2/26/2023 0 Comments The works of archimedesIn general this unconstrained quality will probably be welcome, both to classicists, who will appreciate asides like “in Greek mathematics, you cannot step into the same diagram twice” (p. This format allows the commentary to be much more readable and discursive than a normal commentary there is nothing constrained or compact about it, and matters of editorial choice that would normally be swept under the carpet are made gloriously explicit. The commentary is not presented in the line-by-line or lemma-by-lemma format usual for classical scholarship, but in large chunks interspersed with the translation (two chunks, one on textual matters and one interpretive, after each theorem) and, for smaller points, in the form of footnotes to the translation. Almost the only thing the commentary does not do, in fact, is to explain in terms intelligible to a reader trained in modern mathematical notation what is being said in the corresponding section of the text. It discusses exactly how Archimedes constructed his argument, which portions of it are probably not his own but later interpolations, how the community of mathematicians functioned in the time of Archimedes, how Archimedes’ arguments move from specific cases to general principles (or fail to do so), how the text interacts with the diagrams, and many equally intriguing topics. And the commentary is not only readable, but positively fascinating. Moreover, his interests 1 lie precisely in the differences between ancient mathematical thought and our own, and these issues are extensively explored in the commentary, so that at times the translation seems to be almost filling the role of a vehicle on which to hang the commentary. Netz comments that “the purpose of a scholarly translation as I understand it is to remove all barriers having to do with the foreign language itself, leaving all other barriers intact” (p. The choice to produce so difficult a translation was a very conscious one. No amount of training in modern mathematics, however, will suffice to get a reader through this translation, which presents Greek geometry as it really was: a very different way of thinking from our mathematics. Of course, geometrical proofs are not considered compelling reading by non-mathematicians at the best of times, but most people with a reasonable background (say, that provided in a year of high school geometry) can get through most of the works of Archimedes as presented in a number of other translations, which use modern mathematical notation. The corollary of the translation’s fidelity to the original, however, is that it is almost completely unreadable. It may be doubted whether true scholarly comment can ever be based on anything other than the original text, but if such use is possible for any translation, it is possible for this one. This temptation is deliberate on the part of the author, whose stated goal is to produce “a reliable translation that may serve as basis for scholarly comment” (p. Netz has re-thought many of Heiberg’s editorial decisions and discusses his thoughts at length in the commentary (not only in places where he questions Heiberg’s choices, but also often where he agrees or is unsure), so that at times one is almost tempted to treat the translation as a critical edition in its own right. It is based not only upon the best available Greek text but also upon re-examination of manuscripts, including a palimpsest that had been lost for almost all of the twentieth century. The translation itself is probably the best ever done in terms of faithfulness to the text and to Archimedes’ own way of thinking. The work is of high quality and will undoubtedly remain an important one for years to come - though perhaps less because of the translation itself than because of the accompanying material. The volume includes not only a translation but also extensive commentary, as well as a translation of the important ancient commentary by Eutocius of Ascalon, notes on that commentary, and a critical edition of the diagrams that accompany both texts in the manuscript tradition. The book under review, a translation of the two books On the Sphere and the Cylinder, is an example of particular courage well applied: it is only the first volume of a multi-volume translation project intended to cover all the works of Archimedes included in the standard Greek edition (Teubner, ed. In the case of Archimedes, probably the most famous of ancient mathematicians, the distinction is certainly well deserved, and there is considerable courage involved in any attempt to translate this difficult, elliptical, and interpolated (not to mention highly technical) set of writings. Perhaps the ultimate acknowledgement that a work of classical antiquity is truly impossible to read is the provision of a facing translation in the Teubner text.
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