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. 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.
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.
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In 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. At the same time, the expansiveness seems inseparable from some speculative tendencies that may be less universally applauded. A not insignificant proportion of the comments contain suggestions about questions such as Archimedes' feelings which, while interesting, are so unsusceptible of demonstration as to be normally excluded from the domain of scholarship.
Occasionally such inferences about Archimedes himself, or even other questions, are based on re-interpretations of manuscript evidence with which classicists may not be entirely comfortable. For example, when there are signs of haste or abbreviation in our versions of an ancient text, scholars studying other ancient technical works frequently believe that those works were originally fuller but have been abbreviated in transmission while Netz normally takes any evidence of haste as evidence of Archimedes' own haste.
Perhaps Archimedes' works are different from those of other ancient writers, and Netz is correct in his tacit assumption that deliberate additions were far more likely than deliberate subtractions in the transmission of this text: but one would feel more comfortable if he argued this principle rather than assuming it.
One of the most original and most interesting contributions of Netz's work is a critical edition of the diagrams that accompany Archimedes' text. Netz claims, with a good deal of plausibility, that the diagrams go back to Archimedes himself, and he has carefully documented the various forms in which each appears in the different manuscripts.
Many previous translations of Archimedes have simply redrawn the diagrams to make them adhere to the modern conventions of diagram construction, and even Heiberg was less scrupulous about the diagrams than about the Greek text. Netz is truly a pioneer in his interest in the ancient conventions of mathematical diagrams, and his reconstructions and commentary on them are particularly useful -- not to mention fascinating. The translation of Eutocius' commentaries is another particularly valuable aspect of Netz's work. The commentaries are extremely important, not only because they help us understand what Archimedes actually wrote and what he meant by it for example, a significant amount of Archimedes' text has been lost from the direct manuscript tradition and is preserved only in Eutocius' version , but also because they reveal a great deal about how the ancients understood and used the works of Archimedes and because they preserve substantial amounts of the work of other ancient mathematicians whose writings are now otherwise lost.
For this reason Eutocius' commentaries are included in Heiberg's edition of Archimedes, but they are omitted from most previous translations, thus depriving monolingual English speakers of an important aid to understanding Archimedes. The inclusion of the commentaries in this translation thus gives it a significant advantage over others. Netz also provides notes to Eutocius; though these are much less extensive than his commentary on Archimedes, they are also very valuable, especially given how little work has been done on Eutocius.
A critical edition of Eutocius' diagrams is similarly important. This first volume of Netz's translation contains a work of Archimedes that is already available in two other English versions: T. Dijksterhuis' Dutch version translated into English by C. Reporting from:. Your name.
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Between myth and mathematics: the vicissitudes of Archimedes and his work | SpringerLink
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