[29] So Plato makes Zeno say in the Parmenides, apropos of his philosophy as a whole; and all internal and external evidence supports this view. [30] �With Parmenides,� Hegel says, �philosophising proper began.� Werke (edition of 1840), vol. xiii. p. 274. [31] Parmenides, 128 A�D. [32] This interpretation is combated by Milhaud, Les philosophes-g�om�tres de la Gr�ce, p. 140 n., but his reasons do not seem to me convincing. All the interpretations in what follows are open to question, but all have the support of reputable authorities. [33] Physics, vi. 9. 2396 (R.P. 136�139). [34] Cf. Gaston Milhaud, Les philosophes-g�om�tres de la Gr�ce, p. 140 n.; Paul Tannery, Pour l'histoire de la science hell�ne, p. 249; Burnet, op. cit., p. 362. [35] Cf. R. K. Gaye, �On Aristotle, Physics, Z ix.� Journal of Philology, vol. xxxi., esp. p. 111. Also Moritz Cantor, Vorlesungen �ber Geschichte der Mathematik, 1st ed., vol. i., 1880, p. 168, who, however, subsequently adopted Paul Tannery's opinion, Vorlesungen, 3rd ed. (vol. i. p. 200). [36] �Le mouvement et les partisans des indivisibles,� Revue de M�taphysique et de Morale, vol. i. pp. 382�395. [37] �Le mouvement et les arguments de Z�non d'�l�e,� Revue de M�taphysique et de Morale, vol. i. pp. 107�125. [38] Cf. M. Brochard, �Les pr�tendus sophismes de Z�non d'�l�e,� Revue de M�taphysique et de Morale, vol. i. pp. 209�215. [39] Simplicius, Phys., 140, 28 D (R.P. 133); Burnet, op. cit., pp. 364�365. [40] Op. cit., p. 367. [41] Aristotle's words are: �The first is the one on the non-existence of motion on the ground that what is moved must always attain the middle point sooner than the end-point, on which we gave our opinion in the earlier part of our discourse.� Phys., vi. 9. 939B (R.P. 136). Aristotle seems to refer to Phys., vi. 2. 223AB [R.P. 136A]: �All space is continuous, for time and space are divided into the same and equal divisions�. Wherefore also Zeno's argument is fallacious, that it is impossible to go through an infinite collection or to touch an infinite collection one by one in a finite time. For there are two senses in which the term �infinite� is applied both to length and to time, and in fact to all continuous things, either in regard to divisibility, or in regard to the ends. Now it is not possible to touch things infinite in regard to number in a finite time, but it is possible to touch things infinite in regard to divisibility: for time itself also is infinite in this sense. So that in fact we go through an infinite, [space] in an infinite [time] and not in a finite [time], and we touch infinite things with infinite things, not with finite things.� Philoponus, a sixth-century commentator (R.P. 136A, Exc. Paris Philop. in Arist. Phys., 803, 2.