§6#1Τοῦ δὲ ποσοῦ τὸ μέν ἐστι διωρισμένον, τὸ δὲ συνεχές, καὶ τὸ μὲν ἐκ θέσιν ἐχόντων πρὸς ἄλληλα τῶν ἐν αὑτοῖς μορίων συνέστηκε, τὸ δὲ οὐκ ἐξ ἐχόντων θέσιν.
Of quantity, some is discrete, and some is continuous; and some consists of parts which have position in relation to one another, while some does not consist of parts having position.
Ἔστι δὲ διωρισμένον μὲν οἷον ἀριθμὸς καὶ λόγος, συνεχὲς δὲ οἷον γραμμή, ἐπιφάνεια, σῶμα, ἔτι δὲ παρὰ ταῦτα χρόνος καὶ τόπος.
Discrete is, for example, number and speech; continuous is, for example, line, surface, body, and, besides these, time and place.
Τῶν μὲν γὰρ τοῦ ἀριθμοῦ μορίων οὐδείς ἐστι κοινὸς ὅρος, πρὸς ὃν συνάπτει τὰ μόρια αὐτοῦ, οἷον τὰ πέντε εἰ ἔστι τῶν δέκα μόριον, πρὸς οὐδένα κοινὸν ὅρον συνάπτει τὰ πέντε καὶ τὰ πέντε, ἀλλὰ διώρισται·
For of the parts of number, there is no common boundary at which its parts touch; for example, if five is a part of ten, the five and the five touch at no common boundary, but are discrete.
καὶ τὰ τρία γε καὶ τὰ ἑπτὰ πρὸς οὐδένα κοινὸν ὅρον συνάπτει· οὐδ᾿ ὅλως ἂν ἔχοις ἐπ᾿ ἀριθμοῦ κοινὸν ὅρον λαβεῖν τῶν μορίων, ἀλλ᾿ ἀεὶ διώρισται· ὥστε ὁ μὲν ἀριθμὸς τῶν διωρισμένων ἐστίν.
And three and seven touch at no common boundary; nor indeed could you find any common boundary of parts in number, but they are always discrete; so that number is of the discrete.
Ὡσαύτως δὲ καὶ ὁ λόγος τῶν διωρισμένων ἐστίν.
Likewise, speech also is of the discrete.
Ὅτι μὲν γὰρ ποσόν ἐστιν ὁ λόγος, φανερόν· καταμετρεῖται γὰρ συλλαβῇ βραχείᾳ καὶ μακρᾷ.
For that speech is a quantity is clear, since it is measured by long and short syllables.
Λέγω δὲ αὐτὸν τὸν μετὰ φωνῆς λόγον γιγνόμενον.
And I mean speech that is produced with a voice.
Πρὸς οὐδένα γὰρ κοινὸν ὅρον αὐτοῦ τὰ μόρια συνάπτει· οὐ γὰρ ἔστι κοινὸς ὅρος πρὸς ὃν αἱ συλλαβαὶ συνάπτουσιν, ἀλλ᾿ ἑκάστη διώρισται αὐτὴ καθ᾿ αὑτήν.
For its parts touch at no common boundary; for there is no common boundary at which the syllables touch, but each is discrete itself by itself.
Ἡ δὲ γραμμὴ συνεχής ἐστιν· ἔστι γὰρ λαβεῖν κοινὸν ὅρον πρὸς ὃν τὰ μόρια αὐτῆς συνάπτει, στιγμήν, καὶ τῆς ἐπιφανείας γραμμήν· τὰ γὰρ τοῦ ἐπιπέδου μόρια πρός τινα κοινὸν ὅρον συνάπτει.
The line is continuous; for it is possible to find a common boundary at which its parts touch, namely, a point, and of a surface, a line; for the parts of a plane touch at some common boundary.
Ὡσαύτως δὲ καὶ ἐπὶ τοῦ σώματος ἔχοις ἂν λαβεῖν κοινὸν ὅρον, γραμμὴν ἢ ἐπιφάνειαν, πρὸς ἃ τὰ τοῦ σώματος μόρια συνάπτει.
Likewise, in the case of a body, you could find a common boundary, a line or a surface, at which the parts of the body touch.
Ἔστι δὲ καὶ ὁ χρόνος καὶ ὁ τόπος τῶν τοιούτων· ὁ γὰρ νῦν χρόνος συνάπτει πρὸς τὸν παρεληλυθότα καὶ τὸν μέλλοντα.
And time and place also are of such things; for the present time touches both the past and the future.
Πάλιν ὁ τόπος τῶν συνεχῶν ἐστί· τόπον γάρ τινα τὰ τοῦ σώματος μόρια κατέχει, ἃ πρός τινα κοινὸν ὅρον συνάπτει· οὐκοῦν καὶ τὰ τοῦ τόπου μόρια, ἃ κατέχει ἕκαστον τῶν τοῦ σώματος μορίων, πρὸς τὸν αὐτὸν ὅρον συνάπτει πρὸς ὃν καὶ τὰ τοῦ σώματος μόρια.
Again, place is of the continuous; for the parts of the body occupy some place, which parts touch at some common boundary; therefore, the parts of the place too, which each of the parts of the body occupies, touch at the same boundary at which the parts of the body touch.
Ὥστε συνεχὴς ἂν εἴη καὶ ὁ τόπος· πρὸς γὰρ ἕνα κοινὸν ὅρον αὐτοῦ τὰ μόρια συνάπτει.
Consequently, place too would be continuous; for its parts touch at one common boundary.
Ἔτι δὲ τὰ μὲν ἐκ θέσιν ἐχόντων πρὸς ἄλληλα τῶν ἐν αὑτοῖς μορίων συνέστηκε, τὰ δὲ οὐκ ἐξ ἐχόντων θέσιν, οἷον τὰ μὲν τῆς γραμμῆς μόρια θέσιν ἔχει πρὸς ἄλληλα·
Moreover, some consists of parts having position in relation to one another, while some does not consist of parts having position.
ἕκαστον γὰρ αὐτῶν κεῖταί που, καὶ ἔχοις ἂν διαλαβεῖν καὶ ἀποδοῦναι ὅπου ἕκαστον κεῖται ἐν τῷ ἐπιπέδῳ καὶ πρὸς ποῖον μόριον τῶν λοιπῶν συνάπτει.
For example, the parts of a line have position in relation to one another; for each of them lies somewhere, and you could distinguish and point out where each lies on the plane, and at what part of the remaining parts it touches.
Ὡσαύτως δὲ καὶ τὰ τοῦ ἐπιπέδου μόρια θέσιν ἔχει τινά· ὁμοίως γὰρ ἂν ἀποδοθείη ἕκαστον οὗ κεῖται, καὶ ποῖα συνάπτει πρὸς ἄλληλα.
Likewise, the parts of a surface have some position; for in the same way one could point out where each lies, and which ones touch one another.
καὶ τὰ τοῦ στερεοῦ δὲ ὡσαύτως, καὶ τὰ τοῦ τοποῦ.
And the parts of a solid likewise, and those of place.
Ἐπὶ δέ γε τοῦ ἀριθμοῦ οὐκ ἂν ἔχοι τις ἐπιδεῖξαι ὡς τὰ μόρια αὐτοῦ θέσιν τινὰ ἔχει πρὸς ἄλληλα ἢ κεῖταί που, ἢ ποῖά γε πρὸς ἄλληλα συνάπτει τῶν μορίων.
But in the case of number, one could not show that its parts have any position in relation to one another, or lie anywhere, or which of the parts touch one another.
Οὐδὲ τὰ τοῦ χρόνου· ὑπομένει γὰρ οὐδὲν τῶν τοῦ χρόνου μορίων· ὃ δὲ μή ἐστιν ὑπομένον, πῶς ἂν τοῦτο θέσιν τινὰ ἔχοι;
Nor indeed the parts of time; for none of the parts of time endures; and that which does not endure, how could this have any position?
ἀλλὰ μᾶλλον τάξιν τινὰ εἴποις ἂν ἔχειν τῷ τὸ μὲν πρότερον εἶναι τοῦ χρόνου τὸ δ᾿ ὕστερον.
But rather you would say that it has some order, because one part of time is prior and another is posterior.
Καὶ ἐπὶ τοῦ ἀριθμοῦ δὲ ὡσαύτως τῷ τὸ ἓν πρότερον ἀριθμεῖσθαι τῶν δύο καὶ τὰ δύο τῶν τριῶν· καὶ οὕτω τάξιν τινὰ ἂν ἔχοι, θέσιν δὲ οὐ πάνυ λάβοις ἄν.
And in the case of number likewise, because one is numbered prior to two, and two prior to three; and in this way it would have some order, but you could not possibly grasp position.
Καὶ ὁ λόγος δὲ ὡσαύτως· οὐδὲν γὰρ ὑπομένει τῶν μορίων αὐτοῦ, ἀλλ᾿ εἴρηταί τε καὶ οὐκ ἔστιν ἔτι τοῦτο λαβεῖν, ὥστε οὐκ ἂν εἴη θέσις τῶν μορίων αὐτοῦ, εἴγε μηδὲν ὑπομένει.
And speech likewise; for none of its parts endures, but it has been spoken and it is no longer possible to grasp this, so that there would be no position of its parts, since indeed none endures.
Τὰ μὲν οὖν ἐκ θέσιν ἐχόντων τῶν μορίων συνέστηκε, τὰ δὲ οὐκ ἐξ ἐχόντων θέσιν.
Therefore, some consists of parts having position, and some does not consist of parts having position.
Κυρίως δὲ ποσὰ ταῦτα μόνα λέγεται τὰ εἰρημένα, τὰ δὲ ἄλλα πάντα κατὰ συμβεβηκός· εἰς ταῦτα γὰρ ἀποβλέποντες καὶ τἆλλα ποσὰ λέγομεν, οἷον πολὺ τὸ λευκὸν λέγεται τῷ τὴν ἐπιφάνειαν πολλὴν εἶναι, καὶ ἡ πρᾶξις μακρὰ τῷ γε τὸν χρόνον πολὺν εἶναι, καὶ ἡ κίνησις πολλή.
But strictly only these things mentioned are called quantities, and all the others are so called accidentally; for it is by looking to these that we call other things quantities too, as white is called much because the surface is much, and an action is called long because the time is much, and motion is much.
Οὐ γὰρ καθ᾿ αὑτὸ ἕκαστον τούτων ποσὸν λέγεται.
For each of these is not called a quantity in itself.
Οἷον ἐὰν ἀποδιδῷ τις πόση τις ἡ πρᾶξίς ἐστι, τῷ χρόνῳ ὁριεῖ, ἐνιαυσιαίαν ἢ οὕτω πως ἀποδιδούς.
For example, if one is to state how much an action is, he will define it by time, stating it as a year long or in some such way.
Καὶ τὸ λευκὸν ποσόν τι ἀποδιδοὺς τῇ ἐπιφανείᾳ ὁριεῖ· ὅση γὰρ ἂν ἡ ἐπιφάνεια ᾖ, τοσοῦτον καὶ τὸ λευκὸν φήσειεν ἂν εἶναι.
And in stating how much a white thing is, he will define it by surface; for however large the surface may be, so large would he say the white is also.
Ὥστε μόνα κυρίως καὶ καθ᾿ αὑτὰ ποσὰ λέγεται τὰ εἰρημένα, τῶν δὲ ἄλλων οὐδὲν καθ᾿ αὑτό, ἀλλ᾿ εἰ ἄρα, κατὰ συμβεβηκός.
So that only the things mentioned are called quantities strictly and in themselves, and none of the others in itself, but, if at all, accidentally.