Since, however, the science concerning nature is conversant with magnitudes, motion and time, each of which must necessarily be either infinite or finite; (although not everything is either infinite or finite; as, for instance, passive quality or a point; for, perhaps, it is necessary that no one of things of this kind should be placed in either of these) — since this is the case, it is fit that he who engages in a discussion concerning nature should speculate the infinite, and consider whether it is or not; and if it is what it is. But that the speculation concerning the infinite pertains to this science is indicated by this circumstance, that all those who appear to have touched on a philosophy of this kind in a manner which deserves to be mentioned, have discoursed about the infinite; and all of them consider it has a certain principle of beings. Some, indeed, as the Pythagoreans and Plato, consider it, per se, not as being an accident to anything else, but as having an essential subsistence; except that the Pythagoreans, indeed, consider the infinite as subsisting insensibles; for they do not make number to be separate; and they assert that what is beyond the heavens is infinite; but Plato says that beyond the heavens there is not any body, nor ideas, because these are nowhere: he affirms, however, that the infinite is both insensibles, and in ideas. And the Pythagoreans, indeed, say that the infinite is the even in number; for this being comprehended and bounded by the odd, imparts infinity to beings. They add that this is indicated by what happens in numbers. For gnomons being placed about unity, and also being placed separately, sometimes another form is always produced, and at other times one and the same form remains. But Plato establishes two infinites, namely, the great and the small. All those, however, who discourse concerning nature, always subject a certain other nature of those things which are called elements, to the infinite; as for instance, water, or air, or that which subsists between these. But no one of those who make the elements to be finite introduces infinity. Such, however, as make infinite elements, as Anaxagoras and Democritus, say that the infinite is continuous by contact, the former from similar parts, but the latter from the all-spermatic nature of figures. And the former, indeed, asserts that any part whatever is similarly mingled with the whole, because he saw that everything is generated from everything: for hence he seems to have said that all things once subsisted together; as this flesh, and this bone, and in like manner everything else. All things therefore, thus subsisted, and consequently together: for the principle of separation is not only in each, but likewise of all: for since that which is generated is generated from such a body, and there is a generation of all things, though not together, it is also necessary that there should be a certain principle of generation; but this is one, which he calls intellect. Intellect, however, operates from a certain principle by understanding; so that it is necessary that all things should have once subsisted together, and once have begun to be moved. But Democritus says that none of the principles were produced one from the other; though at the same time common body itself is the principle of all things, differing in magnitude and figure according to the parts. That this theory, therefore, pertains to physical concerns, is, from what has been said, evident. Rationally, too, do all philosophers consider the infinite as a principle; For it cannot be in vain, nor can any other power be present with it than that of a principle: for all things are either the principle, or from the principle; but of the infinite there is no principle, since otherwise it would have been an end. Again, it is also unbegotten and incorruptible, as being a certain principle: for that which is generated must necessarily receive an end; and end is the corruption of everything. Hence, as we have said, there is a principle of this, but this appears to be the principle of other things. It likewise appears to comprehend and govern all things, as those assert who do not introduce other causes beside the infinite, such as intellect or friendship. It would seem also that this is divine: for it is immoral and indestructible, as Anaximander says, and most of the physiologists.
