The Complete Aristotle (eng.)

traversing of the infinite by the finite. For when the
infinite magnitude A is in motion a part of it, say GD, will occupy
the finite and then another, and then another, and so on to
infinity. Thus the two results will coincide: the infinite will
have completed a motion over the finite and the finite will have
traversed the infinite: for it would seem to be impossible for the
motion of the infinite over the finite to occur in any way other
than by the finite traversing the infinite either by locomotion
over it or by measuring it. Therefore, since this is impossible,
the infinite cannot traverse the finite.
    Nor again will the infinite traverse the infinite in a finite
time. Otherwise it would also traverse the finite, for the infinite
includes the finite. We can further prove this in the same way by
taking the time as our starting-point.
    Since, then, it is established that in a finite time neither
will the finite traverse the infinite, nor the infinite the finite,
nor the infinite the infinite, it is evident also that in a finite
time there cannot be infinite motion: for what difference does it
make whether we take the motion or the magnitude to be infinite? If
either of the two is infinite, the other must be so likewise: for
all locomotion is in space.
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8
    Since everything to which motion or rest is natural is in motion
or at rest in the natural time, place, and manner, that which is
coming to a stand, when it is coming to a stand, must be in motion:
for if it is not in motion it must be at rest: but that which is at
rest cannot be coming to rest. From this it evidently follows that
coming to a stand must occupy a period of time: for the motion of
that which is in motion occupies a period of time, and that which
is coming to a stand has been shown to be in motion: consequently
coming to a stand must occupy a period of time.
    Again, since the terms ‘quicker’ and ‘slower’ are used only of
that which occupies a period of time, and the process of coming to
a stand may be quicker or slower, the same conclusion follows.
    And that which is coming to a stand must be coming to a stand in
any part of the primary time in which it is coming to a stand. For
if it is coming to a stand in neither of two parts into which the
time may be divided, it cannot be coming to a stand in the whole
time, with the result that that that which is coming to a stand
will not be coming to a stand. If on the other hand it is coming to
a stand in only one of the two parts of the time, the whole cannot
be the primary time in which it is coming to a stand: for it is
coming to a stand in the whole time not primarily but in virtue of
something distinct from itself, the argument being the same as that
which we used above about things in motion.
    And just as there is no primary time in which that which is in
motion is in motion, so too there is no primary time in which that
which is coming to a stand is coming to a stand, there being no
primary stage either of being in motion or of coming to a stand.
For let AB be the primary time in which a thing is coming to a
stand. Now AB cannot be without parts: for there cannot be motion
in that which is without parts, because the moving thing would
necessarily have been already moved for part of the time of its
movement: and that which is coming to a stand has been shown to be
in motion. But since AB is therefore divisible, the thing is coming
to a stand in every one of the parts of AB: for we have shown above
that it is coming to a stand in every one of the parts in which it
is primarily coming to a stand. Since then, that in which primarily
a thing is coming to a stand must be a period of time and not
something indivisible, and since all time is infinitely divisible,
there cannot be anything in which primarily it is coming to a
stand.
    Nor again can there be a primary time at which the being at rest
of that which is at rest occurred: for it cannot have occurred in
that which has no parts, because there cannot be motion in that
which is indivisible, and that in which rest takes place is the
same as that in which motion takes place: for we defined a state of
rest to be the state of a thing to which motion is natural but
which is not in motion when (that is to say in that in which)
motion would be natural to it. Again, our use of the phrase ‘being
at rest’ also implies that the previous state of a thing is still
unaltered, not one point only but two at