De Rervm Natvra Constantivm Scientia, Principiis Et Affectionibvs Commvnibvs, Dispvtatio

LVII. From this it happened that they fell into various and inexplicable difficulties; for if they established that the parts were finite, they were entangled in these absurdities, namely: that the base in an Isosceles [triangle] is equal to the sides; that the diameter is equal to the individual ribs of a square; that a smaller circle described within a larger one is equal to the larger, etc. If [they established] them as infinite, they took up these other absurdities: that a finite line cannot be traversed; that all lines are equal in length; and finally, whatever absurdities follow from the infinite. But if they had attributed finite parts to quantity and had denied that the principles of the Mathematicians, from which those absurdities were gathered, were true in reality, they would have been forced to accept no absurdity.

LVIII. Therefore, setting aside the opinion of these men, others deny that quantity coalesces from Mathematical indivisibles, and they deny this universally, both regarding finite and infinite [parts]. And there are two ways to explain this opinion. Some explain it so that they believe there are no indivisible parts in reality from which quantity is actually joined, and so they believe all things are divisible into other parts existing in act.

LIX. And they define that there are two genera of parts: some they call "aliquot and incommunicating," of which one is entirely outside the complex of the other; others [they call] "communicating and proportional," of which one is enclosed in another as a part of it. Having posited this, they say that quantity is composed of parts of both genera, infinitely divisible into communicating and proportional parts.

LX. But this opinion follows: that the parts from which quantity is actually built are actually infinite. Since there is no part from which quantity is truly and actually composed that lacks divisibility, without it being able to be divided into other parts actually contained within itself, it necessarily follows that the parts are infinite in act. For the infinite is defined in act as that whose parts are all in act, and so many of them that there is no last one; if, therefore, there is no part which cannot be divided into other parts contained in its complex, it must be that there is no last one among them, yet all are in act, and thus they are infinite in act.