By Jacques Sesiano
This version 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 background of arithmetic in could 1975. Early in 1973, my thesis adviser, Gerald Toomer, realized 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 reproduction of it. In Sep tember 1973, he proposed that the examine of it's the topic of my dissertation. for the reason that obstacles of time forced us to settle on priorities, the 1st aim was once to set up a severe textual content and to translate it. therefore, the Arabic textual content and the English translation seem the following almost as they did in my thesis. significant alterations, despite 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 solely new, as is the reconstruction of the background of the Arithmetica from Diophantine to Arabic occasions. it truly is with the private 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
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. 46 In classical Arabic, the article can be prefixed to the first element instead of the last, since the chain of genitives may be considered as. a single word (cf.
This latter agreement is disputable. Chapter III Tentative Reconstruction of the History of the Arithmetica §8. Formal Subdivisions of a Problem 1. Analysis and Synthesis In the beginning of the seventh Book of his Collection, Pappus mentions two types of analyses and syntheses distinguished by the Greeks. 1 The first, 1tOPIO''tlKOV, type is commonly used by geometers in connection with the demonstration of a proposition, or of an (already known) solution. In the corresponding analysis, what is to be proved is supposed to be true (or known), and must be reduced by passing through its successive consequences, either to an identity or to a known proposition.
Concerning the expression of (mln)A as (lip + llq)A. The representation of some fraction (mln)A as (lIp + llq)A occasionally leads to the case mentioned by Nallino (Opus, II, p. ), 2250 and 3523 seqq. (fo). · k what is in the text expressed as "one half of one eight". 29 Apart from the fractions having their denominators represented as a product of equal factors (see above). , I, pp. 164,9 and 328,13. Part One 42 Introduction (A in the genitive) depending upon two status constructi (l/p and l/q, 1 ~ p,q ~ 10).
Books IV to VII of Diophantus’ Arithmetica : in the Arabic Translation Attributed to Qustā ibn Lūqā by Jacques Sesiano