**Aristotle, De Caelo I**

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**Part 6, 273b 27 - 274a 19**

From what we have said, then, it is clear that the weight of
the infinite body cannot be finite. It must then be infinite. We have therefore
only to show this to be impossible in order to prove an infinite body
impossible. But the impossibility of infinite weight can be shown in the
following way. A given weight moves a given distance in a given time; a weight
which is as great and more moves the same distance in a less time, the times
being in inverse proportion to the weights. For instance, if one weight is
twice another, it will take half as long over a given movement. Further, a
finite weight traverses any finite distance in a finite time. It necessarily
follows from this that infinite weight, if there is such a thing, being, on the
one hand, as great and more than as great as the finite, will move accordingly,
but being, on the other hand, compelled to move in a time inversely
proportionate to its greatness, cannot move at all. The time should be less in
proportion as the weight is greater. But there is no proportion between the
infinite and the finite: proportion can only hold between a less and a greater
finite time. And though you may say that the time of the movement can be
continually diminished, yet there is no minimum. Nor, if there were, would it help
us. For some finite body could have been found greater than the given finite in
the same proportion which is supposed to hold between the infinite and the
given finite; so that an infinite and a finite weight must have traversed an
equal distance in equal time. But that is impossible. Again, whatever the time,
so long as it is finite, in which the infinite performs the motion, a finite
weight must necessarily move a certain finite distance in that same time.
Infinite weight is therefore impossible, and the same reasoning applies also to
infinite lightness. Bodies then of infinite weight and of infinite lightness
are equally impossible.