
On The Heavens
These assumed bodies will be commensurate in mass and in weight alike.
Nor again does it make any difference to our demonstration whether the
total mass has its weight equally or unequally distributed. For it
must always be Possible to take from the infinite mass a body of equal
weight to BD by diminishing or increasing the size of the section to
the necessary extent.
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
