Abstract
We may now provide an overview of the pre-Euclidean theory of incommensurable magnitudes and its relation to the development of the other branches of geometry in the fourth century. Following this we will append some remarks on the nature of the pre-Euclidean ‘foundations crises’ and on the Greek conception of the relation of the fields of arithmetic and geometry.
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Notes
P. Tannery, Géométrie grecque, p. 98; T. L. Heath, Euclid II, pp. 112-3. On this form of the ‘crisis’, see W. Burkert, LS 1972, pp. 455–465.
B. L. van der Waerden, SA 1954, pp. 125–6.
T. L. Heath, Math in Aristotle 1949, pp. 44–47.
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© 1975 D. Reidel Publishing Company, Dordrecht, Holland
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Knorr, W.R. (1975). Conclusions and Syntheses. In: The Evolution of the Euclidean Elements. Synthese Historical Library, vol 15. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-1754-1_9
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DOI: https://doi.org/10.1007/978-94-010-1754-1_9
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