§6.4#2Εἷς μὲν οὖν τρόπος τοῦ μὴ διὰ γνωριμωτέρων ἐστὶ τὸ διὰ τῶν ὑστέρων τὰ πρότερα δηλοῦν, καθάπερ πρότερον εἴπαμεν· ἄλλος, εἰ τοῦ ἐν ἠρεμίᾳ καὶ τοῦ ὡρισμένου διὰ τοῦ ἀορίστου καὶ τοῦ ἐν κινήσει ἀποδέδοται ὁ λόγος· πρότερον γὰρ τὸ μένον καὶ τὸ ὡρισμένον τοῦ ἀορίστου καὶ ἐν κινήσει ὄντος.
One way, then, of not defining through things that are more knowable is to declare prior things through posterior things, just as we said before; another, if the formula of what is at rest and defined is rendered through the indefinite and what is in motion; for what is remaining and defined is prior to the indefinite and what is in motion.
Τοῦ δὲ μὴ ἐκ προτέρων τρεῖς εἰσὶ τρόποι, πρῶτος μὲν εἰ διὰ τοῦ ἀντικειμένου τὸ ἀντικείμενον ὥρισται, οἷον διὰ τοῦ κακοῦ τὸ ἀγαθόν· ἅμα γὰρ τῇ φύσει τὰ ἀντικείμενα.
Of not defining from prior things, there are three ways: first, if the opposite is defined through the opposite, for example, the good through the bad; for opposites are simultaneous by nature.
Ἐνίοις δὲ καὶ ἡ αὐτὴ ἐπιστήμη ἀμφοτέρων δοκεῖ εἶναι, ὥστ᾿ οὐδὲ γνωριμώτερον τὸ ἕτερον τοῦ ἑτέρου.
And to some, the science of both also seems to be the same, so that neither is more knowable than the other.
Δεῖ δὲ μὴ λανθάνειν ὅτι ἔνια ἴσως οὐκ ἔστιν ὁρίσασθαι ἄλλως, οἷον τὸ διπλάσιον ἄνευ τοῦ ἡμίσεος, καὶ ὅσα καθ᾿ αὑτὰ πρός τι λέγεται· πᾶσι γὰρ τοῖς τοιούτοις ταὐτὸν τὸ εἶναι τῷ πρός τί πως ἔχειν, ὥστ᾿ ἀδύνατον ἄνευ θατέρου θάτερον γνωρίζειν, διόπερ ἀναγκαῖον ἐν τῷ τοῦ ἑτέρου λόγῳ συμπεριειλῆφθαι καὶ θάτερον.
But it must not escape notice that some things perhaps cannot be defined otherwise, for example, the double without the half, and as many things as are said to be relative in themselves; for to all such things, to be is the same as to be related in some way to something, so that it is impossible to know one without the other, wherefore it is necessary that in the formula of one, the other also is included.
Γνωρίζειν μὲν οὖν δεῖ τὰ τοιαῦτα πάντα, χρῆσθαι δ᾿ αὐτοῖς ὡς ἂν δοκῇ συμφέρειν.
Now, one must know all such things, but use them as seems to be advantageous.
Ἄλλος, εἰ αὐτῷ κέχρηται τῷ ὁριζομένῳ.
Another, if he has used the defined thing itself.
Λανθάνει δ᾿, ὅταν μὴ αὐτῷ τῷ τοῦ ὁριζομένου ὀνόματι χρήσηται, οἷον εἰ τὸν ἥλιον ἄστρον ἡμεροφανὲς ὡρίσατο· ὁ γὰρ ἡμέρᾳ χρώμενος ἡλίῳ χρῆται.
And this escapes notice when he does not use the name of the defined thing itself, for example, if he defined the sun as 'a star that appears by day'; for he who uses 'day' uses 'the sun'.
Δεῖ δ᾿ ὅπως φωραθῇ τὰ τοιαῦτα μεταλαμβάνειν ἀντὶ τοῦ ὀνόματος τὸν λόγον, οἷον ὅτι ἡμέρα ἡλίου φορὰ ὑπὲρ γῆς ἐστίν· δῆλον γὰρ ὅτι ὁ τὴν φορὰν ἡλίου ὑπὲρ γῆς εἰρηκὼς τὸν ἥλιον εἴρηκεν, ὥστε κέχρηται τῷ ἡλίῳ ὁ τῇ ἡμέρᾳ χρησάμενος.
But in order that such things may be detected, one must substitute the formula for the name, for example, that 'day is the passage of the sun above the earth'; for it is clear that he who has said 'the passage of the sun above the earth' has said 'the sun', so that he who has used 'day' has used 'the sun'.
Πάλιν εἰ τῷ ἀντιδιῃρημένῳ τὸ ἀντιδιῃρημένον ὥρισται, οἷον περιττὸν τὸ μονάδι μεῖζον ἀρτίου.
Again, if the coordinate species is defined by the coordinate species, for example, 'odd' as 'what is greater than an even number by a unit'.
Ἄμα γὰρ τῇ φύσει τὰ ἐκ τοῦ αὐτοῦ γένους ἀντιδιῃρημένα, τὸ δὲ περιττὸν καὶ ἄρτιον ἀντιδιῄρηται· ἄμφω γὰρ ἀριθμοῦ διαφοραί.
For coordinate species from the same genus are simultaneous by nature, and 'odd' and 'even' are coordinate; for both are differences of number.
Ὁμοίως δὲ καὶ εἰ διὰ τῶν ὑποκάτω τὸ ἐπάνω ὥρισται, οἷον ἄρτιον ἀριθμὸν τὸν δίχα διαιρούμενον ἢ τὸ ἀγαθὸν ἕξιν ἀρετῆς· τό τε γὰρ δίχα ἀπὸ τῶν δύο εἴληπται, ἀρτίων ὄντων, καὶ ἡ ἀρετὴ ἀγαθόν τί ἐστιν, ὥσθ᾿ ὑποκάτω ταῦτα ἐκείνων ἐστίν.
And likewise also if what is above is defined through things that are below, for example, 'an even number is one that is divided in two' or 'the good is the state of virtue'; for both 'in two' is taken from 'two', which are even, and 'virtue' is a certain good, so that these are below those.
Ἔτι δ᾿ ἀνάγκη τὸν τῷ ὑποκάτω χρώμενον καὶ αὐτῷ χρῆσθαι.
Moreover, it is necessary that he who uses what is below also uses the thing itself.
Ὅ τε γὰρ τῇ ἀρετῇ χρώμενος χρῆται τῷ ἀγαθῷ, ἐπειδὴ ἀγαθόν τι ἡ ἀρετή· ὁμοίως δὲ καὶ ὁ τῷ δίχα χρώμενος τῷ ἀρτίῳ χρῆται, ἐπειδὴ εἰς δύο διῃρῆσθαι σημαίνει τὸ δίχα, τὰ δὲ δύο ἄρτιά ἐστιν.
For he who uses virtue uses the good, since virtue is a certain good; and likewise also he who uses 'in two' uses the even, since 'in two' signifies being divided into two, and two is even.