[99] That is, we do not consider the sophism of Zeno refuted by the fact that the geometrical progression a(1 + 1/n + 1/n2 + 1/n3 +,... etc.)—in which a designates the initial distance between Achilles and the tortoise, and n the relation of their respective velocities—has a finite sum if n is greater than 1. On this point we may refer to the arguments of F. Evellin, which we regard as conclusive (see Evellin, Infini et quantité, Paris, 1880, pp. 63-97; cf. Revue philosophique, vol. xi., 1881, pp. 564-568). The truth is that mathematics, as we have tried to show in a former work, deals and can deal only with lengths. It has therefore had to seek devices, first, to transfer to the movement, which is not a length, the divisibility of the line passed over, and then to reconcile with experience the idea (contrary to experience and full of absurdities) of a movement that is a length, that is, of a movement placed upon its trajectory and arbitrarily decomposable like it.
[100] Plato, Timaeus, 37 D.
[101] We have tried to bring out what is true and what is false in this idea, so far as spatiality is concerned (see Chapter III.). It seems to us radically false as regards duration.
[102] Aristotle, De anima, 430 a 14 και εστιν ο μεν τοιουτος νους τω πυντυ γινεσθαι, ο δε τω παντα ποιειν, ως εξις τις, οιον το φως. τροπον γαρ τινα κα το φως ποιει τα δυναμει οντα χρωματα ενεργεια χρωματα.
[103] De caelo, ii. 287 a 12 της εσχατης περιφορας ουτε κενον εστιν εξωθεν ουτε τοπος. Phys. iv. 212 a 34 το δε παν εστι μεν ως κινησεται εστι δ' ως ου. ως μεν γαρ ολον, αμα τον τοπον ου μεταβαλλει. κυκλω δε κινησεται, των μοιων γαρ ουτος ο τοπος.
[104] De caelo, i. 279 a 12 ουδε χρονος εστιν εξω του ουρανου. Phys. viii. 251 b 27 ο χρονος παθος τι κινησεως.
[105] Especially have we left almost entirely on one side those admirable but somewhat fugitive intuitions that Plotinus was later to seize, to study and to fix.
[107] Descartes, Principes, ii. § 29.
[108] Descartes, Principes, ii. §§ 36 ff.