March 8, 2017

Books IV to VII of Diophantus’ Arithmetica : in the Arabic by Jacques Sesiano

By Jacques Sesiano

This variation of Books IV to VII of Diophantus' Arithmetica, that are extant purely in a lately came across Arabic translation, is the outgrowth of a doctoral dissertation submitted to the Brown collage division of the background of arithmetic in could 1975. Early in 1973, my thesis adviser, Gerald Toomer, discovered of the lifestyles of this manuscript in A. Gulchln-i Macanl's just-published catalogue of the mathematical manuscripts within the Mashhad Shrine Library, and secured a photographic reproduction of it. In Sep­ tember 1973, he proposed that the research of it's the topic of my dissertation. on the grounds that obstacles of time forced us to settle on priorities, the 1st goal used to be to set up a serious textual content and to translate it. for that reason, the Arabic textual content and the English translation seem the following nearly as they did in my thesis. significant alterations, in spite of the fact that, are present in the mathematical com­ mentary and, much more so, within the Arabic index. The dialogue of Greek and Arabic interpolations is completely new, as is the reconstruction of the heritage of the Arithmetica from Diophantine to Arabic instances. it's with the private gratitude that I recognize my nice debt to Gerald Toomer for his consistent encouragement and useful assistance.

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Additional resources for Books IV to VII of Diophantus’ Arithmetica : in the Arabic Translation Attributed to Qustā ibn Lūqā

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In lines 1771,2242-46,2398-2400; 1473, 1695,2142-46. , lines 571,1313). Finally, lam-lam-alif instead of alif-lam-alif is found in a few cases (with amwal: note 435; with arbaca h : note 614 (reading milli as previous word); with am{iil: note 858). §5. Additions by Earlier Readers (or Copyists) Two kinds of minor additions are incorporated in the manuscript's text: those originating from earlier readers' explanations or corrections, which were originally marginal or supralineal, and those reSUlting from a scribe's mechanical repetition (dittography).

The regularity of its use, however,15 has led us to keep it, nolens volens, in the edition, instead of correcting it each time with a note. (fi) There is another kind of miswriting made by the second copyist, which is found in aggregates in which the initial letters are certain combinations of alif(s) and lames). The spelling alif-lam-alif instead of alif-lam-alif-alif (for ilia + initial alif) is found in several passages (with arbaca h : notes 326, 328, 333, 338, 349, 410, 413, 414, 429, 566; with ilnai: notes 495, 649).

45 Indirectly by Abcnbeder (= Ibn Badr, Suter no. 493): he does not use x 8 , but expresses x 10 by five mal's, and he gi yes for a power x 6n the denominations 2n ka'b's and 3n mal's as equivalent (Compendia, pp. 1516 of the Arabic text). 39 40 46 Part One Introduction d. Grammatical Determination of the Powers We have seen that the powers xn (n ~ 4) are generally expressed in Arabic by a sequence of the form PIP z P 3 ... , the P;'s being either mal or kacb. Thus arises the question of the position of the article when such expressions are determined.

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