§8.10#2ὅτι μὲν οὖν οὐκ ἐνδέχεται ἄπειρον εἶναι δύναμιν ἐν πεπερασμένῳ μεγέθει, οὐδʼ ἐν ἀπείρῳ πεπερασμένην, ἐκ τούτων δῆλον.
That, therefore, it is not possible for an infinite power to reside in a finite magnitude, nor a finite power in an infinite one, is clear from these considerations.
περὶ δὲ τῶν φερομένων ἔχει καλῶς διαπορῆσαί τινα ἀπορίαν πρῶτον.
With regard to things in projectile motion, however, it is well to raise a certain difficulty first.
εἰ γὰρ πᾶν τὸ κινούμενον κινεῖται ὑπὸ τινός, ὅσα μὴ αὐτὰ ἑαυτὰ κινεῖ, πῶς κινεῖται ἔνια συνεχῶς μὴ ἁπτομένου τοῦ κινήσαντος, οἷον τὰ ῥιπτούμενα;
For if everything that is moved is moved by something—excluding those that move themselves—how is it that some things, such as projectiles, continue to be moved continuously when that which set them in motion is no longer in contact with them?
εἰ δʼ ἅμα κινεῖ καὶ ἄλλο τι ὁ κινήσας, οἷον τὸν ἀέρα, ὃς κινούμενος κινεῖ, ὁμοίως ἀδύνατον τοῦ πρώτου μὴ ἁπτομένου μηδὲ κινοῦντος κινεῖσθαι, ἀλλʼ ἄμα πάντα καὶ κινεῖσθαι καὶ πεπαῦσθαι ὅταν τὸ πρῶτον κινοῦν παύσηται, καὶ εἰ ποιεῖ, ὥσπερ ἡ λίθος, οἷόν τε κινεῖν ὃ ἐκίνησεν.
And if the mover moves something else at the same time, such as the air, which being moved then moves [the projectile], it is likewise impossible for motion to take place when the first mover is neither touching nor moving it, but rather all things must both be in motion and have ceased simultaneously when the first mover ceases, even if it makes [the air], just as the stone does, capable of moving what it moved.
ἀνάγκη δὴ τοῦτο μὲν λέγειν, ὅτι τὸ πρῶτον κινῆσαν ποιεῖ οἷόν τε κινεῖν ἢ τὸν ἀέρα ἢ τὸ ὕδωρ ἤ τι ἄλλο τοιοῦτον ὁ πέφυκε κινεῖν καὶ κινεῖσθαι· ἀλλʼ οὐχ ἅμα παύεται κινοῦν καὶ κινούμενον· ἀλλὰ κινούμενον μὲν ἅμα ὅταν ὁ κινῶν παύσηται κινῶν, κινοῦν δὲ ἔτι ἐστίν.
We must indeed say this: that the first mover makes either the air or the water or some other such thing—which is of a nature to move and to be moved—capable of causing motion; but it does not cease causing motion and being moved at the same time; rather, it ceases being moved at the same time when the mover ceases to move it, but it is still capable of causing motion.
διὸ καὶ κινεῖ τι ἄλλο ἐχόμενον· καὶ ἐπὶ τούτου ὁ αὐτὸς λόγος.
Therefore, it also moves something else adjacent to it; and the same account applies to this.
παύεται δέ, ὅταν ἀεὶ ἐλάττων ἡ δύναμις τοῦ κινεῖν ἐγγίγνηται τῷ ἐχομένῳ.
And it ceases when the power of causing motion that is produced in the adjacent thing becomes progressively less.
τέλος δὲ παύεται, ὅταν μηκέτι ποιήση τὸ πρότερον κινοῦν, ἀλλὰ κινούμενον μόνον.
And it finally ceases when [the preceding member] no longer makes the next thing a mover, but only something moved.
ταῦτα δʼ ἀνάγκη ἅμα παύεσθαι, τὸ μὲν κινοῦν τὸ δὲ κινούμενον, καὶ τὴν ὅλην κίνησιν.
And these must cease simultaneously—the one as mover, the other as moved—and so must the whole motion.
αὕτη μὲν οὖν ἐν τοῖς ἐνδεχομένοις ὁτὲ μὲν κινεῖσθαι ὁτὲ δʼ ἠρεμεῖν ἐγγίγνεται ἡ κίνησις, καὶ οὐ συνεχής, ἀλλὰ φαίνεται· ἢ γὰρ ἐφεξῆς ὄντων ἢ ἁπτομένων ἐστίν· οὐ γὰρ ἓν τὸ κινοῦν, ἀλλʼ ἐχόμενα ἀλλήλων.
This motion, then, occurs in things that are capable of sometimes being in motion and sometimes at rest, and it is not continuous, but only appears to be; for it belongs to things that are successive or in contact, since the mover is not one, but things adjacent to one another.
διὸ ἐν ἀέρι καὶ ὕδατι γίγνεται ἡ τοιαύτη κίνησις, ἣν λέγουσί τινες ἀντιπερίστασιν εἶναι.
Therefore, such motion occurs in air and water, which some say is mutual replacement (antiperistasis).
ἀδύνατον δὲ ἄλλως τὰ ἀπορηθέντα λύειν, εἰ μὴ τὸν εἰρημένον τρόπον.
But it is impossible to solve the difficulties raised in any other way than in the manner described.
ἡ δʼ ἀντιπερίστασις ἅμα πάντα κινεῖσθαι ποιεῖ καὶ κινεῖν, ὥστε καὶ παύεσθαι· νῦν δὲ φαίνεταί τι ἓν κινούμενον συνεχῶς·
Mutual replacement, however, makes all things move and be moved at the same time, so that they also cease at the same time; but in fact some single thing appears to be moved continuously.
ὑπὸ τίνος οὖν;
By what, then?
οὐ γὰρ ὑπὸ τοῦ αὐτοῦ.
For it is not by the same thing.
ἐπεὶ δʼ ἐν τοῖς οὖσιν ἀνάγκη κίνησιν εἶναι συνεχῆ, αὕτη δὲ μία ἐστίν, ἀνάγκη δὲ τὴν μίαν μεγέθους τέ τινος εἶναι (οὐ γὰρ κινεῖται τὸ ἀμέγεθες) καὶ ἑνὸς καὶ ὑφʼ ἑνός (οὐ γὰρ ἔσται συνεχής, ἀλλʼ ἐχομένη ἑτέρα ἑτέρας καὶ διηρημένη), τὸ δὴ κινοῦν εἰ ἕν, ἢ κινούμενον κινεῖ ἢ ἀκίνητον ὄν. εἰ μὲν δὴ κινοῦ.
Since, however, there must be a continuous motion among existing things, and this is one, and the single motion must belong to some magnitude (for that which has no magnitude cannot be moved) and be of a single thing and by a single mover (for otherwise it will not be continuous, but successive and divided), if then the mover is one, it must cause motion either while being itself moved or while being unmoved.
μενον, συνακολουθεῖν δεήσει καὶ μεταβάλλειν αὐτό, ἅμα δὲ κινεῖσθαι ὑπό τινος, ὥστε στήσεται καὶ ἥξει εἰς τὸ κινεῖσθαι ὑπὸ ἀκινήτου.
If, then, it causes motion while being moved, it will have to follow along and change itself, and at the same time be moved by something; so that the series will stop and arrive at being moved by an unmoved mover.
τοῦτο γὰρ οὐκ ἀνάγκη συμμεταβάλλειν, ἀλλʼ ἀεί τε δυνήσεται κινεῖν (ἄπονον γὰρ τὸ οὕτω κινεῖν) καὶ ὁμαλὴς αὕτη ἡ κίνησις ἢ μόνη ἢ μάλιστα· οὐ γὰρ ἔχει μεταβολὴν τὸ κινοῦν οὐδεμίαν.
For this [unmoved mover] does not need to change along with it, but will always be able to cause motion (for causing motion in this way is effortless), and this motion is either alone or pre-eminently uniform, since the mover undergoes no change.
δεῖ δὲ οὐδὲ τὸ κινούμενον πρὸς ἐκεῖνο ἔχειν μεταβολήν, ἵνα ὁμοία ᾖ ἡ κίνησις.
Nor must the moved object undergo any change in relation to that mover, so that the motion may be uniform.
ἀνάγκη δὴ ἢ ἐν μέσῳ ἢ ἐν κύκλῳ εἶναι· αὗται γὰρ αἱ ἀρχαί.
It must, then, be either at the center or on the circumference; for these are the starting points.
ἀλλὰ τάχιστα κινεῖται τὰ ἐγγύτατα τοῦ κινοῦντος. τοιαύτη δʼ ἡ τοῦ κύκλου κίνησις·
But the things nearest to the mover are moved fastest; and such is the motion of the circle.
ἐκεῖ ἄρα τὸ κινοῦν.
Therefore, the mover is there.
ἔχει δʼ ἀπορίαν εἰ ἐνδέχεταί τι κινούμενον κινεῖν συνεχῶς, ἀλλὰ μὴ ὥσπερ τὸ θοῦν πάλιν καὶ πάλιν, τῷ ἐφεξῆς εἶναι συνεχῶς·
But there is a difficulty as to whether it is possible for something that is moved to cause motion continuously, and not like that which pushes again and again, being continuous by being successive.
ἢ γὰρ αὐτὸ δεῖ ἀεὶ ὠθεῖν ἢ ἕλκειν ἢ ἄμφω, ἢ ἕτερόν τι ἐκδεχόμενον ἄλλο παρʼ ἄλλου, ὥσπερ πάλαι ἐλέχθη ἐπὶ τῶν ῥιπτουμένων, εἰ διαιρετὸς ὢν ὁ ἀὴρ κινεῖ ἄλλος ἀεὶ κινούμενος.
For either it must itself always push or pull or both, or something else must receive [the motion] from one to another, as was said earlier of projectiles, if the air, being divisible, causes motion by one part always being moved after another.
ἀμφοτέρως δʼ οὐχ οἷόν τε μίαν εἶναι, ἀλλʼ ἐχομένην.
In both ways, however, it is impossible for the motion to be single, but it can only be adjacent.
μόνη ἄρα συνεχὴς ἣν κινεῖ τὸ ἀκίνητον· ἀεὶ γὰρ ὁμοίως ἔχον καὶ πρὸς τὸ κινούμενον ὁμοίως ἕξει καὶ συνεχῶς.
Therefore, the only continuous motion is that which the unmoved mover causes; for, being always in the same state, it will also relate to the moved object in the same way and continuously.
διωρισμένων δὲ τούτων φανερὸν ὅτι ἀδύνατον τὸ πρῶτον κινοῦν καὶ ἀκίνητον ἔχειν τι μέγεθος.
These things having been defined, it is clear that it is impossible for the first and unmoved mover to have any magnitude.
εἰ γὰρ μέγεθος ἔχει, ἀνάγκη ἤτοι πεπερασμένον αὐτὸ εἶναι ἢ ἄπειρον.
For if it has magnitude, it must of necessity be either finite or infinite.
ἄπειρον μὲν οὖν ὅτι οὐκ ἐνδέχεται μέγεθος εἶναι, δέδεικται πρότερον ἐν τοῖς φυσικοῖς· ὅτι δὲ τὸ πεπερασμένον ἀδύνατον ἔχειν δύναμιν ἄπει. ρον, καὶ ὅτι ἀδύνατον ὑπὸ πεπερασμένου κινεῖσθαί τι ἄπει. ρον χρόνου, δέδεικται νῦν.
Now, that there cannot be an infinite magnitude has been shown previously in the Physics; and that it is impossible for a finite magnitude to have an infinite power, and that it is impossible for anything to be moved for an infinite time by a finite thing, has been shown just now.
τὸ δέ γε πρῶτον κινοῦν ἀΐδιον κινεῖ κίνησιν καὶ ἄπειρον χρόνον.
But the first mover causes an eternal motion and for an infinite time.
φανερὸν τοίνυν ὅτι ἀδιαίρετόν ἐστι καὶ ἀμερὲς καὶ οὐδὲν ἔχον μέγεθος.
It is clear, therefore, that it is indivisible, partless, and has no magnitude.