§5.15πρός τι λέγεται τὰ μὲν ὡς διπλάσιον πρὸς ἥμισυ καὶ τριπλάσιον πρὸς τριτημόριον, καὶ ὅλως πολλαπλάσιον πρὸς πολλοστημόριον καὶ ὑπερέχον πρὸς ὑπερεχόμενον· τὰ δʼ ὡς τὸ θερμαντικὸν πρὸς τὸ θερμαντὸν καὶ τὸ τμητικὸν πρὸς τὸ τμητόν, καὶ ὅλως τὸ ποιητικὸν πρὸς τὸ παθητικόν· τὰ δʼ ὡς τὸ μετρητὸν πρὸς τὸ μέτρον καὶ ἐπιστητὸν πρὸς ἐπιστήμην καὶ αἰσθητὸν πρὸς αἴσθησιν.
"Relative" is said, on the one hand, in the way that the double is in relation to the half, and the triple to the third part, and in general the multiple to the fraction, and the exceeding to the exceeded; on the other hand, in the way that what can heat is to what can be heated, and what can cut to what ¦30 can be cut, and in general the active to the passive; and further, in the way that the measurable is to the measure, the knowable to knowledge, and the sensible to sensation.
λέγεται δὲ τὰ μὲν πρῶτα κατʼ ἀριθμὸν ἢ ἁπλῶς ἢ ὡρισμένως, πρὸς αὐτοὺς ἢ πρὸς ἕν (οἷον τὸ μὲν διπλάσιον πρὸς ἓν ἀριθμὸς ὡρισμένος, τὸ δὲ πολλαπλάσιον κατʼ ἀριθμὸν πρὸς ἕν, οὐχ ὡρισμένον δέ, οἷον τόνδε ἢ τόνδε· τὸ δὲ ἡμιόλιον πρὸς τὸ ὑφημιόλιον κατʼ ἀριθμὸν πρὸς ἀριθμὸν ὡρισμένον· τὸ δʼ ἐπιμόριον πρὸς τὸ ὑπεπιμόριον κατὰ ἀόριστον, ὥσπερ τὸ πολλαπλάσιον πρὸς τὸ ἕν· τὸ δʼ ὑπερέχον πρὸς τὸ ὑπερεχόμενον ὅλως ἀόριστον κατʼ ἀριθμόν· ὁ γὰρ ἀριθμὸς σύμμετρος, κατὰ μὴ συμμέτρου δὲ ἀριθμὸς οὐ λέγεται, τὸ δὲ ὑπερέχον πρὸς τὸ ὑπερεχόμενον τοσοῦτόν τέ ἐστι καὶ ἔτι, τοῦτο δʼ ἀόριστον· ὁπότερον γὰρ ἔτυχέν ἐστιν, ἢ ἴσον ἢ οὐκ ἴσον)· ταῦτά τε οὖν τὰ πρός τι πάντα κατʼ ἀριθμὸν λέγεται καὶ ἀριθμοῦ πάθη, καὶ ἔτι τὸ ἴσον καὶ ὅμοιον καὶ ταὐτὸ κατʼ ἄλλον τρόπον (κατὰ γὰρ τὸ ἓν λέγεται πάντα, ταὐτὰ μὲν γὰρ ὧν μία ἡ οὐσία, ὅμοια δʼ ὧν ἡ ποιότης μία, ἴσα δὲ ὧν τὸ ποσὸν ἕν· τὸ δʼ ἓν τοῦ ἀριθμοῦ ἀρχὴ καὶ μέτρον, ὥστε ταῦτα πάντα πρός τι λέγεται κατʼ ἀριθμὸν μέν, οὐ τὸν αὐτὸν δὲ τρόπον)·
Of these, the first class are said in respect of number, either indefinitely or definitely, in relation to the numbers themselves or to one (for example, the double in relation to one is a definite number, but the multiple ¦35 in respect of number is in relation to one, though not a definite one, such as this or that; ¦1021a ¦1 while the sesquialter in relation to its reciprocal is in respect of a definite number in relation to a definite number; and the superparticular in relation to its reciprocal is in respect of an indefinite relation, just as the multiple is in relation to one; and the exceeding in relation to the exceeded is completely indefinite in respect of number; ¦5 for number is commensurable, but number is not said of what is incommensurable, whereas the exceeding in relation to the exceeded is "so much and something more," and this is indefinite; for it is whatever it happens to be, either equal or not equal); these relatives, then, are all said in respect of number and are affections of number; and further, the equal and ¦10 the like and the same in another way (for they are all said in respect of one; for those things are the same whose substance is one, and those are like whose quality is one, and those are equal whose quantity is one; and one is the beginning and measure of number, so that all these are said to be relatives in respect of number, but not in the same way); on the other hand, ¦15 the active and the passive are so called in respect of active and passive potency and the actualizations of these potencies, as for example what can heat is to what can be heated because it has the potency, and again that which heats is to that which is heated, and that which cuts to that which is cut, as actualizing these potencies.
τὰ δὲ ποιητικὰ καὶ παθητικὰ κατὰ δύναμιν ποιητικὴν καὶ παθητικὴν καὶ ἐνεργείας τὰς τῶν δυνάμεων, οἷον τὸ θερμαντικὸν πρὸς τὸ θερμαντὸν ὅτι δύναται, καὶ πάλιν τὸ θερμαῖνον πρὸς τὸ θερμαινόμενον καὶ τὸ τέμνον πρὸς τὸ τεμνόμενον ὡς ἐνεργοῦντα. τῶν δὲ κατʼ ἀριθμὸν οὐκ εἰσὶν ἐνέργειαι ἀλλʼ ἢ ὃν τρόπον ἐν ἑτέροις εἴρηται· αἱ δὲ κατὰ κίνησιν ἐνέργειαι οὐχ ὑπάρχουσιν.
But of the relatives in respect of number there are no actualizations except ¦20 in the way described elsewhere; but actualizations in respect of movement do not belong to them.
τῶν δὲ κατὰ δύναμιν καὶ κατὰ χρόνους ἤδη λέγονται πρός τι οἷον τὸ πεποιηκὸς πρὸς τὸ πεποιημένον καὶ τὸ ποιῆσον πρὸς τὸ ποιησόμενον.
Of those in respect of potency, they are already said to be relatives in respect of times, as for example what has acted to what has been acted upon, and what will act to what will be acted upon.
οὕτω γὰρ καὶ πατὴρ υἱοῦ λέγεται πατήρ· τὸ μὲν γὰρ πεποιηκὸς τὸ δὲ πεπονθός τί ἐστιν.
For it is in this way too that a father is called father of a son; for the one has acted, and the other has been affected ¦25 in some way.
ἔτι ἔνια κατὰ στέρησιν δυνάμεως, ὥσπερ τὸ ἀδύνατον καὶ ὅσα οὕτω λέγεται, οἷον τὸ ἀόρατον.
Further, some are said to be relatives in respect of privation of potency, such as the impotent and whatever is so called, like the invisible.
τὰ μὲν οὖν κατʼ ἀριθμὸν καὶ δύναμιν λεγόμενα πρός τι πάντα ἐστὶ πρός τι τῷ ὅπερ ἐστὶν ἄλλου λέγεσθαι αὐτὸ ὅ ἐστιν, ἀλλὰ μὴ τῷ ἄλλο πρὸς ἐκεῖνο· τὸ δὲ μετρητὸν καὶ τὸ ἐπιστητὸν καὶ τὸ διανοητὸν τῷ ἄλλο πρὸς αὐτὸ λέγεσθαι πρός τι λέγονται.
Now, the relatives which are so called in respect of number and of potency are all relatives because that which they are is said to be of something else, and not because something else is in relation to them; but the measurable and the knowable and the ¦30 object of thought are called relatives because something else is said in relation to them.
τό τε γὰρ διανοητὸν σημαίνει ὅτι ἔστιν αὐτοῦ διάνοια, οὐκ ἔστι δʼ ἡ διάνοια πρὸς τοῦτο οὗ ἐστὶ διάνοια (δὶς γὰρ ταὐτὸν εἰρημένον ἂν εἴη), ὁμοίως δὲ καὶ τινός ἐστιν ἡ ὄψις ὄψις, οὐχ οὗ ἐστὶν ὄψις (καίτοι γʼ ἀληθὲς τοῦτο εἰπεῖν) ἀλλὰ πρὸς χρῶμα ἢ πρὸς ἄλλο τι τοιοῦτον.
For the object of thought signifies that there is thought of it, but thought is not in relation to that of which it is thought (for then the same thing would have been said twice); and similarly sight is the sight of something, not of that of which it is sight (although indeed it is true to say this), but in relation to color or some other such thing.
ἐκείνως δὲ δὶς τὸ αὐτὸ λεχθήσεται, ὅτι ἐστὶν οὗ ἐστὶν ἡ ὄψις.
In the other way, the same thing will be said twice, namely, that it is the sight of that of which it is the sight.
τὰ μὲν οὖν καθʼ ἑαυτὰ λεγόμενα πρός τι τὰ μὲν οὕτω λέγεται, τὰ δὲ ἂν τὰ γένη αὐτῶν ᾖ τοιαῦτα, οἷον ἡ ἰατρικὴ τῶν πρός τι ὅτι τὸ γένος αὐτῆς ἡ ἐπιστήμη δοκεῖ εἶναι πρός τι· ἔτι καθʼ ὅσα τὰ ἔχοντα λέγεται πρός τι, οἷον ἰσότης ὅτι τὸ ἴσον καὶ ὁμοιότης ὅτι τὸ ὅμοιον·
¦1021b ¦1 So of relatives in themselves, some are so called in these ways, others if ¦5 their genera are such, as for example medicine is a relative because its genus, knowledge, is held to be a relative; further, in respect of all those qualities by virtue of which the things having them are called relatives, as equality because of the equal and likeness because of the like.
τὰ δὲ κατὰ συμβεβηκός, οἷον ἅνθρωπος πρός τι ὅτι συμβέβηκεν αὐτῷ διπλασίῳ εἶναι, τοῦτο δʼ ἐστὶ τῶν πρός τι· ἢ τὸ λευκόν, εἰ τῷ αὐτῷ συμβέβηκε διπλασίῳ καὶ λευκῷ εἶναι.
Others are relatives accidentally, as for example a man is a relative because it has happened to him to be double, ¦10 and this is one of the relatives; or what is white, if it has happened to the same subject to be both double and white.