§1.7#2ἀλλά μὴν ἐν ἀπείρῳ γε οὐκ ἔστι κινῆσαι ούδὲ κινηθῆναι· πέρας γὰρ οὐκἔχει, ἢ δὲ ποίησις καὶ τὸ πάθος ἔχει.
But indeed, it is not possible to cause movement or to be moved in an infinite [time]; for it has no limit, but action and passion do have a limit.
οὐδʼ ἄπειρον δὴ ὑπʼ ἀπείρου ἐνδέχεται οὐθὲν παθεῖν.
Nor indeed is it possible for any infinite thing to be acted upon by another infinite thing.
ἔστω γὰρ τὸ ἄπειρον καὶ τὸ Β, χρόνος δʼ ἐν ᾦ ἔπαθε τὸ Β ὑπὸ τοῦ Ἀ,ἐῳʼ ᾧ ΓΔ. τὸ δὴ ἐφʼ ᾧ τὸ E τοῦ ἀπείρου μέρος, ἐπεὶ ὅλον πέπονθε τὸ Β, οὐκ ἐν ἴσῳ χρόνῳ τὸ αὐτό· ὑποκείσθω γὰρ ἐν ἐλάττονι κινεῖσθαι τὸ ἔλαττον χρόνῳ.
For let the infinite [sc. A] and the other [sc. infinite] be B, and let the time in which B was acted upon by A be ΓΔ. Now, regarding E, which is a part of the infinite, since the whole B was acted upon, [E is acted upon] not in an equal time; for let it be assumed that the less is moved in less time.
ἔστω τὸ Σ κεκινημένον ὑπὸ τοῦ Α ἐν τῷ Δ. ὃ δὴ τὸ Δ πρὸς τὸ σ, τὸ E ἐστὶ πρός τι τοῦ Β πεπερασμένον.
Let Σ be that which has been moved by A in the time Δ. Then, whatever ratio [the time] Δ has to σ [the whole time], [the part] E has that same ratio to some finite part of B.
τοῦ τοίνυν ἀνάγκη ὑπὸ τοῦ Ακινηθῆναι ἐν τῷΔχρόνῳ· ὑπὸ γὰρ τοῦ αὐτοῦ ὑποκείσθω ἐν τῷ πλείονι καὶ ἐλάττονι χρόνῳ τὸ μεῖζον καὶ τὸ ἔλαττον πάσχειν, ὅσα ἀνάλογον χρόνῳ διήρηται.
Therefore, it is necessary that this [finite part] be moved by A in the time Δ; for let it be assumed that by the same agent, the greater and the less are acted upon in longer and shorter times, as many as are divided proportionally to the time.
ἐν ούδενὶ ἄρα χρόνῳ δυνατὸν πεπερασμένῳ ἄπειρον ὑπʼ ἀπείρου κινηθῆναι· ἐν ἀπείρῳ ἄρα.
Therefore, it is not possible in any finite time for one infinite to be moved by another infinite; it must therefore be in an infinite time.
ἀλλʼ ὁ μὲν ἄπειρος χρόνος οὐκ ἔχει τέλος, τὸ δὲ κεκινημένον ἔχει.
But whereas infinite time has no end, that which has been moved does have an end.
εἰ τοίνυν πᾶν σῶμα αἰσθητὸν ἔχει δύναμιν ποιητικὴν ἢ παθητικὴν ἢ ἄμφω, ἀδύνατον σῶμα ἄπειρον αἰσθητὸν εἶναι.
If, therefore, every sensible body has a power of acting or being acted upon, or both, it is impossible for there to be an infinite sensible body.
ἀλλὰ μὴν καὶ ὅσα γε σώματα ἐν τόπῳ, πάντα αἰσθητά.
But indeed, all bodies that are in a place are sensible.
οὐκ ἔστιν ἄρα σῶμα ἄπειρον ἔξω τοῦ οὐρανοῦ οὐθέν.
Therefore, there is no infinite body outside the heaven.
ἀλλὰ μὴν ούδὲ μέχρι τινός.
But indeed, neither is there any up to some limit.
οὐθὲν ἄρα ὅλως σῶμα ἔξω τοῦ οὐρανοῦ.
Therefore, there is no body at all outside the heaven.
εἰ μὲν γὰρ νοητόν, ἔσται ἐν τόπῳʼ τὸ γὰρ ἔξω καὶ ἔσω τόπον σημαίνει.
For if it is intelligible, it will be in a place; for "outside" and "inside" signify a place.
ὥστʼ ἔσται αἰσθητὸν. αἰσθητὸν δʼ οὐθὲν μὴ ἐν τόπῳ.
So it will be sensible; and there is no sensible body that is not in a place.
άογιιώτερον δʼ ἔστιν ἐπιχειρεῖν καὶ ὧδε, οὔτε γὰρ κύκλῳ οἷόν τε κινεῖσθαι τὸ ἄπειρον ὁμοιομερὲς ὄν· μέσον μὲν γὰρ τοῦ ἀπείρου οὐκ ἔστι, τὸ δὲ κύκλῳ περὶ τὸ μέσον κινεῖται.
We may also argue more logically [abstractly] as follows: for it is not possible for the infinite, being uniform, to move in a circle; for there is no center of the infinite, and circular motion is about a center.
ἀλλά μὴν οὐδʼ ἐπʼ εὐθείας οἷόν τε φέρεσθαι τὸ ἄπείρον· δεήσει γὰρ ἕτερον εἶναι τοσοῦτον τόπον ἄπειρον εἰς ὁν-οίσθήσεται κατὰ φύσιν, καὶ ἄλλον τοσοῦτον εἰς ὃν παρὰ φύσιν.
But indeed, neither is it possible for the infinite to be carried in a straight line; for there will be need of another equally infinite place into which it will be carried according to nature, and another as large into which it will be carried contrary to nature.
ἔτι εἴτε φύσει ἔχει κίνησιν τοῦ εἰς εὐθὸ εἴτε βίᾳ κινεῖται, ἀμφοτέρως δεήσει ἄπειρον εἶναι τὴν κινοῦσαν ἰσχύν· ἥ τε γὰρ ἄπειρος ἀπείρου καὶ τοῦ ἀπείρου ἄπειρος ἡ ἰσχύς· ὥςτ ἔσται καὶ τὸ κινοῦν ἄπειρον (λόγος δʼ ἐν τοῖς περὶ κινήσεως ὅτι οὐθὲν ἔχει ἄπειρον δύναμιν τῶν πεπερασμένων, ουδὲ τῶν ἀπείρων πεπερασμένην).
Furthermore, whether it has movement in a straight line by nature or is moved by force, in both cases it will be necessary that the moving force be infinite; for infinite force is of the infinite, and the force of the infinite is infinite; so that the moving cause will also be infinite (and there is an argument in the books on motion [Physics] that nothing of finite things has infinite power, nor does any of infinite things have finite power).
εἰ οὖν τὸ κατὰ φύσιν καὶ παρὰ φύσιν ἐνδέχεται κινηθῆναι, ἔσται δύο ἄπειρα, τό τε κινοῦν οὕτω καὶ τὸ κινούμενον.
If, therefore, it is possible to be moved according to nature and contrary to nature, there will be two infinites, both that which moves in this way and that which is moved.
ἔτι τὸ κινοῦν τὸ ἄπειρον τί ἐστιν;
Furthermore, what is that which moves the infinite?
εἰ μὲν γὰρ αὐτὸ ἑαυτό, ἔμψφον ἔσται.
For if it moves itself, it will be animate [living].
τοῦτο δὲ πῶς δυνατὸν ἄπειρον εἶναι ζῷον;
But how is it possible for there to be an infinite animal?
εἰ δʼ ἄλλο τι τὸ κινοῦν, δύο ἔσται ἄπειρα, τὸ τεκινοῦνκαὶ τὸ κινούμενον, διαφέροντα τὴνμορφὴν καὶ τὴν δύναμιν.
But if something else is the mover, there will be two infinites, both the mover and the moved, differing in form and power.
εἰ δὲ μὴ συνεχὲς τὸ πᾶν, ἀλλʼ ὥσπερ λέγει σημόκριτος καὶ Λεύκιππος, διαωρισμένα τῷ κενῷ, μίαν ἀναγκαῖον εἶναι πάντων τὴν κίνησιν.
And if the whole is not continuous, but, as Democritus and Leucippus say, separated by the void, it is necessary that there is one and the same movement for all [the atoms].
διώρισται μὲν γὰρ τοῖς σχήμασιν· τὴν δὲ φύσιν εἶναί φασιν αὐτῶν μίαν, ὥσπερ ἂν εἰ χρυσὸς ἕκαστον εἴη κεχοωρισμένος.
For they are distinguished by their shapes; but they say that their nature is one, as if each were a separate piece of gold.
τούτων δέ, καθάπερ λέγομεν, ἀναγκαῖον εἶναι τὴν αὐτὴν κίνησιν· ὅπου γὰρ μία βῶλος, καὶ ἡ σύμπασα γῆ φέρεται, καὶ τό τε πᾶν πῦρ καὶ σπινθὴρ εἰς τὸν αὐτὸν τόπον.
And for these, as we say, it is necessary that there is the same movement; for where a single clod of earth is carried, there also the entire earth is carried, and both the whole fire and a spark are carried to the same place.
ὥστʼ οὔτε κοῦφον ἁπλῶς οὐθὲν ἔσται τῶν σωμάτων, εἰ πάντʼ ἔχει βάρος· εἷ δὲ κουφότητα, βαρύ οὐδέν.
So that there will be nothing absolutely light among the bodies if all have weight; and if they have lightness, nothing will be heavy.
ἔτι εἰ βάρος ἔχει ἢ κουφότητα, ἔσται ἢ ἔσχατόν τι τοῦ παντὸς ἢ μέσον.
Furthermore, if they have weight or lightness, there will be either some extremity of the whole or a center.
τοῦτο δʼ ἀδύνατον ἀπείρου γʼ ὄντος.
But this is impossible since it is infinite.
ὅλως δʼ, οὗ μή ἐστι μέσον μηδʼ ἔσχατον, μηδὲ τὸ μὲν ἄνω το δὲ κάτω, τόπος οὐθεὶς ἔσται τοῖς σώμασι τῆς φορᾶς.
In general, where there is neither center nor extremity, nor "up" and "down", there will be no place for the bodies to move.
τούτου δὲ μή ὄντος κίνησις οὐκ ἔσται· ἀνάγκη γὰρ κινεῖσθαι ἤτοι κατὰ φύσιν ἢ παρὰ φύσιν, ταῦτα δʼ ὥρισται τοῖς τόποις τοῖς οἰκείοις καὶ τοῖς ἀλλοτρίοις.
And if this does not exist, there will be no motion; for it is necessary to move either according to nature or contrary to nature, and these are defined by their proper places and foreign places.
ἔτι οὖ παρὰ φύσιν τι μένει ἢ φέρεται, ἀνάγκη τινὸς ἄλλου εἷναι τοῦτον τὸν τόπον κατά φύσιν (τοῦτο δὲ πιστὸν ἐκ τῆς ἐπαγαωγῆς)· ἀνάγκη δὴ μὴ πάντα ἢ βάρος ἔχειν ἢ κουφότητα, ἀλλά τὰ μὲν τὰ δʼ οὔ.
Furthermore, where something remains or is carried contrary to nature, it is necessary that this place is according to nature for some other thing (and this is trustworthy from induction); it is necessary, then, that not all things have weight or lightness, but some do and others do not.
ὅτι μὲν τοίνυν οὐκ ἔστι τὸ σῶμα τοῦ παντὸς ἄπειρον, ἐκ τούτων φανερόν.
That, therefore, the body of the universe is not infinite, is clear from these arguments.