§10.1#2ἐν πᾶσι δὴ τούτοις μέτρον καὶ ἀρχὴ ἕν τι καὶ ἀδιαίρετον, ἐπεὶ καὶ ἐν ταῖς γραμμαῖς χρῶνται ὡς ἀτόμῳ τῇ ποδιαίᾳ.
In all these, then, the measure and starting-point is some one and indivisible thing, since even in the case of lines they use the foot-length as indivisible.
πανταχοῦ γὰρ τὸ μέτρον ἕν τι ζητοῦσι καὶ ἀδιαίρετον· τοῦτο δὲ τὸ ἁπλοῦν ἢ τῷ ποιῷ ἢ τῷ ποσῷ.
For everywhere they seek as measure some one and indivisible thing; and this is that which is simple either in quality or in quantity.
ὅπου μὲν οὖν δοκεῖ μὴ εἶναι ἀφελεῖν ἢ προσθεῖναι, τοῦτο ἀκριβὲς τὸ μέτρον (διὸ τὸ τοῦ ἀριθμοῦ ἀκριβέστατον· τὴν γὰρ μονάδα τιθέασι πάντῃ ἀδιαίρετον)· ἐν δὲ τοῖς ἄλλοις μιμοῦνται τὸ τοιοῦτον·
Where, then, it seems not to be possible to subtract or to add, this measure is exact (wherefore that of number is most exact; for they assume the unit to be indivisible in every way); but in other cases they imitate such a thing.
ἀπὸ γὰρ σταδίου καὶ ταλάντου καὶ ἀεὶ τοῦ μείζονος λάθοι ἂν καὶ προστεθέν τι καὶ ἀφαιρεθὲν μᾶλλον ἢ ἀπὸ ἐλάττονος· ὥστε ἀφʼ οὗ πρώτου κατὰ τὴν αἴσθησιν μὴ ἐνδέχεται, τοῦτο πάντες ποιοῦνται μέτρον καὶ ὑγρῶν καὶ ξηρῶν καὶ βάρους καὶ μεγέθους· καὶ τότʼ οἴονται εἰδέναι τὸ ποσόν, ὅταν εἰδῶσι διὰ τούτου τοῦ μέτρου.
For from a stade and a talent and always from a greater thing, anything added or subtracted would escape notice more easily than from a smaller thing; so that the first point at which, according to perception, it is not possible [to do so], this all men make their measure of liquids and solids, of weight and of magnitude; and they think they know the quantity then, when they know it by means of this measure.
καὶ δὴ καὶ κίνησιν τῇ ἁπλῇ κινήσει καὶ τῇ ταχίστῃ (ὀλίγιστον γὰρ αὕτη ἔχει χρόνον)· διὸ ἐν τῇ ἀστρολογίᾳ τὸ τοιοῦτον ἓν ἀρχὴ καὶ μέτρον (τὴν κίνησιν γὰρ ὁμαλὴν ὑποτίθενται καὶ ταχίστην τὴν τοῦ οὐρανοῦ, πρὸς ἣν κρίνουσι τὰς ἄλλας), καὶ ἐν μουσικῇ δίεσις, ὅτι ἐλάχιστον, καὶ ἐν φωνῇ στοιχεῖον.
And indeed they measure motion too by the simple motion and the fastest (for this takes the least time); wherefore in astronomy such a "one" is the starting-point and measure (for they assume the motion of the heaven to be uniform and the fastest, and by comparison with this they judge the others), and in music the quarter-tone, because it is the least, and in speech the element.
καὶ ταῦτα πάντα ἕν τι οὕτως, οὐχ ὡς κοινόν τι τὸ ἓν ἀλλʼ ὥσπερ εἴρηται. —οὐκ ἀεὶ δὲ τῷ ἀριθμῷ ἓν τὸ μέτρον ἀλλʼ ἐνίοτε πλείω, οἷον αἱ διέσεις δύο, αἱ μὴ κατὰ τὴν ἀκοὴν ἀλλʼ ἐν τοῖς λόγοις, καὶ αἱ φωναὶ πλείους αἷς μετροῦμεν, καὶ ἡ διάμετρος δυσὶ μετρεῖται καὶ ἡ πλευρά, καὶ τὰ μεγέθη πάντα.
And all these are a "one" in this way, not because the "one" is some common universal, but in the way we have said.—But the measure is not always one in number, but sometimes more; for example, the quarter-tones are two, those which are not determined by hearing but in the ratios, and the voices by which we measure are more than one, and the diagonal and the side are measured by two [different measures], and so are all magnitudes.
οὕτω δὴ πάντων μέτρον τὸ ἕν, ὅτι γνωρίζομεν ἐξ ὧν ἐστὶν ἡ οὐσία διαιροῦντες ἢ κατὰ τὸ ποσὸν ἢ κατὰ τὸ εἶδος.
Thus, indeed, the "one" is the measure of all things, because we know that of which the substance consists by dividing it either in respect of quantity or of form.
καὶ διὰ τοῦτο τὸ ἓν ἀδιαίρετον, ὅτι τὸ πρῶτον ἑκάστων ἀδιαίρετον.
And for this reason the "one" is indivisible, because the first of each class of things is indivisible.
οὐχ ὁμοίως δὲ πᾶν ἀδιαίρετον, οἷον ποὺς καὶ μονάς, ἀλλὰ τὸ μὲν πάντῃ, τὸ δʼ εἰς ἀδιαίρετα πρὸς τὴν αἴσθησιν θετέον, ὥσπερ εἴρηται ἤδη· ἴσως γὰρ πᾶν συνεχὲς διαιρετόν.
But not every indivisible is so in the same way, as for example the foot and the unit; but the latter is indivisible in every way, while the former must be assumed to be indivisible in respect of perception, as has been said already; for perhaps every continuous thing is divisible.
ἀεὶ δὲ συγγενὲς τὸ μέτρον· μεγεθῶν μὲν γὰρ μέγεθος, καὶ καθʼ ἕκαστον μήκους μῆκος, πλάτους πλάτος, φωνῆς φωνή, βάρους βάρος, μονάδων μονάς.
And the measure is always homogeneous; for the measure of magnitudes is a magnitude, and in particular that of length is a length, of breadth a breadth, of sound a sound, of weight a weight, of units a unit.
οὕτω γὰρ δεῖ λαμβάνειν, ἀλλʼ οὐχ ὅτι ἀριθμῶν ἀριθμός· καίτοι ἔδει, εἰ ὁμοίως·
For we must understand it in this way, and not that the measure of numbers is a number; and yet it should be so, if the analogy held.
ἀλλʼ οὐχ ὁμοίως ἀξιοῖ ἀλλʼ ὥσπερ εἰ μονάδων μονάδας ἀξιώσειε μέτρον ἀλλὰ μὴ μονάδα· ὁ δʼ ἀριθμὸς πλῆθος μονάδων.
But the analogy does not hold in the same way, but it is as if one should claim that the measure of units is units and not a unit; but number is a plurality of units.
καὶ τὴν ἐπιστήμην δὲ μέτρον τῶν πραγμάτων λέγομεν καὶ τὴν αἴσθησιν διὰ τὸ αὐτό, ὅτι γνωρίζομέν τι αὐταῖς, ἐπεὶ μετροῦνται μᾶλλον ἢ μετροῦσιν.
And we speak of science and perception as a measure of things for the same reason, because we know something by them, although they are measured rather than measure.
ἀλλὰ συμβαίνει ἡμῖν ὥσπερ ἂν εἰ ἄλλου ἡμᾶς μετροῦντος ἐγνωρίσαμεν πηλίκοι ἐσμὲν τῷ τὸν πῆχυν ἐπὶ τοσοῦτον ἡμῶν ἐπιβάλλειν.
But it happens to us as if, when another was measuring us, we knew how big we are by his applying the cubit-measure to us so far.
Πρωταγόρας δʼ ἄνθρωπόν φησι πάντων εἶναι μέτρον, ὥσπερ ἂν εἰ τὸν ἐπιστήμονα εἰπὼν ἢ τὸν αἰσθανόμενον· τούτους δʼ ὅτι ἔχουσιν ὁ μὲν αἴσθησιν ὁ δὲ ἐπιστήμην, ἅ φαμεν εἶναι μέτρα τῶν ὑποκειμένων.
And Protagoras says that man is the measure of all things, as if he had said the knower or the perceiver; and these because they possess, the one perception and the other science, which we say are the measures of the subjects.
οὐθὲν δὴ λέγοντες περιττὸν φαίνονταί τι λέγειν.
Thus, while saying nothing extraordinary, they appear to be saying something.
ὅτι μὲν οὖν τὸ ἑνὶ εἶναι μάλιστά ἐστι κατὰ τὸ ὄνομα ἀφορίζοντι μέτρον τι, καὶ κυριώτατα τοῦ ποσοῦ, εἶτα τοῦ ποιοῦ, φανερόν· ἔσται δὲ τοιοῦτον τὸ μὲν ἂν ᾖ ἀδιαίρετον κατὰ τὸ ποσόν, τὸ δὲ ἂν κατὰ τὸ ποιόν· διόπερ ἀδιαίρετον τὸ ἓν ἢ ἁπλῶς ἢ ᾗ ἕν.
It is clear, then, that to be one, if we define it according to the name, is most of all to be a measure, and most properly of quantity, and next of quality; and it will be of this character if it is indivisible in quantity in the one case, and in quality in the other; wherefore the "one" is indivisible, either absolutely or as being one.