§5.3Μετὰ δὲ ταῦτα λέγωμεν τί ἐστιν τὸ ἅμα καὶ χωρίς, καὶ τί τὸ ἅπτεσθαι, καὶ τί τὸ μεταξὺ καὶ τί τὸ ἐφεξῆς καὶ τί τὸ ἐχόμενον καὶ συνεχές, καὶ τοῖς ποίοις ἕκαστον τούτων ὑπάρχειν πέφυκεν.
After this let us state what is "at the same time" and "apart", and what is "touching", and what is "between" and what is "in succession" and what is "contiguous" and "continuous", and to what kind of things each of these is by nature adapted to belong.
ἅμα μὲν οὖν λέγω ταῦτʼ εἶναι κατὰ τόπον, ὅσα ἐν ἑνὶ τόπῳ ἐστὶ πρώτῳ. χωρὶς δὲ ὅσα ἐν ἑτέρῳ, ἅπτεσθαι δὲ ὧν τὰ ἄκρα ἅμα.
Now I say that those things are "at the same time" in respect of place which are in one primary place; and "apart" which are in different places; and "touching" whose extremities are at the same time.
| ἐπεὶ δὲ πᾶσα μεταβολὴ ἐν τοῖς ἀντικειμένοις, τὰ δʼ ἀντικείμενα τά τε ἐναντία καὶ τὰ κατὰ ἀντίφασιν, ἀντιφάσεως δʼ οὐδὲν ἀνὰ μέσου, φανερὸν ὅτι ἐν τοῖς ἐναντίοις ἔσται τὸ μεταξύ.
But since every change is between opposites, and opposites are contraries and contradictories, and there is nothing between contradictories, it is clear that the "between" will be among contraries.
ἐν ἐλαχίστοις δʼ ἐστὶ τὸ μεταξὺ τρισίν·
The "between" is, at least, in three things.
ἔσχατον μὲν γάρ ἐστι τῆς μεταβολῆς τὸ ἐναντίον,| μεταξὺ δὲ εἰς ὃ πέφυκε πρότερον ἀφικνεῖσθαι τὸ μεταβάλλον ἢ εἰς ὃ ἔσχατον μεταβάλλει κατὰ φύσιν συνεχῶς μεταβάλλον.
For the contrary is the extremity of change, and "between" is that into which the changing thing is by nature adapted to arrive before it changes into the extremity, when changing continuously according to nature.
| συνεχῶς δὲ κινεῖται τὸ μηθὲν ἢ ὅτι ὀλίγιστον διαλεῖπον τοῦ πράγματος—μὴ τοῦ χρόνου (οὐδὲν γὰρ κωλύει διαλείποντα, καὶ εὐθὺς δὲ μετὰ τὴν ὑπάτην φθέγξασθαι τὴν νεάτην) ἀλλὰ τοῦ πράγματος ἐν ὧ κινεῖται.
And a thing is moved "continuously" when it leaves no gap, or the least possible, in the thing itself—not in time (for nothing prevents leaving a gap in time, and sounding the highest note immediately after the lowest) but in the thing in which it is moved.
τοῦτο δὲ ἔν τε ταῖς κατὰ τόπον καὶ ἐν ταῖς ἄλλαις μεταβολαῖς φανερόν.
This is clear both in changes in respect of place and in other changes.
ἐναντίον δὲ κατὰ τόπον τὸ κατʼ εὐθεῖαν ἀπέχον πλεῖστον· ἡ γὰρ ἐλαχίστη πεπέρανται, μέτρον δὲ τὸ πεπερασμένον.
And "contrary" in respect of place is that which is most distant in a straight line; for the shortest line is limited, and that which is limited is a measure.
ἐφεξῆς δὲ οὗ μετὰ τὴν ἀρχὴν ὄντος ἢ θέσει ἢ εἴδει ἢ ἄλλῳ τινὶ οὕτως ἀφορισθέντος μηδὲν μεταξύ ἐστι τῶν ἐν ταὐτῷ γένει καὶ οὗ ἐφεξῆς ἐστιν (λέγω δʼ οἶον γραμμὴ γραμμῆς ἢ γραμμαί, ἢ μονάδος μονὰς ἢ μονάδες, ἢ οἰκίας οἰκία· ἄλλο δʼ οὐδὲν κωλύει μεταξὺ εἶναι).
And "in succession" is that which, being after the beginning either in position or in species or in some other way thus determined, has nothing of the same genus between itself and that which it is in succession to (I mean, for instance, a line after a line or lines, a unit after a unit or units, or a house after a house; but nothing prevents something of another kind from being between).
τὸ γὰρ ἐφεξῆς τινὶ ἐφεξῆς καὶ ὕστερόν τι· οὐ γὰρ τὸ ἓν ἐφεξῆς τοῖν δυοῖν, οὐδʼ ἡ νουμηνία τῇ δευτέρᾳ ἐφεξῆς, ἀλλὰ ταῦτʼ ἐκείνοις.
For that which is in succession to something is in succession to it and is something posterior; for "one" is not in succession to "two", nor is the first of the month in succession to the second, but the latter to the former.
ἐχ όμενον δὲ ὃ ἂν ἐφεξῆς ὂν ἅπτηται.
And "contiguous" is that which, being in succession, touches.
τὸ δὲ συνεχὲς ἔστι μὲν ὅπερ ἐχόμενόν τι, λέγω δʼ εἶναι συνεχὲς ὅταν ταὐτὸ γένηται καὶ ἓν τὸ ἑκατέρου πέρας οἶς ἅπτονται, καὶ ὥσπερ σημαίνει τοὔνομα, συνέχηται.
And the "continuous" is indeed a certain species of the contiguous, but I call it "continuous" when the extremity of each of the two things becomes the same and one at the point where they touch, and, just as the name signifies, they are held together.
τοῦτο δʼ οὐχ οἷόν τε δυοῖν ὄντοιν εἶναι τοῖν ἐσχάτοιν.
And this is not possible when the extremities are two.
τούτου δὲ διωρισ μένου φανερὸν ὅτι ἐν τούτοις ἐστὶ τὸ συνεχές, ἐξ ὧν ἕν τι πέφυκε γίγνεσθαι κατὰ τὴν σύναψιν.
This being defined, it is clear that the continuous is among those things from which some one thing is by nature adapted to come to be by their union.
καὶ ὥς ποτε γίγνεται τὸ συνέχον ἕν, οὕτω καὶ τὸ ὅλον ἔσται ἔν, οἷον ἢ γόμφῳ ἢ κόλλῃ ἢ ἁφῇ ἢ προσφύσει. φανερὸν δὲ καὶ ὅτι
πρῶτον τὸ ἐφεξῆς ἐστι·
And in whatever way that which holds them together becomes one, in that way also the whole will be one, for instance, either by a peg, or by glue, or by contact, or by organic union. And it is also clear that "in succession" is primary.
τὸ μὲν γὰρ ἁπτόμενον ἐφεξῆς ἀνἀγκη εἶναι, τὸ δʼ ἐφεξῆς οὐ πᾶν ἅπτεσθαι (διὸ καὶ ἐν προτέροις τῷ λόγῳ τὸ ἐφεξῆς ἔστιν, οἷον ἐν ἀριθμοῖς, ἀρὴ δʼ οὐκ ἔστιν), καὶ εἰ μὲν συνεχές, ἀνάγκη ἅπτεσθαι, εἰ δʼ ἅπτεται, οὔπω συνεχές· οὐ γὰρ ἀνάγκη ἓν εἶναι αὐτῶν τὰ ἄκρα, εἰ ἅμα εἶεν· ἀλλʼ εἰ ἕν, ἀνάγκη καὶ ἅμα.
For that which touches must be in succession, but not everything which is in succession touches (wherefore "in succession" is also in things prior in definition, as in numbers, while touching is not); and if a thing is continuous, it must touch, but if it touches, it is not yet continuous; for it is not necessary that their extremities should be one if they are at the same time; but if they are one, they must also be at the same time.
ὥστε ἡ σύμφυσις ὑστάτη κατὰ τὴν γένεσιν· ἀνάγκη γὰρ ἅψασθαι εἰ συμφύσεται τὰ ἄκρα, τὰ δὲ ἁπτόμενα οὐ πάντα συμπέφυκεν· ἐν οἶς δὲ μὴ ἔστιν ἁρή, δῆλον ὅτι οὐκ ἔστιν οὐδὲ σύμφυσις ἐν τούτοις.
Consequently, organic union is the last in respect of coming to be; for the extremities must touch if they are to unite organically, but things which touch are not all united organically; and in those things in which there is no touching, it is clear that there is also no organic union among them.
ὥστʼ εἰ ἔστι στιγμὴ καὶ μονὰς οἵας λέγουσι κεχαωρισμένας, οὐχ οἶόν τε εἶναι μονάδα καὶ στιγμὴν τὸ αὐτό· ταῖς μὲν γὰρ ὑπάρχει τὸ ἅπτεσθαι, ταῖς δὲ μονάσιν τὸ ἐφεξῆς, καὶ τῶν μὲν ἐνδέχεται εἶναί τι μεταξύ (πᾶσα γὰρ γραμμὴ μεταξὺ στιγμῶν), τῶν δʼ οὐκ ἀνάγκη· οὐδὲ γὰρ μεταξὺ δυάδος καὶ μονάδος.
So if there are points and units as they say, existing separately, it is not possible for a unit and a point to be the same; for touching belongs to points, but to units succession, and in the case of points there can be something between them (for every line is between points), but in the case of units it is not necessary; for there is nothing between a dyad and a unit.
τί μὲν οὖν ἐστι τὸ ἅμα καὶ χαωρίς, καὶ τί τὸ ἄπτεσθαι, καὶ τί τὸ μεταξὺ καὶ τὸ ἐφεξῆς, καὶ τί τὸ ἐχόμενον καὶ τὸ συνεχές, καὶ τοῖς ποίοις ἕκαστον τούτων ὑπάρχει, εἴρηται.
What, then, is "at the same time" and "apart", and what is "touching", and what is "between" and "in succession", and what is "contiguous" and "continuous", and to what kind of things each of these belongs, has been stated.