The Arithmetic of Al-Uqlīdisī

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?’s 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?’s Introduction and Table of Contents ofBook II.- 1. On Doubling.- 2. On Halving.- 3. Halving where Fractions Occur, and Doubling – 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?’s 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.