§8.8#1Ὅτι δʼ ἐνδέχεται εἶναί τινα ἄπειρον, μίαν οὖσαν καὶ συνεχῆ, καὶ αὕτη ἐστὶν ἡ κύκλῳ, λέγωμεν νῦν. πᾶν μὲν γὰρ κινεῖται τὸ φερόμενον ἢ κύκλῳ ἢ εὐθεῖαν ἢ μικτήν, ὥστʼ εἰ μηδʼ ἐκείνων ἡ ἑτέρα συνεχής, οὐδὲ τὴν ἐξ ἀμφοῖν οἷόν τʼ εἶναι συγκειμένην·
let us state that it is possible for there to be some infinite motion which is single and continuous, and that this is circular motion. For everything that is in locomotion is moved either in a circle, or in a straight line, or in a mixture of both, so that if neither of those two is continuous, then neither can the motion composed of both be so.
ὅτι δὲ τὸ φερόμενον τὴν εὐθεῖαν καὶ πεπερασμένην οὐ φέρεται συνεχῶς, δῆλον· ἀνακάμπτει γάρ, τὸ δʼ ἀνακάμπτον τὴν εὐθεῖαν τὰς ἐναντίας κινεῖται κινήσεις·
But that which is carried along a finite straight line does not move continuously is clear; for it turns back, and that which turns back on a straight line moves with contrary motions.
ἐναντία γὰρ κατὰ τόπον ἡ ἄνω τῇ κάτω καὶ ἡ εἰς τὸ πρόσθεν τῇ εἰς τοὔπισθεν καὶ ἡ εἰς ἀριστερὰ τῇ εἰς δεξιά· τόπου γὰρ ἐναντιώσεις αὗται.
For in respect of place, upward motion is contrary to downward, forward to backward, and to the left to to the right; for these are contrarieties of place.
τίς δʼ ἐστὶν ἡ μία καὶ συνεχὴς κίνησις, διώρισται πρότερον, ὅτι ἡ τοῦ ἑνὸς καὶ ἐν ἑνὶ χρόνῳ καὶ ἐν ἀδιαφόρῳ κατʼ εἶδος (τρία γὰρ ἦν, τό τε κινούμενον, οἷον ἄνθρωπος ἢ θεός, καὶ ὅτε, οἷον χρόνος, καὶ τρίτον τὸ ἐν ᾧ·
But what the single and continuous motion is has been defined previously, namely, that of a single subject, in a single time, and in that which is specifically undifferentiated.
τοῦτο δʼ ἐστὶν τόπος ἢ πάθος ἢ εἶδος ἢ μέγεθος).
For there were three things—that which is moved, such as a man or a god; second, when, such as time; and third, that in which; and this is either place, or affection, or form, or magnitude.
τὰ δʼ ἐναντία διαφέρει τῷ εἴδει, καὶ οὐχ ἕν· τόπου δʼ αἱ εἰρημέναι διαφοραί. σημεῖον δʼ ὅτι ἐναντία ἡ κίνησις ἡ ἀπὸ τοῦ Α πρὸς τὸ Β τῇ ἀπὸ τοῦ Β πρὸς τὸ Α, ὅτι ἱστᾶσιν καὶ παύουσιν ἀλλήλας, ἐὰν ἅμα γίγνωνται.
But contraries differ in species and are not one; and the mentioned distinctions are those of place. And a sign that the motion from A to B is contrary to that from B to A is that they stop and check each other if they occur at the same time.
καὶ ἐπὶ κύκλου ὡσαύτως, οἷον ἡ ἀπὸ τοῦ Α ἐπὶ τὸ Β τῇ ἀπὸ τοῦ Α ἐπὶ τὸ Γ (ἱστᾶσι γάρ, κἂν συνεχεῖς ὦσιν καὶ μὴ γίγνηται ἀνάκαμψις, διὰ τὸ τἀναντία φθείρειν καὶ κωλύειν ἄλληλα)· ἀλλʼ οὐχ ἡ εἰς τὸ πλάγιον τῇ ἄνω. μάλιστα δὲ φανερὸν
ὅτι ἀδύνατον εἶναι συνεχῆ τὴν ἐπὶ τῆς εὐθείας κίνησιν, ὅτι ἀνακάμπτον ἀναγκαῖον στῆναι, οὐ μόνου ἐπʼ εὐθείας, ἀλλὰ κὰν κύκλον φέρηται.
And similarly on a circle, as for instance the motion from A toward B is contrary to that from A toward C (for they stop each other, even if they are continuous and no turning back occurs, because contraries destroy and block each other); but motion to the side is not contrary to upward motion. But it is most clear that motion on a straight line cannot be continuous, because that which turns back must necessarily stop, not only on a straight line, but also if it is carried along a circle.
οὐ γὰρ ταὐτὸν κύκλῳ φέρεσθαι καὶ κύκλον· ἔστιν γὰρ ὁτὲ μὲν συνείρειν κινούμενον, ὁτὲ δʼ ἐπὶ τὸ αὐτὸ ἐλθὸν ὅθεν ὡρμήθη ἀνακάμψαι πάλιν.
For to be carried in a circle is not the same as to be carried along a circle; for sometimes a moving thing can continue continuously, but at another time, having come to the same point from which it started, it can turn back again.
ὅτι δʼ ἀνάγκη ἵστασθαι, ἡ πίστις οὐ μόνον ἐπὶ τῆς αἰσθήσεως ἀλλὰ καὶ ἐπὶ τοῦ λόγου.
But that it must necessarily stop, credibility is gained not only from perception but also from argument.
ἀρχὴ δὲ ἥδε.
And the principle is as follows.
τριῶν γὰρ ὄντων, ἀρχῆς μέσου τελευτῆς, τὸ μέσον πρὸς ἑκάτερον ἄμφω ἐστίν, καὶ τῷ μὲν ἀριθμῷ ἕν, τῷ λόγῳ δὲ δύο.
For since there are three things—beginning, middle, and end—the middle is both in relation to each of the others, and while it is one in number, it is two in definition.
ἔτι δὲ ἄλλο ἐστὶν τὸ δυνάμει καὶ τὸ ἐνεργείᾳ, ὥστε τῆς εὐθείας τῶν ἐντὸς τῶν ἄκρων ὁτιοῦν σημεῖον δυνάμει μέν ἐστι μέσον, ἐνεργείᾳ δʼ οὐκ ἔστιν, ἐὰν μὴ διέλη ταύτῃ καὶ ἐπιστὰν πάλιν ἄρξηται κινεῖσθαι·
Further, that which is in potentiality is other than that which is in actuality, so that any point on a straight line between the extremities is a middle in potentiality, but is not so in actuality, unless the moving object divides the line at this point, and having stopped, starts to move again.
οὕτω δὲ τὸ μέσον ἀρχὴ γίγνεται καὶ τελευτή, ἀρχὴ μὲν τῆς ὕστερον, τελευτὴ δὲ τῆς πρώτης (λέγω δʼ οἷον ἐὰν φερόμενον τὸ Α στῇ ἐπὶ τοῦ Β καὶ πάλιν φέρηται ἐπὶ τὸ Γ).
And in this way the middle becomes a beginning and an end: the beginning of the subsequent motion, and the end of the first (I mean, for example, if the moving object A should stop at B and move again toward C).
ὅταν δὲ συνεχῶς φέρηται, οὔτε γεγονέναι οὔτε ἀπογεγονέναι οἷόν τε τὸ Α κατὰ τὸ Β σημεῖον, ἀλλὰ μόνον εἶναι ἐν τῷ νῦν, ἐν χρόνῳ δʼ οὐδενὶ πλὴν οὗ τὸ νῦν ἐστιν διαίρεσις, ἐν τῷ ὅλῳ. (εἰ δὲ γεγονέναι τις θήσει καὶ ἀπογεγονέναι, ἀεὶ στήσεται τὸ Α φερόμενον· ἀδύνατον γὰρ τὸ Α ἅμα γεγονέναι τε ἐπὶ τοῦ Β καὶ ἀπογεγονέναι.
But when it is carried along continuously, it is not possible for A either to have arrived at or to have departed from the point B, but it is only there in the 'now', and not in any time except that of which the 'now' is a division within the whole time. (And if anyone posits that it has arrived and departed, the moving object A will always stop; for it is impossible for A to have arrived at B and to have departed from it at the same time.
ἐν ἄλλῳ ἄρα καὶ ἄλλῳ σημείῳ χρόνου.
Therefore, it must be at different points of time.
χρόνος ἄρα ἔσται ὁ ἐν μέσῳ.
Thus, there will be time in between.
ὥστε ἠρεμήσει τὸ Α ἐπὶ τοῦ Β. ὁμοίως δὲ καὶ ἐπὶ τῶν ἄλλων σημείων·
Consequently, A will be at rest at B.
ὁ γὰρ αὐτὸς λόγος ἐπὶ πάντων. ὅταν δὴ χρήσηται τὸ φερόμενον Α τῷ Β μέσῳ καὶ τελευτῇ καὶ ἀρχῇ, ἀνάγκη στῆναι διὰ τὸ δύο ποιεῖν, ὥσπερ ἂν εἰ καὶ νοήσειεν. ) ἀλλʼ ἀπὸ μὲν τοῦ Α σημείου ἀπογέγονε τῆς ἀρχῆς, ἐπὶ δὲ τοῦ Γ γέγονεν, ὅταν τελευτήσῃ καὶ στῇ.
And similarly for the other points; for the same argument applies to all. When, therefore, the moving object A uses the middle B as both an end and a beginning, it must necessarily stop because it makes it two, just as if one were to conceive it in thought.) But it has departed from the beginning point A, and has arrived at C when it has finished its motion and stopped.