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

By Jacques Sesiano

This variation of Books IV to VII of Diophantus' Arithmetica, that are extant basically in a lately chanced on Arabic translation, is the outgrowth of a doctoral dissertation submitted to the Brown collage division of the heritage of arithmetic in could 1975. Early in 1973, my thesis adviser, Gerald Toomer, realized 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 replica of it. In Sep­ tember 1973, he proposed that the examine of or not it's the topic of my dissertation. considering the fact that boundaries of time forced us to settle on priorities, the 1st target was once to set up a serious textual content and to translate it. as a result, the Arabic textual content and the English translation look the following almost as they did in my thesis. significant alterations, even if, are present in the mathematical com­ mentary and, much more so, within the Arabic index. The dialogue of Greek and Arabic interpolations is totally new, as is the reconstruction of the heritage of the Arithmetica from Diophantine to Arabic instances. it really is with the inner most gratitude that I recognize my nice debt to Gerald Toomer for his consistent encouragement and important 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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I, pp. 4,12-6,8). 34 The relevant passage of St. 206 = Mem. , II, p. 90, and printed in Diels' Doxographi graeci, pp. 556-57. 35 In this system the values of k are generally limited to 0,1,2 only: see below, (h). ano 44 Part One Introduction cubes among the powers is the origin of the designations of the fifth and the seventh powers: &AOYO~ is any power which does not belong to a Q-class {x2n} or to a C-class {x 3n } (in other words any x N with N not divisible by 2 or 3), and of those x 5 is the first and x 7 the second (X ll being the third and so on).

36 The denomination of powers was carried on in the Diophantine way for higher powers, the rules being (in our symbolism) that x 3n is represented by n C's, x 3n 1 (= X 3 (n -1) + 2) by one Q followed by n - 1 C's, and x 3n 2 (=x 3 (n-2)+4) by two Q's followed by n - 2 C's. Thus,forinstance,x 8 is expressed asmal ka'b ka'b andx 9 aska'b ka'bka'b. B. Certain Islamic mathematicians use some different denominations (see below). But quite a different system is that described by Luca Pacioli (Summa, fo1.

Those in the middle of Book VI), though not systematically (see lines 2698, 2728-29, 2801-4, 3088-89 (cf. " fo1. 107r ). ~, of which there are only a few occurrences (see below). ); 196 = t + t· kalso occurs (in IV,22, in the middle of Book VI, and in VII,6); i ~ = + kis used only incidentally (line 402; cf. 2701). Finally, some fractions are decomposed into a sum of fractions having powers of the same number in the denominator: ~~ = %+ %. , the Badf', cf. fo1. 118 v, 124\ 125", 128 V), in some of which it is even quite frequent (as in the Algebra of Abu Kami1).

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