On Nicomachus's Introduction to Arithmetic

IN NICOMACHI ARITHM. INTROD.

those fallen under perception, which share in the true state of being by participation. It would be logical to discuss the technology of all beings simply in this way. The nature of the continuous and the nature of the discrete, in their entirety, are conceived in two ways regarding beings—that is, in the constitution of the entire world: the discrete by way of juxtaposition and aggregation, and the continuous by way of union and concatenation. Properly speaking, the continuous and united might be called magnitude size, and the juxtaposed and discrete, multitude quantity. And according to the essence of magnitude, the world might be conceived and spoken of as one, solid, spherical, grown together with itself, extended, and concatenated. But according to the idea and notion of multitude, the composition and decoration and harmony of the whole might be conceived as having its constitution from such-and-such—let us say—elements, spheres, stars, kinds, animals, plants, contrarieties, and similarities. But as for the united, the division is to infinity from everything, but the increase is to a definite point; and for the multitude, by way of antipeponthēsis reciprocity, the increase is to infinity, but conversely, the division is to a definite point. Since both are infinite by nature according to conception, and therefore are unlimited by sciences—for, according to Philolaus, "there will not even be a beginning of the knowable thing if all are infinite"—and since it is necessary for the nature of science to be seen in beings...