---
title: "Metaphysics · Τὰ Μετὰ τὰ Φυσικά"
author: "Aristotle"
translator: "Hugh Tredennick"
languages: [grc, en]
shelf: "Philosophy"
section: 9 of 27
url: https://scriptura.si/works/aristotle-metaphysics/9/
cite: "Aristotle, tr. Hugh Tredennick, Metaphysics · Τὰ Μετὰ τὰ Φυσικά, section 9. Scriptura (scriptura.si), https://scriptura.si/works/aristotle-metaphysics/9/"
---

# Metaphysics · Τὰ Μετὰ τὰ Φυσικά

*Aristotle, tr. Hugh Tredennick*

First philosophy: being as being, substance, cause, and the unmoved mover.

> Greek: ed. William David Ross, from the Perseus Digital Library (canonical-greekLit, tlg0086.tlg025, CC BY-SA 4.0).

> English: Hugh Tredennick, from the Perseus Digital Library (tlg0086.tlg025.perseus-eng2). Notes are not included.

> Rows follow the references the two texts share (line numbers), cut where both reach the end of a sentence.

## 9. Book V · 1017a–1021a

Source: https://scriptura.si/works/aristotle-metaphysics/9/ · cite a paragraph as https://scriptura.si/works/aristotle-metaphysics/9/#p-N

[¶0] These, then, are the senses in which things are said to “be” accidentally: either because both predicates belong to the same subject, which is; or because the predicate belongs to the subject, which is; or because the subject to which belongs that of which it is itself predicated itself is. (2.) The senses of essential being are those which are indicated by the figures of predication; for “being” has as many senses as there are ways of predication. Now since some predicates indicate (a) what a thing is, and others its (b) quality, (c) quantity, (d) relation, (e) activity or passivity, (f) place, (g) time, to each of these corresponds a sense of “being.” There is no difference between “the man is recovering” and “the man recovers”; or between “the man is walking” or “cutting” and “the man walks” or “cuts”; and similarly in the other cases. (3.) Again, “to be” and “is” mean that a thing is true, and “not to be” that it is false. Similarly too in affirmation and negation; e.g., in “Socrates is cultured” “is” means that this is true; or in “Socrates is not-white” that this is true; but in “the diagonal is not commensurable” “is not” means that the statement is false.

> Greek: καθʼ αὑτὰ δὲ εἶναι λέγεται ὅσαπερ σημαίνει τὰ σχήματα τῆς κατηγορίας· ὁσαχῶς γὰρ λέγεται, τοσαυταχῶς τὸ εἶναι σημαίνει. ἐπεὶ οὖν τῶν κατηγορουμένων τὰ μὲν τί ἐστι σημαίνει, τὰ δὲ ποιόν, τὰ δὲ ποσόν, τὰ δὲ πρός τι, τὰ δὲ ποιεῖν ἢ πάσχειν, τὰ δὲ πού, τὰ δὲ ποτέ, ἑκάστῳ τούτων τὸ εἶναι ταὐτὸ σημαίνει· οὐθὲν γὰρ διαφέρει τὸ ἄνθρωπος ὑγιαίνων ἐστὶν ἢ τὸ ἄνθρωπος ὑγιαίνει, οὐδὲ τὸ ἄνθρωπος βαδίζων ἐστὶν ἢ τέμνων τοῦ ἄνθρωπος βαδίζει ἢ τέμνει, ὁμοίως δὲ καὶ ἐπὶ τῶν ἄλλων. ἔτι τὸ εἶναι σημαίνει καὶ τὸ ἔστιν ὅτι ἀληθές, τὸ δὲ μὴ εἶναι ὅτι οὐκ ἀληθὲς ἀλλὰ ψεῦδος, ὁμοίως ἐπὶ καταφάσεως καὶ ἀποφάσεως, οἷον ὅτι ἔστι Σωκράτης μουσικός, ὅτι ἀληθὲς τοῦτο, ἢ ὅτι ἔστι Σωκράτης οὐ λευκός, ὅτι ἀληθές· τὸ δʼ οὐκ ἔστιν ἡ διάμετρος σύμμετρος, ὅτι ψεῦδος.

[¶1] (4.) Again, “to be” 〈or “is”〉 means that some of these statements can be made in virtue of a potentiality and others in virtue of an actuality. For we say that both that which sees potentially and that which sees actually is “a seeing thing.” And in the same way we call “understanding” both that which can use the understanding, and that which does; and we call “tranquil” both that in which tranquillity is already present, and that which is potentially tranquil. Similarly too in the case of substances. For we say that Hermes is in the stone, and the half of the line in the whole; and we call “corn” what is not yet ripe. But when a thing is potentially existent and when not, must be defined elsewhere. “Substance” means (a) simple bodies, e.g. earth, fire, water and the like; and in general bodies, and the things, animal or divine, including their parts, which are composed of bodies. All these are called substances because they are not predicated of any substrate, but other things are predicated of them. (b) In another sense, whatever, being immanent in such things as are not predicated of a substrate, is the cause of their being; as, e.g., the soul is the cause of being for the animal. (c) All parts immanent in things which define and indicate their individuality, and whose destruction causes the destruction of the whole; as, e.g., the plane is essential to the body (as some hold) and the line to the plane.

> Greek: ἔτι τὸ εἶναι σημαίνει καὶ τὸ ὂν τὸ μὲν δυνάμει ῥητὸν τὸ δʼ ἐντελεχείᾳ τῶν εἰρημένων τούτων· ὁρῶν τε γὰρ εἶναί φαμεν καὶ τὸ δυνάμει ὁρῶν καὶ τὸ ἐντελεχείᾳ, καὶ [τὸ] ἐπίστασθαι ὡσαύτως καὶ τὸ δυνάμενον χρῆσθαι τῇ ἐπιστήμῃ καὶ τὸ χρώμενον, καὶ ἠρεμοῦν καὶ ᾧ ἤδη ὑπάρχει ἠρεμία καὶ τὸ δυνάμενον ἠρεμεῖν. ὁμοίως δὲ καὶ ἐπὶ τῶν οὐσιῶν· καὶ γὰρ Ἑρμῆν ἐν τῷ λίθῳ φαμὲν εἶναι, καὶ τὸ ἥμισυ τῆς γραμμῆς, καὶ σῖτον τὸν μήπω ἁδρόν. πότε δὲ δυνατὸν καὶ πότε οὔπω, ἐν ἄλλοις διοριστέον. οὐσία λέγεται τά τε ἁπλᾶ σώματα, οἷον γῆ καὶ πῦρ καὶ ὕδωρ καὶ ὅσα τοιαῦτα, καὶ ὅλως σώματα καὶ τὰ ἐκ τούτων συνεστῶτα ζῷά τε καὶ δαιμόνια καὶ τὰ μόρια τούτων· ἅπαντα δὲ ταῦτα λέγεται οὐσία ὅτι οὐ καθʼ ὑποκειμένου λέγεται ἀλλὰ κατὰ τούτων τὰ ἄλλα. ἄλλον δὲ τρόπον ὃ ἂν ᾖ αἴτιον τοῦ εἶναι, ἐνυπάρχον ἐν τοῖς τοιούτοις ὅσα μὴ λέγεται καθʼ ὑποκειμένου, οἷον ἡ ψυχὴ τῷ ζῴῳ. ἔτι ὅσα μόρια ἐνυπάρχοντά ἐστιν ἐν τοῖς τοιούτοις ὁρίζοντά τε καὶ τόδε τι σημαίνοντα, ὧν ἀναιρουμένων ἀναιρεῖται τὸ ὅλον, οἷον ἐπιπέδου σῶμα, ὥς φασί τινες, καὶ ἐπίπεδον γραμμῆς·

[¶2] And number in general is thought by some to be of this nature, on the ground that if it is abolished nothing exists, and that it determines everything. (d) Again, the essence, whose formula is the definition, is also called the substance of each particular thing. Thus it follows that “substance” has two senses: the ultimate subject, which cannot be further predicated of something else; and whatever has an individual and separate existence. The shape and form of each particular thing is of this nature. “The same” means (a) accidentally the same. E.g., “white” and “cultured” are the same because they are accidents of the same subject; and “man” is the same as “cultured,” because one is an accident of the other; and “cultured” is the same as “man” because it is an accident of “man”; and “cultured man” is the same as each of the terms “cultured” and “man,” and vice versa; for both “man” and “cultured” are used in the same way as “cultured man,” and the latter in the same way as the former. Hence none of these predications can be made universally. For it is not true to say that every man is the same as “the cultured”; because universal predications are essential to things, but accidental predications are not so, but are made of individuals and with a single application.

> Greek: καὶ ὅλως ὁ ἀριθμὸς δοκεῖ εἶναί τισι τοιοῦτος (ἀναιρουμένου τε γὰρ οὐδὲν εἶναι, καὶ ὁρίζειν πάντα)· ἔτι τὸ τί ἦν εἶναι, οὗ ὁ λόγος ὁρισμός, καὶ τοῦτο οὐσία λέγεται ἑκάστου. συμβαίνει δὴ κατὰ δύο τρόπους τὴν οὐσίαν λέγεσθαι, τό θʼ ὑποκείμενον ἔσχατον, ὃ μηκέτι κατʼ ἄλλου λέγεται, καὶ ὃ ἂν τόδε τι ὂν καὶ χωριστὸν ᾖ· τοιοῦτον δὲ ἑκάστου ἡ μορφὴ καὶ τὸ εἶδος. ταὐτὰ λέγεται τὰ μὲν κατὰ συμβεβηκός, οἷον τὸ λευκὸν καὶ τὸ μουσικὸν τὸ αὐτὸ ὅτι τῷ αὐτῷ συμβέβηκε, καὶ ἄνθρωπος καὶ μουσικὸν ὅτι θάτερον θατέρῳ συμβέβηκεν, τὸ δὲ μουσικὸν ἄνθρωπος ὅτι τῷ ἀνθρώπῳ συμβέβηκεν· ἑκατέρῳ δὲ τοῦτο καὶ τούτῳ ἑκάτερον ἐκείνων, καὶ γὰρ τῷ ἀνθρώπῳ τῷ μουσικῷ καὶ ὁ ἄνθρωπος καὶ τὸ μουσικὸν ταὐτὸ λέγεται, καὶ τούτοις ἐκεῖνο (διὸ καὶ πάντα ταῦτα καθόλου οὐ λέγεται· οὐ γὰρ ἀληθὲς εἰπεῖν ὅτι πᾶς ἄνθρωπος ταὐτὸ καὶ τὸ μουσικόν· τὰ γὰρ καθόλου καθʼ αὑτὰ ὑπάρχει, τὰ δὲ συμβεβηκότα οὐ καθʼ αὑτά·

[¶3] “Socrates” and “cultured Socrates” seem to be the same; but “Socrates” is not a class-name, and hence we do not say “every Socrates” as we say “every man.” Some things are said to be “the same” in this sense, but (b) others in an essential sense, in the same number of senses as “the one” is essentially one; for things whose matter is formally or numerically one, and things whose substance is one, are said to be the same. Thus “sameness” is clearly a kind of unity in the being, either of two or more things, or of one thing treated as more than one; as, e.g., when a thing is consistent with itself; for it is then treated as two. Things are called “other” of which either the forms or the matter or the definition of essence is more than one; and in general “other” is used in the opposite senses to “same.” Things are called “different” which, while being in a sense the same, are “other” not only numerically, but formally or generically or analogically; also things whose genus is not the same; and contraries; and all things which contain “otherness” in their essence. Things are called “like” which have the same attributes in all respects; or more of those attributes the same than different; or whose quality is one. Also that which has a majority or the more important of those attributes of something else in respect of which change is possible (i.e. the contraries) is like that thing. And “unlike” is used in the opposite senses to “like.”

> Greek: ἀλλʼ ἐπὶ τῶν καθʼ ἕκαστα ἁπλῶς λέγεται· ταὐτὸ γὰρ δοκεῖ Σωκράτης καὶ Σωκράτης εἶναι μουσικός· τὸ δὲ Σωκράτης οὐκ ἐπὶ πολλῶν, διὸ οὐ πᾶς Σωκράτης λέγεται ὥσπερ πᾶς ἄνθρωπος)·—καὶ τὰ μὲν οὕτως λέγεται ταὐτά, τὰ δὲ καθʼ αὑτὰ ὁσαχῶσπερ καὶ τὸ ἕν· καὶ γὰρ ὧν ἡ ὕλη μία ἢ εἴδει ἢ ἀριθμῷ ταὐτὰ λέγεται καὶ ὧν ἡ οὐσία μία, ὥστε φανερὸν ὅτι ἡ ταυτότης ἑνότης τίς ἐστιν ἢ πλειόνων τοῦ εἶναι ἢ ὅταν χρῆται ὡς πλείοσιν, οἷον ὅταν λέγῃ αὐτὸ αὑτῷ ταὐτόν· ὡς δυσὶ γὰρ χρῆται αὐτῷ.—ἕτερα δὲ λέγεται ὧν ἢ τὰ εἴδη πλείω ἢ ἡ ὕλη ἢ ὁ λόγος τῆς οὐσίας· καὶ ὅλως ἀντικειμένως τῷ ταὐτῷ λέγεται τὸ ἕτερον. διάφορα δὲ λέγεται ὅσʼ ἕτερά ἐστι τὸ αὐτό τι ὄντα, μὴ μόνον ἀριθμῷ ἀλλʼ ἢ εἴδει ἢ γένει ἢ ἀναλογίᾳ· ἔτι ὧν ἕτερον τὸ γένος, καὶ τὰ ἐναντία, καὶ ὅσα ἔχει ἐν τῇ οὐσίᾳ τὴν ἑτερότητα. ὅμοια λέγεται τά τε πάντῃ ταὐτὸ πεπονθότα, καὶ τὰ πλείω ταὐτὰ πεπονθότα ἢ ἕτερα, καὶ ὧν ἡ ποιότης μία· καὶ καθʼ ὅσα ἀλλοιοῦσθαι ἐνδέχεται τῶν ἐναντίων, τούτων τὸ πλείω ἔχον ἢ κυριώτερα ὅμοιον τούτῳ. ἀντικειμένως δὲ τοῖς ὁμοίοις τὰ ἀνόμοια.

[¶4] The term “opposite” is applied to (a) contradiction; (b) contraries; (c) relative terms; (d) privation; (e) state; (f) extremes; e.g. in the process of generation and destruction. And (g) all things which cannot be present at the same time in that which admits of them both are called opposites; either themselves or their constituents. “Grey” and “white” do not apply at the same time to the same thing, and hence their constituents are opposite. “Contrary” means: (a) attributes, generically different, which cannot apply at the same time to the same thing. (b) The most different attributes in the same genus; or (c) in the same subject; or (d) falling under the same faculty. (e) Things whose difference is greatest absolutely, or in genus, or in species. Other things are called “contrary” either because they possess attributes of this kind, or because they are receptive of them, or because they are productive of or liable to them, or actually produce or incur them, or are rejections or acquisitions or possessions or privations of such attributes. And since “one” and “being” have various meanings, all other terms which are used in relation to “one” and “being” must vary in meaning with them; and so “same,” “other” and “contrary” must so vary, and so must have a separate meaning in accordance with each category. Things are called “other in species” (a) which belong to the same genus and are not subordinate one to the other;

> Greek: ἀντικείμενα λέγεται ἀντίφασις καὶ τἀναντία καὶ τὰ πρός τι καὶ στέρησις καὶ ἕξις καὶ ἐξ ὧν καὶ εἰς ἃ ἔσχατα αἱ γενέσεις καὶ φθοραί· καὶ ὅσα μὴ ἐνδέχεται ἅμα παρεῖναι τῷ ἀμφοῖν δεκτικῷ, ταῦτα ἀντικεῖσθαι λέγεται ἢ αὐτὰ ἢ ἐξ ὧν ἐστίν. φαιὸν γὰρ καὶ λευκὸν ἅμα τῷ αὐτῷ οὐχ ὑπάρχει· διὸ ἐξ ὧν ἐστὶν ἀντίκειται. ἐναντία λέγεται τά τε μὴ δυνατὰ ἅμα τῷ αὐτῷ παρεῖναι τῶν διαφερόντων κατὰ γένος, καὶ τὰ πλεῖστον διαφέροντα τῶν ἐν τῷ αὐτῷ γένει, καὶ τὰ πλεῖστον διαφέροντα τῶν ἐν ταὐτῷ δεκτικῷ, καὶ τὰ πλεῖστον διαφέροντα τῶν ὑπὸ τὴν αὐτὴν δύναμιν, καὶ ὧν ἡ διαφορὰ μεγίστη ἢ ἁπλῶς ἢ κατὰ γένος ἢ κατʼ εἶδος. τὰ δʼ ἄλλα ἐναντία λέγεται τὰ μὲν τῷ τὰ τοιαῦτα ἔχειν, τὰ δὲ τῷ δεκτικὰ εἶναι τῶν τοιούτων, τὰ δὲ τῷ ποιητικὰ ἢ παθητικὰ εἶναι τῶν τοιούτων, ἢ ποιοῦντα ἢ πάσχοντα, ἢ ἀποβολαὶ ἢ λήψεις, ἢ ἕξεις ἢ στερήσεις εἶναι τῶν τοιούτων. ἐπεὶ δὲ τὸ ἓν καὶ τὸ ὂν πολλαχῶς λέγεται, ἀκολουθεῖν ἀνάγκη καὶ τἆλλα ὅσα κατὰ ταῦτα λέγεται, ὥστε καὶ τὸ ταὐτὸν καὶ τὸ ἕτερον καὶ τὸ ἐναντίον, ὥστʼ εἶναι ἕτερον καθʼ ἑκάστην κατηγορίαν.—ἕτερα δὲ τῷ εἴδει λέγεται ὅσα τε ταὐτοῦ γένους ὄντα μὴ ὑπάλληλά ἐστι, καὶ ὅσα ἐν τῷ αὐτῷ γένει ὄντα διαφορὰν ἔχει, καὶ ὅσα ἐν τῇ οὐσίᾳ ἐναντίωσιν ἔχει·

[¶5] or (b) which are in the same genus and contain a differentia; or (c) which contain a contrariety in their essence. (d) Contraries, too (either all of them or those which are called so in a primary sense), are “other in species” than one another; and (e) so are all things of which the formulae are different in the final species of the genus (e.g., “man” and “horse” are generically indivisible, but their formulae are different); and (f) attributes of the same substance which contain a difference. “The same in species” has the opposite meanings to these. “Prior” and “posterior” mean: (1.) (a) In one sense (assuming that there is in each genus some primary thing or starting-point) that which is nearer to some starting-point, determined either absolutely and naturally, or relatively, or locally, or by some agency; e.g., things are prior in space because they are nearer either to some place naturally determined, such as the middle or the extreme, or to some chance relation; and that which is further is posterior. (b) In another sense, prior or posterior in time. Some things are prior as being further from the present, as in the case of past events (for the Trojan is prior to the Persian war, because it is further distant from the present); and others as being nearer the present, as in the case of future events (for the Nemean are prior to the Pythian games because they are nearer to the present, regarded as a starting-point and as primary).

> Greek: καὶ τὰ ἐναντία ἕτερα τῷ εἴδει ἀλλήλων ἢ πάντα ἢ τὰ λεγόμενα πρώτως, καὶ ὅσων ἐν τῷ τελευταίῳ τοῦ γένους εἴδει οἱ λόγοι ἕτεροι (οἷον ἄνθρωπος καὶ ἵππος ἄτομα τῷ γένει οἱ δὲ λόγοι ἕτεροι αὐτῶν), καὶ ὅσα ἐν τῇ αὐτῇ οὐσίᾳ ὄντα ἔχει διαφοράν. ταὐτὰ δὲ τῷ εἴδει τὰ ἀντικειμένως λεγόμενα τούτοις. πρότερα καὶ ὕστερα λέγεται ἔνια μέν, ὡς ὄντος τινὸς πρώτου καὶ ἀρχῆς ἐν ἑκάστῳ γένει, τῷ ἐγγύτερον ⟨εἶναι⟩ ἀρχῆς τινὸς ὡρισμένης ἢ ἁπλῶς καὶ τῇ φύσει ἢ πρός τι ἢ ποὺ ἢ ὑπό τινων, οἷον τὰ μὲν κατὰ τόπον τῷ εἶναι ἐγγύτερον ἢ φύσει τινὸς τόπου ὡρισμένου (οἷον τοῦ μέσου ἢ τοῦ ἐσχάτου) ἢ πρὸς τὸ τυχόν, τὸ δὲ πορρώτερον ὕστερον· τὰ δὲ κατὰ χρόνον (τὰ μὲν γὰρ τῷ πορρώτερον τοῦ νῦν, οἷον ἐπὶ τῶν γενομένων, πρότερον γὰρ τὰ Τρωϊκὰ τῶν Μηδικῶν ὅτι πορρώτερον ἀπέχει τοῦ νῦν· τὰ δὲ τῷ ἐγγύτερον τοῦ νῦν, οἷον ἐπὶ τῶν μελλόντων, πρότερον γὰρ Νέμεα Πυθίων ὅτι ἐγγύτερον τοῦ νῦν τῷ νῦν ὡς ἀρχῇ καὶ πρώτῳ χρησαμένων)· τὰ δὲ κατὰ κίνησιν (τὸ γὰρ ἐγγύτερον τοῦ πρώτου κινήσαντος πρότερον, οἷον παῖς ἀνδρός·

[¶6] (c) In another sense, in respect of motion (for that which is nearer to the prime mover is prior; e.g., the boy is prior to the man). This too is a kind of starting point in an absolute sense. (d) In respect of potency; for that which is superior in potency, or more potent, is prior. Such is that in accordance with whose will the other, or posterior, thing must follow, so that according as the former moves or does not move, the latter is or is not moved. And the will is a “starting-point.” (e) In respect of order; such are all things which are systematically arranged in relation to some one determinate object. E.g., he who is next to the leader of the chorus is prior to him who is next but one, and the seventh string is prior to the eighth; for in one case the leader is the starting-point, and in the other the middle string. In these examples “prior” has this sense; but (2.) in another sense that which is prior in knowledge is treated as absolutely prior; and of things which are prior in this sense the prior in formula are different from the prior in perception. Universals are prior in formula, but particulars in perception. And in formula the attribute is prior to the concrete whole: e.g. “cultured” to “the cultured man”; for the formula will not be a whole without the part. Yet “cultured” cannot exist apart from some cultured person. Again, (3.) attributes of prior subjects are called prior; e.g., straightness is prior to smoothness, because the former is an attribute of the line in itself, and the latter of a surface.

> Greek: ἀρχὴ δὲ καὶ αὕτη τις ἁπλῶς)· τὰ δὲ κατὰ δύναμιν (τὸ γὰρ ὑπερέχον τῇ δυνάμει πρότερον, καὶ τὸ δυνατώτερον· τοιοῦτον δʼ ἐστὶν οὗ κατὰ τὴν προαίρεσιν ἀνάγκη ἀκολουθεῖν θάτερον καὶ τὸ ὕστερον, ὥστε μὴ κινοῦντός τε ἐκείνου μὴ κινεῖσθαι καὶ κινοῦντος κινεῖσθαι· ἡ δὲ προαίρεσις ἀρχή)· τὰ δὲ κατὰ τάξιν (ταῦτα δʼ ἐστὶν ὅσα πρός τι ἓν ὡρισμένον διέστηκε κατά τινα λόγον, οἷον παραστάτης τριτοστάτου πρότερον καὶ παρανήτη νήτης· ἔνθα μὲν γὰρ ὁ κορυφαῖος ἔνθα δὲ ἡ μέση ἀρχή)·—ταῦτα μὲν οὖν πρότερα τοῦτον λέγεται τὸν τρόπον, ἄλλον δὲ τρόπον τὸ τῇ γνώσει πρότερον ὡς καὶ ἁπλῶς πρότερον. τούτων δὲ ἄλλως τὰ κατὰ τὸν λόγον καὶ τὰ κατὰ τὴν αἴσθησιν. κατὰ μὲν γὰρ τὸν λόγον τὰ καθόλου πρότερα κατὰ δὲ τὴν αἴσθησιν τὰ καθʼ ἕκαστα· καὶ κατὰ τὸν λόγον δὲ τὸ συμβεβηκὸς τοῦ ὅλου πρότερον, οἷον τὸ μουσικὸν τοῦ μουσικοῦ ἀνθρώπου· οὐ γὰρ ἔσται ὁ λόγος ὅλος ἄνευ τοῦ μέρους· καίτοι οὐκ ἐνδέχεται μουσικὸν εἶναι μὴ ὄντος μουσικοῦ τινός. ἔτι πρότερα λέγεται τὰ τῶν προτέρων πάθη, οἷον εὐθύτης λειότητος· τὸ μὲν γὰρ γραμμῆς καθʼ αὑτὴν πάθος τὸ δὲ ἐπιφανείας.

[¶7] Some things, then, are called prior and posterior in this sense; but others (iv.) in virtue of their nature and substance, namely all things which can exist apart from other things, whereas other things cannot exist without them. This distinction was used by Plato. (And since “being” has various meanings, (a) the substrate, and therefore substance, is prior; (b) potential priority is different from actual priority. Some things are prior potentially, and some actually; e.g., potentially the half-line is prior to the whole, or the part to the whole, or the matter to the substance; but actually it is posterior, because it is only upon dissolution that it will actually exist.) Indeed, in a sense all things which are called “prior” or “posterior” are so called in this connection; for some things can exist apart from others in generation (e.g. the whole without the parts), and others in destruction (e.g. the parts without the whole). And similarly with the other examples. “Potency” means: (a) the source of motion or change which is in something other than the thing changed, or in it qua other. E.g., the science of building is a potency which is not present in the thing built; but the science of medicine, which is a potency, may be present in the patient, although not qua patient. Thus “potency” means the source in general of change or motion in another thing, or in the same thing qua other;

> Greek: τὰ μὲν δὴ οὕτω λέγεται πρότερα καὶ ὕστερα, τὰ δὲ κατὰ φύσιν καὶ οὐσίαν, ὅσα ἐνδέχεται εἶναι ἄνευ ἄλλων, ἐκεῖνα δὲ ἄνευ ἐκείνων μή· ᾗ διαιρέσει ἐχρήσατο Πλάτων. (ἐπεὶ δὲ τὸ εἶναι πολλαχῶς, πρῶτον μὲν τὸ ὑποκείμενον πρότερον, διὸ ἡ οὐσία πρότερον, ἔπειτα ἄλλως τὰ κατὰ δύναμιν καὶ κατʼ ἐντελέχειαν· τὰ μὲν γὰρ κατὰ δύναμιν πρότερά ἐστι τὰ δὲ κατὰ ἐντελέχειαν, οἷον κατὰ δύναμιν μὲν ἡ ἡμίσεια τῆς ὅλης καὶ τὸ μόριον τοῦ ὅλου καὶ ἡ ὕλη τῆς οὐσίας, κατʼ ἐντελέχειαν δʼ ὕστερον· διαλυθέντος γὰρ κατʼ ἐντελέχειαν ἔσται.) τρόπον δή τινα πάντα τὰ πρότερον καὶ ὕστερον λεγόμενα κατὰ ταῦτα λέγεται· τὰ μὲν γὰρ κατὰ γένεσιν ἐνδέχεται ἄνευ τῶν ἑτέρων εἶναι, οἷον τὸ ὅλον τῶν μορίων, τὰ δὲ κατὰ φθοράν, οἷον τὸ μόριον τοῦ ὅλου. ὁμοίως δὲ καὶ τἆλλα. δύναμις λέγεται ἡ μὲν ἀρχὴ κινήσεως ἢ μεταβολῆς ἡ ἐν ἑτέρῳ ἢ ᾗ ἕτερον, οἷον ἡ οἰκοδομικὴ δύναμίς ἐστιν ἣ οὐχ ὑπάρχει ἐν τῷ οἰκοδομουμένῳ, ἀλλʼ ἡ ἰατρικὴ δύναμις οὖσα ὑπάρχοι ἂν ἐν τῷ ἰατρευομένῳ, ἀλλʼ οὐχ ᾗ ἰατρευόμενος. ἡ μὲν οὖν ὅλως ἀρχὴ μεταβολῆς ἢ κινήσεως λέγεται δύναμις ἐν ἑτέρῳ ἢ ᾗ ἕτερον, ἡ δʼ ὑφʼ ἑτέρου ἢ ᾗ ἕτερον (καθʼ ἣν γὰρ τὸ πάσχον πάσχει τι, ὁτὲ μὲν ἐὰν ὁτιοῦν, δυνατὸν αὐτό φαμεν εἶναι παθεῖν, ὁτὲ δʼ οὐ κατὰ πᾶν πάθος ἀλλʼ ἂν ἐπὶ τὸ βέλτιον)·

[¶8] or the source of a thing’s being moved or changed by another thing, or by itself qua other (for in virtue of that principle by which the passive thing is affected in any way we call it capable of being affected; sometimes if it is affected at all, and sometimes not in respect of every affection, but only if it is changed for the better). (b) The power of performing this well or according to intention; because sometimes we say that those who can merely take a walk, or speak, without doing it as well as they intended, cannot speak or walk. And similarly in the case of passivity. (c) All states in virtue of which things are unaffected generally, or are unchangeable, or cannot readily deteriorate, are called “potencies.” For things are broken and worn out and bent and in general destroyed not through potency but through impotence and deficiency of some sort; and things are unaffected by such processes which are scarcely or slightly affected because they have a potency and are potent and are in a definite state. Since “potency” has all these meanings, “potent” (or “capable”) will mean (a) that which contains a source of motion or change (for even what is static is “potent” in a sense) which takes place in another thing, or in itself qua other.

> Greek: ἔτι ἡ τοῦ καλῶς τοῦτʼ ἐπιτελεῖν ἢ κατὰ προαίρεσιν· ἐνίοτε γὰρ τοὺς μόνον ἂν πορευθέντας ἢ εἰπόντας, μὴ καλῶς δὲ ἢ μὴ ὡς προείλοντο, οὔ φαμεν δύνασθαι λέγειν ἢ βαδίζειν· ὁμοίως δὲ καὶ ἐπὶ τοῦ πάσχειν. ἔτι ὅσαι ἕξεις καθʼ ἃς ἀπαθῆ ὅλως ἢ ἀμετάβλητα ἢ μὴ ῥᾳδίως ἐπὶ τὸ χεῖρον εὐμετακίνητα, δυνάμεις λέγονται· κλᾶται μὲν γὰρ καὶ συντρίβεται καὶ κάμπτεται καὶ ὅλως φθείρεται οὐ τῷ δύνασθαι ἀλλὰ τῷ μὴ δύνασθαι καὶ ἐλλείπειν τινός· ἀπαθῆ δὲ τῶν τοιούτων ἃ μόλις καὶ ἠρέμα πάσχει διὰ δύναμιν καὶ τῷ δύνασθαι καὶ τῷ ἔχειν πώς. λεγομένης δὲ τῆς δυνάμεως τοσαυταχῶς, καὶ τὸ δυνατὸν ἕνα μὲν τρόπον λεχθήσεται τὸ ἔχον κινήσεως ἀρχὴν ἢ μεταβολῆς (καὶ γὰρ τὸ στατικὸν δυνατόν τι) ἐν ἑτέρῳ ἢ ᾗ ἕτερον, ἕνα δʼ ἐὰν ἔχῃ τι αὐτοῦ ἄλλο δύναμιν τοιαύτην, ἕνα δʼ ἐὰν ἔχῃ μεταβάλλειν ἐφʼ ὁτιοῦν δύναμιν, εἴτʼ ἐπὶ τὸ χεῖρον εἴτʼ ἐπὶ τὸ βέλτιον (καὶ γὰρ τὸ φθειρόμενον δοκεῖ δυνατὸν εἶναι φθείρεσθαι, ἢ οὐκ ἂν φθαρῆναι εἰ ἦν ἀδύνατον·

[¶9] (b) That over which something else has a potency of this kind. (c) That which has the potency of changing things, either for the worse or for the better (for it seems that even that which perishes is “capable” of perishing; otherwise, if it had been incapable, it would not have perished. As it is, it has a kind of disposition or cause or principle which induces such an affection. Sometimes it seems to be such as it is because it has something, and sometimes because it is deprived of something; but if privation is in a sense a state or “habit,” everything will be “potent” through having something; and so a thing is “potent” in virtue of having a certain “habit” or principle, and also in virtue of having the privation of that “habit,” if it can have privation; and if privation is not in a sense “habit,” the term “potent” is equivocal). (d) A thing is “potent” if neither any other thing nor itself qua other contains a potency or principle destructive of it. (e) All these things are “potent” either because they merely might chance to happen or not to happen, or because they might do so well. Even in inanimate things this kind of potency is found; e.g. in instruments; for they say that one lyre “can” be played, and another not at all, if it has not a good tone. “Impotence” is a privation of potency—a kind of abolition of the principle which has been described—either in general or in something which would naturally possess that principle, or even at a time when it would naturally already possess it (for we should not use “impotence”—in respect of begetting—in the same sense of a boy, a man and a eunuch).

> Greek: νῦν δὲ ἔχει τινὰ διάθεσιν καὶ αἰτίαν καὶ ἀρχὴν τοῦ τοιούτου πάθους· ὁτὲ μὲν δὴ τῷ ἔχειν τι δοκεῖ, ὁτὲ δὲ τῷ ἐστερῆσθαι τοιοῦτον εἶναι· εἰ δʼ ἡ στέρησίς ἐστιν ἕξις πως, πάντα τῷ ἔχειν ἂν εἴη τι, [εἰ δὲ μὴ] ὥστε τῷ τε ἔχειν ἕξιν τινὰ καὶ ἀρχήν ἐστι δυνατὸν [ὁμωνύμως] καὶ τῷ ἔχειν τὴν τούτου στέρησιν, εἰ ἐνδέχεται ἔχειν στέρησιν· ⟨εἰ δὲ μή, ὁμωνύμως⟩)· ἕνα δὲ τῷ μὴ ἔχειν αὐτοῦ δύναμιν ἢ ἀρχὴν ἄλλο ἢ ᾗ ἄλλο φθαρτικήν. ἔτι δὲ ταῦτα πάντα ἢ τῷ μόνον ἂν συμβῆναι γενέσθαι ἢ μὴ γενέσθαι, ἢ τῷ καλῶς. καὶ γὰρ ἐν τοῖς ἀψύχοις ἔνεστιν ἡ τοιαύτη δύναμις, οἷον ἐν τοῖς ὀργάνοις· τὴν μὲν γὰρ δύνασθαί φασι φθέγγεσθαι λύραν, τὴν δʼ οὐδέν, ἂν ᾖ μὴ εὔφωνος. ἀδυναμία δὲ ἐστὶ στέρησις δυνάμεως καὶ τῆς τοιαύτης ἀρχῆς οἵα εἴρηται, ἢ ὅλως ἢ τῷ πεφυκότι ἔχειν, ἢ καὶ ὅτε πέφυκεν ἤδη ἔχειν· οὐ γὰρ ὁμοίως ἂν φαῖεν ἀδύνατον εἶναι γεννᾶν παῖδα καὶ ἄνδρα καὶ εὐνοῦχον. ἔτι δὲ καθʼ ἑκατέραν δύναμιν ἔστιν ἀδυναμία ἀντικειμένη, τῇ τε μόνον κινητικῇ καὶ τῇ καλῶς κινητικῇ.

[¶10] Again, there is an “impotence” corresponding to each kind of potency; both to the kinetic and to the successfully kinetic. Some things are said to be “impotent” in accordance with this meaning of “impotence,” but others in a different sense, namely “possible” and “impossible.” “Impossible” means: (a) that whose contrary is necessarily true; e.g., it is impossible that the diagonal of a square should be commensurable with the sides, because such a thing is a lie, whose contrary is not only true but inevitable. Hence that it is commensurable is not only a lie but necessarily a lie. And the contrary of the impossible, i.e. the possible, is when the contrary is not necessarily a lie; e.g., it is possible that a man should be seated, for it is not necessarily a lie that he should not be seated. “Possible,” then, means in one sense, as we have said, that which is not necessarily a lie; in another, that which is true; and in another, that which may be true. (The “power” in geometry is so called by an extension of meaning.) These are the senses of “potent” which do not correspond to “potency.” Those which do correspond to it all refer to the first meaning, i.e.

> Greek: καὶ ἀδύνατα δὴ τὰ μὲν κατὰ τὴν ἀδυναμίαν ταύτην λέγεται, τὰ δὲ ἄλλον τρόπον, οἷον δυνατόν τε καὶ ἀδύνατον, ἀδύνατον μὲν οὗ τὸ ἐναντίον ἐξ ἀνάγκης ἀληθές (οἷον τὸ τὴν διάμετρον σύμμετρον εἶναι ἀδύνατον ὅτι ψεῦδος τὸ τοιοῦτον οὗ τὸ ἐναντίον οὐ μόνον ἀληθὲς ἀλλὰ καὶ ἀνάγκη [ἀσύμμετρον εἶναι]· τὸ ἄρα σύμμετρον οὐ μόνον ψεῦδος ἀλλὰ καὶ ἐξ ἀνάγκης ψεῦδος)· τὸ δʼ ἐναντίον τούτῳ, τὸ δυνατόν, ὅταν μὴ ἀναγκαῖον ᾖ τὸ ἐναντίον ψεῦδος εἶναι, οἷον τὸ καθῆσθαι ἄνθρωπον δυνατόν· οὐ γὰρ ἐξ ἀνάγκης τὸ μὴ καθῆσθαι ψεῦδος. τὸ μὲν οὖν δυνατὸν ἕνα μὲν τρόπον, ὥσπερ εἴρηται, τὸ μὴ ἐξ ἀνάγκης ψεῦδος σημαίνει, ἕνα δὲ τὸ ἀληθές [εἶναι], ἕνα δὲ τὸ ἐνδεχόμενον ἀληθὲς εἶναι. κατὰ μεταφορὰν δὲ ἡ ἐν γεωμετρίᾳ λέγεται δύναμις. ταῦτα μὲν οὖν τὰ δυνατὰ οὐ κατὰ δύναμιν· τὰ δὲ λεγόμενα κατὰ δύναμιν πάντα λέγεται πρὸς τὴν πρώτην [μίαν]·

[¶11] “a source of change which exists in something other than that in which the change takes place, or in the same thing qua other.” Other things are said to be “potent” because something else has such a potency over them; others because it does not possess it; others because it possesses it in a particular way. The term “impotent” is similarly used. Thus the authoritative definition of “potency” in the primary sense will be “a principle producing change, which is in something other than that in which the change takes place, or in the same thing qua other.” “Quantity” means that which is divisible into constituent parts, each or every one of which is by nature some one individual thing. Thus plurality, if it is numerically calculable, is a kind of quantity; and so is magnitude, if it is measurable. “Plurality” means that which is potentially divisible into non-continuous parts; and “magnitude” that which is potentially divisible into continuous parts. Of kinds of magnitude, that which is continuous in one direction is length; in two directions, breadth; in three, depth. And of these, plurality, when limited, is a number; length, a line; breadth, a plane; depth, a body. Again, some things are essentially quantitative, but others only accidentally; e.g. the line is essentially, but “cultured” accidentally quantitative. And of the former class some are quantitative in virtue of their substance, e.g. the fine (because the definition which describes it is quantitative in some form);

> Greek: αὕτη δʼ ἐστὶν ἀρχὴ μεταβολῆς ἐν ἄλλῳ ἢ ᾗ ἄλλο. τὰ γὰρ ἄλλα λέγεται δυνατὰ τῷ τὰ μὲν ἔχειν αὐτῶν ἄλλο τι τοιαύτην δύναμιν τὰ δὲ μὴ ἔχειν τὰ δὲ ὡδὶ ἔχειν. ὁμοίως δὲ καὶ τὰ ἀδύνατα. ὥστε ὁ κύριος ὅρος τῆς πρώτης δυνάμεως ἂν εἴη ἀρχὴ μεταβλητικὴ ἐν ἄλλῳ ἢ ᾗ ἄλλο. ποσὸν λέγεται τὸ διαιρετὸν εἰς ἐνυπάρχοντα ὧν ἑκάτερον ἢ ἕκαστον ἕν τι καὶ τόδε τι πέφυκεν εἶναι. πλῆθος μὲν οὖν ποσόν τι ἐὰν ἀριθμητὸν ᾖ, μέγεθος δὲ ἂν μετρητὸν ᾖ. λέγεται δὲ πλῆθος μὲν τὸ διαιρετὸν δυνάμει εἰς μὴ συνεχῆ, μέγεθος δὲ τὸ εἰς συνεχῆ· μεγέθους δὲ τὸ μὲν ἐφʼ ἓν συνεχὲς μῆκος τὸ δʼ ἐπὶ δύο πλάτος τὸ δʼ ἐπὶ τρία βάθος. τούτων δὲ πλῆθος μὲν τὸ πεπερασμένον ἀριθμὸς μῆκος δὲ γραμμὴ πλάτος δὲ ἐπιφάνεια βάθος δὲ σῶμα. ἔτι τὰ μὲν λέγεται καθʼ αὑτὰ ποσά, τὰ δὲ κατὰ συμβεβηκός, οἷον ἡ μὲν γραμμὴ ποσόν τι καθʼ ἑαυτό, τὸ δὲ μουσικὸν κατὰ συμβεβηκός. τῶν δὲ καθʼ αὑτὰ τὰ μὲν κατʼ οὐσίαν ἐστίν, οἷον ἡ γραμμὴ ποσόν τι (ἐν γὰρ τῷ λόγῳ τῷ τί ἐστι λέγοντι τὸ ποσόν τι ὑπάρχει), τὰ δὲ πάθη καὶ ἕξεις τῆς τοιαύτης ἐστὶν οὐσίας, οἷον τὸ πολὺ καὶ τὸ ὀλίγον, καὶ μακρὸν καὶ βραχύ, καὶ πλατὺ καὶ στενόν, καὶ βαθὺ καὶ ταπεινόν, καὶ βαρὺ καὶ κοῦφον, καὶ τὰ ἄλλα τὰ τοιαῦτα.

[¶12] and others are attributes and conditions of a substance of this kind— e.g., “much” and “little,” “long” and “short,” “broad” and “narrow,” “deep” and “shallow,” “heavy” and “light,” etc. Moreover, “great” and “small,” and “greater” and “smaller,” whether used absolutely or relatively to one another, are essential attributes of quantity; by an extension of meaning, however, these terms are also applied to other things. Of things called quantitative in an accidental sense, one kind is so called in the sense in which we said above that “cultured” or “white” is quantitative—because the subject to which they belong is quantitative; and others in the sense that motion and time are so called—for these too are said in a sense to be quantitative and continuous, since the subjects of which they are attributes are divisible. I mean, not the thing moved, but that through or along which the motion has taken place; for it is because the latter is quantitative that the motion is quantitative, and because the motion is quantitative that the time is also. “Quality” means (a) in one sense, the differentia of essence; e.g., a man is an animal of a certain quality because he is two-footed; and so is a horse, because it is four-footed. Also a circle is a geometrical figure of a certain quality, because it has no angles;

> Greek: ἔστι δὲ καὶ τὸ μέγα καὶ τὸ μικρὸν καὶ μεῖζον καὶ ἔλαττον, καὶ καθʼ αὑτὰ καὶ πρὸς ἄλληλα λεγόμενα, τοῦ ποσοῦ πάθη καθʼ αὑτά· μεταφέρονται μέντοι καὶ ἐπʼ ἄλλα ταῦτα τὰ ὀνόματα. τῶν δὲ κατὰ συμβεβηκὸς λεγομένων ποσῶν τὰ μὲν οὕτως λέγεται ὥσπερ ἐλέχθη ὅτι τὸ μουσικὸν ποσὸν καὶ τὸ λευκὸν τῷ εἶναι ποσόν τι ᾧ ὑπάρχουσι, τὰ δὲ ὡς κίνησις καὶ χρόνος· καὶ γὰρ ταῦτα πόσʼ ἄττα λέγεται καὶ συνεχῆ τῷ ἐκεῖνα διαιρετὰ εἶναι ὧν ἐστὶ ταῦτα πάθη. λέγω δὲ οὐ τὸ κινούμενον ἀλλʼ ὃ ἐκινήθη· τῷ γὰρ ποσὸν εἶναι ἐκεῖνο καὶ ἡ κίνησις ποσή, ὁ δὲ χρόνος τῷ ταύτην. [τὸ] ποιὸν λέγεται ἕνα μὲν τρόπον ἡ διαφορὰ τῆς οὐσίας, οἷον ποιόν τι ἄνθρωπος ζῷον ὅτι δίπουν, ἵππος δὲ τετράπουν, καὶ κύκλος ποιόν τι σχῆμα ὅτι ἀγώνιον, ὡς τῆς διαφορᾶς τῆς κατὰ τὴν οὐσίαν ποιότητος οὔσης·

[¶13] which shows that the essential differentia is quality. In this one sense, then, “quality” means differentia of essence; but (b) in another it is used as of immovable and mathematical objects, in the sense that numbers are in a way qualitative—e.g. such as are composite and are represented geometrically not by a line but by a plane or solid (these are products respectively of two and of three factors)—and in general means that which is present besides quantity in the essence. For the essence of each number is that which goes into it once; e.g. that of 6 is not what goes twice or three times, but what goes once; for 6 is once 6. (c) All affections of substance in motion in respect of which bodies become different when they (the affections) change—e.g. heat and cold, whiteness and blackness, heaviness and lightness, etc. (d) The term is used with reference to goodness and badness, and in general to good and bad. Thus there are, roughly speaking, two meanings which the term “quality” can bear, and of these one is more fundamental than the other. Quality in the primary sense is the differentia of the essence; and quality in numbers falls under this sense, because it is a kind of differentia of essences, but of things either not in motion or not qua in motion. Secondly, there are the affections of things in motion qua in motion, and the differentiae of motions. Goodness and badness fall under these affections, because they denote differentiae of the motion or functioning in respect of which things in motion act or are acted upon well or badly.

> Greek: —ἕνα μὲν δὴ τρόπον τοῦτον λέγεται ἡ ποιότης διαφορὰ οὐσίας, ἕνα δὲ ὡς τὰ ἀκίνητα καὶ τὰ μαθηματικά, ὥσπερ οἱ ἀριθμοὶ ποιοί τινες, οἷον οἱ σύνθετοι καὶ μὴ μόνον ἐφʼ ἓν ὄντες ἀλλʼ ὧν μίμημα τὸ ἐπίπεδον καὶ τὸ στερεόν (οὗτοι δʼ εἰσὶν οἱ ποσάκις ποσοὶ ἢ ποσάκις ποσάκις ποσοί), καὶ ὅλως ὃ παρὰ τὸ ποσὸν ὑπάρχει ἐν τῇ οὐσίᾳ· οὐσία γὰρ ἑκάστου ὃ ἅπαξ, οἷον τῶν ἓξ οὐχ ὃ δὶς ἢ τρὶς εἰσὶν ἀλλʼ ὃ ἅπαξ· ἓξ γὰρ ἅπαξ ἕξ. ἔτι ὅσα πάθη τῶν κινουμένων οὐσιῶν, οἷον θερμότης καὶ ψυχρότης, καὶ λευκότης καὶ μελανία, καὶ βαρύτης καὶ κουφότης, καὶ ὅσα τοιαῦτα, καθʼ ἃ λέγονται καὶ ἀλλοιοῦσθαι τὰ σώματα μεταβαλλόντων. ἔτι κατʼ ἀρετὴν καὶ κακίαν καὶ ὅλως τὸ κακὸν καὶ ἀγαθόν. σχεδὸν δὴ κατὰ δύο τρόπους λέγοιτʼ ἂν τὸ ποιόν, καὶ τούτων ἕνα τὸν κυριώτατον· πρώτη μὲν γὰρ ποιότης ἡ τῆς οὐσίας διαφορά (ταύτης δέ τι καὶ ἡ ἐν τοῖς ἀριθμοῖς ποιότης μέρος· διαφορὰ γάρ τις οὐσιῶν, ἀλλʼ ἢ οὐ κινουμένων ἢ οὐχ ᾗ κινούμενα), τὰ δὲ πάθη τῶν κινουμένων ᾗ κινούμενα, καὶ αἱ τῶν κινήσεων διαφοραί. ἀρετὴ δὲ καὶ κακία τῶν παθημάτων μέρος τι· διαφορὰς γὰρ δηλοῦσι τῆς κινήσεως καὶ τῆς ἐνεργείας, καθʼ ἃς ποιοῦσιν ἢ πάσχουσι καλῶς ἢ φαύλως τὰ ἐν κινήσει ὄντα·

[¶14] For that which can function or be moved in such-and-such a way is good, and that which can function in such-and-such a way and in the contrary way is bad. Quality refers especially to “good” and “bad” in the case of living things, and of these especially in the case of such as possess choice. Things are called “relative” (a) In the sense that “the double” is relative to the half, and “the triple” to the third; and in general the “many times greater” to the “many times smaller,” and that which exceeds to the thing exceeded. (b) In the sense that the thing which heats or cuts is relative to the thing heated or cut; and in general the active to the passive. (c) In the sense that the measurable is relative to the measure, and the knowable to knowledge, and the sensible to sensation. (a) In the first sense they are said to be numerically relative; either simply, or in a definite relation to numbers or to 1. E.g., “the double” in relation to 1 is a definite number; the “many times as great” is in a numerical relation to 1, but not in a definite relation such as this or that;

> Greek: τὸ μὲν γὰρ ὡδὶ δυνάμενον κινεῖσθαι ἢ ἐνεργεῖν ἀγαθὸν τὸ δʼ ὡδὶ καὶ ἐναντίως μοχθηρόν. μάλιστα δὲ τὸ ἀγαθὸν καὶ τὸ κακὸν σημαίνει τὸ ποιὸν ἐπὶ τῶν ἐμψύχων, καὶ τούτων μάλιστα ἐπὶ τοῖς ἔχουσι προαίρεσιν. πρός 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. 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·

[¶15] the relation of that which is 1.5 times something else to that something is a definite numerical relation to a number; and that which is (n+1)/n times something else is in an indefinite relation to a number, just as “the many times as great” is in an indefinite relation to 1. The relation of that which exceeds to that which is exceeded is numerically quite indefinite, for number is commensurate, and is not predicated of the incommensurate; whereas that which exceeds, in relation to that which is exceeded, is “so much” plus something more; and this something more is indefinite, for it is indifferently equal or not equal to the “so much.” Thus not only are all these things said to be relative in respect of number, but also the “equal” and “like” and “same,” though in another way: for all these terms are used in respect of “one”. Things are “the same” whose essence is one; “like” whose quality is one; “equal” whose quantity is one. Now “one” is the starting-point and standard of number; and so all these relations involve number, though not all in the same way. (b) Active and passive things are called relative in virtue of an active or passive potentiality or actualization of the potentialities; e.g., that which can heat is called relative to that which can be heated, because it can heat; and again the thing heating is called relative to the thing heated, and the thing cutting to the thing cut, because their potentialities are actualized. Numerical relations, on the other hand, are not actualized (except as has been described elsewhere); they have no actualizations in respect of motion.

> Greek: 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)· 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·