The Complete Aristotle (eng.)

do not mean
this, nor are we examining this sort of infinite, but the infinite
as untraversable. Further, how can an infinite exist by itself,
unless number and magnitude also exist by themselvess-since
infinity is an attribute of these? Further, if the infinite is an
accident of something else, it cannot be qua infinite an element in
things, as the invisible is not an element in speech, though the
voice is invisible. And evidently the infinite cannot exist
actually. For then any part of it that might be taken would be
infinite (for ‘to be infinite’ and ‘the infinite’ are the same, if
the infinite is substance and not predicated of a subject).
Therefore it is either indivisible, or if it is partible, it is
divisible into infinites; but the same thing cannot be many
infinites (as a part of air is air, so a part of the infinite would
be infinite, if the infinite is substance and a principle).
Therefore it must be impartible and indivisible. But the actually
infinite cannot be indivisible; for it must be of a certain
quantity. Therefore infinity belongs to its subject incidentally.
But if so, then (as we have said) it cannot be it that is a
principle, but that of which it is an accident-the air or the even
number.
    This inquiry is universal; but that the infinite is not among
sensible things, is evident from the following argument. If the
definition of a body is ‘that which is bounded by planes’, there
cannot be an infinite body either sensible or intelligible; nor a
separate and infinite number, for number or that which has a number
is numerable. Concretely, the truth is evident from the following
argument. The infinite can neither be composite nor simple. For (a)
it cannot be a composite body, since the elements are limited in
multitude. For the contraries must be equal and no one of them must
be infinite; for if one of the two bodies falls at all short of the
other in potency, the finite will be destroyed by the infinite. And
that each should be infinite is impossible. For body is that which
has extension in all directions, and the infinite is the
boundlessly extended, so that if the infinite is a body it will be
infinite in every direction. Nor (b) can the infinite body be one
and simple-neither, as some say, something apart from the elements,
from which they generate these (for there is no such body apart
from the elements; for everything can be resolved into that of
which it consists, but no such product of analysis is observed
except the simple bodies), nor fire nor any other of the elements.
For apart from the question how any of them could be infinite, the
All, even if it is finite, cannot either be or become any one of
them, as Heraclitus says all things sometime become fire. The same
argument applies to this as to the One which the natural
philosophers posit besides the elements. For everything changes
from contrary to contrary, e.g. from hot to cold.
    Further, a sensible body is somewhere, and whole and part have
the same proper place, e.g. the whole earth and part of the earth.
Therefore if (a) the infinite body is homogeneous, it will be
unmovable or it will be always moving. But this is impossible; for
why should it rather rest, or move, down, up, or anywhere, rather
than anywhere else? E.g. if there were a clod which were part of an
infinite body, where will this move or rest? The proper place of
the body which is homogeneous with it is infinite. Will the clod
occupy the whole place, then? And how? (This is impossible.) What
then is its rest or its movement? It will either rest everywhere,
and then it cannot move; or it will move everywhere, and then it
cannot be still. But (b) if the All has unlike parts, the proper
places of the parts are unlike also, and, firstly, the body of the
All is not one except by contact, and, secondly, the parts will be
either finite or infinite in variety of kind. Finite they cannot
be; for then those of one kind will be infinite in quantity and
those of another will not (if the All is infinite), e.g. fire or
water would be infinite, but such an infinite element would be
destruction to the contrary elements. But if the parts are infinite
and simple, their places also are infinite and there will be an
infinite number of elements; and if this is impossible, and the
places are finite, the All also must be limited.
    In general, there cannot be an infinite body and also a proper
place for bodies, if every sensible body has either weight or
lightness. For it must move