§5.6#1ἓν λέγεται τὸ μὲν κατὰ συμβεβηκὸς τὸ δὲ καθʼ αὑτό, κατὰ συμβεβηκὸς μὲν οἷον Κορίσκος καὶ τὸ μουσικόν, καὶ Κορίσκος μουσικός (ταὐτὸ γὰρ εἰπεῖν Κορίσκος καὶ τὸ μουσικόν, καὶ Κορίσκος μουσικός), καὶ τὸ μουσικὸν καὶ τὸ δίκαιον, καὶ μουσικὸς Κορίσκος καὶ δίκαιος Κορίσκος·
'One' is spoken of, in one way, as accidental, and in another, as in itself. Accidental is, for instance, Coriscus and what is musical, and musical Coriscus (for it is the same to say Coriscus and what is musical, and musical Coriscus); and what is musical and what is just, and musical Coriscus and just Coriscus.
πάντα γὰρ ταῦτα ἓν λέγεται κατὰ συμβεβηκός, τὸ μὲν δίκαιον καὶ τὸ μουσικὸν ὅτι μιᾷ οὐσίᾳ συμβέβηκεν, τὸ δὲ μουσικὸν καὶ Κορίσκος ὅτι θάτερον θατέρῳ συμβέβηκεν·
For all these are called one accidentally: the just and the musical because they are accidents of one substance, and the musical and Coriscus because the one is an accident of the other.
ὁμοίως δὲ τρόπον τινὰ καὶ ὁ μουσικὸς Κορίσκος τῷ Κορίσκῳ ἓν ὅτι θάτερον τῶν μορίων θατέρῳ συμβέβηκε τῶν ἐν τῷ λόγῳ, οἷον τὸ μουσικὸν τῷ Κορίσκῳ· καὶ ὁ μουσικὸς Κορίσκος δικαίῳ Κορίσκῳ ὅτι ἑκατέρου μέρος τῷ αὐτῷ ἑνὶ συμβέβηκεν ἕν.
Similarly, in a way, musical Coriscus is one with Coriscus because one of the parts in the formula is an accident of the other, for instance, the musical of Coriscus; and musical Coriscus is one with just Coriscus because a part of each is an accident of the same one thing.
ὡσαύτως δὲ κἂν ἐπὶ γένους κἂν ἐπὶ τῶν καθόλου τινὸς ὀνομάτων λέγηται τὸ συμβεβηκός, οἷον ὅτι ἄνθρωπος τὸ αὐτὸ καὶ μουσικὸς ἄνθρωπος· ἢ γὰρ ὅτι τῷ ἀνθρώπῳ μιᾷ οὔσῃ οὐσίᾳ συμβέβηκε τὸ μουσικόν, ἢ ὅτι ἄμφω τῶν καθʼ ἕκαστόν τινι συμβέβηκεν, οἷον Κορίσκῳ.
And it is the same even if the accident is spoken of in the case of a genus or of some universal terms, as that man is the same as musical man; for this is either because the musical is an accident of man, which is one substance, or because both are accidents of some individual, for instance, Coriscus.
πλὴν οὐ τὸν αὐτὸν τρόπον ἄμφω ὑπάρχει, ἀλλὰ τὸ μὲν ἴσως ὡς γένος καὶ ἐν τῇ οὐσίᾳ τὸ δὲ ὡς ἕξις ἢ πάθος τῆς οὐσίας.
Except that both do not belong in the same way, but the one perhaps as a genus and in the substance, and the other as a state or affection of the substance.
—ὅσα μὲν οὖν κατὰ συμβεβηκὸς λέγεται ἕν, τοῦτον τὸν τρόπον λέγεται·
Those things, then, which are called one accidentally, are so called in this way.
τῶν δὲ καθʼ ἑαυτὰ ἓν λεγομένων τὰ μὲν λέγεται τῷ συνεχῆ εἶναι, οἷον φάκελος δεσμῷ καὶ ξύλα κόλλῃ·
But of those which are called one in themselves, some are so called by being continuous, for instance, a bundle by its band, and pieces of wood by glue.
καὶ γραμμή, κἂν κεκαμμένη ᾖ, συνεχὴς δέ, μία λέγεται, ὥσπερ καὶ τῶν μερῶν ἕκαστον, οἷον σκέλος καὶ βραχίων.
And a line, even if it is bent, if it is continuous, is called one, just as each of the limbs is, for instance, a leg and an arm.
αὐτῶν δὲ τούτων μᾶλλον ἓν τὰ φύσει συνεχῆ ἢ τέχνῃ.
Of these themselves, those which are continuous by nature are more one than those by art.
συνεχὲς δὲ λέγεται οὗ κίνησις μία καθʼ αὑτὸ καὶ μὴ οἷόν τε ἄλλως· μία δʼ οὗ ἀδιαίρετος, ἀδιαίρετος δὲ κατὰ χρόνον.
And that is called continuous whose motion is one in itself and cannot be otherwise; and motion is one when it is indivisible, and indivisible in time.
καθʼ αὑτὰ δὲ συνεχῆ ὅσα μὴ ἁφῇ ἕν· εἰ γὰρ θείης ἁπτόμενα ἀλλήλων ξύλα, οὐ φήσεις ταῦτα εἶναι ἓν οὔτε ξύλον οὔτε σῶμα οὔτʼ ἄλλο συνεχὲς οὐδέν.
And those things are continuous in themselves which are one not by contact; for if you put pieces of wood touching one another, you will not say that these are one, neither one piece of wood, nor one body, nor any other continuous thing.
τά τε δὴ ὅλως συνεχῆ ἓν λέγεται κἂν ἔχῃ κάμψιν, καὶ ἔτι μᾶλλον τὰ μὴ ἔχοντα κάμψιν, οἷον κνήμη ἢ μηρὸς σκέλους, ὅτι ἐνδέχεται μὴ μίαν εἶναι τὴν κίνησιν τοῦ σκέλους.
And things which are continuous in general are called one even if they have a bend, and still more those which have no bend, for instance, the shin or the thigh of a leg, because it is possible for the motion of the leg not to be one.
καὶ ἡ εὐθεῖα τῆς κεκαμμένης μᾶλλον ἕν· τὴν δὲ κεκαμμένην καὶ ἔχουσαν γωνίαν καὶ μίαν καὶ οὐ μίαν λέγομεν, ὅτι ἐνδέχεται καὶ μὴ ἅμα τὴν κίνησιν αὐτῆς εἶναι καὶ ἅμα· τῆς δʼ εὐθείας ἀεὶ ἅμα, καὶ οὐδὲν μόριον ἔχον μέγεθος τὸ μὲν ἠρεμεῖ τὸ δὲ κινεῖται, ὥσπερ τῆς κεκαμμένης.
And the straight line is more one than the bent; and we call the bent line which has an angle both one and not one, because it is possible for its motion to be both not simultaneous and simultaneous; but that of the straight line is always simultaneous, and no part of it which has magnitude is at rest while another is in motion, as in the bent line.
ἔτι ἄλλον τρόπον ἓν λέγεται τῷ τὸ ὑποκείμενον τῷ εἴδει εἶναι ἀδιάφορον· ἀδιάφορον δʼ ὧν ἀδιαίρετον τὸ εἶδος κατὰ τὴν αἴσθησιν·
Further, in another way, a thing is called one because the substrate is indistinguishable in form; and it is indistinguishable when its form is indivisible according to sensation.
τὸ δʼ ὑποκείμενον ἢ τὸ πρῶτον ἢ τὸ τελευταῖον πρὸς τὸ τέλος·
And the substrate is either the first or the last in relation to the end.
καὶ γὰρ οἶνος εἷς λέγεται καὶ ὕδωρ ἕν, ᾗ ἀδιαίρετον κατὰ τὸ εἶδος, καὶ οἱ χυμοὶ πάντες λέγονται ἕν (οἷον ἔλαιον οἶνος) καὶ τὰ τηκτά, ὅτι πάντων τὸ ἔσχατον ὑποκείμενον τὸ αὐτό· ὕδωρ γὰρ ἢ ἀὴρ πάντα ταῦτα.
For wine is called one and water one, in so far as they are indivisible in form; and all juices (for instance, oil and wine) and things that can be melted are called one, because the ultimate substrate of all of them is the same, for all these are water or air.
λέγεται δʼ ἓν καὶ ὧν τὸ γένος ἓν διαφέρον ταῖς ἀντικειμέναις διαφοραῖς—καὶ ταῦτα λέγεται πάντα ἓν ὅτι τὸ γένος ἓν τὸ ὑποκείμενον ταῖς διαφοραῖς (οἷον ἵππος ἄνθρωπος κύων ἕν τι ὅτι πάντα ζῷα), καὶ τρόπον δὴ παραπλήσιον ὥσπερ ἡ ὕλη μία.
And those things are also called one whose genus is one, though differing by opposite differences; and all these are called one because the genus which is the substrate of the differences is one (for instance, horse, man, and dog are a certain one because they are all animals), in a manner very similar to that in which the matter is one.
ταῦτα δὲ ὁτὲ μὲν οὕτως ἓν λέγεται, ὁτὲ δὲ τὸ ἄνω γένος ταὐτὸν λέγεται —ἂν ᾖ τελευταῖα τοῦ γένους εἴδη—τὸ ἀνωτέρω τούτων, οἷον τὸ ἰσοσκελὲς καὶ τὸ ἰσόπλευρον ταὐτὸ καὶ ἓν σχῆμα ὅτι ἄμφω τρίγωνα· τρίγωνα δʼ οὐ ταὐτά.
These are sometimes called one in this way, and sometimes the higher genus is said to be the same, if they are the ultimate species of the genus, that which is higher than these, for instance, the isosceles and the equilateral are the same and one figure because both are triangles, but they are not the same triangles.