Author | al-แธคasan Ahmad, Abลซ. author |
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Title | The Arithmetic of Al-Uqlฤซdisฤซ [electronic resource] : The Story of Hindu-Arabic Arithmetic as told in Kitฤb al-Fuแนฃลซl fฤซ al-แธคisฤb al-Hindฤซ / by Abลซ al-แธคasan Ahmad, Ibrฤhim al-Uqlฤซdisฤซ |
Imprint | Dordrecht : Springer Netherlands, 1978 |
Connect to | http://dx.doi.org/10.1007/978-94-009-9772-1 |
Descript | XVII, 492 p. online resource |
I - Introduction -- 1.1. Past Attempts in the Study of Islamic Arithmetic -- 1.2. The Present Work -- 1.3. Transliteration -- 1.4. Outline of Islamic Contact with Indian Science -- 1.5. Arithmetic Systems in Arabic Texts; General Remarks -- 1.6. The Sexagesimal Scale -- 1.7. Finger-Reckoning -- 1.8. Indian Arithmetic -- 1.9. Greek Arithmetica -- 1.10. Types of Texts -- 1.11. Hindi and Hindu -- 1.12. Kit?b al Fus?l F? al-?is?b al-Hind?, by Ab? al-?assan, A?mad ibn Ibr?h?m, Al-Uql?dis? -- 1.13. The Subsidiary Texts: A-Type -- 1.14. Subsidiary Texts: H-Type -- 1.15. Subsidiary Texts: HA-Type -- 1.16. Subsidiary Texts: Islamic Type -- 1.17. Subsidiary Texts to Hindu Sources -- II - The Text The Arithmetic of Al-Uql?dis? -- Frontispiece -- Al-Uql?dis?โs Introduction and Table of Contents of Book I -- Book I -- 1. On the Nine Letters and the Places -- 2. On Doubling and Halving -- 3. On Increasing and Decreasing -- 4. On Multiplication -- 5. On Division -- 6. Multiplication of Fractions by Numbers -- 7. Combining Fractions and Parts -- 8. On Multiplying a Number with Fractions by a Number -- 9. Multiplying Fractions by Fractions -- 10. On Multiplying a Number with Fractions by Fractions -- 11. Multiplying a Number with Fractions by a Number with Fractions -- 12. On Extracting Roots of Numbers, Open and Asamm -- 13. On Extracting the Roots of Fractions, Isolated or Joined to Units -- 14. On Division in General -- 15. The Arithmetic of Degrees and the Concepts It Involves -- 16. Halving the Degree and Doubling It -- 17. On Increasing and Decreasing -- 18. Multiplication of Degrees and Minutes -- 19. On Division of Degrees and Minutes -- 20. On Extracting the Roots of Degrees and Minutes -- 21. Extracting the Roots of A$amm Numbers -- Book II -- Al-Uql?dis?โs Introduction and Table of Contents of Book II -- 1. On Doubling -- 2. On Halving -- 3. Halving where Fractions Occur, and Doubling โ All Methods -- 4. Increasing, Unlike the Preceding (Type) -- 5. On Decreasing of the Preceding Type -- 6. On the Preceding Type of Increasing and Decreasing; Minute (Problems) -- 7. Exhausting One Number by Another -- 8. Queries on the Curiosities of Casting Out -- 9. Multiplication of Integers - All Methods: The Upright and the Branching -- 10. On Multiplication by (the Method of) Houses -- 11. Curiosities in Multiplication -- 12. On Division -- 13. On the Balances -- 14. On Multiplying Integers and Fractions by Integers and Fractions, Upright and Branching -- 15. On Which Is More, Such Parts of This Number or Such Parts of That? -- 16. On Multiplying Fractions of Fractions of Fractions -- 17. On Making Perfect Squares to Extract Their Roots -- 18. On Extracting the Root of the Asamm -- 19. Extracting the Roots of the Asamm and Testing Them -- 20. On Degrees and Minutes and the Concepts They Involve -- Book III -- Table of Contents of Book III -- 1. Justifications of the Hindi (Arithmetic) and Its Whys and Hows -- 2. Queries on Doubling and Halving -- 3. Queries on Increasing and Decreasing -- 4. Queries on Multiplication -- 5. Queries on Division -- 6. Queries on Roots -- 7. On Checking by Balancing and Its Justifications -- 8. Balances of Fractions -- 9. Queries on Doubling and Halving -- 10. Queries on Increasing and Decreasing -- 11. Queries on Adding Different Kinds -- 12. Queries on Increasing and Decreasing (Coming) Together -- 13. Curiosities in the Multiplication of Nines -- 14. Extracting Roots by Zeros Where Fractions Occur -- 15. On Converting Fractions and Parts, One to Another -- 16. On Decreasing Fractions and Parts, One from the Other -- 17. Queries on Minutes and Their Minute Parts -- 18. Division by the Upright (Method) -- 19. Queries on Root (Extraction) by the Upright (Method) -- 20. Queries About Profit, Involving a Curiosity -- 21. On the Justification of (the Method of) Extracting the Side of the Cube -- Book IV -- Al-Uql?dis?โs Introduction and Table of Contents of Book IV -- 1. The Method of Addition -- 2. On Doubling -- 3. On Halving -- 4. On Increasing -- 5. On Decreasing -- 6. On Multiplication -- 7. On Division -- 8. On Multiplying Fractions by Numbers -- 9. On Adding Fractions and Parts -- 10. On Multiplying a Number with Fractions by a Number -- 11. On Multiplying Fractions by Fractions -- 12. On Multiplying a Number with Fractions by Fractions -- 13. On Multiplying Integers and Fractions by Integers and Fractions -- 14. General, on Division -- 15. On Differentiating Between Fractions -- 16. On Converting Fractions and Parts from one Number to Another Number -- 17. On Extracting Roots of Numbers -- 18. On Extracting Roots Where Fractions Occur -- 19. On Degrees and Their Schemes -- 20. On Adding Degrees, Minutes and Lower Orders -- 21. Decreasing Degrees, Minutes and Lower Orders from Each Other -- 22. Reducing Degrees and Whatever Minutes and Seconds Follow to Their Lowest Places -- 23. Multiplication of Degrees, Minutes, Seconds, and Lower Orders, by Equal or Different Orders -- 24. On the Division of Degrees and Minutes and Lower Orders by Degrees and Minutes and Lower Orders -- 25. On Extracting the Roots of Degrees, Minutes and Lower Orders -- 26. On Working Out All That Is Needed of Hindi Arithmetic Without the Nine Letters -- 27. By Hindi: Writings, Names, Calculations - Everything We Want -- 28. A Calculating (Tool) for the Blind and the Weak-Sighted -- 29. On Extracting the Side of the Cube -- 30. On Knowing Fractions That Are Cubic and Extracting Their Sides, Single or Combined to Units -- 31. On Extracting the Sides of Numbers Which Have No Roots -- 32. On Doubling One, Sixty-Four Times -- III - Remarks and Comparative Studies -- Unit 1. Aims and Contents of the Four Books (The Introductions to the Four Books) -- Unit 2. The Numerals -- Unit 3. Duplation and Mediation -- Unit 4. Addition and Subtraction -- Unit 5. Multiplication -- Unit 6. Division -- Unit 7. Fractions -- Unit 8. Square Roots -- Unit 9. Cube Roots -- Unit 10. Checking -- Unit 11. Profit and Loss -- Unit 12. Remarks on Decimal Fractions -- A Recapitulation -- Index of Auxiliary Works and Authors -- Table of Important Remarks