§4.12#1Ἐλάχιστος δὲ ἀριθμὸς ὁ μὲν ἁπλῶς ἐστὶν ἡ δυάς·
Now, the minimum number in an absolute sense is the dyad; but of a particular number, in one sense there is a minimum, and in another there is not.
τὶς δὲ ἀριθμὸς ἔστι μὲν ὡς ἔστιν, ἔστι δʼ ὡς οὐκ ἔστιν, οἷον γραμμῆς ἐλάχιστος πλήθει μέν ἐστιν αἱ δύο ἢ ἡ μία, μεγέθει δʼ οὐκ ἔστιν ἐλάχιστος· ἀεὶ γὰρ διαιρεῖται πᾶσα γραμμή.
For instance, of a line, the minimum in respect of multiplicity is two or one, but in magnitude there is no minimum; for every line is always divided.
ὥστε ὁμοίως καὶ χρόνος· ἐλάχιστος γὰρ κατὰ μὲν ἀριθμόν ἐστιν ὁ εἷς ἢ οἱ δύο, κατὰ μέγεθος δʼ οὐκ ἔστιν. φανερὸν
δὲ καὶ ὅτι ταχὺς μὲν καὶ βραδὺς οὐ λέγεται, πολὺς δὲ καὶ ὀλίγος καὶ μακρὸς καὶ βραχύς.
So it is likewise with time; for the minimum in respect of number is one or two, but in respect of magnitude there is none. And it is also clear that time is not said to be fast or slow, but much and little, and long and short.
ᾗ μὲν γὰρ συνεχής, μακρὸς καὶ βραχύς, ᾗ δὲ ἀριθμός, πολὺς καὶ ὀλίγος.
For in so far as it is continuous, it is long and short, but in so far as it is number, it is much and little.
ταχὺς δὲ καὶ βραδὺς οὐκ ἔστιν· οὐδὲ γὰρ ἀριθμὸς ᾧ ἀριθμοῦμεν ταχὺς καὶ βραδὺς οὐδείς. καὶ ὁ αὐτὸς δὲ πανταχοῦ
ἅμα· πρότερον δὲ καὶ ὕστερον οὐχ ὁ αὐτός, ὅτι καὶ ἡ μεταβολὴ ἡ μὲν παροῦσα μία, ἡ δὲ γεγενημένη καὶ ἡ μέλλουσα ἑτέρα, ὁ δὲ χρόνος ἀριθμός ἐστιν οὐχ ᾧ ἀριθμοῦμεν ἀλλʼ ὁ ἀριθμούμενος, οὗτος δὲ συμβαίνει πρότερον καὶ ὕστερον ἀεὶ ἕτερος· τὰ γὰρ νῦν ἕτερα.
But it is not fast and slow; for indeed, no number by which we number is fast or slow. And time is the same everywhere simultaneously; but in respect of prior and posterior it is not the same, because change also is one in the present, but past and future change are different, and time is not the number by which we number but the number which is numbered, and this happens to be always different in prior and posterior, because the "nows" are different.
ἔστι δὲ ὁ ἀριθμὸς εἷς μὲν καὶ ὁ αὐτὸς ὁ τῶν ἑκατὸν ἵππων καὶ ὁ τῶν ἑκατὸν ἀνθρώπων, ὧν δʼ ἀριθμός, ἕτερα, οἱ ἵπποι τῶν ἀνθρώπων.
And the number of a hundred horses and that of a hundred men is one and the same, but the things of which it is the number—the horses and the men—are different.
ἔτι ὡς ἐνδέχεται κίνησιν εἶναι τὴν αὐτὴν καὶ μίαν πάλιν καὶ πάλιν, οὕτω καὶ χρόνον, οἷον ἐνιαυτὸν ἢ ἔαρ ἢ μετόπωρον.
Further, just as it is possible for the same and single motion to occur again and again, so also for time, such as a year or spring or autumn.
οὐ
μόνον δὲ τὴν κίνησιν τῷ χρόνῳ μετροῦμεν, ἀλλὰ καὶ τῇ κινήσει τὸν χρόνον διὰ τὸ ὁρίζεσθαι ὑπʼ ἀλλήλων· ὁ μὲν γὰρ χρόνος ὁρίζει τὴν κίνησιν ἀριθμὸς ὢν αὐτῆς, ἡ δὲ κίνησις τὸν χρόνον.
And not only do we measure motion by time, but also time by motion, because they are defined by each other; for time defines motion, being its number, and motion defines time.
καὶ λέγομεν πολὺν καὶ ὀλίγον χρόνον τῇ κινήσει μετροῦντες, καθάπερ καὶ τῷ ἀριθμητῷ τὸν ἀριθμόν, οἷον τῷ ἑνὶ ἵππῳ τὸν τῶν ἵππων ἀριθμόν.
And we speak of much and little time, measuring it by motion, just as we measure number by the countable, as, for instance, the number of horses by the single horse.
τῷ μὲν γὰρ ἀριθμῷ τὸ τῶν ἵππων πλῆθος γνωρίζομεν, πάλιν δὲ τῷ ἑνὶ ἵππῳ τὸν τῶν ἵππων ἀριθμὸν αὐτόν.
For by number we know the multiplicity of horses, and again by the single horse we know the number of horses itself.
ὁμοίως δὲ καὶ ἐπὶ τοῦ χρόνου καὶ τῆς κινήσεως· τῷ μὲν γὰρ χρόνῳ τὴν κίνησιν, τῇ δὲ κινήσει τὸν χρόνον μετροῦμεν.
Likewise also in the case of time and motion; for we measure motion by time, and time by motion.
καὶ τοῦτʼ εὐλόγως συμβέβηκεν· ἀκολουθεῖ γὰρ τῷ μὲν μεγέθει ἡ κίνησις, τῇ δὲ κινήσει ὁ χρόνος, τῷ καὶ ποσὰ καὶ συνεχῆ καὶ διαιρετὰ εἶναι·
And this happens reasonably; for motion follows magnitude, and time follows motion, in respect of being quantities, continuous, and divisible.
διὰ μὲν γὰρ τὸ τὸ μέγεθος εἶναι τοιοῦτον ἡ κίνησις ταῦτα πέπονθεν, διὰ δὲ τὴν κίνησιν ὁ χρόνος.
For because magnitude is of this nature, motion has these properties, and because of motion, time has them.
καὶ μετροῦμεν καὶ τὸ μέγεθος τῇ κινήσει καὶ τὴν κίνησιν τῷ μεγέθει· πολλὴν γὰρ εἶναί φαμεν τὴν ὁδόν, ἂν ἡ πορεία πολλή, καὶ ταύτην πολλήν, ἂν ἡ ὁδὸς πολλή· καὶ τὸν χρόνον, ἂν ἡ κίνησις, καὶ τὴν κίνησιν, ἂν ὁ χρόνος.
And we measure both magnitude by motion, and motion by magnitude; for we say that the road is long if the journey is long, and that this is long if the road is long; and time if the motion is, and the motion if the time is.
ἐπεὶ δʼ ἐστὶν ὁ χρόνος μέτρον
κινήσεως καὶ τοῦ κινεῖσθαι, μετρεῖ δʼ οὗτος τὴν κίνησιν τῷ ὁρίσαι τινὰ κίνησιν ἣ καταμετρήσει τὴν ὅλην (ὥσπερ καὶ τὸ μῆκος ὁ πῆχυς τῷ ὁρίσαι τι μέγεθος ὃ ἀναμετρήσει τὸ ὅλον), καὶ ἔστιν τῇ κινήσει τὸ ἐν χρόνῳ εἶναι τὸ μετρεῖσθαι τῷ χρόνῳ καὶ αὐτὴν καὶ τὸ εἶναι αὐτῆς (ἅμα γὰρ τὴν κίνησιν καὶ τὸ εἶναι τῆς κινήσεως μετρεῖ, καὶ τοῦτʼ ἔστιν αὐτῇ τὸ ἐν χρόνῳ εἶναι, τὸ μετρεῖσθαι αὐτῆς τὸ εἶναι), δῆλον ὅτι καὶ τοῖς ἄλλοις τοῦτʼ ἔστι τὸ ἐν χρόνῳ εἶναι, τὸ μετρεῖσθαι αὐτῶν τὸ εἶναι ὑπὸ τοῦ χρόνου.
Since, then, time is the measure of motion and of being moved, and it measures motion by defining a certain motion which will measure out the whole (just as the cubit measures length by defining a certain magnitude which will measure out the whole), and since for motion to be in time is to be measured by time, both itself and its being (for it measures simultaneously both motion and the being of motion, and this is what it is for it to be in time, namely, for its being to be measured), it is clear that for other things too, this is to be in time, namely, for their being to be measured by time.
τὸ γὰρ ἐν χρόνῳ εἶναι δυοῖν ἐστιν θάτερον, ἓν μὲν τὸ εἶναι τότε ὅτε ὁ χρόνος ἔστιν, ἓν δὲ ὥσπερ ἔνια λέγομεν ὅτι ἐν ἀριθμῷ ἐστιν. τοῦτο δὲ σημαίνει ἤτοι ὡς μέρος ἀριθμοῦ καὶ πάθος, καὶ ὅλως ὅτι τοῦ ἀριθμοῦ τι, ἢ ὅτι ἔστιν αὐτοῦ ἀριθμός.
For to be in time is one of two things: one, to be when time is; the other, just as we say of some things that they are "in number." And this means either that it is as a part of number and an affection of it, and generally that it is something belonging to number, or that there is a number of it.
ἐπεὶ δʼ ἀριθμὸς ὁ χρόνος, τὸ μὲν νῦν καὶ τὸ πρότερον καὶ ὅσα τοιαῦτα οὕτως ἐν χρόνῳ ὡς ἐν ἀριθμῷ μονὰς καὶ τὸ περιττὸν καὶ ἄρτιον (τὰ μὲν γὰρ τοῦ ἀριθμοῦ τι, τὰ δὲ τοῦ χρόνου τί ἐστιν)· τὰ δὲ πράγματα ὡς ἐν ἀριθμῷ τῷ χρόνῳ ἐστίν.
And since time is a number, the "now" and the "prior" and all such things are in time just as the unit, the odd, and the even are in number (for some are things belonging to number, and others are things belonging to time); but things are in time as being in number.
εἰ δὲ τοῦτο, περιέχεται ὑπὸ χρόνου ὥσπερ καὶ τὰ ἐν ἀριθμῷ ὑπʼ ἀριθμοῦ καὶ τὰ ἐν τόπῳ ὑπὸ τόπου.
And if this is so, they are contained by time just as things in number are contained by number, and things in place by place.
φανερὸν δὲ καὶ ὅτι οὐκ ἔστιν τὸ ἐν χρόνῳ εἶναι τὸ εἶναι ὅτε ὁ χρόνος ἔστιν, ὥσπερ οὐδὲ τὸ ἐν κινήσει εἶναι οὐδὲ τὸ ἐν τόπῳ ὅτε ἡ κίνησις καὶ ὁ τόπος ἔστιν.
It is also clear that to be in time is not to be when time is, just as to be in motion or to be in place is not to be when motion or place is.
εἰ γὰρ ἔσται τὸ ἔν τινι οὕτω, πάντα τὰ πράγματα ἐν ὁτῳοῦν ἔσται, καὶ ὁ οὐρανὸς ἐν τῇ κέγχρῳ· ὅτε γὰρ ἡ κέγχρος ἔστιν, ἔστι καὶ ὁ οὐρανός.
For if being "in" something is to be so, all things will be in anything whatever, and the heaven will be in a millet-seed; for when the millet-seed is, the heaven also is.
ἀλλὰ τοῦτο μὲν συμβέβηκεν, ἐκεῖνο δʼ ἀνάγκη παρακολουθεῖν, καὶ τῷ ὄντι ἐν χρόνῳ εἶναί τινα χρόνον ὅτε κἀκεῖνο ἔστιν, καὶ τῷ ἐν κινήσει ὄντι εἶναι τότε κίνησιν.
But this is accidental, whereas the other must follow: both for that which is in time, that there is some time when it also is, and for that which is in motion, that there is then motion.