§57οὔτε γὰρ ὅπως, ἐπειδὰν ἅπαξ τις εἴπῃ ὅτι ἄπειροι ὄγκοι ἔν τινι ὑπάρχουσιν ἢ ὁπηλίκοι οὖν, ἔστι νοῆσαι· πῶς τ’ ἂν ἔτι τοῦτο πεπερασμένον εἴη τὸ μέγεθος;
For once someone says that infinite particles, of whatever size, exist in a certain thing, it is impossible to conceive how this can be; and how could this size still be limited?
πηλίκοι γάρ τινες δῆλον ὡς οἱ ἄπειροί εἰσιν ὄγκοι· καὶ οὗτοι [ἐξ ὧν] ὁπηλίκοι ἄν ποτε ὦσιν, ἄπειρον ἂν ἦν καὶ τὸ μέγεθος.
For it is clear that the infinite particles are of some size; and whatever size these may be, the whole size also would have been infinite.
ἄκρον τε ἔχοντος τοῦ πεπερασμένου διαληπτόν, εἰ μὴ καὶ καθ’ ἑαυτὸ θεωρητόν, οὐκ ἔστι μὴ οὐ καὶ τὸ ἑξῆς τούτου τοιοῦτον νοεῖν καὶ οὕτω κατὰ τὸ ἑξῆς εἰς τοὔμπροσθεν βαδίζοντα εἰς τὸ ἄπειρον ὑπάρχειν καὶ τὸ τοιοῦτον ἀφικνεῖσθαι τῇ ἐννοίᾳ.
And since the limited has a distinguishable extremity, even if it is not observable by itself, it is impossible not to conceive the next point after this as being of the same nature, and thus by proceeding forward, to arrive in thought at infinity.
§58τό τε ἐλάχιστον τὸ ἐν τῇ αἰσθήσει δεῖ κατανοεῖν ὅτι οὔτε τοιοῦτόν ἐστιν οἷον τὸ τὰς μεταβάσεις ἔχον οὔτε πάντῃ πάντως ἀνόμοιον, ἀλλ’ ἔχον μέν τινα κοινότητα τῶν μεταβατῶν, διάληψιν δὲ μερῶν οὐκ ἔχον· ἀλλ’ ὅταν διὰ τὴν τῆς κοινότητος προσεμφέρειαν οἰηθῶμεν διαλήψεσθαί τι αὐτοῦ, τὸ μὲν ἐπιτάδε, τὸ δὲ ἐπέκεινα, τὸ ἴσον ἡμῖν δεῖ προσπίπτειν.
And one must understand that the minimum in sensation is neither such as to have transitions nor altogether dissimilar, but rather having a certain community with things that have transitions, yet having no distinction of parts; but whenever, through the similarity of this community, we think we can distinguish some part of it, one on this side and another on that side, the equal must present itself to us.
ἑξῆς τε θεωροῦμεν ταῦτα ἀπὸ τοῦ πρώτου καταρχόμενοι καὶ οὐκ ἐν τῷ αὐτῷ, οὐδὲ μέρεσι μερῶν ἁπτόμενα, ἀλλ’ ἢ ἐν τῇ ἰδιότητι τῇ ἑαυτῶν τὰ μεγέθη καταμετροῦντα, τὰ πλείω πλεῖον καὶ τὰ ἐλάττω ἔλαττον.
And we observe these in succession, beginning from the first and not in the same place, nor with parts touching parts, but rather measuring sizes in their own peculiarity, the more being greater and the fewer being smaller.
ταύτῃ τῇ ἀναλογίᾳ νομιστέον καὶ τὸ ἐν τῇ ἀτόμῳ ἐλάχιστον κεχρῆσθαι· §59μικρότητι γὰρ ἐκεῖνο δῆλον ὡς διαφέρει τοῦ κατὰ τὴν αἴσθησιν θεωρουμένου, ἀναλογίᾳ δὲ τῇ αὐτῇ κέχρηται.
By this analogy we must believe that the minimum in the atom also behaves; for in smallness it clearly differs from that which is observed through sensation, but it preserves the same analogy.
ἐπεί περ καὶ ὅτι μέγεθος ἔχει ἡ ἄτομος, κατὰ τὴν ἐνταῦθα ἀναλογίαν κατηγορήσαμεν, μικρόν τι μόνον μακρὰν ἐκβαλόντες.
Indeed, we asserted that the atom has size according to this analogy, only casting it far away as something small.
ἔτι τε τὰ ἐλάχιστα καὶ ἀμερῆ πέρατα δεῖ νομίζειν τῶν μηκῶν τὸ καταμέτρημα ἐξ αὑτῶν πρώτων τοῖς μείζοσι καὶ ἐλάττοσι παρασκευάζοντα τῇ διὰ λόγου θεωρίᾳ ἐπὶ τῶν ἀοράτων.
Furthermore, we must believe that these minimal and partless extremities provide the first measure from themselves for greater and smaller sizes in the rational contemplation of invisible things.
ἡ γὰρ κοινότης ἡ ὑπάρχουσα αὐτοῖς πρὸς τὰ †ἀμετάβολα ἱκανὴ τὸ μέχρι τούτου συντελέσαι, συμφόρησιν δὲ ἐκ τούτων κίνησιν ἐχόντων οὐχ οἷόν τε γίνεσθαι.
For the community that exists between them and the unchanging things is sufficient to accomplish up to this point, but it is impossible for a compound to arise from these if they have independent motion.
§60Καὶ μὴν καὶ τοῦ ἀπείρου ὡς μὲν ἀνωτάτω ἢ κατωτάτω οὐ δεῖ κατηγορεῖν τὸ ἄνω ἢ κάτω.
Moreover, one must not predicate "up" or "down" of the infinite in the sense of an absolute highest or lowest.
† εἰς μέντοι τὸ ὑπὲρ κεφαλῆς, ὅθεν ἂν στῶμεν, εἰς ἄπειρον ἄγειν †ὂν† μηδέποτε φανεῖσθαι τοῦτο ἡμῖν· ἢ τὸ ὑποκάτω τοῦ νοηθέντος εἰς ἄπειρον ἅμα ἄνω τε εἶναι καὶ κάτω πρὸς τὸ αὐτό†· τοῦτο γὰρ ἀδύνατον διανοηθῆναι.
However, to extend to infinity into the region above our heads, wherever we may stand, will never appear to us as a limit; nor can that which extends to infinity below the conceived point be at the same time both up and down with respect to the same thing, for this is impossible to conceive.
ὥστε ἔστι μίαν λαβεῖν φορὰν τὴν ἄνω νοουμένην εἰς ἄπειρον καὶ μίαν τὴν κάτω, ἂν καὶ μυριάκις πρὸς τοὺς πόδας τῶν ἐπάνω τὸ παρ’ ἡμῶν φερόμενον 〈εἰς〉 τοὺς ὑπὲρ κεφαλῆς ἡμῶν τόπους ἀφικνῆται ἢ ἐπὶ τὴν κεφαλὴν τῶν ὑποκάτω τὸ παρ’ ἡμῶν κάτω φερόμενον· ἡ γὰρ ὅλη φορὰ οὐθὲν ἧττον ἑκατέρα ἑκατέρᾳ ἀντικειμένη ἐπ’ ἄπειρον νοεῖται.
Consequently, it is possible to assume one upward motion conceived to infinity, and one downward, even if that which is carried from us to the regions above our heads should arrive ten thousand times at the feet of those above us, or that which is carried downward from us at the head of those below us; for the whole motion in each direction is nonetheless conceived as opposed to the other to infinity.
§61Καὶ μὴν καὶ ἰσοταχεῖς ἀναγκαῖον τὰς ἀτόμους εἶναι, ὅταν διὰ τοῦ κενοῦ εἰσφέρωνται μηθενὸς ἀντικόπτοντος.
Moreover, the atoms must be equal in speed when they are carried through the void and nothing opposes them.
οὔτε γὰρ τὰ βαρέα θᾶττον οἰσθήσεται τῶν μικρῶν καὶ κούφων, ὅταν γε δὴ μηδὲν ἀπαντᾷ αὐτοῖς· οὔτε τὰ μικρὰ τῶν μεγάλων, πάντα πόρον σύμμετρον ἔχοντα, ὅταν μηθὲν μηδὲ ἐκείνοις ἀντικόπτῃ· οὔθ’ ἡ ἄνω οὔθ’ ἡ εἰς τὸ πλάγιον διὰ τῶν κρούσεων φορά, οὔθ’ ἡ κάτω διὰ τῶν ἰδίων βαρῶν.
For neither will the heavy ones be carried faster than the small and light ones, as long as nothing meets them; nor will the small ones be carried faster than the large ones, all having a commensurate path, when nothing opposes them either; neither the motion upward nor sideways due to collisions, nor that downward due to their own weights.
ἐφ’ ὁπόσον γὰρ ἂν κατίσχῃ ἑκάτερον, ἐπὶ τοσοῦτον ἅμα νοήματι τὴν φορὰν σχήσει, ἕως ἀντικόψῃ ἢ ἔξωθεν ἢ ἐκ τοῦ ἰδίου βάρους πρὸς τὴν τοῦ πλήξαντος δύναμιν.
For as long as either of the two motions prevails, it will maintain its course as fast as thought, until it is opposed either from without or by its own weight against the power of that which struck it.