Cambridge Ludic Proof Greek Mathematics And The Alexandrian by Reviel Netz

By Reviel Netz

This booklet represents a brand new departure in technology reviews: an research of a systematic form of writing, situating it in the context of the modern sort of literature. Its philosophical importance is that it offers a unique approach of constructing feel of the proposal of a systematic sort. For the 1st time, the Hellenistic mathematical corpus - some of the most large extant for the interval - is put centre-stage within the dialogue of Hellenistic tradition as a complete. Professor Netz argues that Hellenistic mathematical writings undertake a story approach in keeping with shock, a compositional shape in line with a mosaic of it appears unrelated parts, and a carnivalesque large quantity of element. He additional investigates how such stylistic personal tastes derive from, and throw gentle on, the fashion of Hellenistic poetry. this crucial e-book might be welcomed by means of all students of Hellenistic civilization in addition to historians of historical technology and Western arithmetic.

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I assumed – as a generation of scholars was trained to assume – that Greek mathematics, certainly in its canonical form seen in the works of Euclid, Apollonius, and Archimedes, systematically foregrounded geometrical considerations. This would lead one to look for a geometrical study having to do with the tangram shapes of the Stomachion – which indeed must have formed part of the structure of Archimedes’ treatise. ” The translation of a single, crucial word is difficult, as the word is both difficult to read and, likely, corrupt.

In fact any permutation of propositional order within a deductively sound treatise still remains deductively sound: deductive soundness depends not on the sequence of presentation (at heart, a stylistic concern), but on the absence of circular paths of demonstration. The Measurement of the Circle as it stands is therefore deductively sound. Still, it is remarkably outside the norm of Greek mathematical writing which – as a very strong rule – does not allow such permutations of propositions. This, coupled with the falseness of proposition , makes most modern readers believe proposition  is a late interpolation.

It is also remarkable in its aesthetic structure, where variety and surprise are systematically deployed to good effect. Archimedes’ immortality is firmly based on mathematical achievement. The same mathematical content, expressed ponderously and clumsily, would still have earned Archimedes his glory, although as we have suggested already, it would be difficult to present a result as striking as that of Spiral Lines without something of its brilliance shining through the style of the writing. And conversely: the same rhetorical structure, expressing poorly thought-out mathematics, would have been quickly forgotten.

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