Page:Blaise Pascal works.djvu/450

 multiplied several times, exceed any number whatsoever, it is precisely of the same kind with numbers through its essence and its immutable nature, in the meaning of the same Euclid who would not have it called a number.

It is not the same thing with an indivisible in respect to an extension. For it not only differs in name, which is voluntary, but it differs in kind, by the same definition; since an indivisible, multiplied as many times as we like, is so far from being able to exceed an extension, that it can never form any thing else than a single and exclusive indivisible; which is natural and necessary, as has been already shown. And as this last proof is founded upon the definition of these two things, indivisible and extension, we will proceed to finish and perfect the demonstration.

An indivisible is that which has no part, and extension is that which has divers separate parts.

According to these definitions, I affirm that two indivisibles united do not make an extension.

For when they are united, they touch each other in some part; and thus the parts whereby they come in contact are not separate, since otherwise they would not touch each other. Now, by their definition, they have no other parts; therefore they have no separate parts; therefore they are not an extension by the definition of extension which involves the separation of parts.

The same thing will be shown of all the other indivisibles that may be brought into junction, for the same reason. And consequently an indivisible, multiplied as many times as we like, will not make an extension. Therefore it is not of the same kind as extension, by the definition of things of the same kind.

It is in this manner that we demonstrate that indivisibles are not of the same species as numbers. Hence it arises that two units may indeed make a number, because they are pf the same kind; and that two indivisibles do not make a extension, because they are not of the same kind.

Hence we see how little reason there is in comparing the relation that exists between unity and numbers with that which exists between indivisibles and extension.

But if we wish to take in numbers a comparison that