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he places double and half and such things under the category of "relative to something." We say, therefore, that it is possible for the same thing to be referred to one category and another according to one purpose and another. For as indicating number and measure, the aforementioned things are referred to quantity, but as having a relation to one another and as being spoken of in relation to one another, they are referred to "relative to something"; for the large is called large in relation to the small, and the double in relation to the half, and likewise the rest. A body, insofar as it is physical, is referred to substance, but insofar as it is mathematical, that is, measured, it is referred to quantity. Furthermore, of quantity, one part is magnitude, the other multitude. Magnitude, therefore, is measured, while multitude is numbered. "How large" follows magnitude, and "how many" follows multitude. There are three properties of quantity, which are called concomitants: first, that it has no contrary in itself; for a body in and of itself has no contrary, but insofar as it happens to be white, it has a contrary, black. One must know that the number two has no other number as its contrary; for if it did, there would be many. For all other numbers would be contraries, and nature is found to be unjust in opposing many to one; for it is not possible for many things to be contrary to one. Second, that it does not admit of more and less. For two palm trees are not more two than two men are. And that which has no contrary does not admit of more and less. Third, what belongs only and to all quantity, is the equal and unequal. For a line is equal to a line and unequal. 51 Concerning things relative to something. Things relative to something are those things which, being what they are, are said to be of other things, or are in some other way in relation to another. And they are said to be of other things, as a father of a son; for a father is in every case called the father of a son. But in relation to another, as large is in relation to small, and much to little; for it is not said "of little, much" but "in relation to little." One must know that when something is considered in itself, it is not relative to something, but when it has a relation to another, then it is called relative to something. Thus, this is the being of relatives, and this is their substance, in being spoken of in relation to another, that is, in having a relation to another; for the relation to one another makes things relative. Of relatives, some are named with the same name, as a friend is a friend of a friend, an enemy an enemy of an enemy, but others with a different name, as a father is a father of a son, a teacher a teacher of a student. Again, of relatives, some are according to excess, as the greater is greater than the less, -others according to the judging and the judged, as knowledge is knowledge of the knowable; for knowledge judges the knowable, that is, cognition judges the cognizable, and perception is perception of the perceptible, and position is position of what is posited, and standing is standing of what can stand, and reclining is reclining of what can recline, and such things; -others according to power and powerlessness, power as in the hot and the heated, and powerlessness according to the privation of power, as we say sight has the powerlessness to see the starless sphere; - and others according to the cause and the caused, as a father is father of a son. A property of relatives is to be spoken of in relation to their correlatives; for a friend is a friend of a friend, and a friend is a friend of a friend, a teacher is a teacher of a student, and a student is a student of a teacher; -and to be simultaneous by nature. To be simultaneous by nature is to contribute to and be contributed to, and to cancel out and be cancelled out together; for if there is a father, there will certainly be a son, and if there is a son, there will certainly be a father, and if there is not a father, there will not be a son, - for whose son will he be if there is no father? -and if there is not a son, there will not be a father; for he who does not have a son will not be a father. Thus the son is cancelled out with the father and the father with the son, but what is cancelled out is not his substance but the relation. For even if the son remains, he does not remain a son; for not having a father, how will he be a son? And if we do speak of the son of one who has died, either we do not speak properly but by an extension of meaning, or on the grounds that the father has not perished and passed into non-being, because of the immortality of the soul. One must know that each category is a most general genus and has both subordinate genera and species, and differences that divide the genera and constitute the species, and most specific species and individuals; but neither are the constitutive differences called essential, except for those of substance alone, nor the individuals

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διπλάσιον καὶ ἥμισυ καὶ τὰ τοιαῦτα ὑπὸ τὰ πρός τι τίθησι. Λέγομεν οὖν, ὅτι δυνατὸν τὸ αὐτὸ πρᾶγμα κατ' ἄλλον καὶ ἄλλον σκοπὸν ὑπὸ ἄλλην καὶ ἄλλην κατηγορίαν ἀνάγεσθαι. Ὡς μὲν γὰρ ἀριθμὸν καὶ μέτρον δηλοῦντα τὰ προειρημένα ὑπὸ τὸ ποσὸν ἀνάγονται, ὡς δὲ σχέσιν ἔχοντα πρὸς ἄλληλα καὶ ὡς πρὸς ἄλληλα λεγόμενα ὑπὸ τὰ πρός τι· τὸ γὰρ μέγα πρὸς τὸ μικρὸν λέγεται μέγα καὶ τὸ διπλάσιον πρὸς τὸ ἥμισυ, ὁμοίως καὶ τὰ λοιπά. Τὸ δὲ σῶμα, καθὸ μὲν φυσικόν ἐστιν, ὑπὸ τὴν οὐσίαν ἀνάγεται, καθὸ δὲ μαθηματικὸν ἤγουν μετρούμενον, ὑπὸ τὸ ποσόν. Ἔτι τοῦ ποσοῦ τὸ μὲν μέγεθος, τὸ δὲ πλῆθος. Τὸ μὲν οὖν μέγεθος μετρεῖται, τὸ δὲ πλῆθος ἀριθμεῖται. Ἀκολουθεῖ δὲ τὸ πηλίκον τῷ μεγέθει, τὸ δὲ ποσὸν τῷ πλήθει. Ἴδια δέ εἰσι τοῦ ποσοῦ τρία, ἅτινα λέγονται παρακολουθήματα· πρῶτον τὸ μὴ ἔχειν τι ἐναντίον καθ' αὑτό· τὸ γὰρ σῶμα αὐτὸ καθ' αὑτὸ οὐκ ἔχει τι ἐναντίον, καθὸ δέ ἐστι τυχὸν λευκόν, ἔχει τι ἐναντίον, τὸ μέλαν. Χρὴ δὲ γινώσκειν, ὅτι τῷ δύο ἀριθμῷ οὐκ ἔστιν ἐναντίος ἄλλος ἀριθμός· εἰ γὰρ ἔσται, πολλοὶ ἔσονται. Πάντες γὰρ οἱ ἄλλοι ἀριθμοὶ ἐναντίοι ἔσονται, καὶ εὑρίσκεται ἡ φύσις ἄδικος ἑνὶ πολλὰ ἀντιτάξασα· οὐ γὰρ ἐνδέχεται ἑνὶ πολλὰ εἶναι ἐναντία. ∆εύτερον τὸ μὴ ἐπιδέχεσθαι τὸ μᾶλλον καὶ ἧττον. Οὐδὲ γὰρ οἱ δύο φοίνικές εἰσι μᾶλλον δύο ἤπερ οἱ δύο ἄνθρωποι. Τὸ δὲ μὴ ἔχον ἐναντίον οὐκ ἐπιδέχεται τὸ μᾶλλον καὶ ἧττον. Τρίτον δέ, ὃ μόνῳ καὶ παντὶ τῷ ποσῷ, τὸ ἴσον καὶ ἄνισον. Γραμμὴ γὰρ γραμμῆς ἴση ἐστὶ καὶ ἄνισος. 51 Περὶ τῶν πρός τι. Πρός τι ταῦτά εἰσιν, ὅσα αὐτά, ἅπερ ἐστίν, ἑτέρων εἶναι λέγεται ἢ ὁπωσοῦν ἄλλως πρὸς ἕτερον. Καὶ ἑτέρων μὲν εἶναι λέγεται ὡς πατὴρ υἱοῦ· ὁ γὰρ πατὴρ πάντως υἱοῦ λέγεται πατήρ. Πρὸς ἕτερον δὲ ὡς μέγα πρὸς μικρὸν καὶ πολὺ πρὸς ὀλίγον· οὐ γὰρ λέγεται ὀλίγου πολὺ ἀλλὰ πρὸς ὀλίγον. Χρὴ δὲ γινώσκειν, ὅτι, ὅταν τι καθ' ἑαυτὸ θεωρῆται, οὐκ ἔστι πρός τι, ἡνίκα δὲ σχῇ σχέσιν πρὸς ἕτερον, τότε λέγεται πρός τι. Ὥστε τοῦτό ἐστι τὸ εἶναι τῶν πρός τι καὶ αὕτη αὐτῶν ἐστιν ἡ ὑπόστασις, ἐν τῷ πρὸς ἕτερον λέγεσθαι ἤγουν ἐν τῷ ἔχειν σχέσιν πρὸς ἕτερον· ἡ γὰρ πρὸς ἄλληλα σχέσις τὰ πρός τι ποιεῖ. Τῶν δὲ πρός τι τὰ μὲν ἐν τῷ αὐτῷ ὀνόματι ὀνομάζονται, ὡς φίλος φίλου φίλος, ἐχθρὸς ἐχθροῦ ἐχθρός, τὰ δὲ ἑτέρῳ ὀνόματι, ὡς πατὴρ υἱοῦ πατήρ, διδάσκαλος μαθητοῦ διδάσκαλος. Πάλιν τῶν πρός τι τὰ μὲν καθ' ὑπεροχήν, ὡς τὸ μεῖζον ἐλάττονος μεῖζον, -τὰ δὲ κατὰ τὸ κρῖνον καὶ κρινόμενον, ὡς ἐπιστήμη ἐπιστητοῦ ἐπιστήμη· ἡ γὰρ ἐπιστήμη κρίνει τὸ ἐπιστητὸν ἤγουν ἡ γνῶσις κρίνει τὸ γνωστόν, καὶ αἴσθησις αἰσθητοῦ αἴσθησις καὶ θέσις θετοῦ θέσις καὶ στάσις στατοῦ στάσις καὶ ἀνάκλισις ἀνακλιτοῦ ἀνάκλισις καὶ τὰ τοιαῦτα· -τὰ δὲ κατὰ δύναμιν καὶ ἀδυναμίαν, δύναμιν μὲν ὡς τὸ θερμὸν καὶ τὸ θερμαινόμενον, ἀδυναμίαν δὲ τὸ κατὰ στέρησιν τῆς δυνάμεως, ὡς λέγομεν ἀδυναμίαν ἔχειν τὴν ὄψιν ὁρᾶν τὴν ἄναστρον σφαῖραν· - τὰ δὲ κατὰ τὸ αἴτιον καὶ αἰτιατόν, ὡς πατὴρ υἱοῦ πατήρ. Ἴδιον δὲ τῶν πρός τι τὸ πρὸς ἀντιστρέφοντα λέγεσθαι· φίλος γὰρ φίλου φίλος καὶ φίλος φίλου φίλος, διδάσκαλος μαθητοῦ διδάσκαλος καὶ μαθητὴς διδασκάλου μαθητής· -καὶ τὸ ἅμα τῇ φύσει εἶναι. Τὸ δὲ ἅμα τῇ φύσει ἐστὶ τὸ συνεισφέρειν καὶ συνεισφέρεσθαι καὶ συναναιρεῖν καὶ συναναιρεῖσθαι· πατρὸς γὰρ ὄντος πάντως καὶ υἱὸς ἔσται, καὶ υἱοῦ ὄντος πάντως καὶ πατὴρ ἔσται καὶ πατρὸς μὴ ὄντος οὐδὲ υἱὸς ἔσται, - τίνος γὰρ ἔσται υἱὸς μὴ ὄντος πατρός; -καὶ υἱοῦ μὴ ὄντος οὐδὲ πατὴρ ἔσται· ὁ γὰρ μὴ ἔχων υἱὸν οὐκ ἔσται πατήρ. Ὥστε συναναιρεῖται ὁ υἱὸς τῷ πατρὶ καὶ ὁ πατὴρ τῷ υἱῷ, συναναιρεῖται δὲ οὐχ ἡ ὑπόστασις αὐτοῦ ἀλλ' ἡ σχέσις. Εἰ γὰρ καὶ μένει ὁ υἱός, ἀλλ' οὐχ υἱὸς μένει· μὴ ἔχων γὰρ πατέρα πῶς ἔσται υἱός; Εἰ δὲ καὶ λέγομεν υἱὸν τοῦ τετελευτηκότος, ἢ οὐ κυρίως λέγομεν ἀλλὰ καταχρηστικῶς, ἢ ὡς μὴ ἀπολομένου τοῦ πατρὸς καὶ εἰς τὸ μὴ εἶναι χωρήσαντος διὰ τὸ τῆς ψυχῆς ἀθάνατον. Χρὴ δὲ εἰδέναι, ὅτι ἑκάστη κατηγορία γενικώτατον γένος ἐστὶ καὶ ἔχει καὶ γένη καὶ εἴδη ὑπάλληλα καὶ διαιρετικὰς τῶν γενῶν καὶ συστατικὰς τῶν εἰδῶν διαφορὰς καὶ εἰδικώτατα εἴδη καὶ ἄτομα· οὔτε δὲ αἱ συστατικαὶ διαφοραὶ λέγονται οὐσιώδεις, εἰ μὴ μόνης τῆς οὐσίας, οὐδὲ τὰ ἄτομα