§1.3.66 συμβεβηκὸς γάρ τι τῷ τριγώνῳ τὸ δυσὶν ὀρθαῖς θαῖς ἴσας ἔχειν τὰς γωνίας.
6 For having its angles equal to two right angles is some accident to the triangle.
ἔτι τοῖς ἀντικειμένοις διαιρεῖν.
Furthermore, one must divide by opposites.
διάφορα γὰρ ἀλλήλοις τἀντικείμενα, οἷον λευκότης καὶ μελανία καὶ εὐθύτης καὶ καμπυλότης.
For opposites are different from one another, such as whiteness and blackness, or straightness and curvedness.
ἐὰν οὖν θάτερα διάφορα ᾖ, τῷ ἀντικειμένῳ διαιρετέον καὶ μὴ τὸ μὲν νεύσει τὸ δὲ χρώματι.
Therefore, if one of the two is different, one must divide by the opposite, and not one by inclination and the other by color.
πρὸς δὲ τούτοις τά γʼ ἔμψυχα τοῖς κοινοῖς ἔργοις τού σήματος καὶ τῆς ψυχῆς, οἷον καὶ ἐν ταῖς ῥηθείσαις νν πορευτικὰ καὶ πτηνά· ἔστι γάρ τινα γένη οἷς ἄμεφω ὑπάρχει καὶ ἔστι πτηνὰ καὶ ἄπτερα, καθάπερ τὸ τῶν μυρμήκων γένος.
And in addition to these, living things [should be divided] by the common functions of the body and the soul, as, in those [divisions] just mentioned, 'pedestrian' and 'winged'; for there are some genera to which both belong, and they are winged and wingless, just like the genus of ants.
καὶ τῷ ἀγρίῳ καὶ τῷ ἡμέρῳ διαιρεῖσθαι·
And to divide by 'wild' and 'tame' [is also inappropriate]; for in the same way, this would seem to divide the same species.
ὡσαύτως γὰρ ἂν δόξειε ταὐτὰ εἴδη διαιρεῖν πάντα γὰρ ὡς εἰπεῖν, ὅσα ἥμερα, καὶ ἄγρια τυγχάνει ὄντα, οἷον ἄνθρωποι, ἵκποι, βόες, κύνες ἐν τῇ Ἰνδικῇ, ὕες, αἶγες, πρόβατα· ὧν ἕκαστον, εἰ μὲν ὁμώνυμον, οὐ διῄρηται χωρίς, εἰ δὲ ταῦτα ἓν εἴδει, οὐχ οἷόν τʼ εἶναι διαφορὰν τὸ ἄγριον καὶ τὸ ἥμερον.
For almost all things, so to speak, that are tame happen to be wild as well, such as humans, horses, cattle, dogs in India, pigs, goats, sheep; of each of these, if they are homonymous, they have not been divided separately, but if they are one in species, it is not possible for 'wild' and 'tame' to be a difference.
§1.3.77 ὅλως δʼ ὁποιανοῦν διαφορὰν μιᾷ διαιροῦντι τοῦτο συμβαίνειν ἀναγκαῖον.
7 In general, it is necessary that this happens to anyone who divides by any single difference.
ἀλλὰ δεῖ πειρᾶσθαι λαμβάνειν κατὰ γένη τὰ ζῷα, ὡς ὑφήγηνθʼ οἱ πολλοὶ διορίσαντες ὄρνιθος γένος καὶ ἐχθύος.
But one must try to grasp the animals according to genera, as the many have led the way by defining the genus of bird and of fish.
τούτων δʼ ἕκαστον πολλαῖς ὥκισται διαφσραῖς, οὐ κατὰ τὴν διχοτομίαν.
And each of these is defined by many differences, not according to dichotomy.
οὕτω μὲν γὰρ ἤτοι τὸ παράπαν οὐκ ἔστι λαβεῖν (τὸ αὐτὸ γὰρ εἰς πλείους ἐμπίπτει διαιρέσεις καὶ τὰ ἐναντία εἰς τὴν αὑτήν), ἢ μία μόνον διαφορὰ ἔσται, καὶ αὕτη ἤτοι ἁπλῆ, ἢ ἐκ συμπλοκῆς τὸ τελευταῖον ἔσται εἶδος.
For in that way, either it is altogether impossible to grasp [the species] (for the same thing falls into several divisions and opposites into the same division), or there will be only one difference, and this itself will be either simple, or the ultimate species will be from a combination.
§1.3.8ἐὰν δὲ μὴ διαφορᾶς λαμβάνῃ τὴν 8 διαφοράν, ἀναγκαῖον, ὥσπερ συνδέσμῳ τὸν λόγον ἕνα ποιοῦντας οὕτω καὶ τὴν διαίρεσιν συνεχῆ ποιεῖν.
8 But if one does not grasp the difference as a difference of a difference, it is necessary, just as they make the definition one by a conjunction, so also to make the division continuous.
λέγω δʼ οἷον συμβαίνει τοῖς διαιρουμένοις τὸ μὲν ἄπτερον τὸ δὲ πτερωτόν, πτερωτοῦ δὲ τὸ μὲν ἥμερον τὸ δ᾿ ἄγριον, ἢ τὸ μὲν λευκὸν τὸ δὲ μέλαν· οὐ γὰρ διαφορὰ τοῦ πτερωτοῦ τὸ ἥμερον οὐδὲ τὸ λευκόν, ἀλλʼ ἑτέρας ἀρχὴ διαφορᾶς· ἐκεῖ δὲ κατὰ συμβεβηκός.
I mean, for example, what happens to those who divide, where one is wingless and the other winged, and of the winged one is tame and the other wild, or one is white and the other black; for being tame or being white is not a difference of the winged, but the beginning of another difference, and in that case it is accidental.
διὸ πολλαῖς τὸ ἓν εὐθέως διαιρετέον, ὡσπερ λέγομεν.
Therefore, one must divide the one immediately by many differences, as we say.
καὶ γὰρ οὕτω μὲν αἱ στερήσεις ποιήσουσι δια φοράν, ἐν δὲ τῇ διχοτομία οὐ ποιήσουσιν.
For in this way privations will make a difference, but in dichotomy they will not.
§1.3.9ὅτι δʼ 9 οὐκ ἐνδέχεται τῶν καθʼ ἔκαστον εἰδῶν λαμβάνειν οὐδὲν διαιροῦσι δίχα τὸ γένος, ὥσπερ τινὲς ᾠήθησαν, καὶ ἐκ τῶνδε φανερὸν.
9 And that it is not possible to grasp any of the particular species by dividing the genus into two, as some have thought, is clear also from the following.
ἀδύνατον γὰρ μίαν ὑπάρχειν διαφορὰν τῶν καθʼ ἕκαστον διαιρετῶν, ἐάν θʼ ἁπλά λαμβάνῃ ἐάν τε συμπεπλεγμένα.
For it is impossible for there to belong a single difference of the particular divided things, whether one takes simple or combined ones.
λέγω δὲ ἁπλᾶ μέν, ἐάν τʼ ἔχῃ διαφοράν, ἐάν τε μὴ ἔχῃ, οἷον τὸ πολυσχιδὲς πρὸς τὸ σχιζόπουν, συμπεπλεγμένα δέ, οἷον τὴν σχιζοποδίαν.
By 'simple' I mean, whether it has a difference or not, such as 'many-cleft' compared to 'cloven-footed'; and by 'combined' I mean, for example, 'cloven-footedness'.
τοῦτο γὰρ ἡ συνέχεια βούλεται τῶν ἀπὸ τοῦ γένους κατὰ τὴν διαίρεσιν διαφορῶν ὡς ἕν τι τὸ πᾶν ὄν.
For this is what the continuity of the differences starting from the genus according to division wants, as the whole being some single thing.
ἀλλὰ παρὰ τὴν λέξινσυμβαίνει δοκεῖν τὴν τελευταίαν μόνην εἶναι διαφοράν, σἷον τὸ πολυσχιδὲς ἢ τὸ δίπουν, τὸ δʼ ὑπόπουν καὶ πολύπουν περίεργα.
But due to the phrasing, it happens that only the last seems to be a difference, such as 'many-cleft' or 'two-footed', while 'having feet' and 'many-footed' are redundant.
§1.3.10ὅτι δʼ ἀδύνατον πλείους εἶναι τοιαύτας, 10 δῆλου· ἀεὶ γὰρ βαδίζων ἐπὶ τὴν ἐσχάτην διαφορὰν ἀφικνεῖται, ἀλλʼ οὐκ ἐπὶ τὴν τελευταίαν καὶ τὸ εἶδος.
10 And that it is impossible for there to be more than one such is clear; for by always proceeding, one arrives at the ultimate difference, but not at the last and the species.
αὕτη δʼ ἐστὶν τὸ σχιζόπουν μόνον, ἢ πάσα ἡ σύμπλεξις, ἐὰν διαιρῆται ἅνθρωπον, οἷον εἴ τις συνθείη ὑπόπουν, δίπουν, σχιζόπουν.
And this is 'cloven-footed' alone, or the whole combination, if one is dividing 'man', for example, if one were to combine 'having feet', 'two-footed', and 'cloven-footed'.
εἰ δʼ ἦν ὁ ἄνθρωπος σχιζόπουν μόνον, οὕτως ἐγίνετʼ ἂν αὕτη μία διαφορά.
If man were 'cloven-footed' alone, in this way this would have become a single difference.
νῦν δʼ ἐπειδὴ οὐκ ἔστιν, ἀνάγκη πολλὰς εἶναι μὴ ὑπὸ μίαν διαίρεσιν.
But as it is not so, it is necessary that there are many differences not under a single division.
ἀλλὰ μὴν πλείους γε τοῦ αὐτοῦ οὐκ ἔστιν ὑπὸ μίαν διχοτομίαν εἶναι, ἀλλὰ μίαν κατὰ μίαν τελευτᾶν.
However, there cannot be several differences of the same thing under a single dichotomy, but they must end in one by one.
ὥστε ἀδύνατον ὁτιοῦν λαβεῖν τῶν καθʼ ἕκαστον ζῴων δίχα διαιρουμένους.
Consequently, it is impossible for those who divide into two to grasp any of the particular animals.