Abstract
The date and manner of the first discovery of incommensurability have not been preserved for us by any credible witness. Three authors, seven hundred years after the fact, offer us some information of the origins of the theory of incommensurability, but it is difficult to judge how much, if any, historical validity this information has.
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Notes
Pappus, Commentary…on Book X of Euclid’s Elements, ed. G. Junge and W. Thomson, 1930, pp. 63, 64. The same story is told in a Greek scholium to the Tenth Book; cf. Euclid, Elementa, ed, J. L. Heiberg, V, p. 417. Here the terms for “irrational” are bXoyov and dveiSeov. This scholium may derive from Proclus; cf. J. H. Knoche, Scholien des Proklus Diadochus zu Euklids Elementen 1865, pp. 17 - 28.
Proclus, In Primum Euclidis Elementorum Librum, ed. G. Friedlein, 1873, p. 65.
T. L. Heath, HGM 1921, 1, p. 154. The abbreviated version of the Eudemean summary appears in Hero, Definitiones, etc. (Opera, ed. J. L. Heiberg, IV, p. 108 ).
J. L. Heiberg, ‘Mathematisches zu Aristoteles’, AbhGMW 1904, 18, p. 24; also H. Vogt, ‘Entdeckungsgeschichte’, BM 1909–10, pp. 148–9.
O. Becker, in Das mathematische Denken der Antike, 1957, p. 51, has offered a similar argument for showing the impossibility of solving the relation A2=2B2 in integers, via the pebble-arithmetic of the Pythagoreans.
H.Diels, FV 1951, 29A25, I, p. 253. The Achilles-paradox (ibid., A26) involves similar principles.
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© 1975 D. Reidel Publishing Company, Dordrecht, Holland
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Knorr, W.R. (1975). The Side and the Diameter. In: The Evolution of the Euclidean Elements. Synthese Historical Library, vol 15. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-1754-1_2
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