§3.4#1Ἐπεὶ δʼ ἐστὶν ἡ περὶ φύσεως ἐπιστήμη περὶ μεγέθη καὶ κίνησιν καὶ χρόνον, ὦν ἕκαστον ἀναγκαῖον ἢ ἄπειρον ἢ πεπερασμένον εἶναι, εἰ καὶ μὴ πᾶν ἐστιν ἄπειρον ἢ πεπερασμένον, οἷον πάθος ἢ στιγμή (τῶν γὰρ τοιούτων ἴσως οὐδὲν ἀναγκαῖον ἐν θατέρῳ τούτων εἶναι, προσῆκον ἂν εἴη τὸν περὶ φύσεως πραγματευόμενον θεωρῆσαι περὶ ἀπείρου, εἰ ἔστιν ἢ μή, καὶ εἰ ἔστιν, τί ἐστιν.
Since the science of nature is concerned with magnitudes, motion, and time, each of which must be either infinite or finite, even if not everything is infinite or finite, such as an affection or a point (for perhaps nothing of such things is necessarily in either of these), it would be appropriate for the student of nature to consider concerning the infinite, whether it exists or not, and if it exists, what it is.
σημεῖον δʼ ὅτι ταύτης τῆς ἐπιστήμης οἰκεία ἡ θεωρία ἡ περὶ αὐτοῦ· πάντες γὰρ οἱ δοκοῦντες ἀξιολόγως ἦφθαι τῆς τοιαύτης φιλοσοφίας πεποίηνται λόγον περὶ τοῦ ἀπείρου, καὶ πάντες ὡς ἀρχήν τινα τιθέασι τῶν ὄντων, οἱ μέν, ὥσπερ οἱ Πυθαγόρειοι καὶ Πλάτων, καθʼ αὐτό, οὐχ ὡς συμβεβηκός τινι ἑτέρῳ ἀλλʼ οὐσίαν αὐτὸ ὂν τὸ ἄπειρον.
And a sign that the study of it is appropriate to this science is this: for all those who seem to have touched upon this kind of philosophy in a noteworthy way have made an account concerning the infinite, and all posit it as a kind of principle of things that are; some, like the Pythagoreans and Plato, [posit it] in itself, not as an attribute to some other thing, but the infinite itself being a substance.
πλὴν οἱ μὲν Πυθαγόρειοι ἐν τοῖς αἰσθητοῖς (οὐ γὰρ χωριστὸν ποιοῦσιν τὸν ἀριθμόν), καὶ εἶναι τὸ ἔξω τοῦ οὐρανοῦ ἄπειρον, Πλάτων δὲ ἔξω μὲν οὐδὲν εἶναι σῶμα, οὐδὲ τὰς ἰδέας, διὰ τὸ μηδὲ ποὺ εἶναι αὐτάς, τὸ μέντοι ἄπειρον καὶ ἐν τοῖς αἰσθητοῖς καὶ ἐν ἐκείναις εἶναι·
Except that the Pythagoreans place it in sensible things (for they do not make number separate), and say that what is outside the heaven is infinite, while Plato says that there is no body outside, nor are the ideas [outside] because of their not even being anywhere, yet the infinite is both in sensible things and in those [ideas].
καὶ οἱ μὲν τὸ ἄπειρον εἶναι τὸ ἄρτιον (τοῦτο γὰρ ἐναπολαμβανόμενον καὶ ὑπὸ τοῦ περιττοῦ περαινόμενον παρέχειν τοῖς οὖσι τὴν ἀπειρίαν· σημεῖον δʼ εἶναι τούτου τὸ συμβαῖνον ἐπὶ τῶν ἀριθμῶν· περιτιθεμένων γὰρ τῶν γνωμόνων περὶ τὸ ἓν καὶ χωρὶς ὁτὲ μὲν ἄλλο ἀεὶ γίγνεσθαι τὸ εἶδος, ὁτὲ δὲ ἕν), Πλάτων δὲ δύο τὰ ἄπειρα, τὸ μέγα καὶ τὸ μικρόν.
And the former [say] that the infinite is the even (for this, being enclosed and limited by the odd, provides infinity to things; and a sign of this is what happens in the case of numbers; for when gnomons are placed around the one, and also separately, in one case the form always becomes different, in another case it becomes one), but Plato [makes] the infinites two, the Great and the Small.
οἱ δὲ περὶ φύσεως πάντες
ὑποτιθέασιν ἑτέραν τινὰ φύσιν τῷ ἀπείρῳ τῶν λεγομένων στοιχείων, οἷον ὕδωρ ἢ ἀέρα ἢ τὸ μεταξὺ τούτων.
But all the writers on nature assume some other nature for the infinite from among the so-called elements, such as water or air or the medium between these.
τῶν δὲ πεπερασμένα ποιούντων στοιχεῖα οὐθεὶς ἄπειρα ποιεῖ·
And of those who make the elements finite, no one makes them infinite.
ὅσοι δʼ ἄπειρα ποιοῦσι τὰ στοιχεῖα, καθάπερ Ἀναξαγόρας καὶ Δημόκριτος, ὁ μὲν ἐκ τῶν ὁμοιομερῶν, ὁ δʼ ἐκ τῆς πανσπερμίας τῶν σχημάτων, τῇ ἁφῇ συνεχὲς τὸ ἄπειρον εἶναι φασίν·
But as many as make the elements infinite, like Anaxagoras and Democritus, the former from the homoeomeries, the latter from the panspermia of shapes, say that the infinite is continuous by contact.
καὶ ὁ μὲν ὁτιοῦν τῶν μορίων εἶναι μίγμα ὁμοίως τῷ παντὶ διὰ τὸ ὁρᾶν ὁτιοῦν ἐξ ὁτουοῦν γιγνόμενον·
And the former says that any of the parts is a mixture in like manner to the whole, because of seeing anything generated out of anything.
ἐντεῦθεν γὰρ ἔοικε καὶ ὁμοῦ ποτὲ πάντα χρήματα φάναι εἶναι, οἷον ἥδε ἡ σὰρξ καὶ τόδε τὸ ὁστοῦν, καὶ οὕτως ὁτιοῦν· καὶ πάντα ἄρα· καὶ ἅμα τοίνυν·
For from this he seems also to say that all things were once together, as this flesh and this bone, and so with anything; and therefore all things; and therefore at the same time.
ἀρχὴ γὰρ οὐ μόνον ἐν ἑκάστῳ ἔστι τῆς διακρίσεως, ἀλλὰ καὶ πάντων.
For there is a principle of separation not only in each, but also of all.
ἐπεὶ γὰρ τὸ γιγνόμενον ἐκ τοῦ τοιούτου γίγνεται σώματος, πάντων δʼ ἔστι γένεσις πλὴν οὐχ ἅμα, καί τινα ἀρχὴν δεῖ εἶναι τῆς γενέσεως, αὕτη δʼ ἐστὶν μία, οἷον ἐκεῖνος καλεῖ νοῦν, ὁ δὲ νοῦς ἀπʼ ἀρχῆς τινος ἐργάζεται νοήσας· ὥστε ἀνάγκη ὁμοῦ ποτε πάντα εἶναι καὶ ἄρξασθαί ποτε κινούμενα.
For since what is generated comes from such a body, and there is generation of all things though not at the same time, and there must be some principle of generation, and this is one, which he calls Intellect, and Intellect works from some beginning, having thought; so that it is necessary that all things were once together and began at some time to be moved.
Δημόκριτος δʼ οὐδὲν ἕτερον ἐξ ἑτέρου γίγνεσθαι τῶν πρώτων φησίν· ἀλλʼ ὅμως γε αὐτῷ τὸ κοινὸν σῶμα πάντων ἐστὶν ἀρχή, μεγέθει κατὰ μόρια καὶ σχήματι διαφέρον.
But Democritus says that none of the primary things is generated from another; but nevertheless for him the common body of all is the principle, differing in its parts by magnitude and shape.