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1 online resource (308 pages) |
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text txt rdacontent |
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computer c rdamedia |
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online resource cr rdacarrier |
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Intro -- Preface -- Contents -- Chapter 1 Two Curious Mathematical Cuneiform Texts from Old Babylonian Mari -- 1.1. M. 7857. A Fanciful Interpretation of a Geometric Progression -- 1.1 a. M. 7857. A text with three kinds of counting numbers -- 1.1 b. OB texts with ascending or descending geometric progressions -- 1.1 c. A Late Babylonian text using the trailing part algorithm -- 1.1 d. The sum of a geometric progression in an Old Babylonian text -- 1.1 e. The sum of a geometric progression in a Seleucid text -- 1.1 f. P.Rhind # 79: a parallel to M. 7857 in a hieratic papyrus -- 1.1 g. Summary. The Mesopotamian roots of a Mother Goose riddle -- 1.1. M. 8631. Another Curious Mathematical Text from OB Mari -- 1.1 a. M. 8631. A fanciful interpretation of 30 doublings -- 1.2 b. The Old Babylonian doubling and halving algorithm -- 1.2 c. P.IFAO 88: A parallel to M. 8631 in a Greek-Egyptian papyrus -- 1.2 d. Summary. The Mesopotamian roots of a well known legend -- Chapter 2 Hieratic Mathematical Papyri and Cuneiform Mathematical Texts -- 2.1. Themes in P.Rhind, a Hieratic Mathematical Papyrus Roll -- 2.1 a. P.Rhind, a hieratic mathematical recombination text -- 2.1 b. Theme E: division problems (P.Rhind ## 24-38) -- 2.1 c. Theme F: sharing problems (P.Rhind ## 39-40, 63-65, 68) -- 2.1 d. Theme G: geometry problems (P.Rhind ## 41-46, 48-60) -- 2.1 e. Theme H: baking or brewing numbers (P.Rhind ## 69-78) -- 2.1 f. Theme I: a combined price problem (P.Rhind # 62) -- 2.2. Themes in P.Moscow, a Smaller Hieratic Mathematical Papyrus -- 2.2 a. P.Moscow: Another Egyptian mathematical recombination text -- 2.2 b. P.Moscow # 23: A combined work norm -- 2.2 c. P.Moscow ## 6-7, 17: Metric algebra -- 2.2 d. P.Moscow # 14: The volume of a truncated pyramid -- 2.2 e. P.Moscow # 10: The area of a semicircle(?) -- 2.3. Hieratic Mathematical Papyrus Fragments |
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2.3 a. P.Berlin 6619 # 1: Metric algebra -- 2.3 b. P.UC 32160 (= Kahun IV.3) # 1: A cylindrical granary -- 2.3 c. P.UC 32160 # 2: An arithmetic progression with 10 terms -- 2.3 d. P.UC 32161 (= Kahun XLV. 1): A list of large numbers -- 2.4. Conclusion -- New thoughts about the nature of P.Rhind -- Summary: Comparison of hieratic Egyptian and OB mathematics -- Chapter 3 Demotic Mathematical Papyri and Cuneiform Mathematical Texts -- 3.1. Themes in P.Cairo (Ptolemaic, the 3rd C. BCE) -- 3.1 a. P.Cairo, a hieratic mathematical recombination text -- 3.1 b. P.Cairo 8 (DMP ## 24-31). A pole against a wall -- 3.1 c. P.Cairo 1 (DMP ## 2-3). Two closely related division problems -- 3.1 d. P.Cairo 2 (DMP ## 4-6). Completion problems -- 3.1 e. P.Cairo 3 (DMP ## 7, 15-16, 18). A rectangular sail -- 3.1 f. P.Cairo 4 (DMP ## 8-12, 14, 17). Reshaping a rectangular cloth -- 3.1 g. P.Cairo 7 (DMP # 23). Shares in a geometric progression -- 3.1 h. P.Cairo 9 (DMP ## 32-33). Diameter of a circle with given area -- 3.1 i. P.Cairo 10 (DMP ## 34-35). Metric algebra -- 3.1 j . P.Cairo 11 (DMP ## 36, 38). An equilateral triangle in a circle -- 3.1 k. P.Cairo 12 (DMP # 37). A square inscribed in a circle -- 3.1.1. P.Cairo 13-14 (DMP ## 39-40). Pyramids with a square base -- 3.1 m. P.Cairo 15-16 (## "32-33"). Metric algebra -- 3.2. P.British Museum 10399 (Ptolemaic, Later than P.Cairo) -- 3.2 a. P.BM 10399 1 (DMP # 41). A circle-and-chord problem -- 3.2 b. P.BM 10399 2 (DMP ## 42-45). Masts (truncated cones) -- 3.2 c. P.BM 10399 3 (DMP ## 46-51). The reciprocal of 1 + 1/n, etc. -- 3.3. P.British Museum 10520 (Early(?) Roman) -- 3.3 a. P.BM 10520 1 (DMP # 53). The iterated sum of 1 through 10 -- 3.3 b. P.BM 10520 2 (DMP # 54). A multiplication table for 64 -- 3.3 c. P.BM 10520 3 (DMP # 55). A new multiplication rule |
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3.3 d. P.BM 10520 4 (DMP # 56). 2/35 expressed as a sum of parts -- 3.3 e. P.BM 10520 5 (DMP ## 57-61). Operations with fractions -- 3.3 f. P.BM 10520 6 (DMP ## 62-63). The square side rule -- 3.3 g. P.BM 10520 7 (DMP ## 64-65). The quadrilateral area rule -- 3.4. P.British Museum 10794 (Date Uncertain) -- Multiplication tables for 90 and 150 (DMP ## 66-67) -- 3.5. P.Carlsberg 30 (Probably 2nd Century BCE)29 -- 3.5 a. P.Carlsberg 30 # 1 (DMP # 69). The diagonal of a square, etc. -- 3.5 b. P.Carlsberg 30 # 2 (DMP ## 71-72). A system of linear equations -- 3.6. P.Griffith Inst. I. E. 7 (Late Ptolemaic or Early Roman) -- A theme text with linear equations -- 3.7. P.Heidelberg 663 (Ptolemaic, 2nd or 1st C. BCE) -- 3.7 a. P.Heidelberg 663 # 1. A vertically striped trapezoid -- 3.7 b. P.Heidelberg 663 # 2. A horizontally striped trapezoid -- 3.7 c. P.Heidelberg 663. Parallel texts -- 3.8. Conclusion -- The importance of P.Cairo for the history of mathematics -- The other demotic mathematical papyri -- Chapter 4 Greek-Egyptian Mathematical Documents and Cuneiform Mathematical Texts -- 4.1. O.Bodl. ii 1847 (30 BCE), an Ostracon with Schematic Field Plans -- 4.2. P.Oxyrhynchus iii 470 (3rd C. CE). A Water Clock -- 4.3. P. Vindobonensis G. 26740. Five Illustrated Geometric Exercises -- 4.3 a. P.Vindob. G. 26740 # 1. A segment of a circular band -- 4.3 b. P. Vindob. G. 26740 ## 2-4. A circle area found in three ways -- 4.3 c. P.Vindob. G. 26740 # 5. The area of a semicircle -- 4.4. P.Mich. 620. Systems of Linear Equations. Tabular Arrays -- 4.4 a. P.Mich. 620 # 1. A system of linear equations: four unknowns -- 4.4 b. P.Mich. 620 # 2. A system of linear equations: two unknowns -- 4.4 c. P.Mich. 620 # 3. A system of linear equations: three unknowns -- 4.5. P.Akhmîm (7th C. CE). Calculations with Fractions -- 4.5 a. P.Akhmîm. Ten tables of fractions |
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4.5 b. P.Akhmîm 1. The capacity measure(?) of a truncated cone -- 4.5 c. P.Akhmîm 2. The capacity measure of a rectangular granary -- 4.5 d. P.Akhmîm 3, 5. Unequal sharing, and division exercises -- 4.5 e. P.Akhmîm 4-10. Examples of counting with fractions -- 4.5 f. P.Akhmîm 9. Prices and market rates -- 4.6. WT.Michael 62 (7th? C. CE). Prices and Market Rates -- 4.7. Problems for Right Triangles and Quadrilaterals -- 4.7 a. P.Genève 259. Problems for the sides of a right triangle -- 4.7 b. P.Chicago litt. 3. Three types of non-symmetric trapezoids -- 4.7 c. P.Cornell 69. Non-symmetric trapezoids, and a birectangle -- 4.8. P.Vindobonensis G. 19996 (1st C. CE?). Stereometric Exercises -- 4.8 a. P.Vindob. G. 19996: Contents -- 4.8 b. P.Vindob. G. 19996 # 10. A pyramid with a triangular base -- 4.8 c. P.Vindob. G. 19996 # 13. A truncated triangular pyramid -- 4.8 d. P.Vindob. G. 19996 # 18. A square pyramid -- 4.8 e. P.Vindob. G. 19996 # 19. A truncated square pyramid -- 4.8 f. P.Vindob. G. 19996 # 24. A truncated circular cone -- 4.8 g. Pyramids and cones in Old Babylonian mathematical texts -- 4.9. Conclusion -- Relations between Greek-Egyptian and Babylonian mathematics -- New Thoughts About the History of Ancient Mathematics -- Index of Texts -- Index of Subjects -- Bibliography |
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Key Features:Extensive surveys of known Egyptian mathematical textsNew interpretations of particularly difficult Egyptian or Babylonian mathematical exercisesMany detailed diagrams and figures, using computer-aided methods of presentationsInteresting observations of experiments with new ways of representing fractions in demotic and Greek-Egyptian mathematical texts |
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Description based on publisher supplied metadata and other sources |
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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2020. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries |
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Print version: Friberg, Joran Unexpected Links Between Egyptian And Babylonian Mathematics
Singapore : World Scientific Publishing Company,c2005 9789812563286
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| Subject |
Mathematics, Ancient.;Mathematics, Babylonian.;Mathematics, Egyptian
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Electronic books
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