Plato's mathematical construction

Classical Quarterly

Volumn 53, Issue 2, 2003, Pages 500-509

  Netz, Reviel ^a  

^a STANFORD UNIVERSITY   (United States)

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Indexed keywords

EID: 62949236252     PISSN: 00098388     EISSN: 14716844     Source Type: Journal    
DOI: 10.1093/cq/53.2.500     Document Type: Article

References (7)

1. J. L. Heiberg, Archimedis opera omnia III (Teubner, 1915), 56.13-58.14. The text, as well as its context, is translated below
2. W. R. Knorr, The Ancient Tradition of Geometric Problems (New York, 1986), 57-61
3. id., Textual Studies in Ancient and Medieval Geometry (Boston, 1989), 78-80
4. The following translation of Heiberg (n. 1), 54.26-58.14 follows the conventions used, for example, in R. Netz, Archimedes transformed: the case of a result stating a maximum for a cubic equation', Archive for History of Exact Sciences 54 (1999), 1-47. In particular, I mark, for ease of reference, steps of the construction by Latin letters, and steps of the proof by Arabic numerals
5. See the discussion in S. Cuomo, Pappus of Alexandria and the Mathematics of Late Antiquity (Cambridge, 2000)
6. See G. E. R. Lloyd, 'The Meno and the mysteries of mathematics', Phronesis 37 (1992), 166-83, for an account of Plato's, more typical, intended indeterminacy in mathematical descriptions
7. L. Zhmud, 'Plato as "architect of science"', Phronesis 43 (1998), 211-44, surveys the general phenomenon of this mathematical construction of Plato. Perhaps the example closest to the process suggested in this article is Simplicius' account of Plato's role in the early history of astronomy, perhaps derived from Sosigenes. According to this account (Simplicius in De Caelo 488.20-4), Plato set an explicit task to mathematical astronomers, 'to find what are the uniform and ordered movements by the assumption of which the apparent movements of the planets can be accounted for'. This is clearly a reading - as if it was meant to be read in such theoretically precise terms - of a vague and discursive passage in the Laws, 821b5-822c9. Astronomy was extracted out of Plato; so, I suggest, was stereometry