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 in simple terms in a lately chanced on Arabic translation, is the outgrowth of a doctoral dissertation submitted to the Brown collage division of the historical past of arithmetic in might 1975. Early in 1973, my thesis adviser, Gerald Toomer, discovered of the life 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 replica of it. In Sep­ tember 1973, he proposed that the learn of or not it's the topic of my dissertation. on account that boundaries of time pressured us to settle on priorities, the 1st target was once to set up a serious textual content and to translate it. therefore, the Arabic textual content and the English translation look right here almost as they did in my thesis. significant alterations, although, are present in the mathematical com­ mentary and, much more so, within the Arabic index. The dialogue of Greek and Arabic interpolations is fullyyt new, as is the reconstruction of the historical past of the Arithmetica from Diophantine to Arabic occasions. it really is with the inner most gratitude that I recognize my nice debt to Gerald Toomer for his consistent encouragement and valuable assistance.

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

Example text

Simon, Anatomie des Galen, I, p. xxi). For all these cases, we have standardized the spelling by adopting the classical orthography. 13 2. Particular Endings The following uses, though not peculiar to our manuscript (see Graf, Sprachgebrauch, pp. 8-9), are worthy of note: an alif otiosum (alif al-wiqaya h) which is appended to the form yatlii (note 3); (b) the ending -i takes the place of the ending _in, in two places, once by each hand (notes 15, 771); otherwise the spelling is correct; (c) again exceptional is the writing of an alif where an ought to be used, which occurs twice in the second handwriting (notes 172, 579).

Pp. , I, p. 1484). , 695, 783, 863, 865, 866). , lines 187, 188,475,649, 736. , 440,1475, and 321, 499-500). Those numerals which are construed with the genitive of the numbered object ought, in classical Arabic, not to have the article themselves, since they are in the status constructus. But this rule is not always observed (cf. CaspariWright, II, p. 244). While the "classical" case is poorly represented in our text (see lines 149, 523,524-25; cf. note 398), the other two combinations appear frequently.

44 In Books VI and VII, x 8 is designated as QQQQ (mal mal mal mal). The usage of this denomination in Arabic times is confirmed by its repeated appearance in Abu Kamil's Algebra (fol. 45 What the Greek Arithmetica had in these places we do not know; but one should keep in mind that an expression of x 8 by means of Qonly is known to have existed in Greek times (the 'tE'tP(X1tA:ii ()UV(Xlll~ mentioned above). See also p. B. Remark. Powers in the denominator occur in our text in problem VI,23 only.

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