Lives and Opinions of Eminent Philosophers

"And one must understand that the minimum in sensation is neither such as that which admits of transitions, nor entirely dissimilar in every respect, but possesses a certain commonality with things admitting transitions, yet has no distinction of parts. But whenever, through the resemblance of this commonality, we think we shall distinguish something of it, one part on this side and one on that, an equal part must present itself to us. And we observe these consecutively, beginning from the first, and not in the same place, nor touching parts with parts, but either measuring magnitudes in their own proper nature, the greater number measuring a greater magnitude, and the smaller number a smaller magnitude.

"By this analogy one must believe that the minimum in the atom also functions; for it is obvious that it differs in smallness from what is observed by sensation, but it follows the same analogy. Since indeed that the atom has magnitude, we also predicated according to the analogy found here, merely projecting it far in a small degree. Furthermore, one must believe that these minimal and uncompounded limits supply from themselves as primary units the measurement of lengths for greater and smaller bodies in the rational investigation of invisible things. For the commonality which belongs to them with respect to unchangeable things is sufficient to accomplish this much, but an aggregation consisting of these as possessing motion cannot occur.

"Furthermore, in reference to the infinite, one must not predicate 'up' or 'down' as though there were a highest or lowest point. We know, however, that what is above our head, wherever we may stand, extends to infinity, and that this could never appear to us—nor what is below that which is conceived to infinity—to be at the same time both up and down with respect to the same point; for this is impossible to conceive. Consequently, it is possible to take one motion conceived upward to infinity, and one downward, even if a myriad of times that which moves from us toward the places above our head should reach the feet of those above, or that which moves downward from us should reach the head of those below; for the whole motion in each case is nonetheless conceived as opposed to the other to infinity.

"Moreover, it is also necessary that the atoms be of equal speed, whenever they travel through the void with nothing resisting them. For the heavy bodies will not move faster than the small and light, whenever indeed nothing meets them; nor will the small move faster than the large, having every passage commensurate with them, whenever nothing either resists them; nor will the motion upward or sideways caused by collisions, nor that downward caused by their own weights. For as long as either prevails, it will maintain its motion as quick as thought, until something resists it either from without or from its own weight against the power of that which struck it.

"Yet within compounds one body will be carried faster than another, although the atoms are of equal speed, by reason of the atoms in the aggregates moving in one direction during the minimum continuous time, even if not in one direction during the times contemplated by reason; but they collide frequently, until the continuity of the motion falls under sensation. For the opinion added concerning the invisible, that the times contemplated by reason will also have continuity of motion, is not true in the case of such things; since everything that is actually observed or apprehended by the mind in an act of attention is true."