The Complete Aristotle (eng.)

all and the whole is not like
joining two pieces of string; for it is from this they get the
dignity they ascribe to the infinite-its containing all things and
holding the all in itself-from its having a certain similarity to
the whole. It is in fact the matter of the completeness which
belongs to size, and what is potentially a whole, though not in the
full sense. It is divisible both in the direction of reduction and
of the inverse addition. It is a whole and limited; not, however,
in virtue of its own nature, but in virtue of what is other than
it. It does not contain, but, in so far as it is infinite, is
contained. Consequently, also, it is unknowable, qua infinite; for
the matter has no form. (Hence it is plain that the infinite stands
in the relation of part rather than of whole. For the matter is
part of the whole, as the bronze is of the bronze statue.) If it
contains in the case of sensible things, in the case of
intelligible things the great and the small ought to contain them.
But it is absurd and impossible to suppose that the unknowable and
indeterminate should contain and determine.
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7
    It is reasonable that there should not be held to be an infinite
in respect of addition such as to surpass every magnitude, but that
there should be thought to be such an infinite in the direction of
division. For the matter and the infinite are contained inside what
contains them, while it is the form which contains. It is natural
too to suppose that in number there is a limit in the direction of
the minimum, and that in the other direction every assigned number
is surpassed. In magnitude, on the contrary, every assigned
magnitude is surpassed in the direction of smallness, while in the
other direction there is no infinite magnitude. The reason is that
what is one is indivisible whatever it may be, e.g. a man is one
man, not many. Number on the other hand is a plurality of ‘ones’
and a certain quantity of them. Hence number must stop at the
indivisible: for ‘two’ and ‘three’ are merely derivative terms, and
so with each of the other numbers. But in the direction of
largeness it is always possible to think of a larger number: for
the number of times a magnitude can be bisected is infinite. Hence
this infinite is potential, never actual: the number of parts that
can be taken always surpasses any assigned number. But this number
is not separable from the process of bisection, and its infinity is
not a permanent actuality but consists in a process of coming to
be, like time and the number of time.
    With magnitudes the contrary holds. What is continuous is
divided ad infinitum, but there is no infinite in the direction of
increase. For the size which it can potentially be, it can also
actually be. Hence since no sensible magnitude is infinite, it is
impossible to exceed every assigned magnitude; for if it were
possible there would be something bigger than the heavens.
    The infinite is not the same in magnitude and movement and time,
in the sense of a single nature, but its secondary sense depends on
its primary sense, i.e. movement is called infinite in virtue of
the magnitude covered by the movement (or alteration or growth),
and time because of the movement. (I use these terms for the
moment. Later I shall explain what each of them means, and also why
every magnitude is divisible into magnitudes.)
    Our account does not rob the mathematicians of their science, by
disproving the actual existence of the infinite in the direction of
increase, in the sense of the untraversable. In point of fact they
do not need the infinite and do not use it. They postulate only
that the finite straight line may be produced as far as they wish.
It is possible to have divided in the same ratio as the largest
quantity another magnitude of any size you like. Hence, for the
purposes of proof, it will make no difference to them to have such
an infinite instead, while its existence will be in the sphere of
real magnitudes.
    In the fourfold scheme of causes, it is plain that the infinite
is a cause in the sense of matter, and that its essence is
privation, the subject as such being what is continuous and
sensible. All the other thinkers, too, evidently treat the infinite
as matter-that is why it is inconsistent in them to make it what
contains, and not what is contained.
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    div id="section26" class="section" title="8">
8
    It remains to dispose of the arguments which are supposed to
support