Books IV to VII of Diophantus' Arithmetica: In the Arabic Translation Attributed to Qustā Ibn Lūqā

ISBN-13: 9781461381761 / Angielski / Miękka / 2011 / 502 str.

Jacques Sesiano

Opis

This edition of Books IV to VII of Diophantus' Arithmetica, which are extant only in a recently discovered Arabic translation, is the outgrowth of a doctoral dissertation submitted to the Brown University Department of the History of Mathematics in May 1975. Early in 1973, my thesis adviser, Gerald Toomer, learned of the existence of this manuscript in A. Gulchln-i Macanl's just-published catalogue of the mathematical manuscripts in the Mashhad Shrine Library, and secured a photographic copy of it. In Sep tember 1973, he proposed that the study of it be the subject of my dissertation. Since limitations of time compelled us to decide on priorities, the first objective was to establish a critical text and to translate it. For this reason, the Arabic text and the English translation appear here virtually as they did in my thesis. Major changes, however, are found in the mathematical com mentary and, even more so, in the Arabic index. The discussion of Greek and Arabic interpolations is entirely new, as is the reconstruction of the history of the Arithmetica from Diophantine to Arabic times. It is with the deepest gratitude that I acknowledge my great debt to Gerald Toomer for his constant encouragement and invaluable assistance."

Spis treści

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 $$ A{x^} + Bx + C = \square $$.- 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.