§1.3.13 Ἔτι στερήσει μὲν ἀναγκαῖον διαιρεῖν, καὶ διαιροῦσιν οἱ διχοτομοῦντες.
3 Furthermore, it is necessary to divide by privation, and those who divide into two do so.
οὐκ ἔστι δὲ διαφορὰ στερήσεως ᾗ στέρησις·
But there is no difference of a privation qua privation.
ἀδύνατον γὰρ εἴδη εἶναι τοὺ μὴ ὄντος, οἷον τῆς ἀποδίας ἢ τοῦ ἀπτέρου ὥσπερ πτερώσεως καὶ ποδῶν.
For it is impossible for there to be species of non-being, such as of the footless or of the wingless, in the way that there are of wingedness and of feet.
δεῖ δὲ τῆς καθόλου διαφορᾶς εἴδη εἶναι· εἰ γὰρ μὴ ἔσται, διὰ τί ἂν εἴη τῶν καθόλου καὶ οὐ τῶν καθʼ ἕκαστον;
But there must be species of a universal difference; for if there will not be, why would it belong to the universals and not to the particulars?
τῶν δὲ διαφορῶν αἱ μὲν καθόλου εἰσὶ καὶ ἔχουσιν εἴθη, οἷον πτερότης· τὸ μὲν γὰρ ἄσχιστον τὸ δʼ ἐσχισμένον ἐστὶ πτερόν.
Of differences, some are universal and have species, such as wingedness; for one wing is undivided, while another is divided.
καὶ ποδότης ὡσαύτως ἡ μὲν πολυσχιδὴς, ἡ δὲ δισχιδής, οἷον τὰ διχαλά, ἡ δʼ ἀσχιδὴς καὶ ἀδιαίρετες, οἷον τὰ μώνυχα.
And likewise footedness: one is many-cleft, another two-cleft, such as cloven-hoofed animals, and another undivided and indivisible, such as solid-hoofed animals.
§1.3.22 χαλεπὸν μὲν οὖν διαλαβεῖν καὶ εἰς τοιαύτας διαφορὰς ὧν ἔστιν εἴδη, ὥσθ᾿ ὁτιοῦν ζῷον ἐν ταύταις ὑπάρχειν καὶ μὴ ἐν πλείοσι ταὐτόν, οἷον πτερωτὸν καὶ ἄπτερον (ἔστι γὰρ ἄμφω ταὐτόν, οἷον μύρμηξ καὶ λαμπυρὶς καὶ ἕτερά τινα), πάντων δὲ χαλεπώτατον ἢ ἀδύνατον εἰς τὰ ἄναιμα.
2 Therefore, it is difficult to distinguish into such differences of which there are species, so that any animal whatever falls under these, and the same animal does not fall under more than one, such as "winged" and "wingless" (for the same animal is both, such as the ant, the firefly, and certain others); but of all things, this is most difficult or impossible in the case of bloodless animals.
ἀναγκαῖον γὰρ τῶν καθʼ ἕκαστον ὑπάρχειν τινὶ τῶν διαφορῶν ἑκάστην, ὥστε καὶ τὴν ἀντικειμένην.
For it is necessary that each of the differences belongs to some of the particulars, and so too the opposite difference.
§1.3.3εἰ δὲ 3 μὴ ἐνδέχεται τοῖς εἴδει διαφέρουσιν ὑπάρχειν εἶδός τι τῆς οὐσίας ἄτομον καὶ ἕν, ἀλλʼ ἀεὶ διαφορὰν ἕξει, οἷον ὄρνις ἀνθρώπου (ἡ διποδία γὰρ ἄλλη καὶ διάφορος), κἂν εἰ ἔναιμα, τὸ αἷμα διάφορον· ἢ οὐδὲν τῆς οὐσίας τὸ αἷμα θετέον.
And if 3 it is not possible for some indivisible and single species of substance to belong to things that differ in species, but they will always have a difference, as a bird does from a man (for their two-footedness is other and different), and even if they are blooded, their blood is different, or else blood must not be posited as any part of their substance.
εἰ δʼ οὕτως ἐστίν, ἡ μία διαφορὰ δυσὶν ὑπάρξει.
But if this is so, one difference will belong to two things.
εἰ δὲ τοῦτο, δῆλον ὅτι ἀδύνατον στέρησιν εἶναι διαφοράν.
And if this, it is clear that it is impossible for a privation to be a difference.
ἔσονται δʼ αἱ διαφοραὶ ἴσαι τοῖς ἀτόμοις ζῴοις, εἴπερ ἄτομά τε ταύτα καὶ αἱ διαφοραὶ ἄτομοι, κοινὴ δὲ μὴ ἐστιν.
And the differences will be equal to the indivisible animals, if indeed these are indivisible and the differences are indivisible, and there is no common one.
εἰ δʼ ἐνδέχεται μὴ ὑπάρχειν καὶ κοινήν, ἄτομον δέ, δῆλον ὅτι κατά γε τὴν κοινὴν ἐν τῷ αὐτῷ ἐστίν, ἕτερα ὄντα τῷ εἴδει ζῷα.
But if it is possible that there is no common difference, but only an indivisible one, it is clear that, at least in respect of the common one, animals that are different in species are in the same.
ὥστʼ ἀναγκαῖον, εἰ ἴδιοι αἱ διαφοραὶ εἰς ἃς ἅπαντα ἐμπίπτει τὰ ἄτομα, μηδεμίαν αὐτῶν εἶναι κοινὴν.
Thus, if the differences into which all the indivisibles fall are peculiar, it is necessary that none of them is common.
εἰ δὲ μή, ἕτερα ὄντα εἰς τὴν αὐτὴν βαδιεῖται.
Otherwise, being different, they will go into the same.
§1.3.4δεῖ δʼ οὔτε τὸ αὐτὸ καὶ 4 ἄτομον εἰς ἑτέραν καὶ ἑτέραν ἰέναι διαφορὰν τῶν διῃρημένων, οὔτʼ εἰς τὴν αὐτὴν ἕτερα, καὶ ἅπαντα εἰς ταὐτάς.
And we must 4 neither have the same indivisible thing go into one and then another of the divided differences, nor have different things go into the same, and all must go into these same ones.
φανερὸν τοίνυν ὅτι οὐκ ἔστι λαβεῖν τὰ ἄτομα εἴδη ὡς διαιροῦνται οἱ εἰς δύο διαιροῦντες τὰ ζῷα ἢ καὶ ἄλλο ὁτιοῦν γένος.
It is manifest, then, that it is not possible to grasp the indivisible species in the way that those who divide animals, or indeed any other genus, into two make their divisions.
καὶ γὰρ κατ’ ἐκείνους ἀναγκαῖον ἴσας τὰς ἐσχάτας εἶναι διαφορὰς τοῖς ζῴοις πάσι τοῖς ἀτόμοις τῷ εἴδει.
For indeed, according to them, it is necessary that the ultimate differences are equal to all the animals that are indivisible in species.
ὄντος γὰρ τοῦδέ τινος γένους, οὗ διαφοραὶ πράται τὰ λευκά, τούτων δʼ ἑκατέρου ἄλλαι, καὶ οὕτως εἰς τὸ πρόσω ἕως τῶν ἀτόμων, αἱ τελευταῖαι τέτταρες ἔσονται ἄλλο τι πλῆθος τῶν ἀφʼ ἑνὸς διπλασιαζομένων· τοσαῦτα δὲ καὶ τὰ εἴδη.
For if there is some genus of which the first differences are "white," and of each of these there are others, and so on forward until the indivisibles, the last four differences will be some other multitude of those doubled from one; and there will be just as many species.
§1.3.5ἔστι δʼ ἡ διαφορὰ τὸ εἶδος ἐν τῇ ὕλῃ. 5 οὔτε γὰρ ἄνευ ὕλης οὐδὲν ζῴου μόριον, οὕτε μόνη ἡ ὕλη· οὐ γὰρ πάντως ἔχον σῶμα ἔσται ζῷον, οὐδὲ τῶν μορίων οὐδέν, ὥσπερ πολλάκις εἴρηται.
And the difference is the form in the matter. 5 For no part of an animal is without matter, nor is the matter alone; for a body in just any state will not be an animal, nor will any of its parts, as has been said many times.
ἔτι διαιρεῖν χρὴ τοῖς ἐν τῇ οὐσίᾳ καὶ μὴ τοῖς συμβεβηκόσι καθʼ αὐτό, οἷον εἴ τις τὰ σχήματα διαιροίη, ὅτι τὰ μὲν δυσὶν ὀρθαῖς ἴσας ἔχει τὰς γωνίας, τὰ δὲ πλείοσιν·
Furthermore, one must divide by what is in the substance, and not by what is accidental in itself, for example, if one were to divide figures by saying that some have angles equal to two right angles, and others to more.