§1.2#2ὁπότε γὰρ ἥπτοντο καὶ ὃν ἦν μέγεθος καὶ ἄμα ἦσαν, οὐδὲν ἐποίουν μεῖζον τὸ πᾶν.
For when they touched and were a single magnitude and were together, they made the whole no larger.
διαιρεθέντος γὰρ εἰς δύο καὶ πλείω, οὐδὲν ἔλαττον οὐδὲ μεῖζον τὸ πᾶν τοῦ πρότερον, ὥστε κὲν πᾶσαι συντεθῶσιν, οὐδὲν ποιήσουσι μέγεθος.
For when it is divided into two or more, the whole is no smaller nor larger than before, so that even if all are put together, they will produce no magnitude.
ἀλλὰ μὴν καὶ εἴ τι διαιρουμένου οἷον ἔκπρισμα γίνεται τοῦ σώματος, καὶ οὕτως ἐκ τοῦ μεγέθους σῶμά τι ἀπέρχεται, ὁ αὐτὸς λόγος, ἐκεῖνο πῶς διαιρετόν;
But indeed, even if when divided something like a sawing-dust comes to be from the body, and in this way some body departs from the magnitude, the same argument applies: how is that divisible?
εἰ δὲ μὴ σῶμα ἀλλ᾿ εἶδός τι χωριστὸν ἢ πάθος ὅ ἀπῆλθεν, καὶ ἔστι τὸ μέγεθος στιγμαὶ ἢ ἁφαὶ τοδὶ παθοῦσαι, ἄτοπον ἐκ μὴ μεγεθῶν μέγεθος εἶναι.
But if it is not a body but some separable form or affection which departed, and the magnitude is points or contacts having undergone this affection, it is absurd for magnitude to come from non-magnitudes.
ἔτι δὲ ποῦ ἔσονται καὶ ἀκίνητοι ἢ κινούμεναι αἱ στιγμαί;
Further, where will the points be, and will they be unmoved or moved?
ἁφή τε ἀεὶ μία δυοῖν τινῶν, ὡς ὄντος τινὸς παρὰ τὴν ἁφὴν καὶ τὴν διαίρεσιν καὶ τὴν στιγμήν.
And contact is always one between some two, as if there were something besides the contact, the division, and the point.
εἰ δή τις θήσεται ἁτιοῦν ἢ ὁπηλικονοῦν σῶμα εἶναι πάντῃ διαιρετόν, πάντα ταῦτα συμβαίνει.
If, then, anyone posits any body whatever or of whatever size to be divisible everywhere, all these consequences follow.
ἔτι ἐὰν διελὼν συνθῶ τὸ ξύλον ἤ τι ἄλλο, πάλιν ἴσον τε καὶ ἕν.
Further, if having divided I put together the wood or something else, it is again equal and one.
οὐκοῦν οὕτως ἔχει δηλονότι κἂν τέμω τὸ ξύλον καθ᾿ ὁτιοῦν σημεῖον.
Therefore, it is clearly so even if I cut the wood at any point whatever.
πάντῃ ἄρα διῄται δυνάμει.
It is therefore divided everywhere potentially.
τί οὖν ἔστι παρὰ τὴν διαίρεσιν;
What, then, is there besides the division?
εἰ γὰρ καὶ ἔστι τι πάθος, ἀλλὰ πῶς εἰς ταῦτα διαλύεται καὶ γίνεται ἐκ τούτων;
For even if there is indeed some affection, yet how is it dissolved into these and comes to be from these?
ἢ πῶς χωρίζεται ταῦτα;
Or how are these separated?
ὥστ᾿ εἴπερ ἀδύνατον ἐξ ἁφῶν ἢ στιγμῶν εἶναι τὰ μεγέθη, ἀνάγκη εἶναι σώματα ἀδιαίρετα καὶ μεγέθη.
So that if indeed it is impossible for magnitudes to be from contacts or points, it is necessary that there are indivisible bodies and magnitudes.
οὐ μὴν ἀλλὰ καὶ ταῦτα θεμένοις οὐχ ἧττον συμβαίνει ἀδύνατον.
Yet to those who posit these, no less impossible consequences follow.
ἔσκεπται δὲ περὶ αὐτῶν ἐν ἑτέροις.
But they have been investigated in other works.
ἀλλὰ ταῦτα πειρατέον λύειν· διὸ πάλιν ἐξ ἀρχῆς τὴν ἀπορίαν λεκτέον.
Yet we must try to resolve these; therefore, we must state the difficulty again from the beginning.
Τὸ μὲν οὖν ἅπαν σῶμα αἰσθητὸν εἶναι διαιρετὸν καθ᾿ ὁτιοῦν σημεῖον καὶ ἀδιαίρετον οὐδὲν ἄτοπον· τὸ μὲν γὰρ δυνάμει διαιρετόν, τὸ δ᾿ ἐντελεχείᾳ ὑπάρξει.
Now, for every sensible body to be divisible at any point whatever and indivisible is nothing absurd; for the one will belong to it potentially, and the other in actuality.
τὸ δ᾿ εἶναι ἅμα πάντῃ διαιρετὸν δυνάμει ἀδύνατον δόξειεν ἂν εἶναι.
But to be simultaneously divisible everywhere potentially would seem to be impossible.
εἰ γὰρ δυνατόν, κἂν γένοιτο, οὐχ ὥστε εἶναι ἄμα ἄμφω ἐντελεχείᾳ ἀδιαίρετον καὶ διῃρημένον, ἀλλὰ διῃρημένον καθ᾿ ὁτιοῦν σημεῖον.
For if it were possible, it could also happen, not so as to be simultaneously both in actuality indivisible and divided, but divided at any point whatever.
οὐδὲν ἄρα ἔσται λοιπόν, καὶ εἰς ἀσώματον ἐφθαρμένον τὸ σῶμα, καὶ γένοιτο δ᾿ ἂν πάλιν ἤτοι ἐκ στιγμῶν ἢ ὅλως ἐξ οὐδενός.
Therefore, nothing will remain, and the body will have perished into something incorporeal, and could come to be again either from points or entirely from nothing.
καὶ τοῦτο πῶς δυνατόν;
And how is this possible?
Ἀλλὰ μὴν ὅτι γε διαιρεῖται εἰς χωριστὰ καὶ ἀεὶ εἰς ἐλάττω μεγέθη καὶ εἰς ἀπέχοντα καὶ κεχωρισμένα, φανερόν.
But indeed, that it is divided into separable and always smaller magnitudes and into distant and separated parts is clear.
οὔτε δὴ κατὰ μέρος διαιροῦντι εἴη ἂν ἄπειρος ἡ θρύψις, οὔτε ἄμα οἶόν τε διαιρεθῆναι κατὰ πᾶν σημεῖον (οὐ γὰρ δυνατόν) ἀλλὰ μέχρι του.
Neither, then, for one who divides part by part would the crushing be infinite, nor is it possible to be divided simultaneously at every point (for it is not possible) but only up to a certain point.
ἀνάγκη ἄρα ἄτομα ἐνυπάρχειν μεγέθη ἀόρατα, ἄλλως τε καὶ εἶπερ ἔσται γένεσις καὶ φθορὰ ἡ μὲν διακρίσει ἡ δὲ συγκρίσει.
It is necessary, therefore, that indivisible invisible magnitudes are inherent, especially if generation and destruction are to be, the one by dissociation and the other by association.
ὁ μὲν οὖν ἀναγκάζειν δοκῶν λόγος εἶναι μεγέθη ἄτομα οὗτος ἐστίν· ὅτι δὲ λανθάνει παραλογιζόμενος, καὶ ᾗ λανθάνει, λέγωμεν.
This, then, is the argument that seems to compel the existence of indivisible magnitudes; but let us state that it is a hidden paralogism, and how it is hidden.
Ἐπεὶ γὰρ οὐκ ἔστι στιγμὴ στιγμῆς ἐχομένη, τὸ πάντῃ εἶναι διαιρετὸν ἔστι μὲν ὡς ὑπάρχει τοῖς μεγέθεσιν, ἔστι δ᾿ ὡς οὔ.
For since point is not next to point, being divisible everywhere is in one way present in magnitudes, and in another way not.
δοκεῖ δ᾿ ὅταν τοῦτο τεθῇ, καὶ ὁπῃοῦν καὶ πάντῃ στιγμὴν εἶναι, ὥστ᾿ ἀναγκαῖον εἶναι διαιρεθῆναι τὸ μέγεθος εἰς μηδέν· πάντῃ γὰρ εἶναι στιγμήν· ὥστε ἢ ἐξ ἁφῶν ἢ ἐκ στιγμῶν εἶναι.
But it seems, when this is posited, that there is a point anywhere and everywhere, so that it is necessary for the magnitude to be divided into nothing; for there is a point everywhere; so that it consists either of contacts or of points.
τὸ δ᾿ ἔστιν ὡς ὑπάρχει πάντῃ, ὅτι μία ὁπῃοῦν ἐστί, καὶ πᾶσαι ὡς ἑκάστη, πλείους δὲ μιᾶς οὐκ εἰσίν (ἐφεξῆς γὰρ οὐκ εἰσι), ὥστ᾿ οὐ πάντῃ.
But the truth is that it is present everywhere in the sense that there is one anywhere, and all as each, but there are not more than one (for they are not consecutive), so that not everywhere.
εἰ γὰρ κατὰ μέσον διαιρετόν, καὶ κατ᾿ ἐχομένην στιγμὴν ἔσται διαιρετόν· οὐχὶ δέ¹· οὐ γάρ ἐστιν ἐχόμενον σημεῖον σημείου ἢ στιγμὴ στιγμῆς.
For if it is divisible at the middle, it will also be divisible at the next point; but it is not so; for point is not next to point or point to point.
τοῦτο δ᾿ ἐστὶ διαίρεσις καὶ² σύνθεσις.
And this is division and composition.
Ὥστ᾿ ἔστι καὶ διάκρισις καὶ σύγκρισις, ἀλλ᾿ οὔτ᾿ εἰς ἄτομα καὶ ἐξ ἀτόμων (πολλὰ γὰρ τὰ ἀδύνατα) οὔτε οὕτως ὥστε πάντῃ διαίρεσιν γενέσθαι (εἰ γὰρ ἦν ἐχομένη στιγμὴ στιγμῆς, τοῦτ᾿ ἂν ἧν), ἀλλ᾿ εἰς μικρὰ καὶ ἐλάττω ἐστί, καὶ σύγκρισις ἐξ ἐλαττόνων.
So that there is both dissociation and association, but neither into indivisible parts nor from indivisible parts (for many impossible consequences follow) nor in such a way that division occurs everywhere (for if point were next to point, this would be so), but it is into small and smaller parts, and association is from smaller parts.
ἀλλ᾿ οὐχ ἡ ἁπλῆ καὶ τελεία γένεσις συγκρίσει καὶ διακρίσει ὥρισται, ὥς τινές φασιν, τὴν δ᾿ ἐν τῷ συνεχεῖ μεταβολὴν ἀλλοίωσιν.
But simple and complete generation is not defined by association and dissociation, as some say, while calling the change in the continuous alteration.
ἀλλὰ τοῦτ᾿ ἐστὶν ἐν ᾧ σφάλλεται πάντα.
But this is what everyone is mistaken about.
ἔστι γὰρ γένεσις ἁπλῆ καὶ φθορὰ οὐ συγκρίσει καὶ διακρίσει, ἀλλ᾿ ὅταν μεταβάλλῃ ἐκ τοῦδε εἰς τόδε ὅλον.
For simple generation and destruction are not by association and dissociation, but when it changes from this to that as a whole.
οἱ δὲ οἴονται ἀλλοίωσιν πᾶσαν εἶναι τὴν τοιαύτην μεταβολήν· τὸ δὲ διαφέρει.
But they think that all such change is alteration; but it differs.
ἐν γὰρ τῷ ὑποκειμένῳ τὸ μέν ἐστι κατὰ τὸν λόγον, τὸ δὲ κατὰ τὴν ὕλην.
For in the underlying subject, one part is according to the definition, and the other according to the matter.
ὅταν μὲν οὖν ἐν τούτοις ᾖ ἡ μεταβολή, γένεσις ἔσται ἢ φθορά, ὅταν δ᾿ ἐν τοῖς πάθεσι καὶ κατὰ συμβεβηκός, ἀλλοίωσις.
When, therefore, the change is in these, it will be generation or destruction, but when in the affections and accidentally, alteration.
διακρινόμενα δὲ καὶ συγκρινόμενα εὔφραρτα γίνεται.
But things dissociated and associated become easily destroyed.
ἐὰν μὲν γὰρ εἰς ἐλάττω ὑδάτια διαιρεθῇ, θᾶττον ἀὴρ γίνεται, ἐὰν δὲ συγκριθῇ, βραδύτερον.
For if water is divided into smaller droplets, it becomes air more quickly, but if associated, more slowly.
μᾶλλον δ᾿ ἔσται δῆλον ἐν τοῖς ὕστερον.
But this will be clearer in what follows.
νῦν δὲ τοσοῦτον διωρίσθω, ὅτι ἀδύνατον εἶναι τὴν γένεσιν σύγκρισιν, οἴαν δή τινές φασιν.
For now, let this much be defined, that it is impossible for generation to be association of the kind that some say.