Proclus' division of the mathematical proposition into parts: How and why was it formulated?

Classical Quarterly

Volumn 49, Issue 1, 1999, Pages 282-303

  Netz, Reviel ^a  

^a GONVILLE AND CAIUS COLLEGE   (United Kingdom)

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EID: 34247100717     PISSN: 00098388     EISSN: 14716844     Source Type: Journal    
DOI: 10.1093/cq/49.1.282     Document Type: Review

References (13)

1. R. Netz, The Shaping of Deduction in Greek Mathematics (Cambridge, forthcoming)
2. W. Knorr, 'On the early history of axiomatics: the interaction of mathematics and philosophy in Greek antiquity', in J. Hintikka et al. (edd.), Theory Change, Ancient Axiomatics. and Galileo's Methodology (Dordrecht, 1981) pp. 145-86, esp. pp. 172ff. The main interest of Knorr there is large-scale style (the organization of treatises), not small-scale style (the organization of individual propositions)
3. It is endorsed, for example, in I. Mueller, 'Greek mathematics and Greek logic', in J. Corcoran (ed.), Ancient Logic and its Modern Interpretation (Dordrecht, 1974), p. 67, n. 4
4. D. Fowler notes in The Mathematics of Plato's Academy (Oxford, 1987), p. 367, n. 54, that it may not have been always strictly followed
5. I cannot do justice in this brief compass to the logical detail of the method; all I need to stress is that the method has a standard stylistic format (which however, again, is not absolutely rigid). On the logical side, see especially the discussion in J. Hintikka and U. Remes, The Method of Analysis (Dordrecht, 1974)
6. B. Einarson, 'On certain mathematical terms in Aristotle's logic', American Journal of Philology 57 (1936), 33-54, 151-172
7. See M. Mignucci, 'Expository proofs in Aristotle's Syllogistic', Oxford Studies in Ancient Philosophy (1991), suppl., 9-28, with references to earlier literature
8. Archimedes, Sphere and Cylinder 2.4 (190.25)
9. Apollonius, Introduction to Conies 4 (2.17)
10. The best philological analysis of this difficult passage remains O. Becker, 'Zur Textgestellung des Eudemischen Berichts über die Quadratur der Möndchen durch Hippokrates von Chios', Quelien und Studien zur Geschichte der Mathematik, Astronomie und Physik 3 (1936), 411-19, which includes the above quotation in Eudemus' fragment
11. See G. E. R. Lloyd, Magic Reason and Experience (Cambridge.1979), pp. 102-25
12. C. Rosen, Sonata Forms (New York, 1988)
13. See I. Mueler, foreword to second edition of Proclus: A Commentary on the First Book of Euclid's Elements, trans. G. Morrow (Princeton, 1992), pp. xlviii-1