toise, 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 quantite_, 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.]

[Footnote 100: Plato, _Timaeus_, 37 D.]

[Footnote 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_.]

[Footnote 102: Aristotle, _De anima_, 430 a 14 [Greek: kai hestin ho men
toioutos nous to pynta ginesthai, ho de to panta poiein, os hexis tis,
oion to phos. tropon gar tina ka to phos poiei ta dynamei onta chromata
energeia chromata].]

[Footnote 103: _De caelo_, ii. 287 a 12 [Greek: tes eschates periphoras
oute kenon estin exothen oute topos.] _Phys._ iv. 212 a 34 [Greek: to de
pan esti men hos kinesetai hesti d' hos ou. hos men gar holon, hama ton
topon hou metaballei. kyklo de kinesetai, ton morion gar outos ho
topos].]

[Footnote 104: _De caelo_, i. 279 a 12 [Greek: oude chronos hestin hexo
tou ouranou]. _Phys._ viii. 251 b 27 [Greek: ho chronos pathos ti
kineseos].]

[Footnote 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.]

[Footnote 106: See page 10.]

[Footnote 107: Descartes, _Principes_, ii. Sec. 29.]

[Footnote 108: Descartes, _Principes_, ii. Sec.Sec. 36 ff.]

[Footnote 109: In a course of lectures on Plotinus, given at the College
de France in 1897-1898, we tried to bring out these resemblances. They
are numerous and impressive. The analogy is continued even in the
formulae employed on each side.]

[Footnote 110: "Le Paralogisme psycho-physiologique" (_Revue de
metaphysique et de morale_, Nov. 1904, pp. 895-908). Cf. _Matiere et
memoire_, Paris, 1896, chap. i.]

INDEX

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