The Complete Aristotle (eng.)

motion occupies a
period of time, and a greater magnitude is traversed in a longer
time, it is impossible that a thing should undergo a finite motion
in an infinite time, if this is understood to mean not that the
same motion or a part of it is continually repeated, but that the
whole infinite time is occupied by the whole finite motion. In all
cases where a thing is in motion with uniform velocity it is clear
that the finite magnitude is traversed in a finite time. For if we
take a part of the motion which shall be a measure of the whole,
the whole motion is completed in as many equal periods of the time
as there are parts of the motion. Consequently, since these parts
are finite, both in size individually and in number collectively,
the whole time must also be finite: for it will be a multiple of
the portion, equal to the time occupied in completing the aforesaid
part multiplied by the number of the parts.
    But it makes no difference even if the velocity is not uniform.
For let us suppose that the line AB represents a finite stretch
over which a thing has been moved in the given time, and let GD be
the infinite time. Now if one part of the stretch must have been
traversed before another part (this is clear, that in the earlier
and in the later part of the time a different part of the stretch
has been traversed: for as the time lengthens a different part of
the motion will always be completed in it, whether the thing in
motion changes with uniform velocity or not: and whether the rate
of motion increases or diminishes or remains stationary this is
none the less so), let us then take AE a part of the whole stretch
of motion AB which shall be a measure of AB. Now this part of the
motion occupies a certain period of the infinite time: it cannot
itself occupy an infinite time, for we are assuming that that is
occupied by the whole AB. And if again I take another part equal to
AE, that also must occupy a finite time in consequence of the same
assumption. And if I go on taking parts in this way, on the one
hand there is no part which will be a measure of the infinite time
(for the infinite cannot be composed of finite parts whether equal
or unequal, because there must be some unity which will be a
measure of things finite in multitude or in magnitude, which,
whether they are equal or unequal, are none the less limited in
magnitude); while on the other hand the finite stretch of motion AB
is a certain multiple of AE: consequently the motion AB must be
accomplished in a finite time. Moreover it is the same with coming
to rest as with motion. And so it is impossible for one and the
same thing to be infinitely in process of becoming or of perishing.
The reasoning he will prove that in a finite time there cannot be
an infinite extent of motion or of coming to rest, whether the
motion is regular or irregular. For if we take a part which shall
be a measure of the whole time, in this part a certain fraction,
not the whole, of the magnitude will be traversed, because we
assume that the traversing of the whole occupies all the time.
Again, in another equal part of the time another part of the
magnitude will be traversed: and similarly in each part of the time
that we take, whether equal or unequal to the part originally
taken. It makes no difference whether the parts are equal or not,
if only each is finite: for it is clear that while the time is
exhausted by the subtraction of its parts, the infinite magnitude
will not be thus exhausted, since the process of subtraction is
finite both in respect of the quantity subtracted and of the number
of times a subtraction is made. Consequently the infinite magnitude
will not be traversed in finite time: and it makes no difference
whether the magnitude is infinite in only one direction or in both:
for the same reasoning will hold good.
    This having been proved, it is evident that neither can a finite
magnitude traverse an infinite magnitude in a finite time, the
reason being the same as that given above: in part of the time it
will traverse a finite magnitude and in each several part likewise,
so that in the whole time it will traverse a finite magnitude.
    And since a finite magnitude will not traverse an infinite in a
finite time, it is clear that neither will an infinite traverse a
finite in a finite time. For if the infinite could traverse the
finite, the finite could traverse the infinite; for it makes no
difference which of the two is the thing in motion; either case
involves the