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Books IV to VII of Diophantus' Arithmetica : in the Arabic translation attributed to Quṣtā ibn Lūqā

Author: Jacques Sesiano
Publisher: New York ;Berlin [u.a.] : Springer, 1982.
Dissertation: Diss.--Brown Univ., 1975.
Series: Sources in the history of mathematics and physical sciences, 3.
Edition/Format:   Thesis/dissertation : Thesis/dissertation : Manuscript   Archival Material
Database:WorldCat
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Named Person: Diophantus, <Alexandrinus>; Diophant, von Alexandria.
Material Type: Thesis/dissertation, Manuscript
Document Type: Book, Archival Material
All Authors / Contributors: Jacques Sesiano
ISBN: 0387906908 9780387906904 3540906908 9783540906902
OCLC Number: 246311940
Description: XII, 502 S : Ill.
Contents: One: Introduction.- I. The Four Arabic Books and the Arithmetica.- 1. Authenticity of the Arabic Books@.- 1. That the Arabic Books Belong to the Arithmetica.- 2. Concerning Their Place Within the Arithmetica.- a. Placement of the Arabic Book IV.- b. Basic Methods Used in the Arabic Books.- c. Placement of the Four Arabic Books.- 2. Diophantus in Islamic, and Byzantine, Times.- 1. Qust? ibn L?q? and the Arithmetica.- 2. Islamic Mathematicians and the Arithmetica.- a. Ab? K?mil.- b. Al-?azn.- c. Ab?'l-Waf?'.- d. Al-Karaji?.- e. Ibn al-Hai ?am.- f. Samaw'al ibn Ya?y?.- Appendix. Designation of the Arithmetica in Arabic.- 3. Mathematicians and the Arithmetica in Byzantium.- a. The Time of Leon the Mathematician.- ?. The Seventh and Eighth Centuries.- ss. The Century of Leon.- ?. From Leon to Planudes.- b. The Time of Maximus Planudes.- c. Oldest Greek Manuscripts Still Extant.- ?. Non-Planudean Class.- ss. Planudean Class.- II. The Extant Arabic Text.- 3. Description of the Manuscript.- 4. Orthographical Remarks.- 1. Writing of the hamzah.- 2. Particular Endings.- 3. Numerals.- 4. Repeated, Erroneous Spellings.- 5. Additions by Earlier Readers (or Copyists).- 6. On the Progenitor of Our Manuscript.- 7. Grammatical and Lexicological Remarks.- 1. Numbers and Powers.- A. Integers.- a. Grammatical Peculiarities.- b. Determination.- B. Fractions.- a. General Fractions.- ?. Expression.- ss. Determination.- b. Aliquot Fractions and Related Cases.- ?. Expression.- ss. Decomposition of Some Fractions.- ?. Grammatical Peculiarities Connected with Aliquot Fractions.- C. Grammatical Number of a Mathematical Expression.- a. Units.- b. Multiple of a Power.- c. Algebraic Polynomial Expression.- D. Powers.- a. The Greek Power-system.- b. The Arabic Power-system.- c. The Power-system in Our Text.- ?. x5.- ss. x8.- d. Grammatical Determination of the Powers.- ?. Two Elements.- ss. Three Elements.- 2. Some Grammatical Remarks on Verbs.- a. Verbal Persons Used.- b. Jussives of Weak Verbs.- c. The Verb Hadala.- ?. Agreement of Hadala.- ss. Agreement of the Auxiliary of Hadala.- III. Tentative Reconstruction of the History of the Arithmetica.- 8. Formal Subdivisions of a Problem.- 1. Analysis and Synthesis.- 2. Subdivisions of a Problem.- 9. Major, Unsystematic Supplements in the Arithmetica.- 1. Interpolated Problems in the Arithmetica.- 2. Alternative Resolutions (?????).- a. In the Greek Books.- b. In the Arabic Books.- 3. Other Supplements.- a. Corollaries.- b. Remarks.- c. Additional Computations.- Appendix. A Comparison Between al-Karaji?'s Version and the Extant Arithmetica.- 10. Errors in the Problems of the Arabic Books.- 11. Quality of the Translation.- 1. Imperfections in the Translation.- 2. General Character of the Translation.- 12. Genealogy of the Mashhad Manuscript.- 1. Earliest Additions.- 2. The Major Commentary.- a. Additions Originating with the Major Commentary.- a. Additions in the Analysis.- ss. Additions in the Synthesis.- b. Value of This Commentary.- c. Possible Authorship of the Major Commentary.- 3. The Addition of the Final Statements.- 4. The Arabic Diophantus.- 5. Genealogical Tree of the Mashhad Manuscript.- 13. On the Missing Part of the Arithmetica.- 1. New Aspects of the Problem.- 2. The Announcement in the Greek Introduction.- 3. Diophantus and the Equation $$ A{x^{2}} + Bx + C = \square $$.- 4. On Some Problems of a Diophantine Nature Found in Islamic Mathematics but Not in the Extant Arithmetica.- a. Problems of Ab? K?mil.- b. Problems of al-Karaji?.- 5. Conclusion.- Two: Translation.- Book IV.- Book V.- Book VI.- Book VII.- Three: Mathematical Commentary.- Book IV.- Book V.- Book VI.- Book VII.- Four: Text.- Book IV.- Book V.- Book VI.- Book VII.- Five: Arabic Index.- General Index.
Series Title: Sources in the history of mathematics and physical sciences, 3.
Other Titles: Diophantus' Arithmetica
Responsibility: Jacques Sesiano.

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