"It is properly debated whether irrational numbers are true numbers or fictions. For if we lack rational numbers in geometrical figures, their place is taken by irrationals, which prove precisely those things that rational numbers could not; certainly from the demonstrations they show us we are moved and compelled to admit that they really exist from their effects, which we perceive to be real, sure, and constant. On the other hand, other things move us to a different assertion, namely that we are forced to deny that irrational numbers are numbers. Namely, where we might try to subject them to numeration [decimal representation] and to make them proportional to rational numbers, we find that they flee perpetually, so that none of them in itself can be freely grasped: a fact that we perceive in the resolving of them... Moreover, it is not possible to call that a true number which is such as to lack precision and which has no known proportion to true numbers. Just as an infinite number is not a number, so an irrational number is not a true number and is hidden under a sort of cloud of infinity. And thus the ratio of an irrational number to a rational number is no less uncertain than that of an infinite to a finite."