The Complete Aristotle (eng.)

will be divisible into periods equal in number to
the segments into which the magnitude is divisible. Moreover, if it
is the case that infinite time is not occupied in passing over
every magnitude, but it is possible to ass over some magnitude, say
BE, in a finite time, and if this BE measures the whole of which it
is a part, and if an equal magnitude is passed over in an equal
time, then it follows that the time like the magnitude is finite.
That infinite time will not be occupied in passing over BE is
evident if the time be taken as limited in one direction: for as
the part will be passed over in less time than the whole, the time
occupied in traversing this part must be finite, the limit in one
direction being given. The same reasoning will also show the
falsity of the assumption that infinite length can be traversed in
a finite time. It is evident, then, from what has been said that
neither a line nor a surface nor in fact anything continuous can be
indivisible.
    This conclusion follows not only from the present argument but
from the consideration that the opposite assumption implies the
divisibility of the indivisible. For since the distinction of
quicker and slower may apply to motions occupying any period of
time and in an equal time the quicker passes over a greater length,
it may happen that it will pass over a length twice, or one and a
half times, as great as that passed over by the slower: for their
respective velocities may stand to one another in this proportion.
Suppose, then, that the quicker has in the same time been carried
over a length one and a half times as great as that traversed by
the slower, and that the respective magnitudes are divided, that of
the quicker, the magnitude ABGD, into three indivisibles, and that
of the slower into the two indivisibles EZ, ZH. Then the time may
also be divided into three indivisibles, for an equal magnitude
will be passed over in an equal time. Suppose then that it is thus
divided into KL, LM, MN. Again, since in the same time the slower
has been carried over EZ, ZH, the time may also be similarly
divided into two. Thus the indivisible will be divisible, and that
which has no parts will be passed over not in an indivisible but in
a greater time. It is evident, therefore, that nothing continuous
is without parts.
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3
    The present also is necessarily indivisible-the present, that
is, not in the sense in which the word is applied to one thing in
virtue of another, but in its proper and primary sense; in which
sense it is inherent in all time. For the present is something that
is an extremity of the past (no part of the future being on this
side of it) and also of the future (no part of the past being on
the other side of it): it is, as we have said, a limit of both. And
if it is once shown that it is essentially of this character and
one and the same, it will at once be evident also that it is
indivisible.
    Now the present that is the extremity of both times must be one
and the same: for if each extremity were different, the one could
not be in succession to the other, because nothing continuous can
be composed of things having no parts: and if the one is apart from
the other, there will be time intermediate between them, because
everything continuous is such that there is something intermediate
between its limits and described by the same name as itself. But if
the intermediate thing is time, it will be divisible: for all time
has been shown to be divisible. Thus on this assumption the present
is divisible. But if the present is divisible, there will be part
of the past in the future and part of the future in the past: for
past time will be marked off from future time at the actual point
of division. Also the present will be a present not in the proper
sense but in virtue of something else: for the division which
yields it will not be a division proper. Furthermore, there will be
a part of the present that is past and a part that is future, and
it will not always be the same part that is past or future: in fact
one and the same present will not be simultaneous: for the time may
be divided at many points. If, therefore, the present cannot
possibly have these characteristics, it follows that it must be the
same present that belongs to each of the two times. But if this is
so it is evident that the present is also indivisible: for if it is
divisible it will be involved in the same implications as before.
It is clear,