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Showing papers by "Reviel Netz published in 2003"



Journal ArticleDOI
Reviel Netz1
TL;DR: In this paper, the authorship of Eutocius' ascription to Eudoxus is discussed. But the authors focus on the second part of the puzzle, which is to identify the real author of the solution, and explain how the solution could have been falsely ascribed to Plato, in the context of a commentary on Archimedes, of finding two mean proportionals.
Abstract: A relatively well-known puzzle in the history of Greek mathematics arises from Eutocius’ ascription to Plato, in the context of a commentary on Archimedes, of a mechanical solution to the problem of finding two mean proportionals.1 That a mathematical text by Plato may have existed in antiquity, have survived until the sixth century A.D., and yet have left no other trace before or since, is incredible. On the other hand, there is no doubt that Eutocius intended his ascription—and so, probably, did his source—to refer to the famous philosopher Plato, and not to some otherwise unknown flat-footed ancient author. Other things being equal, a Plato is a Plato is a Plato.2 Thus Eutocius certainly makes a false ascription, most probably reflecting one in a lost source. The arising puzzle is twofold: first, to identify the real author of the solution; second, to explain how the solution could have been falsely ascribed to Plato. The first part of the puzzle was discussed by Knorr (who, for reasons that will become apparent below, considers the solution to be ultimately by Eudoxus).3 In this article, I concentrate on the second part of the puzzle. That something meaningful can be said concerning such questions of ascription— always very difficult to analyse—is due to the presence of another puzzle in the immediate vicinity of this one. Putting the two puzzles together, some pattern may emerge, possibly offering clues for the solution.

7 citations


Journal ArticleDOI
01 Jan 2003-Apeiron
TL;DR: In this article, the authors discuss the goal of Archimedes' Sand-Reckoner, which is related to a more general question in the history of the western exact sciences.
Abstract: Before discussing the goal of Archimedes' Sand-Reckoner, I should perhaps explain the goal of the article itself. The primary question, What is the goal of the Sand-Reckoner?, is related to a more general question in the history of the western exact sciences. It is often assumed that one major difference between ancient and modern science involves the latter's growing reliance on the numerical. Ancient mathematics frequently fails even to mention specific numbers; in modem mathematics everything, including geometrical objects, is considered through the prism of numerical values. This assumption is related to the thesis of Klein (1934-1936 /1968), where ancient mathematics is seen as more 'concrete' or first-order (and so typically related to the qualitative properties of geometrical objects) while modern mathematics is seen as more 'symbolic' or second-order (which in practice means the algebraic treatment of objects understood in terms of real numbers). More recently, it was argued in Fowler (1987, 2 ed. 1999) that Greek mathematics was non-arithmetized so that geometrical objects bore no numerical value of their size at all. It is also often noted that the modern exact sciences, much more than their ancient counterparts, are based on detailed calculation (modem calculation made possible, for instance, by the use of modem tools such as logarithms). Whether as a matter of concept or of practice, then, this standard — and, I believe, correct — picture contrasts a Greek mathematics based on geometrical figures with a modem mathematics based on the symbolic manipulation of numerical terms. Now, one major tool of this modern symbolic manipulation of numerical terms is the modem numerical system itself. Thus general histories of mathematics

4 citations