¹ Booth, N. B., ‘Zeno's Paradoxes’, JHS lxxvii (1957) 199–200Google Scholar; ‘Were Zeno's Arguments a Reply to Attacks upon Parmenides?’ Phronesis ii (1957) 5–6.

² E.g. Vlastos, G., ‘A Note on Zeno B1’, in Allen, and Furley, (ed.), Studies in Presocratic Philosophy (1975) 177–83Google Scholar; id., chapter on Zeno, in Philosophic Classics (ed. Kaufmann, W., 1961), 27–45Google Scholar; Solmsen, F., ‘The Tradition about Zeno of Elea Re-examined’ in Mourelatos, A. P. D. (ed.), The Presocratics (1974)Google Scholar; Abraham, W. E., ‘The Nature of Zeno's Argument Against Plurality in DK 29 B1’, Phronesis xvii (1972) 46–52Google Scholar; Furley, D. J., Two Studies in the Atomists (1967) ch. 5CrossRefGoogle Scholar; Hussey, E., The Presocratics (1972) 101Google Scholar; Untersteiner, M., Zenone, Testimonianze e Frammenti (1963) 201Google Scholar.

³ Earlier studies have included those of Heidel, W. A. in Proc. Amer. Acad. Arts and Sciences xlviii (1913)Google Scholar, Fraenkel, H. in Wege und Formen fruehgriechischen Denkens (Munich 1955)Google Scholar, Lee, H. D. P. in Zeno of Elea (Cambridge 1936)Google Scholar.

⁴ Vlastos takes ἀπέχєιν to mean ‘extend beyond’, basing such an interpretation on the use of the word on rare occasions in highly specialized contexts (see references to his articles in n. 2). Objections to his interpretation are:

(i) It is most implausible that Zeno would use ἀπ- and προ- to mean virtually the same thing within so close range of each other; ἀπέχєιν should mean ‘be separate from’ unless there is something in the context to bring out a different nuance.

(ii) It is really very difficult to obtain from the text, as Vlastos translates it, the geometric sequence which he wants; each successive item, in his interpretation, is first one thing, then it suddenly changes into another.

(iii) The symmetric relation between the two ἕτєρα is obscured or even lost in his interpretation; ‘right’ and ‘left’ seem to matter in his interpretation whereas in the text there is no such differentiation. (This point is made by Abraham [loc. cit. 42–3].)

⁵ Those who argue for the meaning ‘in the lead’ base their case strongly on the Achilles, argument (Phys. 239b 17–19)Google Scholar, in which προέχєιν is used of the ‘Slower’ still being a bit ahead at every stage. But the meaning there is to ‘be ahead in a race’, and it applies only accidentally to successive points in a geometric progression.

⁶ As is suggested by H. D. P. Lee (loc. cit.) who translates τοῦ προύχοντος correctly as ‘successor’ (or ‘the one beyond’), but takes this in the physical sense of points going along a line, each one ‘beyond’ its predecessor. How near he was!

⁷ One might note here mat E. Hussey takes τοῦ προύχοντος in the non-physical sense of ‘the former’, which is dubious Greek and, in my view, makes little sense.

⁸ One and Many in Presocratic Philosophy (1971) 185 n. 32. It would have been easier for Furley's interpretation if ‘παρὰ ἕκαστον τῶν Α’ had been written here instead of ‘παρὰ τὰ Α’ as it is, the plural may indicate that the meaning is ‘since both spend an equal time in going past all the A's’.