New mathematical cuneiform texts - Friberg, Jöran 1934-; Rāwī, Fārūk N. H. al- 1943- (Cham Springer Nature, 2016)
Preface -- Contents -- 1. Late Babylonian Tables of Many-Place Regular Sexagesimal Numbers, from Babylon, Sippar, and Uruk -- 1.1 Late Babylonian Texts Concerned with Many-Place Regular Sexagesimal Numbers -- 1.2 Table B (Babylon). Fragments of a Seleucid Many-Place Table of Reciprocals, with n from 1 to 2 -- 1.2.1 BM 35568. A List of Squares of Many-Place Regular Sexagesimal Numbers -- 1.2.2 Attested Many-Place Regular Numbers n in the Fragments and in Tables U and S -- 1.2.3 Table R: A Reconstructed Common Ancestor to Tables B, U, and S -- 1.2.4 The Numerical Algorithms Used for the Construction of Table R -- 1.2.5 The Double 6-Place Hexagon and the 12-Place Flower in the Index Grid -- 1.2.6 An Error in a Table of Squares Related to the Enlarged Table B* -- 1.3 Table U = W 23283+22905 (Uruk). An Achaemenid Many-Place Table of Reciprocals, with n from 1 to 4 -- 1.3.1 Mathematical and Metrological Tablets from a House in Achaemenid Uruk -- 1.3.2 A Curious Incipit, and a Colophon -- 1.3.3 A Curious Use of the Technical Term íb.si in Table U -- 1.3.4 Numerical Errors in Table U -- 1.3.5 A Curious Extra Line in Table U -- 1.3.6 Table U. New Photos and Transliterations -- 1.4 Table S = Sippar 2175/12. A Neo-Babylonian Many-Place Table of Reciprocals, with n f rom 1 to 3 -- 1.4.1 Numerical Errors and Missing Pairs in Table S -- 1.4.2 Table S. Hand Copies and Conform Transliterations -- 1.5 Table V = AO 6456 (Uruk). A Seleucid Many-Place Table of Reciprocals, with n from 1 to 3 -- 1.5.1 An Invocation, a Many-Place Table of Reciprocals, a Description, and a Colophon -- 1.5.2 Numerical Errors and Missing Pairs in Table V -- 1.5.3 Representation in the Index Grid, Inside a 6-place Double Triangle -- 1.5.4 Table U. New Photos -- 1.6 Table W = W 23281, rev. (Uruk). An Atypical Achaemenid Many-Place Table of Reciprocals
1.6.1 An Atypical Many-Place Table of Reciprocals -- 1.6.2 The Numerical Algorithms Used for the Construction of Table W -- 1.6.3 A Partly Preserved Colophon -- 2. Direct and Inverse Factorization Algorithms for Many-Place Regular Sexagesimal Numbers -- 2.1 BM 46550. A Neo-Babylonian Tablet with Direct and Inverse Factorization Algorithms -- 2.1.1 Description of the Tablet and New Photos -- 2.1.2 A Spectacular Old Babylonian Example of a Many-Place Pair of Reciprocals -- 2.1.3 An Application of a Last Place Factorization Algorithm -- 2.1.4 An Application of an Inverse Last Place Factorization Algorithm -- 2.1.5 Last Place Traces in a Triaxial Index Grid -- 2.1.6 A Faulty Application of the Last Place Factorization Algorithm -- 2.1.7 On the Choice of the Initial Number n = 1 01 02 06 33 45 -- 2.1.8 Errors in BM 46550 -- 2.2 CBS 1215 and the Old Babylonian Trailing Part Factorization Algorithm -- 2.3 Reconstructions of Factorization Algorithms on Three Seleucid Tablet Fragments -- 2.3.1 BM 34517. A Descending Table of Powers of 9 -- 2.3.2 BM 34958. A Last Place Factorization Algorithm for a Large Number of Class I -- 2.3.3 BM 34907. A Direct and an Inverse Last Place Factorization Algorithm -- 2.4 Old Babylonian Ascending and Descending Tables of Powers -- 2.4.1 IM 630174. An Ascending Table of Powers from Old Babylonian Bikasi -- 3. Metrological Table Texts from Achaemenid Uruk -- 3.1 W 23281, obv. A Metrological Recombination Text from Achaemenid Uruk -- 3.1.1 1. A Series of Structure Tables for Traditional Length Measure -- 3.1.2 2. A Conversion Table from Area Measure to Kassite Seed Measure -- 3.1.3 3. A Structure Table for Area Measure -- 3.1.4 4. A Badly Preserved Range Table for Lengths and Square Areas -- 3.1.5 5. The Linear Growth of a Child in its Mother's Womb -- 3.1.6 6. A Catalog of Equations from the 1st Millennium BC
3.1.7 7. Parallel Metrological Lists for Length, Silver, and Grain Numbers -- 3.2 W 23273. Another Metrological Recombination Text from Achaemenid Uruk -- 3.2.1 1. Gods' Names and Gods' Numbers (reads from right to left) -- 3.2.2 2. A Conversion Table from Length Numbers to Sexagesimal nindan Multiples (reads from right to left) -- 3.2.3 3. A Reverse Conversion Table from Sexagesimal nindan Multiples to Length Numbers (reads from right to left) -- 3.2.4 4. A Conversion Table from Length Numbers to Sexagesimal Cubit Multiples (reads from right to left) -- 3.2.5 5. A Reverse Conversion Table from Sexagesimal Cubit Multiples to Length Numbers (reads from right to left) -- 3.2.6 6. A Range Table from (Squares of) Length Measures to Area Measures -- 3.2.7 7. A Conversion Table from Area Numbers to Sexagesimal sar Multiples (reads from right to left) -- 3.2.8 8. A Reverse Conversion Table from Sexagesimal Mina Multiples to Weight Numbers and Grain Multiples -- 3.2.9 9. A Catch Line Referring to Tables for Capacity Measures -- 3.2.10 10. A Shadow Length Table: Months' Names and Cubit Multiples (reads from right to left) -- 3.2.11 11. A Reverse Shadow Length Table (reads from right to left) -- 3.2.12 12. A Colophon -- 3.2.13 W 23273. Photos of the Tablet -- 3.3 W 22309. A Small Fragment of a Metrological Recombination Text from Achaemenid Uruk -- 3.3.1 W 22309, obv. A Structure Table for Traditional Length Measures -- 3.3.2 W 22309, rev. A Metrological Table for Traditional Capacity Measures -- 3.4 W 22260. A Large Fragment of a Metrological/Mathematical Recombination Text from Achaemenid Uruk -- 3.4.1 1. A Conversion Table from Decimal Grain Multiples to Sexagesimal Mina Fractions (reads from right to left) -- 3.4.2 2. A Decimal-Sexagesimal Table of Reciprocals (reads from right to left)
3.4.3 3. [A Conversion Table from Decimal Cubit Multiples to Sexagesimal nindan Multiples] (reads from right to left) -- 3.4.4 4. A Conversion Table from Decimal Cubit Multiples to Sexagesimal 100-Cubit Multiples (reads from right to left) -- 4. CBS 8539. A Mixed Metrological Table Text from Achaemenid Nippur -- 4.1 CBS 8539. Metrological Tables for Systems L (4 variants), M, and C -- 4.1.1 1. A Conversion Table from Traditional Length Measures to Sexagesimal nindan Multiples (reads from right to left) -- 4.1.2 2. A Conversion Table from Traditional Length Numbers to Sexagesimal Cubit Fractions (reads from right to left) -- 4.1.3 3. A Conversion Table from Common Length Numbers to Sexagesimal Cubit Fractions (reads from right to left) -- 4.1.4 4. A Conversion Table from Variant Length Numbers to Sexagesimal 100-Cubit Multiples (reads from right to left) -- 4.1.5 5. A Conversion Table from Weight Names and Grain Multiples to Sexagesimal Mina Fractions (reads from right to left) -- 4.1.6 6. A Conversion Table from Capacity Numbers to Sexagesimal bariga Multiples (reads from right to left) -- 4.2 CBS 11032 and 11019. Two Metrological Tables for Shekel Fractions from Nippur -- 5. Five Texts from Old Babylonian Mê-Turran (Tell Haddad), Ishchali and Shaduppûm (Tell Harmal) with Rectangular-Linear Problems for Figures of a Given Form -- 5.1 IM 121613. A Recombination Text from Mê-Turran with Metric Algebra Problems for Rectangles -- 5.1.1 # 1. A Form and Magnitude Problem for a Rectangle -- 5.1.2 # 2. A Rectangle of a Given Form with a Given Sum of the Field and the Length -- 5.1.3 # 3. A Rectangle of a Given Form with a Given Sum of the Field and Twice the Front -- 5.1.4 # 4. A Rectangle of a Given Form and a Given Sum of Two Rectangular Fields
5.1.5 # 5. A Rectangle of a Given Form with a Given Sum of the Field, the Length, and the Front -- 5.1.6 # 6. A Rectangle of a Given Form with a Given Sum of Many Terms -- 5.1.7 # 7. A Rectangle of a Given Form with a Given Sum of the Field and the Squares on the Length and the Front -- 5.1.8 # 8. A Rectangle of a Given Form with a Given Product of the Field and the Length -- 5.1.9 # 9. A Rectangle of a Given Form with a Given Sum of the Field and Half the Length -- 5.1.10 # 10. A Rectangle of a Given Form with a Given Square of the Sum of the Length -- 5.1.11 # 11. A Rectangle of a Given Form with a Given Excess of the Length over -- 5.1.12 # 12. A Rectangle of a Given Form with a Given Excess of the Front over the Field -- 5.1.13 # 13. A Rectangle of a Given Form with a Given Excess of the Length over the Field -- 5.1.14 # 14. A Rectangle of a Given Form with a Given Excess of the Field over Half -- 5.1.15 # 15. A Rectangle of a Given Form with a Given Field of a Certain Kind -- 5.1.16 # 16. Another Rectangle of a Given Form with a Given Field of a Certain Kind -- 5.1.17 # 17. A Rectangle of a Given Form with a Given Excess of a Certain Kind -- 5.1.18 # 18. A Rectangle of a Given Form with a Given Excess of the Length and -- 5.1.19 # 19. A Rectangle of a Given Form with a Given Shortened and Broadened Field -- 5.1.20 Subscripts -- 5.1.21 The Vocabulary of IM 121316 -- 5.1.22 A Proposed Reconstruction of the Original Theme Text -- 5.1.23 Solution Procedures in Terms of a Square Band (a Ring of Rectangles) -- 5.1.24 Fig. 5.1.19a. The plaque mentioned by Aldo Bonet. Photo: Philipp Bernard (RNM). IM 121613. Hand Copies of the Tablet -- 5.2 IM 43993. A Small Text from Shaduppûm(?) with an Interesting Metric Algebra Problem for a Rectangle -- 5.2.1 A Rectangle of a Given Form with a Given Sum of the Area and the Two Sides
5.2.2 The Vocabulary of IM 43993
Keywords: History; Semitic languages; Mathematics