Other philosophers, moreover, must consistently with their theories recognize something contrary to Wisdom and to the most venerable Cognition. But we are under no such necessity; for there is nothing contrary to the First (τῷ πρώτῳ). All contraries involve Matter, and are in potentiality the same: one of the two contraries is ignorance in regard to the other; but the First has no contrary (p. 1075, b. 24).
Again, if there be no Entia beyond the Perceptibilia, there can be no beginning, no arrangement in order, no generation, no celestial bodies or proceedings (i.e., all these will remain unexplained). There will always be a beginning behind the beginning, ad infinitum; as there is in the theories of all the theologians and physical philosophers (p. 1075, b. 27). And, even if we recognize, beyond the Perceptibilia, Ideas or Numbers, these are causes of nothing; or, if causes of any thing, they are certainly not causes of motion. How, moreover, can Magnitude, and a Continuum arise out of that which has no Magnitude? Number cannot, either as Movent or as Form, produce a Continuum (b. 30).
Again, (Contraries cannot be principles, because) no Contrary can be essentially Constructive and essentially Movent (p. 1075, b. 31); for Contraries involve Matter and Potentiality, and may possibly, therefore, not exist. And, if there be Potentiality, it will come prior to Actuality: upon that supposition therefore (i.e., of Contraries as the fundamental principles) Entia could not be eternal. But Entia are eternal; therefore these theories must be in part amended: we have shown how (b. 34).
Farther, none of these theories explains how it is that numbers coalesce into One; or soul and body into One; or Form and Matter into one Concrete. Nor can they explain this, unless they adopt our doctrine, that the Movent brings about this coalition (p. 1075, b. 37).
Those philosophers (like Speusippus) who recognize many different grades and species of Entia (first the Mathematical Number, &c.), with separate principles for each, make the Essence of the Universe to be incoherent (ἐπεισοδιώδη — p. 1076, a. 1) and set up many distinct principles; for none of these Essences contributes to or bears upon the remainder, whether it exists or does not exist. Now Entia are not willing to be badly governed (τὰ δὲ ὄντα οὐ βούλεται πολιτεύεσθαι κακῶς. “οὐκ ἀγαθὸν πολυκοιρανίη· εἷς κοίρανος.â€� — p. 1076, a. 4).
[IV.]
DE CÅ’LO.
Book I.
CH. 1. — The science of Nature has for its principal object — Bodies, Magnitudes, and the various affections and movements of Bodies and Magnitudes; also the beginnings or principles of this sort of Essence. The Continuous is that which is divisible into parts perpetually divisible: and Body is that which is divisible in every direction. Of magnitudes, some (lines) are divisible only in one direction; others (planes) only in two directions; others again (bodies) in three directions. This is the maximum: there is no other magnitude beyond; for three are all, and to say “in three directionsâ€� is the same as to say “in all directions.â€� As the Pythagoreans say, The Universe and All Things are determined by Three: in End, Middle, and Beginning, lies the number of the Universe, or the Triad. We have received these as laws from nature, and we accordingly employ this number (Three) for solemnities in honour of the Gods. Moreover, we apply our predicates on the same principle; for we call Two, and The Two — Both, but we do not call them all. Three is the first number to which we apply the predicate All. Herein (as was observed before) we follow the lead of Nature herself. Since therefore these three phrases — All Things, The Universe, The Perfect or Complete — do not specifically differ from each other, but are distinguished only in respect of the matter or occasions on which they are applied. Body is the only kind of magnitude which can be declared Perfect or Complete, that is, All; for it is the only magnitude determined or defined by the Three. Being divisible in three directions, it is divisible every way; other magnitudes are divisible either only in one way or only in two. Magnitudes are both divisible and continuous according to the number by which they are designated — continuous in one direction, in two, in three, or all. All divisible magnitudes are also continuous: whether all continuous magnitudes are divisible, is not yet clear. But what is clear is — that there is no upward transition to a higher genus beyond Body, as there is from line to surface, and from surface to Body. If there were, Body would not be perfect or complete as a magnitude; for the transition would be made at the point of deficiency; but the perfect or complete can have no deficiency: it stretches every way. Such is each body included as a part in the universe: it has dimensions in every direction. Yet each is distinguished from its neighbour by contact, and each therefore in a certain sense is many. But the Universe (τὸ πᾶν) including all these parts is of necessity perfect and complete; extending not merely in one way, and in another way not, but πάντῃ, as the word literally means (ss. 1-4).