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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

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