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

LXI. By this argument, we are compelled to think that this opinion is less consistent; and for that reason, we think it must be explained otherwise, in what manner quantity is not composed of indivisibles. A distinction must be made between parts that are in the continuous in act, and those that are only by potentiality. We say the former are finite, and physically "minimal" or "indivisible" (for this is necessarily proven from the preceding); the latter, from which potentiality exists, are truly infinite and always infinitely divisible. This latter is to be believed with the same probability with which it is truly believed that when one part of the continuous has collapsed and been destroyed, another continuous [part] can succeed in the place of the destroyed one, and this by perpetual succession. And we consider this interpretation not only true but also more conformable to the opinion of Aristotle.

LXI. It remains to explain what was second in order, namely, how the parts of quantity from which it is actually composed are continued among themselves. Regarding this matter, our opinion is this: the continuation of parts consists in three things: that all parts are of the same genus; that they are coupled among themselves immediately without the interposition of another; that each one has the power of apprehending or coupling another to itself, whether this power is innate to the parts or adheres as an extrinsic addition. Parts formal to living things possess this kind of power; of this kind is humidity, by which the parts of water are continued among themselves.

LXII. We do not require points, lines, and surfaces—which some believe to be certain bonds by which parts of quantity are tied and continued among themselves—beyond the parts themselves. First, because no reason induces us to think about attributing such indivisibles to quantity. Second, because we hold it as an absurdity to introduce a new and hitherto unheard-of category, distinct from the other ten, for the sake of coordinating points among themselves, which nevertheless would have to be invented if that opinion were granted, since points are absolute beings and not parts of any being in themselves.

LXIII. Nor, however, is it our intention to do away with these indivisibles entirely. Rather, we establish that they are the parts of quantity themselves, in the respect that they are joined among themselves with such proximity that they found the concept by which we truly see one part as divided from the other. For this reason, we consider these definitions convenient, by which we explain the nature of those things: that we define a "point" as a part, which we deny is truly divided from another and which we remove in the mind from that divisibility which it has; a "line" as a part which, when we deny it is separated from another, we recognize is divisible in length; and "surface" in its own way. And these things [are said] concerning quantity viewed in itself; now we will deal with it regarding natural substance, which is the proper business of the Physicist.