Page:Blaise Pascal works.djvu/451

 with accuracy what we are considering in extension, this must be the relation of zero to numbers; for zero is not of the same kind as numbers, since, being multiplied, it cannot exceed them: so that it is the true indivisibility of number, as indivisibility is the true zero of extension. And a like one will be found between rest and motion, and between an instant and time; for all these things are heterogeneous in their magnitudes, since being infinitely multiplied, they can never make any thing else than indivisibles, any more than the indivisibles of extension, and for the same reason. And then we shall find a perfect correspondence between these things; for all these magnitudes are divisible ad infinitum, without ever falling into their indivisibles, so that they all hold a middle place between infinity and nothingness.

Such is the admirable relation that nature has established between these things, and the two marvellous infinities which she has proposed to mankind, not to comprehend, but to admire; and to finish the consideration of this by a last remark, I will add that these two infinites, although infinitely different, are notwithstanding relative to each other, in such a manner that the knowledge of the one leads necessarily to the knowledge of the other.

For in numbers, inasmuch as they can be continually augmented, it absolutely follows that they can be continually diminished, and this clearly; for if a number can be multiplied to 100,000, for example, 100,000th part can also be taken from it, by dividing it by the same number by which it is multiplied; and thus every term of augmentation will become a term of division, by changing the whole into a fraction. So that infinite augmentation also includes necessarily infinite division.

And in space the same relation is seen between these two contrary infinites; that is, that inasmuch as a space can be infinitely prolonged, it follows that it may be infinitely diminished, as appears in this example: If we look through a glass at a vessel that recedes continually in a straight line, it is evident that any point of the vessel observed will continually advance by a perpetual flow in proportion as the ship recedes. Therefore if the course of the vessel is extended ad infinitum, this point will continually recede; and