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Book VII
Sesiano J.
Sources in the History of Mathematics and Physical Sciences,
1982,
цитирований: 1,
doi.org,
Abstract
The introduction to Book VII consists of a single sentence, which is to all appearances genuine—although the elucidation of its meaning poses some difficulty. In it the following three points are made.
Seventh Book of the Treatise of Diophantus
Sesiano J.
Sources in the History of Mathematics and Physical Sciences,
1982,
цитирований: 1,
doi.org,
Abstract
Our intention is to expound in the present Book many arithmetical problems without their departing from the type of problems seen previously in the fourth and fifth Books—even if they are different in species1—in order that it be an opportunity for (acquiring) proficiency and an increase in ex-2925 perience and skill.
The Extant Arabic Text
Sesiano J.
Sources in the History of Mathematics and Physical Sciences,
1982,
цитирований: 0,
doi.org,
Abstract
Books IV to VII of Diophantus’ Arithmetica are found in a codex, apparently a unicum, which is described under the number 295 in the eighth volume of the catalogue of the manuscripts kept in the library attached to the shrine of Imam Rezā at Mashhad (cf. Gulchīn-i Macānī, Fihrist, pp. 235-36). This codex is said to have come to the Shrine Library as the result of an endowment (waqf) made in 1932 by a certain Mirza Reza Khan from Nā’īn (Mīrzā Ridā Ḫān Nā’īnī).1 The manuscript is protected by a cardboard cover bound with and reinforced on the corners by leather. In recent times its eighty reddish-brown leaves (175 x 130 mm) have been numbered as pages.2 On each of these—except for the title-page and the last page—figure twenty lines of text (128 x 92 mm).3
Fifth Book of the Treatise of Diophantus the Alexandrian on Arithmetical Problems
Sesiano J.
Sources in the History of Mathematics and Physical Sciences,
1982,
цитирований: 0,
doi.org,
Abstract
We wish to find two numbers, one square and the other cubic, such that when we add to the square of the square a given multiple of the cubic number, 1620 the result is a square number, and when we subtract from the same another given multiple1 of the cubic number, the remainder is a square number.
Tentative Reconstruction of the History of the Arithmetica
Sesiano J.
Sources in the History of Mathematics and Physical Sciences,
1982,
цитирований: 0,
doi.org,
Abstract
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, ποριστικóν, 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. The synthesis then reverses the process. The second kind of analysis, of the ζητητικóν type, is used in the finding of a solution to a problem. Supposing the problem solved, the mathematician establishes between the known and the unknown magnitudes some relation, which is then reduced, by elimination, to a final relation containing the smallest number of unknowns possible (one for a determinate problem). This is the analysis. The synthesis simply verifies the exactness of the solution found.
Fourth Book of the Treatise of Diophantus on Squares and Cubes
Sesiano J.
Sources in the History of Mathematics and Physical Sciences,
1982,
цитирований: 0,
doi.org,
Abstract
I have presented in detail, in the preceding part of this treatise on arithmetical problems, many problems in which we ultimately, after the restoration and the reduction1, arrived at one term equal to one term, (namely) 10 those (problems) involving (either of) the two species of linear and plane number and also those which are composite. I have done that according to categories which beginners can memorize and grasp the nature of.
The Four Arabic Books and the Arithmetica
Sesiano J.
Sources in the History of Mathematics and Physical Sciences,
1982,
цитирований: 1,
doi.org,
Abstract
The Greek mathematician Diophantus of Alexandria is known with certainty to have lived between 150 B.C. and A.D. 350, as we infer from his having mentioned Hypsicles and from his having been mentioned by The on of Alexandria; it seems fairly probable, though, that he flourished about A.D. 250.1 We can be sure that he wrote at least two treatises: one dealing with problems in indeterminate analysis, the Arithmetica, and another, smaller, tract on polygonal numbers, both of which are only partially extant today.
