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The Readings of Apollonius' On the Cutting off of a Ratio

Published online by Cambridge University Press:  27 February 2012

Ioannis M. Vandoulakis
Ioannis M. Vandoulakis*
Affiliation:
University of the Aegean, Department of Cultural Technology and Communication, University Hill, 81100 Mytilene, Greece
*
Email: [email protected]
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Extract

During the second half of the twentieth century an attention of historians of mathematics shifted to mathematics of the Late Antiquity and its subsequent development by mathematicians of the Arabic world. Many critical editions of works of mathematicians of the Hellenistic era have made their appearance, giving rise to a new, more detailed historical picture. Among these are the critical editions of the works of Diophantus, Apollonius, Archimedes, Pappus, Diocles, and others.

Type
Essay-Review
Information
Arabic Sciences and Philosophy , Volume 22 , Issue 1 , March 2012 , pp. 137 - 149
Copyright
Copyright © Cambridge University Press 2012

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References

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18 This interpretation is adopted, for instance, by Heath (Euclid, The Thirteen Books of The Elements, tr. Thomas Little Heath, 2nd edn, 3 vols. (New York, 1956; orig. publ. Cambridge, 1925, I, pp. 138–9Google Scholar). This imposes on Pappus the view that analysis and synthesis are deductively symmetrical. See also Cherniss, Harold, “Plato as mathematician,” Review of Metaphysics, 4.3 (1951): 395–425Google Scholar.

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22 Marini Philosophi Commentarius in Euclidis Data, in Euclid's Data in Euclidis opera omnia, ed. H. Menge, vol. 6 (Leipzig 1896), p. 234; Taisbak, Christian Marinus (ed.), Euclid's Data: The Importance of Being Given, Acta Historica Scientiarum Naturalium Et Medicinalium 45 (Copenhagen, 2003), p. 243Google Scholar.

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24 Gardies, Jean Louis, “Do mathematical constructions escape logic?” Synthese, 134 (2003): 3–24CrossRefGoogle Scholar.

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26 Per Erik Rutger Martin-Löf, Intuitionistic Type Theory (Naples, 1984).

27 Bellosta, “Ibrāhīm ibn Sinān: on analysis and synthesis”, p. 212.

28 Pappus of Alexandria, Book 7 of the Collection, ed. Jones, vol. 1, p. 67.

29 Ian Mueller, Review of: The Method of Analysis: Its Geometrical Origin and Its General Significance by Jaakko Hintikka and Unto Remes, in The Journal of Philosophy, vol. 73, no. 6 (Mar. 25, 1976): 158–62; 160–1CrossRefGoogle Scholar.

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33 Bellosta, “Ibrāhīm ibn Sinān: on analysis and synthesis”, p. 211.

34 See also Rashed, “Analysis and synthesis according to Ibn al-Haytham”, pp. 121–40.

35 Ibid., pp. 131–2.

36 Apollonius de Perge, La section des droites selon des rapports, p. 17.