excellent in all things else, that are shocked by these infinities and can in no wise assent to them.
I have never known any person who thought that a space could not be increased. But I have seen some, very capable in other respects, who affirmed that a space could be divided into two indivisible parts, however absurd the idea may seem.
I have applied myself to investigating what could be the cause of this obscurity, and have found that it chiefly consisted in this, that they could not conceive of a continuity divisible ad infinitum, whence they concluded that it was not divisible.
It is an infirmity natural to man to believe that he possesses truth directly; and thence it comes that he is always disposed to deny every thing that is incomprehensible to him; whilst in fact he knows naturally nothing but falsehood, and whilst he ought to receive as true only those things the contrary of which appear to him as false.
And hence, whenever a proposition is inconceivable, it is necessary to suspend the judgment on it and not to deny it from this indication, but to examine its opposite; and if this is found to be manifestly false, we can boldly affirm the former, however incomprehensible it may be. Let us apply this rule to our subject.
There is no geometrician that does not believe space divisible ad infinitum. He can no more be such without this principle than man can exist without a soul. And nevertheless there is none who comprehends an infinite division; and he only assures himself of this truth by this one, but certainly sufficient reason, that he perfectly comprehends that it is false that by dividing a space we can reach an indivisible part, that, is, one that has no extent.
For what is there more absurd than to pretend that by continually dividing a space, we shall finally arrive at such a division that on dividing it into two, each of the halves shall remain indivisible and without any extent, and that thus the two negations of extensions will together compose an extent? For I would ask those who hold this idea, whether they conceive clearly two indivisibles being brought into contact; if this is throughout, they are only the same thing,
