
On The Heavens
(1. The infinite cannot be acted upon by the finite.) Let A be an
infinite, B a finite, C the time of a given movement produced by one
in the other. Suppose, then, that A was heated, or impelled, or
modified in any way, or caused to undergo any sort of movement
whatever, by in the time C. Let D be less than B; and, assuming that a
lesser agent moves a lesser patient in an equal time, call the
quantity thus modified by D, E. Then, as D is to B, so is E to some
finite quantum. We assume that the alteration of equal by equal
takes equal time, and the alteration of less by less or of greater
by greater takes the same time, if the quantity of the patient is such
as to keep the proportion which obtains between the agents, greater
and less. If so, no movement can be caused in the infinite by any
finite agent in any time whatever. For a less agent will produce
that movement in a less patient in an equal time, and the
proportionate equivalent of that patient will be a finite quantity,
since no proportion holds between finite and infinite.
(2. The infinite cannot act upon the finite.) Nor, again, can
the infinite produce a movement in the finite in any time whatever.
Let A be an infinite, B a finite, C the time of action. In the time C,
D will produce that motion in a patient less than B, say F. Then
take E, bearing the same proportion to D as the whole BF bears to F. E
will produce the motion in BF in the time C. Thus the finite and
infinite effect the same alteration in equal times. But this is
impossible; for the assumption is that the greater effects it in a
shorter time. It will be the same with any time that can be taken,
so that there will no time in which the infinite can effect this
movement. And, as to infinite time, in that nothing can move another
or be moved by it. For such time has no limit, while the action and
reaction have.
(3. There is no interaction between infinites.) Nor can infinite
be acted upon in any way by infinite. Let A and B be infinites, CD
being the time of the action A of upon B. Now the whole B was modified
