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 and consequently the two together are indivisible; and if it is not throughout, it is then but in a part; then they have parts, therefore they are not indivisible.

If they confess, as in fact they admit when pressed, that their proposition is as inconceivable as the other, they acknowledge that it is not by our capacity for conceiving these things that we should judge of their truth, since these two contraries being both inconceivable, it is nevertheless necessarily certain that one of the two is true.

But as to these chimerical difficulties, which have relation only to our weakness, they oppose this natural clearness and these solid truths: if it were true that space was composed of a certain finite number of indivisibles, it would follow that two spaces, each of which should be square, that is, equal and similar on every side, being the one the double of the other, the one would contain a number of these indivisibles double the number of the indivisibles of the other. Let them bear this consequence well in mind, and let them then apply themselves to ranging points in squares until they shall have formed two, the one of which shall have double the points of the other; and then I will make every geometrician in the world yield to them. But if the thing is naturally impossible, that is, if it is an insuperable impossibility to range squares of points, the one of which shall have double the number of the other, as I would demonstrate on the spot did the thing merit that we should dwell on it, let them draw therefrom the consequence.

And to console them for the trouble they would have in certain junctures, as in conceiving that a space may have an infinity of divisibles, seeing that these are run over in so little time during which this infinity of divisibles would be run over, we must admonish them that they should not compare things so disproportionate as is the infinity of divisibles with the little time in which they are run over: but let them compare the entire space with the entire time, and the infinite divisibles of the space with the infinite moments of the time; and thus they will find that we pass over an infinity of divisibles in an infinity of moments, and a little space in a little time; in which there is no longer the disproportion that astonished them.