§11Ἦι δὲ γραμμή, διαίρεσις κατὰ στιγμμήν, καὶ ὁμοίως καθ’ ὁποιανοῦν ἀπείρους ἂν ἔχοι διαιρέσεις ἅπασα ἡ μὴ ἄτομος, Ἔνιαι δὲ τούτων εἰς μακρὰ καὶ ἄπειροι οἱ λόγοι.
Insofar as it is a line, division is by a point, and likewise by any point whatever, every line that is not indivisible would have infinite divisions. And some of these are long, and their ratios are infinite.
Πᾶσαν δὲ τμηθῆναι τὸν ἐπιταχθέντα δυνατὸν τὴν μὴ ἄτομον.
Also, it is possible for every line that is not indivisible to be cut in the assigned ratio.
Ἔτι εἰ τὸ μέγα ἐκ μικρῶν τινῶν σύγκειται, ἢ οὐθὲν ἔσται τὸ μέγα, ἢ τὸ πεπερασμένας ἔχον διαιρέσεις οὐ μέγα ἔσται.
Furthermore, if the great is composed of certain small things, either the great will be nothing, or that which has finite divisions will not be great.
§12Τὸ γὰρ ὅλον τὰς τῶν μερῶν ἔχει διαιρέσεις ὁμοίως.
For the whole has the divisions of its parts likewise.
Εὕλογον δ' ἐστὶ τό τε σμικρὸν πεπερασμένας ἔχειν διαιρέσεις καὶ τὸ μέγα ἀπείρους, οὕτως ἀξιοῦσιν.
And it is reasonable for the small to have finite divisions and the great infinite ones, as they claim.
Ὤστε φανερὸν ὅτι οὐκ ἐν τούτῳ λέγοιτο τὸ μέγα καὶ τὸ μικρόν, τῷ πεπερασμένας ἔχειν καὶ ἀπείρους διαιρέσεις.
So it is clear that the great and the small would not be defined by this—namely, by having finite and infinite divisions.
§13Εἰ δ’ ὅτι καὶ ἐν ἀριθμοῖς τὸ ὀλίγον πεπερασμένας ἔχει διαιρέσεις, καὶ ἐν γραμμαῖς τις ἀξιοίη τὸ μικρόν, εὔηθες.
But if, because in numbers 'few' has finite divisions, someone should claim that 'small' in lines also does, that is foolish.
Ἔκεῖ μὲν γὰρ ἐξ ἀμερῶν τε ἡ γένεσις, καὶ ἔστι τι ὃ τῶν ἀριθμῶν ἀρχή ἐστι, καὶ πᾶς ὁ μὴ ἄπειρος πεπερασμένας ἔχει διαιρέσεις· ἐπὶ δὲ τῶν μεγεθῶν οὐχ ὁμοίως.
For there, generation is from indivisibles, and there is something which is the principle of numbers, and every number that is not infinite has finite divisions; but in the case of magnitudes it is not likewise.
§14Οἱ δ' ἐν τοῖς εἴδεσι τὰς ἀτόμους κατασκευάζοντες τοὔλαττον ἴσως ἀξίωμα λαμβάνουσι τοῦ προρεῖ κειμένου, τὸ τιθέναι τούτων ἰδέας· καὶ τρόπον τινὰ ταῦτ’ ἀναιροῦσι δι' ὦν δεικνύουσιν.
And those who construct indivisibles in the Forms accept a premise that is perhaps less certain than the proposition in question, namely, the positing of Ideas of these things; and in a way they destroy these by the very means through which they demonstrate them.
Καὶ γὰρ διὰ τούτων τῶν λόγων ἀναιρεῖται τὰ εἴδη.
For indeed, by these very arguments the Forms are destroyed.
Πάλιν δὲ τῶν σωματικῶν στοιχείων εὔηθες τὸ ἀμερῆ ἀξιοῦν.
On the other hand, to claim that the physical elements are indivisible is also foolish.
§15Εἰ γὰρ αὗ καὶ ἀποφαίνονταί τινες οὕτως, ἀλλὰ πρός γε τὴν ὑποκειμένην σκέψιν αὐτὸ τὸ ἐξ ἀρχῆς λαμβάνουσιν.
For even if some people declare it to be so, yet in relation to the inquiry before us they are assuming the very point at issue.
Μᾶλλον δὲ ὅσῳ μᾶλλον τὸ ἐξ ἀρχῆς δόξειαν ἀναλαμβάνεσθαι, τόσῳ μᾶλλον δοκεῖ διαιρετὸν εἶναι σῶμα καὶ μῆκος καὶ τοῖς ὄγκοις καὶ τοῖς διαστήμασιν.
Indeed, the more they might seem to take up the point at issue, the more body and length appear to be divisible, both in their bulks and in their intervals.
§16Ὁ δὲ τοῦ Ζήνωνος λόγος οὐ συμβιβάζει οὐ συμπεπερασμένῳ χρόνῳ τῶν ἀπείρων ἅπτεσθαι τὸ φερόμενον ὡδὶ τὸν αὐτὸν τρόπον.
And Zeno's argument does not prove that what is moved touches infinitely many things in a finite time in this way, in the same manner.
Ὁ γὰρ χρόνος καὶ τὸ μῆκος ἄπειρον καὶ πεπερασμένον λέγεται, καὶ τόσας ἔχει διαιρέσεις.
For time and length are both called infinite and finite, and have the same number of divisions.
§17Οὐδὲ δὴ τὸ καθ’ ἕκαστον ἅπτεσθαι τῶν ἀπείρων τὴν διάνοιαν οὐκ ἔστιν ἀριθμεῖν, εἰ ἄρα τις καὶ νοήσειεν οὕτως ἐφάπτεσθαι τῶν ἀπείρων τὴν διάνοιαν.
Nor indeed is the thought's touching of infinitely many things individually a case of counting, even if someone were to conceive that the thought does touch the infinite in this way.
Ὄπερ ἴσως ἀδύνατον· οὐ γὰρ ἐν συνεχέσι καὶ ὑποκειμένοις ἡ τῆς διανοίας κίνησις, ὥσπερ ἡ τῶν φερομένων.
Which is perhaps impossible; for the movement of thought is not in continuous and underlying subjects, as is the movement of things carried along.
§18Εἰ δ’ οὖν καὶ ἑγχωρεῖ κινεῖσθαι οὕτως, οὐκ ἔστι τοῦτο ἀριθμεῖν· τὸ γὰρ ἀριθμεῖν ἐστὶ τὸ μετὰ ἐπιστάσεως.
But even if it is indeed possible to move in this way, this is not counting; for counting is that which is accompanied by a pause.
Ἀλλ’ ἄτοπον ἴσως τὸ μὴ δυναμένους λύειν τὸν λόγον δουλεύειν τῇ ἀσθενείᾳ, καὶ προσεξαπατᾶν ἑαυτοὺς μείζους ἀπάτας, βοηθοῦντας τῇ ἀδυναμίᾳ.
But it is perhaps absurd that those who are unable to solve the argument should be slaves to their weakness, and deceive themselves with even greater deceptions, trying to help their own inability.
§19Τὸ δ' ἐπὶ τῶν συμμμέτρων γραμμῶν, ὡς ὅτι αἱ πᾶσαί τῷ αὐτῷ τινὶ καὶ ἑνὶ μετροῦνται, κομιδῇ σοφιστικὸν καὶ ἥκιστα κατὰ τὴν ὑπόθεσιν τὴν ἐν τοῖς μαθήμασιν· οὔτε γὰρ ὑποτίθενται οὕτως, οὔτε χρήσιμον αὐτοῖς ἐστίν.
And the argument concerning commensurable lines, to the effect that all lines are measured by one and the same certain thing, is entirely sophistical and least of all in accordance with the hypothesis in mathematics; for they neither hypothesize in this way, nor is it useful to them.
Ἄμα δὲ καὶ ἐναντίον πᾶσαν μὲν γραμμὴν σύμμετρον γίνεσθαι, πασῶν δὲ τῶν συμμέτρων κοινὸν μέτρον εἶναι ἀξιοῦν.
And at the same time, it is contradictory to claim both that every line becomes commensurable, and that there is a common measure of all commensurable lines.
§20Ὤστε γελοῖον τὸ κατὰ τὰς ἐκείνων δόξας καὶ ἐξ ὦν αὐτοὶ λέγουσι φάσκοντες δείξειν, εἰς ἐριστικὸν ἅμα καὶ σοφιστικὸν ἐκκλίνειν λόγον, καὶ ταῦθ’ οὕτως ἀσθενῆ.
So it is ridiculous, while claiming to demonstrate on the basis of their opinions and from what they themselves say, to decline into an eristic and at the same time sophistical argument, and that too one so weak.
Πολλαχῇ γὰρ ἀσθενής ἐστι καὶ πάντα τρόπον διαφυγεῖν καὶ τὰ παράδοξα καὶ τοὺς ἐλέγχους.
For it is weak in many ways, and tries in every manner to escape both paradoxes and refutations.
§21Ἔτι δ' ἄτοπον ἄν εἴη διὰ μὲν τὸν Ζήνωνος λόγον παραπεπεῖσθαί τινας ἀτόμους ποιεῖν γραμμάς, τῷ μὴ ἔχειν ἀντειπεῖν, διὰ δὲ τῆς εὐθείας εἰς τὴν ἡμιόλιον κίνησιν, ἢν ἀναγκαῖον εὐθύς τέμνειν ἀπείρων μεταξὺ πιπτουσῶν περιφερειῶν καὶ διαστημάτων ὄντων, καὶ πάλιν διὰ τὴν τῶν ἴσων κύκλων εὔπειστον, ὅτι ἀνάγκη ἂν ὅτι κινηθῇ, μεῖζον ἡμικύκλιον κινεῖσθαι, καὶ ὅσα ἄλλα τοιαῦτα τεθεώρηται περὶ τὰς γραμμὰς μὴ οἶόν τε ἐνδέχεσθαι τοιαύτην δή τινα γενέσθαι κίνησιν ὥστ’ ἐφ’ ἑκάστην τῶν μεταξὺ μὴ πίπτειν πρότερον· πολὺ γὰρ ταῦτα μᾶλλον ὁμολογούμενα ἐκείνων.
Furthermore, it would be absurd, on the one hand, to be persuaded by Zeno's argument to make lines indivisible because of having no reply to make, and on the other hand, because of the movement of a straight line into a sesquialter ratio—where it is immediately necessary to cut because of the infinite circumferences and intervals falling in between—and again because of the persuasive argument of equal circles, namely that whatever moves must move a greater semicircle, and all other such facts observed about lines, not to admit that it is impossible for such a movement to occur without previously falling on each of the intermediates; for these latter are much more agreed upon than those former.