Arist. _Phys._ Ζ, 9. 239 b 14 (R. P. 137).
The “hypothesis” of the second argument is the same as that in the
first, namely, that the line is a series of points; but the reasoning is
complicated by the introduction of another moving object. The
difference, accordingly, is not a half every time, but diminishes in a
constant ratio. Again, the first argument shows that no moving object
can ever traverse any distance at all, however fast it may move; the
second emphasises the fact that, however slowly it moves, it will
traverse an infinite distance.
(3) The arrow in flight is at rest. For, if everything is at rest when
it occupies a space equal to itself, and what is in flight at any
given moment always occupies a space equal to itself, it cannot
move.[893]
Footnote 893:
_Phys._ Ζ, 9. 239 b 30 (R. P. 138); _ib._ 239 b 5 (R. P. 138 a). The
latter passage is corrupt, though the meaning is plain. I have
translated Zeller’s version of it εἰ γάρ, φησίν, ἠρεμεῖ πᾶν ὅταν ᾖ
κατὰ τὸ ἴσον, ἔστι δ’ ἀεὶ τὸ φερόμενον ἐν τῷ νῦν κατὰ τὸ ἴσον,
ἀκίνητον, κ.τ.λ. Of course ἀεί means “at any time,” not “always,” and
κατὰ τὸ ἴσον is, literally, “on a level with a space equal (to
itself).” For other readings, see Zeller, p. 598, n. 3; and Diels,
_Vors._ p. 131, 44.
Here a further complication is introduced. The moving object itself has
length, and its successive positions are not points but lines. The
successive moments in which it occupies them are still, however, points
of time. It may help to make this clear if we remember that the flight
of the arrow as represented by the cinematograph would be exactly of
this nature.
(4) Half the time may be equal to double the time. Let us suppose
three rows of bodies,[894] one of which (A) is at rest while the other
two (B, C) are moving with equal velocity in opposite directions (Fig.
1). By the time they are all in the same part of the course, B will
have passed twice as many of the bodies in C as in A (Fig. 2).
FIG. 1
A. ● ● ● ●
B. ● ● ● ● →
C. ← ● ● ● ●
FIG. 2
A. ● ● ● ●
B. ● ● ● ●
C. ● ● ● ●
Therefore the time which it takes to pass C is twice as long as the
time it takes to pass A. But the time which B and C take to reach the
position of A is the same. Therefore double the time is equal to the
half.[895]
Footnote 894:
The word is ὄγκοι; cf. Chap. VII. p. 338, _n._ 794. The name is very
appropriate for the Pythagorean units, which Zeno had shown to have
length, breadth, and thickness (fr. 1).
Footnote 895:
Public-domain text, read in full here on John Shaqi.
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