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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

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