EVERYTHING that is in motion must be moved by something. For if it
has not the source of its motion in itself it is evident that it is
moved by something other than itself, for there must be something else
that moves it. If on the other hand it has the source of its motion in
itself, let AB be taken to represent that which is in motion
essentially of itself and not in virtue of the fact that something
belonging to it is in motion. Now in the first place to assume that
AB, because it is in motion as a whole and is not moved by anything
external to itself, is therefore moved by itself-this is just as if,
supposing that KL is moving LM and is also itself in motion, we were
to deny that KM is moved by anything on the ground that it is not
evident which is the part that is moving it and which the part that is
moved. In the second place that which is in motion without being moved
by anything does not necessarily cease from its motion because
something else is at rest, but a thing must be moved by something if
the fact of something else having ceased from its motion causes it
to be at rest. Thus, if this is accepted, everything that is in motion
must be moved by something. For AB, which has been taken to
represent that which is in motion, must be divisible since
everything that is in motion is divisible. Let it be divided, then, at
G. Now if GB is not in motion, then AB will not be in motion: for if
it is, it is clear that AG would be in motion while BG is at rest, and
thus AB cannot be in motion essentially and primarily. But ex
hypothesi AB is in motion essentially and primarily. Therefore if GB
is not in motion AB will be at rest. But we have agreed that that
which is at rest if something else is not in motion must be moved by
something. Consequently, everything that is in motion must be moved by
something: for that which is in motion will always be divisible, and
if a part of it is not in motion the whole must be at rest.

    Since everything that is in motion must be moved by something, let
us take the case in which a thing is in locomotion and is moved by
something that is itself in motion, and that again is moved by
something else that is in motion, and that by something else, and so
on continually: then the series cannot go on to infinity, but there
must be some first movent. For let us suppose that this is not so
and take the series to be infinite. Let A then be moved by B, B by
G, G by D, and so on, each member of the series being moved by that
which comes next to it. Then since ex hypothesi the movent while
causing motion is also itself in motion, and the motion of the moved
and the motion of the movent must proceed simultaneously (for the
movent is causing motion and the moved is being moved
simultaneously) it is evident that the respective motions of A, B,
G, and each of the other moved movents are simultaneous. Let us take
the motion of each separately and let E be the motion of A, Z of B,
and H and O respectively the motions of G and D: for though they are
all moved severally one by another, yet we may still take the motion
of each as numerically one, since every motion is from something to
something and is not infinite in respect of its extreme points. By a
motion that is numerically one I mean a motion that proceeds from
something numerically one and the same to something numerically one
and the same in a period of time numerically one and the same: for a
motion may be the same generically, specifically, or numerically: it
is generically the same if it belongs to the same category, e.g.
substance or quality: it is specifically the same if it proceeds
from something specifically the same to something specifically the
same, e.g. from white to black or from good to bad, which is not of
a kind specifically distinct: it is numerically the same if it
proceeds from something numerically one to something numerically one
in the same period of time, e.g. from a particular white to a
particular black, or from a particular place to a particular place, in
a particular period of time: for if the period of time were not one
and the same, the motion would no longer be numerically one though
it would still be specifically one.

    We have dealt with this question above. Now let us further take
the time in which A has completed its motion, and let it be
represented by K. Then since the motion of A is finite the time will
also be finite. But since the movents and the things moved are
infinite, the motion EZHO, i.e. the motion that is composed of all the
individual motions, must be infinite. For the motions of A, B, and the
others may be equal, or the motions of the others may be greater:
but assuming what is conceivable, we find that whether they are
equal or some are greater, in both cases the whole motion is infinite.
And since the motion of A and that of each of the others are
simultaneous, the whole motion must occupy the same time as the motion
of A: but the time occupied by the motion of A is finite: consequently
the motion will be infinite in a finite time, which is impossible.

    It might be thought that what we set out to prove has thus been
shown, but our argument so far does not prove it, because it does
not yet prove that anything impossible results from the contrary
supposition: for in a finite time there may be an infinite motion,
though not of one thing, but of many: and in the case that we are
considering this is so: for each thing accomplishes its own motion,
and there is no impossibility in many things being in motion
simultaneously. But if (as we see to be universally the case) that
which primarily is moved locally and corporeally must be either in
contact with or continuous with that which moves it, the things
moved and the movents must be continuous or in contact with one
another, so that together they all form a single unity: whether this
unity is finite or infinite makes no difference to our present
argument; for in any case since the things in motion are infinite in
number the whole motion will be infinite, if, as is theoretically
possible, each motion is either equal to or greater than that which
follows it in the series: for we shall take as actual that which is
theoretically possible. If, then, A, B, G, D form an infinite
magnitude that passes through the motion EZHO in the finite time K,
this involves the conclusion that an infinite motion is passed through
in a finite time: and whether the magnitude in question is finite or
infinite this is in either case impossible. Therefore the series
must come to an end, and there must be a first movent and a first
moved: for the fact that this impossibility results only from the
assumption of a particular case is immaterial, since the case
assumed is theoretically possible, and the assumption of a
theoretically possible case ought not to give rise to any impossible
result.