'
. 130
4.5.
MS
5088.55
Assorted Weight Stones Found Together in a Damaged Bronze Pot
. 131
4.6.
YBC
4652.
Weight Stones in an Old Babylonian Mathematical Theme Text
. 133
4.7.
YBC
4669 § 1.
Measuring Vessels in an Old Babylonian Mathematical Theme Text
. 134
5.
Neo-Sumerian Field Plans (Ur III)
.137
5.1.
MS
1984.
A Field Plan Text from Umma with a Summary on the Reverse
.137
5.2.
MS
1850.
A Field Plan Text without a Summary on the Reverse
.140
5.3.
Four
Urlii
Field Plan Texts, Published in
1915,1898,1922,
and
1962.142
6.
An Old
Sumerian
Metro-Mathematical Table Text (Early Dynastic Ilia)
.147
6.1.
Three Previously Published Metro-Mathematical School Texts from Shuruppak
.147
6.2.
MS
3047.
An Old
Sumerian
Metro-Mathematical Table Text
.150
6.2
a. MS
3047,
obv. The Sum of the Areas of a Series of Similar Large Rectangles
.151
6.2
b. MS
3047,
rev. A Geometric Progression of Areas(?)
.152
7.
Old Babylonian Hand Tablets with Practical Mathematics
. 155
7.1.
MS
2317.
Division of a Funny Number by a Non-Regular Factor
.155
7.1a. Interpretation of the Three Numbers in the Text
.155
7.1
b. A
Proposed Solution Algorithm for the Division Problem
.156
7.1
cUETő,
121 § 2.
A Parallel Text from Early Old Babylonian Ur
.157
7.2.
Combined Market Rate Exercises
.157
7.2
a. Combined Market Rate Exercises with Regular Sexagesimal Market Rates
.157
7.2
b. YBC
7234,7235,7354,7355,7358,
and
11127,
Six Parallel Texts in MCT
.161
7.2
с
Combined Market Rate Exercises with One Non-Regular Factor in the Data
.162
7.2
d. N
3914,
a Parallel Text with
10
Given Numbers
.163
Table
of Contents
xvii
7.2
e.
Combined Market Rate Exercises with Several Non-Regular Factors in the Data
. 165
7.2
f. VAT
7530.
A Theme Text with Combined Market Rate Problems
. 166
7.3.
Old Babylonian Brick Types and Brick Constants
.169
7.3
a. MS
2221,
obv. Walking Numbers, Loading Numbers, and Carrying Number
for Three Kinds of Bricks, and for Mud
. 169
7.3
b. On Carrying Numbers in Old Babylonian Metro-Mathematical Problem Texts
. 174
7.3
с
MS
2221,
rev. A Combined Carrying Number Problem for Three Types of Bricks
. 175
7.3
d. Other Texts with Combined Work Norm Problems Involving Bricks and Mud
. 176
7.3
e. An Early Text with a Brick Problem and Sexagesimal Numbers in Place Value Notation
. 178
7.4.
Inheritance Problems with the Shares Forming a Geometric Progression
.179
7.4
a. MS
2830,
obv. A Theme Text with Five Inheritance Problems
. 179
7.4
b. MS
1844.
A Lentil with the Solution Algorithm for an Inheritance Problem
. 182
7.4
с
The Terms of a Geometric Progression
. 182
7.4
d. The Sum of the Geometric Progression
. 185
7.4
e. The Intended Application of the Algorithm
. 185
7.4
f. UET
5,121.
A Parallel Text from Early Old Babylonian Ur
. 187
8.
Old Babylonian Hand Tablets with Geometric Exercises
.189
8.1.
Triangles and
Trapezoide
.189
8.1
a. MS
3042.
The Area of a Triangle
. 189
8.1
b. MS
2107.
The Area of
a Trapezoid.
An Almost Round Area Number
. 189
8.1
с
Examples of Proto-Literate Field-Sides and Field-Area Texts
. 194
8.1
d. MS
3908.
A Trapezoid
Divided into Three Stripes
. 195
8.1
e. Ash.
1922.168, IM 43996,
Two More Texts with Striped Trapezoids or Triangles
. 197
8.1
f. MS
1938/2.
An Arithmetical Progression of Stripes in
a Trapezoid
.200
8.1
g.
MS
3853/2.
A Doodle on the Reverse of a Single Multiplication Table
.201
8.2.
Figures Within Figures
.202
8.2
a. MS
2192.
A Triangular Band between two Concentric Equilateral Triangles
. 202
8.2
b. An Assignment: To Compute the Area between the Two Equilateral Triangles
.203
8.2
с
MS
3051.
An Equilateral Triangle Inscribed in a Circle
.207
8.2
d. MS
3050.
A Square with Diagonals, Inscribed in a Circle
. 210
8.2
e. MS
2985
A Circle in the Middle of a Square
. 212
8.2
f. MS
1938/2.
A Circle in the Middle of a 6-Front
. 216
8.3.
Labyrinths, Mazes, and Decorative Patterns
.219
8.3
a. MS
4515.
A Babylonian Square Labyrinth
. 219
8.3
b. The Greek Labyrinth
. 221
8.3
с
MS
3194.
A Babylonian Rectangular Labyrinth
. 224
8.3
d. MS
4516.
A Geometric Theme text with
8
Assorted Mazes
. 227
8.3
e. MS
3940.
A Pattern Superimposed on a Dense Grid of Guide Lines
. 229
8.3
f. MS
3031.
The Ground Plan of a Palace
. 229
9.
The Beginning and the End of the
Sumerian
King List
.231
9.1.
The
Sumerian
King List
. 231
9.2.
MS
1686.
A New Version of the Ur-Isin King List
. 233
9.3.
MS
2855.
A New Version of the Antediluvian Part of the
Sumerian
King List
. 236
9.4.
The Numbers in the Antediluvian King List
. 242
9.5.
Mesopotamian Year Names
.242
10.
Three Old Babylonian Mathematical Problem Texts from
Uruk
.245
10.1.
MS
3971.
A Double-Column Mathematical Recombination Text
.245
10.1
a. MS
3971 § 1.
A Broken Reed Problem of a New Type
. 245
10.1
b. Other Examples of Broken Reed Problems with Arithmetical Progressions
.247
10.1
с
Other Examples of Broken Reed Problems for Rectangles or Trapezoids
.250
10.1
d. MS
3971 § 2.
To Find a Rectangle with a Given Diagonal and a Given Area
.251
10.1
e. A Parallel Text:
IM 67118
(=Db2-146)
.252
10.1
f.MS
3971 § 3.
Five Examples of igi-igi.bi Problems
.252
10.1
g. MS
3971 § 4.
A Scaling Problem for a Rectangle with its Diagonal
.254
10.2.
MS
3052.
A Single-Column Mathematical Recombination Text
.254
10.2
a. MS
3052 § 1.
Mud Walls Partitioned into Two or More Separate Layers
.258
xviii
Table
of Contents
MS
3052 § 1
a. Repairing a Breach in a Wall with Mud from the Top of the Wall
.258
MS
3052 § 1
b. Measuring the Thickness of a Wall by Drilling a Hole through It
.260
MS
3052 § 1
с
Another Example of a Wall with a Hole Drilled through It
.263
MS
3052 § 1
d. A Wall with a Hole Drilled through it and a Breach Repaired
.267
Earlier Published Parallel Texts: YBC
4673 § 12, Str. 364,
and VAT
8512.270
MS
3052 § 1
e. A Badly Preserved Exercise Dealing with a Mud Wall with a Breach
. 274
10.2
b. MS
3052 § 2.
A 'Diagonal'. The Basic igi-igi.bi Problem
.274
10.2
с
MS
3052 § 3.
An 'Excavation' of the igi-igi.bi Type
.275
10.2
d. MS
3052 § 4.
A 'Square'. Another Badly Damaged Exercise
.275
10.2
e. MS
3052,
Subscript. A List of the Separate Topics in the Text
.278
10.3.
MS
2792.
Two Exercises Dealing with a Divided Ramp
.278
10.3
a. MS
2792 # 1.
A Layer on Top of a Ramp Divided Equally along the Length
.278
10.3
b. MS
2792 # 2.
A Layer on Top of a Ramp Divided Unequally along the Length
.285
10.3
с
The Work Norm for Building a Ramp
. 290
10.3
d. The Construction of the Data for the Two Problems
.290
A Related Text:
Str. 362 # 6.
A Combined Work Norm for Carrying and Building
.293
11.
Three Problem Texts Not Belonging to Any Known Group of Texts
. 295
11.1.
MS
3049.
A Fragment of a Mathematical Recombination Text
.295
11.1
a. MS
3049 § 1
a. Computing the Length of a Chord in a Circle
.295
A Couple of Parallel Texts in the Mathematical Recombination Text BM
85194.298
11.1
b. MS
3049,
Subscript. A List of the Separate Topics in the Text
.299
11.1
с
MS
3049, § 4
с
A Small Fragment of a Problem for a 'Brick Mold'
.299
11.1
d. MS
3049, § 5.
The Inner Diagonal of a Rectangular Gate in a Wall
.301
Explanation of the Calculations in the Text of
§ 5.301
The Diagonal Rule for a Rectangular Prism
.303
BM
96957 +
VAT
649 §§ 5-7.
A Related Theme Text for the Dimensions of a Gate
.304
11.2.
MS
5112.
A Text with Equations for Squares and Rectangles
.308
MS
5112,
obv. Metric Algebra Problems for One or More Squares
.309
11.2
a. MS
5112 § 1.
Old Babylonian Metric Algebra: Completing the Square
. 309
11.2
b. BM
13901 # 23.
A Related Text, with a Four Ways Extended Square Field
.311
11.2
с
MS
5112 §2
a. A trivial Problem for Two Squares
.312
11.2
d. MS
5112 § 2
b. A
Standard Quadratic-Linear System of Equations
.314
A Parallel Text: BM
13901 # 8.315
11.2 e.
MS
5112 §2
с
A Quadratic-Rectangular System of Equations
.316
11.2
f.MS
5112 § 3.
Three Squares With their Sides in an Arithmetical Progression
.318
11.2
g. MS
5112 §4.
A Quadratic-Linear System of Equations for Two Squares
.319
11.2
h. MS
5112 § 5.
Finding the Number of Terms in an Arithmetical Progression
.321
11.2
i. MS
5112 § 6.
A Quadratic Equation with Incorrect Data
.323
MS
5112,
rev.: Metric Algebra Problems for the Length and Front of a Rectangle
.326
11.2
j. MS
5112 § 7
а
-b.
Two Badly Preserved Rectangular-Linear Systems
.326
11.2
k. MS
5112 § 8.
A Rectangle where the Area is Equal to the Length Plus the Front
.327
A Parallel Text:
АО
8862 § 1
d.
328
Another Related Text:
АО
6770 # 1.328
Other Texts Mentioning the Sum of the Length, the Front, and the Area
.329
11.21.
MS
5112 § 9.
Changing the Form of a Rectangle while Keeping the Area
.332
11.2
m. MS
5112 § 10.
A System of Linear Equations for the Length and the Front
.333
Other Old Babylonian Mathematical Texts with Systems of Linear Equations
.334
11.2
n. MS
5112 § 11.
One of the Basic Rectangular-Linear Systems of Equations
.336
YBC
6967,
a Related Text With an igi-igi.bi Equation
.337
11.2
o.MS
5112 § 12.
A Rectangular-Linear System of Equations
.338
11.2
p. MS
5112 § 13.
Another Rectangular-Linear System of Equations
.340
Table
of
Contents
xix
11.3.
MS
3876.
Three Problems for
20
Equilateral Triangles and a 'Horn-Figure'
.342
11.3
a. Computation of the Weight of a 'Horn-Figure'
.342
11.3
b. Constants for Copper and Silver in Mathematical Cuneiform Texts
.347
11.3
с
A'Horn-Figure'Consisting of
20
Equilateral Triangles
.349
11.4.
On the Dating of the Texts in Chapter
11.352
Appendix
1.
Subtractive Notations for Numbers in Mathematical Cuneiform Texts
.355
Al
.1.
Hilprecht's List of Signs for
'19'
in Multiplication Tables from Nippur
.355
Al
.2. Ist.
Τ
7375.
An
Ur
III Table of Reciprocals with Subtractive Number Notations
.356
Al
.3.
A
681.
A Table Text from ED
ШЬ
Adab with Subtractive Number Notations
.357
Appendix
2.
The Old Babylonian Combined Multiplication Table
.361
Appendix
3.
An Old Babylonian Combined Arithmetical Algorithm
.367
A3.1.
CBS
10201.
Hilprecht's Misunderstood Algorithm Text from Nippur
.367
A3.2. UM 29.13.21.
A Fragment of a Multiple Algorithm Text from Nippur
.368
A3.3. CBS
1215.
An Algorithm Text with Explicit Computations
.369
Appendix
4.
Cuneiform Systems of Notations for Numbers and Measures
.373
A4.1. Proto-Literate/Traditional Sexagesimal Counting Numbers
.373
A4.2.
Proto-literate Bisexagesimal Counting Numbers
.375
A4.3.Proto-Elamite
Decimal Counting Numbers
.375
A4.4.
Proto-Literate and Traditional Capacity Numbers
.376
A4.5.
Proto-Cuneiform and Traditional Weight Numbers
.377
A4.6.
Proto-Literate/Traditional Area Numbers
.377
A4.7.
Old Akkadian and Neo-Sumerian/Old Babylonian Length Numbers
.378
A4.8.
Proto-Cuneiform Time Numbers
.379
A4.9.
An Integrated Family of Numbers and Measures
.379
A4.10. Pre-Literate Number Tokens
.380
Appendix
5.
Old Babylonian Complete Metrological Tables
.385
A5.1
.
The Complete Metrological Table for System CCNS/OB)
.385
A5.2. The Complete Metrological Table for System
M(NS/OB).387
A5.3. The Complete Metrological table for System A(NS/OB)
.389
A5.4. The Complete Metrological tables for Systems
L«(NS/OB)
and LcCNS/OB)
.391
A5.5. Old Babylonian (and Other) Combined Metrological Lists
.395
A5.6. Old Babylonian Combined Metrological Tables
.398
. On Prisms, Cylinders, and a Family of Subscripts
.398
Appendix
6.
Metro-Mathematical Cuneiform Texts from the Third Millennium
ВС
.401
A6.1
.
Two Old Akkadian Applications of the Field Expansion Procedure
.401
A6.2. Old Akkadian Square-Side-and-Area Exercises
.403
A6.3. Old Akkadian Metric Division Exercises
.407
A6.4.
IM 58045.
An Old Akkadian
Trapezoid
Partition Problem
.409
A6.5. TM.75.G.1392 (Ebla). A Division Algorithm in Decimal Numbers
.410
A6.6. TM.75.G.2346 (Ebla). Another Decimal Division Algorithm
.412
A6.7. TSS
50,671
(Shuruppak). Sexagesimal Metric Division Exercises (ED
Ша)
.414
A6.8. Examples of Complicated Designs
.416
xx
Table
of
Contents
Appendix
7.
A
Combined Metro-Mathematical Table Text
with Areas of Large and Small Squares (ED Illb)
.419
A7.1
.
CUNES
50-08-001.
An Early Dynastic Metro-Mathematical Table Text
.419
A7.2. A Parallel Text from Adab (ED
ШЬ)
.425
A7.3. The Historical Importance of the Combined Table Text
CUNES
50-08-001.425
A7.4.
CUNES
47-12-176.
An Old Akkadian Lexical Text with Fractions of the
Mina
.426
A7.5.
RA
35,
Texts
1-2
and
IM 96183.
Old Babylonian Table Texts Related to
CUNES
50-08-001.428
Appendix
8.
Plimpton
322,
a Table of Parameters for igi-igi.bi Problems
. 433
Ae.l. Plimpton
322.
A Description of the Preserved Part of the Table Text
.434
A8.2. Related Texts: Texts with igi-igi.bi Problems
.436
A8.3. A Suggested Reconstruction of the Lost Columns on Plimpton
322.440
A8.4. The Old Babylonian Rectangle Parameter Equations. Restrictions on the Parameters
.441
A8.5. The Purpose of the Tables on Plimpton
322.447
A8.6. The Diagonal Rule in the Corpus of Mathematical Cuneiform Texts
.449
Appendix
9.
Many-Place Squares of Squares in Late Babylonian Mathematical Texts
.453
A9.1. Squares of Squares of Many-Place Regular Sexagesimal Numbers
.454
A9.2. An Explicit Late Babylonian Multiplication Algorithm
.456
Appendix
10.
Color Photos of
70
Selected Texts
.465
Vocabulary for the MS Texts
. 503
Index of Subjects
. 509
Index of Texts
. 515
References
. 521
Remark. The successive chapters of this book have been ordered into what initially seemed to be a logical succession of
increasingly sophisticated topics. After the work with the book had been finished, much too late to be considered,
С
Proust's
dissertation TMN
(2004)
became available, with its thorough statistical analysis of nearly the whole corpus of known mathe¬
matical cuneiform texts from Nippur. According to Proust, at the elementary level of the education in the Old Babylonian scribe
schools at Nippur, metrological and mathematical table texts were studied in the following order: a) metrological lists for
systems C, M. A, L, b) metrological tables for systems
С, М.
A, Ln, Lc, c) tables of reciprocals, multiplication tables, tables of
squares, d) tables of square sides and cube sides. All other mathematical cuneiform texts are relegated by Proust to the category
of exercises at an advanced level.
It is not clear to what extent the results of Proust's analysis are applicable to the mathematical cuneiform texts in the Sch0yen
Collection. The great majority of the mathematical texts used by Proust for her statistical analysis are (fragments of) clay tablets
of the so called type Ila/IIb
,
and very few belong to what she calls the advanced level
.
In contrast to this
,
of the Old
В
abylonian
mathematical tablets in the Sch0yen Collection very few, if any, are of type
Па/ПЬ,
and all the texts discussed in Chapters l(?),
7,8,10,
and
11
of this book belong to what Proust calls the advanced level. |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Friberg, Jöran 1934- |
| author_GND | (DE-588)1051628709 |
| author_facet | Friberg, Jöran 1934- |
| author_role | aut |
| author_sort | Friberg, Jöran 1934- |
| author_variant | j f jf |
| building | Verbundindex |
| bvnumber | BV022784911 |
| classification_rvk | EM 2150 SG 510 |
| ctrlnum | (gbd)0891958 (OCoLC)255266852 (DE-599)GBV51124634X |
| discipline | Außereuropäische Sprachen und Literaturen Mathematik Literaturwissenschaft |
| discipline_str_mv | Außereuropäische Sprachen und Literaturen Mathematik Literaturwissenschaft |
| era | Geschichte 2600-500 v. Ch. gnd |
| era_facet | Geschichte 2600-500 v. Ch. |
| format | Book |
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| geographic | Babylonien (DE-588)4004102-5 gnd |
| geographic_facet | Babylonien |
| id | DE-604.BV022784911 |
| illustrated | Illustrated |
| index_date | 2024-07-02T18:37:41Z |
| indexdate | 2024-07-09T21:06:05Z |
| institution | BVB |
| isbn | 9780387345437 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-015990359 |
| oclc_num | 255266852 |
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| owner | DE-12 DE-19 DE-BY-UBM DE-20 DE-11 DE-83 DE-188 |
| owner_facet | DE-12 DE-19 DE-BY-UBM DE-20 DE-11 DE-83 DE-188 |
| physical | XX, 533 S. zahlr. Ill., graph. Darst. |
| psigel | gbd_4_0711 |
| publishDate | 2007 |
| publishDateSearch | 2007 |
| publishDateSort | 2007 |
| publisher | Springer |
| record_format | marc |
| series | Manuscripts in the Schøyen Collection |
| series2 | Manuscripts in the Schøyen Collection : Cuneiform texts Sources and studies in the history of mathematics and physical series |
| spelling | Friberg, Jöran 1934- Verfasser (DE-588)1051628709 aut A remarkable collection of Babylonian mathematical texts Jöran Friberg Berlin, New York [u.a.] Springer 2007 XX, 533 S. zahlr. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Manuscripts in the Schøyen Collection : Cuneiform texts 1 Sources and studies in the history of mathematics and physical series Literaturverz. S. 521 - 533 Schøyen Collection (DE-588)5222053-9 gnd rswk-swf Geschichte 2600-500 v. Ch. gnd rswk-swf Mathematik (DE-588)4037944-9 gnd rswk-swf Keilschrifttext (DE-588)4130946-7 gnd rswk-swf Babylonien (DE-588)4004102-5 gnd rswk-swf Mathematik der Antike (DE-2581)TH000007621 gbd Schøyen Collection (DE-588)5222053-9 b Mathematik (DE-588)4037944-9 s Keilschrifttext (DE-588)4130946-7 s DE-604 Babylonien (DE-588)4004102-5 g Geschichte 2600-500 v. Ch. z Erscheint auch als (DE-604)BV023083795 Manuscripts in the Schøyen Collection Cuneiform texts ; 1 (DE-604)BV022784900 1 http://deposit.dnb.de/cgi-bin/dokserv?id=2798757&prov=M&dok_var=1&dok_ext=htm Digitalisierung BSBMuenchen application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015990359&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Friberg, Jöran 1934- A remarkable collection of Babylonian mathematical texts Manuscripts in the Schøyen Collection Schøyen Collection (DE-588)5222053-9 gnd Mathematik (DE-588)4037944-9 gnd Keilschrifttext (DE-588)4130946-7 gnd |
| subject_GND | (DE-588)5222053-9 (DE-588)4037944-9 (DE-588)4130946-7 (DE-588)4004102-5 |
| title | A remarkable collection of Babylonian mathematical texts |
| title_auth | A remarkable collection of Babylonian mathematical texts |
| title_exact_search | A remarkable collection of Babylonian mathematical texts |
| title_exact_search_txtP | A remarkable collection of Babylonian mathematical texts |
| title_full | A remarkable collection of Babylonian mathematical texts Jöran Friberg |
| title_fullStr | A remarkable collection of Babylonian mathematical texts Jöran Friberg |
| title_full_unstemmed | A remarkable collection of Babylonian mathematical texts Jöran Friberg |
| title_short | A remarkable collection of Babylonian mathematical texts |
| title_sort | a remarkable collection of babylonian mathematical texts |
| topic | Schøyen Collection (DE-588)5222053-9 gnd Mathematik (DE-588)4037944-9 gnd Keilschrifttext (DE-588)4130946-7 gnd |
| topic_facet | Schøyen Collection Mathematik Keilschrifttext Babylonien |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=2798757&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015990359&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV022784900 |
| work_keys_str_mv | AT fribergjoran aremarkablecollectionofbabylonianmathematicaltexts |