§3.12Ἔστι μὲν οὖν οὕτως ὑπολαβεῖν πλείους εἶναι χρόας παρὰ τὸ λευκὸν καὶ τὸ μέλαν, πολλὰς δὲ τῷ λόγῳ· τρία γὰρ πρὸς δύο, καὶ τρία πρὸς τέτταρα, καὶ κατ’ ἄλλους ἀριθμοὺς ἔστι παρ’ ἄλληλα κεῖσθαι, τὰ δ’ ὅλως κατὰ μὲν λόγον μηδένα, καθ’ ὑπεροχὴν δέ τινα καὶ ἔλλειψιν ἀσύμμετρον, καὶ τὸν αὐτὸν δὴ τρόπον ἔχειν ταῦτα ταῖς συμφωνίαις·
It is possible, then, to assume in this way that there are more colors besides white and black, and many according to proportion; for they can be placed alongside one other in the ratio of three to two, and three to four, and according to other numbers, while others are altogether in no proportion, but in some incommensurable excess and defect, and these have the same relation as consonances.
τὰ μὲν γὰρ ἐν ἀριθμοῖς εὐλογίστοις χρώματα, καθάπερ ἐκεῖ τὰς συμφωνίας, τὰ ἥδιστα τῶν χρωμάτων εἶναι δοκοῦντα, οἷον τὸ ἁλουργὸν καὶ φοινικοῦν καὶ ὀλίγ’ ἄττα τοιαῦτα, δι’ ἥνπερ αἰτίαν καὶ αἱ συμφωνίαι ὀλίγαι, τὰ δὲ μὴ ἐν ἀριθμοῖς τἆλλα χρώματα, ἢ καὶ πάσας τὰς χρόας ἐν ἀριθμοῖς εἶναι, τὰς μὲν τεταγμένας τὰς δὲ ἀτάκτους, καὶ αὐτὰς ταύτας, ὅταν μὴ καθαραὶ ὦσι, διὰ τὸ μὴ ἐν ἀριθμοῖς εἶναι τοιαύτας γίνεσθαι.
For those colors which are in simple numerical ratios, just like consonances in that other field, seem to be the most pleasant of colors, such as purple, crimson, and a few other such, for which very reason consonances also are few; while the other colors are those not in numerical ratios; or else all colors are in numerical ratios, some ordered and others disordered, and these latter themselves, when they are not pure, become such because they are not in numerical ratios.
§3.13Εἷς μὲν οὖν τρόπος τῆς γενέσεως τῶν χρωμάτων οὗτος, εἷς δὲ τὸ φαίνεσθαι δι’ ἀλλήλων, οἷον ἐνίοτε οἱ γραφῆς ποιοῦσιν, ἑτέραν χρόαν ἐφ’ ἑτέραν ἐναργεστέραν ἐπαλείφουσιν, ὥσπερ ὅταν ἐν ὕδατί τι ἢ ἐν ἀέρι βούλωνται ποιῆσαι φαινόμενον, καὶ οἷον ὁ ἥλιος καθ’ αὑτὸν μὲν λευκὸς φαίνεται, διὰ δ’ ἀχλύος καὶ καπνοῦ φοινικοῦς.
This, then, is one way of the generation of colors, and another is their appearing through one another, as painters sometimes do when they overlay one color upon another more vivid one, for instance when they want to represent something as seen in water or in air, and as the sun appears white in itself, but crimson through mist and smoke.
§3.14Πολλαὶ δὲ καὶ οὕτως ἔσονται χρόαι τὸν αὐτὸν τρόπον τῷ πρότερον εἰρημένῳ· λόγος γὰρ ἂν εἴη τις τῶν ἐπιπολῆς πρὸς τὰ ἐν βάθει, τὰ δὲ καὶ ὅλως οὐκ ἐν λόγῳ.
And in this way too there will be many colors in the same manner as previously stated; for there would be some ratio of those on the surface to those in the depth, and others altogether not in any ratio.
§3.15Τὸ μὲν οὖν, ὥσπερ καὶ οἱ ἀρχαῖοι, λέγειν ἀπορροίας εἶναι τὰς χροίας καὶ ὁρᾶσθαι διὰ τοιαύτην αἰτίαν ἄτοπον· πάντως γὰρ δι’ ἁφῆς ἀναγκαῖον αὐτοῖς ποιεῖν τὴν αἴσθησιν, ὥστ’ εὐθὺς κρεῖττον φάναι τῷ κινεῖσθαι τὸ μεταξὺ τῆς αἰσθήσεως ὑπὸ τοῦ αἰσθητοῦ γίνεσθαι τὴν αἴσθησιν, ἁφῇ καὶ μὴ ταῖς ἀπορροίαις.
Therefore, to say, as the ancients did, that colors are effluxes and that they are seen for such a cause is absurd; for they must in any case make sensation occur through touch, so that it is immediately better to say that sensation occurs by the medium between the sensation and the sensible object being moved by the sensible object, through touch and not by effluxes.
§3.16Ἐπὶ μὲν οὖν τῶν παρ’ ἄλληλα κειμένων ἀνάγκη ὥσπερ καὶ μέγεθος λαμβάνειν ἀόρατον, οὕτω καὶ χρόνον ἀναίσθητον, ἵνα λάθωσιν αἱ κινήσεις ἀφικνούμεναι καὶ ἓν δοκῇ εἶναι διὰ τὸ ἅμα φαίνεσθαι.
Now, in the case of things placed alongside one another, just as it is necessary to assume an invisible magnitude, so also an imperceptible time, so that the arriving motions may escape notice and seem to be one because of appearing at the same time.
Ἐνταῦθα δὲ οὐδεμία ἀνάγκη, ἀλλὰ τὸ ἐπιπολῆς χρῶμα ἀκίνητον ὂν καὶ κινούμενον ὑπὸ τοῦ ὑποκειμένου οὐχ ὁμοίαν ποιήσει τὴν κίνησιν.
But here there is no such necessity, but the surface color, being stationary and being moved by the underlying one, will not produce a similar motion.
Διὸ καὶ ἕτερον φαίνεται καὶ οὔτε λευκὸν οὔτε μέλαν.
Therefore it appears as something else and neither white nor black.
§3.17Ὥστ’ εἰ μὴ ἐνδέχεται μηδὲν εἶναι μέγεθος ἀόρατον, ἀλλὰ πᾶν ἔκ τινος ἀποστήματος ὁρατόν, καὶ αὕτη τις ἂν εἴη χρωμάτων μίξις.
So if it is impossible for there to be any invisible magnitude, but everything is visible from some distance, this too would be a certain mixture of colors.
Κἀκείνως δ’ οὐδὲν κωλύει φαίνεσθαί τινα χρόαν κοινὴν τοῖς πόρρωθεν· ὅτι γὰρ οὐκ ἔστιν οὐδὲν μέγεθος ἀόρατον, ἐν τοῖς ὕστερον ἐπισκεπτέον.
And in that other way too, nothing prevents some common color from appearing to those at a distance; for that there is no invisible magnitude must be investigated later.
§3.18Εἰ δ’ ἐστὶ μίξις τῶν σωμάτων μὴ μόνον τὸν τρόπον τοῦτον ὅνπερ οἴονταί τινες, παρ’ ἄλληλα τῶν ἐλαχίστων τιθεμένων, ἀδήλων δ’ ἡμῖν διὰ τὴν αἴσθησιν, ἀλλ’ ὅλως πάντῃ πάντως, ὥσπερ ἐν τοῖς περὶ μίξεως εἴρηται καθόλου περὶ πάντων.
But if there is a mixture of bodies, not only in the way some think—by the smallest parts being placed alongside one another, though unperceived by us through sensation—but completely in every way, as has been said in On Mixture in general concerning all things.
§3.19Ἐκείνως μὲν γὰρ μίγνυται ταῦτα μόνον ὅσα ἐνδέχεται διελεῖν εἰς τὰ ἐλάχιστα, καθάπερ ἀνθρώπους ἵππους ἢ τὰ σπέρματα· τῶν μὲν γὰρ ἀνθρώπων ἄνθρωπος ἐλάχιστος, τῶν δ’ ἵππων ἵππος·
For in that way only those things are mixed which can be divided into the smallest parts, just as men, horses, or seeds; for of men, a man is the smallest, and of horses, a horse.
ὥστε τῇ τούτων παρ’ ἄλληλα θέσει τὸ πλῆθος μέμικται τῶν συναμφοτέρων· ἄνθρωπον δὲ ἕνα ἑνὶ ἵππῳ οὐ λέγομεν μεμῖχθαι.
So that by placing these alongside one another, the multitude of both together is mixed; but we do not say that one man is mixed with one horse.
§3.20Ὅσα δὲ μὴ διαιρεῖται εἰς τὸ ἐλάχιστον, τούτων οὐκ ἐνδέχεται μίξιν γενέσθαι τὸν τρόπον τοῦτον ἀλλὰ τῷ πάντῃ μεμῖχθαι, ἅπερ καὶ μάλιστα μίγνυσθαι πέφυκεν.
But for those which are not divided into a smallest part, a mixture cannot occur in this way but by being mixed in every part, which are also by nature most of all inclined to be mixed.
Πῶς δὲ τοῦτο γίγνεσθαι δυνατόν, ἐν τοῖς περὶ μίξεως εἴρηται πρότερον.
But how this can happen has been said before in On Mixture.
§3.21Ἀλλ’ ὅτι ἀνάγκη μιγνυμένων καὶ τὰς χρόας μίγνυσθαι, δῆλον, καὶ ταύτην τὴν αἰτίαν εἶναι κυρίαν τοῦ πολλὰς εἶναι χροίας, ἀλλὰ μὴ τὴν ἐπιπόλασιν μηδὲ τὴν παρ’ ἄλληλα θέσιν· οὐ γὰρ πόρρωθεν μὲν ἐγγύθεν δ’ οὒ φαίνεται μία χρόα τῶν μεμιγμένων, ἀλλὰ πάντοθεν.
But that, when things are mixed, the colors too must be mixed is clear, and that this cause is the principal one for there being many colors, and not surface overlaying nor placement alongside one other; for the color of mixed things does not appear single from a distance but not close up, but from every point of view.
§3.22Πολλαὶ δ’ ἔσονται χρόαι διὰ τὸ κατὰ πολλοὺς λόγους ἐνδέχεσθαι μίγνυσθαι ἀλλήλοις τὰ μιγνύμενα, καὶ τὰ μὲν ἐν ἀριθμοῖς τὰ δὲ καθ’ ὑπεροχὴν μόνον.
And there will be many colors because the things mixed can be mixed with one another in many ratios, some in numerical proportions, and others in excess only.
§3.23Καὶ τἆλλα δὴ τὸν αὐτὸν τρόπον ὅν περ ἐπὶ τῶν παρ’ ἄλληλα τιθεμένων χρωμάτων ἢ ἐπιπολῆς, ἐνδέχεται λέγειν καὶ περὶ τῶν μιγνυμένων· διὰ τίνα δ’ αἰτίαν εἴδη τῶν χρωμάτων ἐστὶν ὡρισμένα καὶ οὐκ ἄπειρα, καὶ χυμῶν καὶ ψόφων, ὕστερον ἐροῦμεν.
And indeed, in the same way as in the case of colors placed alongside one another or on the surface, we can speak also concerning those that are mixed; but for what cause the kinds of colors, tastes, and sounds are determinate and not infinite, we shall speak later.