the added amount must bear some ratio to the remainder, as when one finite quantity exceeds another. Yet it is impossible for two non-finite quantities to bear the ratio that holds between two finite quantities.

Furthermore, if one totality exceeds the other by a finite amount, bring their two other ends into one-to-one correspondence: take a posited amount from the final end of one totality, and an equal amount from the other, and continue in this manner. If the process continues indefinitely, the smaller totality must equal the larger at both ends, which is impossible.

If, however, the smaller totality falls short at the end that has no limit, it has proved finite. The larger exceeds the smaller only by a finite amount, and anything that exceeds a finite quantity by a finite amount is itself finite.”

He said:

“This is not sound, either on the principles of the philosophers or on those of the theologians.”