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that which is ever-moving is immortal; the soul, therefore, is immortal. It must be understood, however, that syllogisms belong to the demonstrative method. But one must know that the analytic method is threefold: for there is the physical, as was said before; and there is also logical analysis, when we break down the proposed syllogism into its proper figure; and there is mathematical, when we take the thing being sought as if it were agreed upon and arrive at something agreed upon, from which the proposed topic is established. For example, let the thing being sought be whether the soul is immortal. This thing being sought I take as agreed upon and I say: Since the soul is immortal, there are recompenses for evil and good deeds; if there are recompenses, there are tribunals under the earth; if there are tribunals under the earth, there is that which is judged and that which judges; if there is that which is judged and that which judges, there is a providential being and providence, which is agreed upon by all. From here, then, by synthesis I say: Since there is providence and a judge, there are tribunals under the earth; if these exist, there are recompenses; if there are recompenses, there is that which is judged; if there is that which is judged, the soul, therefore, is immortal.

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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 προλεχθεῖσα· ἔστι δὲ καὶ λογικὴ ἀνάλυσις, ὅταν τὸν προταχθέντα συλλογισμὸν ἀναλύσωμεν εἰς τὸ οἰκεῖον σχῆμα· ἔστι καὶ μαθηματική, ὅταν λάβωμεν τὸ ζητούμενον ὡς ὁμολογούμενον καὶ καταντήσωμεν εἴς τι ὁμολογούμενον, ὅθεν ἀγρεύεται τὸ προκείμενον. Οἷον ἔστω 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, εἰσὶ τὰ ὑπὸ γῆν δικαιωτήρια· εἰ δέ εἰσι τὰ ὑπὸ γῆν δικαιωτήρια, ἔστι τὸ δικαζόμενον καὶ δικάζον· εἰ δέ ἐστι τὸ δικαζόμενον καὶ δικάζον, ἔστι προνοητὴς καὶ πρόνοια, ἥτις παρὰ πᾶσιν ὁμολογεῖται. Ἔνθεν λοιπὸν κατὰ σύνθεσιν λέγω· Ἐπειδὴ ἔστι πρόνοια καὶ δικαστής, εἰσὶ τὰ ὑπὸ γῆν δικαιωτήρια· εἰ δέ εἰσι ταῦτα, εἰσὶν ἀμοιβαί· εἰ δέ εἰσιν ἀμοιβαί, ἔστι τὸ κρινόμενον· εἰ δὲ ἔστι τὸ κρινόμενον, ἀθάνατος ἄρα ἡ ψυχή.