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and in the case of the other species of mathematics. Practical philosophy adorns character and teaches how one ought to conduct oneself in a state; and if it educates one person, it is called ethics, if a whole household, it is called economics, if a whole city, it is called politics. It must be known that there are four dialectical, or logical, methods: 1. the divisive, which divides the genus into species by means of differences; 2. the definitive, which from the genus and the differences that the divisive method distinguished, defines the subject; 3. the analytic, which analyzes the more composite into the simpler, that is, the body into the humors, the humors into the fruits, the fruits into the four elements, the elements into matter and form; 4. the demonstrative, which demonstrates the proposition by means of a middle term; for instance, it is proposed for me to show that the soul is immortal; I take a certain middle term, 'ever-moving,' and I reason thus: The soul is ever-moving; the ever-moving is immortal; therefore the soul is immortal. It must be known, however, that the syllogisms belong to the demonstrative method. And one must know that the analytic method is threefold: for there is the physical, as was stated before; there is also logical analysis, when we analyze the proposed syllogism into its proper figure; and there is also mathematical, when we take what is sought as being agreed upon and arrive at something agreed upon, from which the proposition is hunted down. For instance, let the question be: Is the soul immortal? I take this question as agreed upon and I say: Since the soul is immortal, there are recompenses for evil and good actions; if there are recompenses, there is that which is judged and that which judges; if there is that which is judged and that which judges, there is a provider and providence. We have arrived, then, at providence, which is agreed upon by all. From this point, then, by synthesis I say: Since there is providence and a judge, there are recompenses; since there are recompenses, there is that which is judged; if there is that which is judged, then the soul is immortal. 67 Concerning the hypostatic union. It is necessary to know that the hypostatic union brings about one composite hypostasis of the things united, preserving in itself the natures that came together for union and their difference and their natural properties unconfused and unchanged. But this has no hypostatic difference in relation to itself; for the characteristic differences of each of those that came together for union, by which each is separated from those of the same species, become its own, as is the case with soul and body. For one composite hypostasis, say of Peter or Paul, is composed from both, and it preserves in itself the two perfect natures, that of the soul and that of the body, and their difference unmingled and their natural properties unconfused. And it has in itself the characteristic properties of each: those of the soul that separate it from other souls, and those of the body that separate it from other bodies, in no way separating the soul from the body but uniting and joining them, and at the same time separating the one hypostasis composed from them from the other hypostases of the same species. And once the natures have received hypostatic union with each other, they remain completely indivisible forever. For even if the soul is separated from the body in death, yet the hypostasis of both is one and the same; for hypostasis is the very coming together at the beginning of each one's existence. Therefore the body and the soul remain, always having the one beginning of their own existence and hypostasis, even if they are separated from each other. And it is necessary to know that it is possible for natures to be united to one another hypostatically, as in the case of man, and it is possible for a nature to be assumed by a hypostasis and to subsist in it, both of which are observed in the case of Christ—for in him both the natures, the divine and the human, were united, and in the pre-existing hypostasis of God the Word, his ensouled flesh subsisted and had its hypostasis in it,—but for one composite nature to be composed from two natures, or one hypostasis from two hypostases, is completely impossible; because

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καὶ ἐπὶ τῶν λοιπῶν εἰδῶν τοῦ μαθηματικοῦ. Τὸ δὲ πρακτικὸν ἦθος κοσμεῖ καὶ τὸ πῶς δεῖ πολιτεύεσθαι διδάσκει· καὶ εἰ μὲν ἕνα ἄνθρωπον παιδεύει, λέγεται ἠθικόν, εἰ δὲ οἶκον ὅλον, λέγεται οἰκονομικόν, εἰ δὲ πόλιν ὁλόκληρον, λέγεται πολιτικόν. Ἰστέον, ὡς τέσσαρές εἰσιν αἱ διαλεκτικαὶ μέθοδοι ἤγουν λογικαί· αʹ διαιρετική, ἥτις διαιρεῖ τὸ γένος εἰς εἴδη διὰ μέσων τῶν διαφορῶν· βʹ ὁριστική, ἥτις ἀπὸ τοῦ γένους καὶ τῶν διαφορῶν, ὧν διεῖλεν ἡ διαιρετική, ὁρίζει τὸ ὑποκείμενον· γʹ ἀναλυτικὴ ἡ τὸ συνθετικώτερον ἀναλύουσα εἰς τὰ ἁπλούστερα, τουτέστι τὸ σῶμα εἰς τοὺς χυμούς, τοὺς χυμοὺς εἰς τοὺς καρπούς, τοὺς καρποὺς εἰς τὰ τέσσαρα στοιχεῖα, τὰ στοιχεῖα εἰς ὕλην καὶ εἶδος· δʹ ἀποδεικτικὴ ἡ διὰ μέσου τινὸς δεικνύουσα τὸ προκείμενον· οἷον πρόκειταί μοι δεῖξαι, ὅτι ἡ ψυχὴ ἀθάνατός ἐστι· λαμβάνω τι μέσον, τὸ ἀεικίνητον, καὶ συλλογίζομαι οὕτως· Ἡ ψυχὴ ἀεικίνητός ἐστι· τὸ ἀεικίνητον ἀθάνατον· ἡ ψυχὴ ἄρα ἀθάνατος. Ἰστέον δέ, ὡς οἱ συλλογισμοὶ τῆς ἀποδεικτικῆς εἰσι. ∆εῖ δὲ γινώσκειν, ὅτι ἡ ἀναλυτικὴ τρισσή τίς ἐστιν· ἔστι γὰρ φυσικὴ ὡς ἡ προλεχθεῖσα· ἔστι δὲ καὶ λογικὴ ἀνάλυσις, ὅταν τὸν προτεθέντα συλλογισμὸν ἀναλύσωμεν εἰς τὸ οἰκεῖον σχῆμα· ἔστι δὲ καὶ μαθηματική, ὅταν λάβωμεν τὸ ζητούμενον ὡς ὁμολογούμενον καὶ καταντήσωμεν εἴς τι ὁμολογούμενον, ὅθεν ἀγρεύεται τὸ προκείμενον. Οἷον ἔστω τὸ ζητούμενον· Εἰ ἀθάνατος ἡ ψυχή. Τοῦτο τὸ ζητούμενον λαμβάνω ὡς ὁμολογούμενον καὶ λέγω· Ἐπειδὴ ἀθάνατος ἡ ψυχή, εἰσὶν ἀμοιβαὶ τῶν φαύλων καὶ ἀγαθῶν πράξεων· εἰ δέ εἰσιν ἀμοιβαί, ἔστι τὸ δικαζόμενον καὶ δικάζον· εἰ δέ ἐστι τὸ δικαζόμενον καὶ δικάζον, ἔστι προνοητὴς καὶ πρόνοια. Κατηντήσαμεν τοίνυν εἰς τὴν πρόνοιαν, ἥτις παρὰ πᾶσιν ὁμολογεῖται. Ἔνθεν λοιπὸν κατὰ σύνθεσιν λέγω· Ἐπειδὴ ἔστι πρόνοια καὶ δικαστής, εἰσὶν ἀμοιβαί· ἐπειδὴ εἰσὶν ἀμοιβαί, ἔστι τὸ κρινόμενον· εἰ δὲ ἔστι τὸ κρινόμενον, ἀθάνατος ἄρα ἡ ψυχή. 67 Περὶ τῆς καθ' ὑπόστασιν ἑνώσεως. Χρὴ γινώσκειν, ὅτι ἡ καθ' ὑπόστασιν ἕνωσις μίαν ὑπόστασιν τῶν ἑνουμένων ἀποτελεῖ σύνθετον σῴζουσα τὰς συνελθούσας πρὸς ἕνωσιν φύσεις καὶ τὴν τούτων διαφορὰν καὶ τὰ τούτων φυσικὰ ἰδιώματα ἀσύγχυτά τε καὶ ἄτρεπτα ἐν ἑαυτῇ. Αὕτη δὲ πρὸς ἑαυτὴν οὐδεμίαν ὑποστατικὴν ἔχει διαφοράν· αὐτῆς γὰρ γίνονται αἱ ἑκατέρου τῶν συνελθόντων πρὸς ἕνωσιν χαρακτηριστικαὶ διαφοραί, αἷς ἑκατέρων ἐκ τῶν ὁμοειδῶν χωρίζονται, ὡς ἐπὶ ψυχῆς ἔχει καὶ σώματος. Μία μὲν γὰρ ἐξ ἀμφοτέρων ἀποτελεῖται ἡ τοῦ Πέτρου τυχὸν ἢ τοῦ Παύλου ὑπόστασις σύνθετος, σῴζει δὲ ἐν ἑαυτῇ τὰς δύο τελείας φύσεις, τήν τε τῆς ψυχῆς καὶ τοῦ σώματος, καὶ τὴν τούτων διαφορὰν ἀσύμφυρτον καὶ τὰ τούτων φυσικὰ ἰδιώματα ἀσύγχυτα. Ἔχει δὲ ἐν ἑαυτῇ τὰ ἑκατέρας χαρακτηριστικὰ ἰδιώματα τά τε τῆς ψυχῆς τὰ χωρίζοντα αὐτὴν ἐκ τῶν λοιπῶν ψυχῶν καὶ τὰ τοῦ σώματος τὰ χωρίζοντα αὐτὸ ἐκ τῶν λοιπῶν σωμάτων, μηδαμῶς χωρίζοντα τὴν ψυχὴν ἐκ τοῦ σώματος ἀλλ' ἑνοῦντα καὶ συνάπτοντα, ἅμα δὲ τὴν ἐξ αὐτῶν συντεθειμένην μίαν ὑπόστασιν χωρίζοντα τῶν λοιπῶν ὁμοειδῶν ὑποστάσεων. Ἐπειδὰν δὲ ἅπαξ αἱ φύσεις τὴν πρὸς ἄλληλα καθ' ὑπόστασιν δέξωνται ἕνωσιν, ἀδιαίρετοι μένουσιν εἰς τὸ παντελές. Εἰ γὰρ καὶ χωρίζεται ἡ ψυχὴ τοῦ σώματος ἐν τῷ θανάτῳ, ἀλλ' ἡ ὑπόστασις ἀμφοτέρων μία καὶ ἡ αὐτή ἐστιν· ὑπόστασις γάρ ἐστιν ἡ ἐν τῇ ἀρχῇ τῆς ἑκάστου ὑπάρξεως κατ' αὐτὸ σύμπηξις. Μένει οὖν τό τε σῶμα καὶ ἡ ψυχή, ἀεὶ μίαν τὴν ἀρχὴν τῆς ἑαυτῶν ἔχοντα ὑπάρξεώς τε καὶ ὑποστάσεως, εἰ καὶ χωρισθῶσιν ἀλλήλων. ∆εῖ δὲ γινώσκειν, ὅτι φύσεις μὲν ἑνωθῆναι ἀλλήλαις καθ' ὑπόστασιν ἐνδέχεται ὡς ἐπὶ τοῦ ἀνθρώπου καὶ φύσιν προσληφθῆναι ὑπὸ ὑποστάσεως καὶ ἐν αὑτῇ ὑποστῆναι δυνατόν, ἅπερ ἀμφότερα ἐπὶ τοῦ Χριστοῦ θεωροῦνται-καὶ γὰρ ἐν αὐτῷ καὶ αἱ φύσεις, ἡ θεία τε καὶ ἡ ἀνθρωπίνη, ἡνώθησαν, καὶ ἐν τῇ προϋπαρχούσῃ τοῦ θεοῦ λόγου ὑποστάσει ὑπέστη ἡ ἔμψυχος αὐτοῦ σὰρξ καὶ αὐτὴν ἔσχεν ὑπόστασιν, -ἐκ δύο δὲ φύσεων ἀποτελεσθῆναι μίαν φύσιν σύνθετον ἢ ἐκ δύο ὑποστάσεων μίαν ὑπό στασιν παντελῶς ἀδύνατον· διότι