concerning form, matter and cause, for example "the matter of the celestial bodies is not the four elements, but a certain fifth, spherical one, as being most capacious or on account of the fittingness of such a shape, which has neither beginning nor end; it is moved in a circle in imitation of the intellects above it which incline toward themselves; for intellect, seeing the forms, sees itself and vice versa; and that intellect is everywhere." And these things the natural philosopher [says]; on account of these things, therefore, he will render the definition from matter and form. The particular art, that is, medicine or carpentry, from which natural philosophy differs in that it also assigns causes from more remote principles. For instance, a physician might assign as cause the four humors or the four elements, but the natural philosopher [assigns] both the matter and the form. Dialectic, which will render definitions from the cause, is occupied with these things, just as it also defines anger as a desire for retaliation. Mathematics, which renders the definitions of the forms in themselves by abstraction. First philosophy will discourse on the forms that are 38 entirely separate from matter. How then do the first philosopher and the mathematician differ? The principles of the forms in matter are both in our soul and in the demiurgic intellect. And of those in the soul, some are extended, those in the imagination, while others are without parts and unextended, as those in the rational faculty. The geometer, therefore, will discourse on the extended forms in the imagination; for he uses the imagination as an abacus, operating divisibly and measuring and cutting distances. But the first philosopher will discourse on the forms in the rational faculty and those in the demiurgic [intellect]. Now, those in the rational faculty are images of the first ones, while those in the demiurgic intellect are archetypal and productive. Concerning the former, one has spoken as a purifier of passions and ignorance, but concerning the latter, as a theoretician. The definition from matter and form is that of the natural philosopher, that from form is of the dialectician, that from matter belongs to no one; for no art is concerned with matter alone. Anger is threefold: that which is separate from every earthly, airy body, that in the spirit which is separate only from the earthly, and that which is inseparable from the body, that is, the boiling of the blood around the heart. Some say that a clod of earth does not move downwards according to nature; for the earth occupies the middle region and not the lower, nor fire upwards, because the whole [universe] has a circular motion. Solution: Such motions are not according to nature, but paths to what is according to nature, just as we call healing according to nature, but becoming sick, as it were, contrary to nature, because the one leads to what is according to nature, and the other to what is contrary to nature. The divine, standing unmoved, moves all things, but other things, while moving [others], are themselves moved. Beauty and an image move [things] without being moved. Rhythm, according to the Abderites, is the shape, turning is the disposition, contact is the arrangement. Plato calls the soul self-moving, not on account of locomotion, but on account of motion according to will and thought. There are five genera according to Plato: being, sameness, otherness, motion, rest, not subordinate as in the other philosophers, but as pervading everywhere. For in all things there is being on account of their existence, sameness on account of the one principle, otherness because we are a multitude, motion (not the imperfect kind, but the 39 activity of certain things, of the hot to heat, of the cold to cool), and rest, that which is in beings and in eternal things. For even in the ever-moving, rest is observed, not because the whole comes to a halt, but because this very state of being ever-moving is a kind of rest for it. We know all things either by sameness, as white by the juxtaposition of white (for we know it as similar), or by unlikeness, as white through black (for we know it as other). Aristotle wrote a book *On the Good*, in which he sets down the unwritten doctrines of Plato. The Pythagoreans honored the monad, dyad, triad, and tetrad; the tetrad, because there are four kinds of living things: celestial, aerial, terrestrial, and aquatic; and because in sensible things there are point, line, plane, solid; and because all things are from the four [elements], and because it is generative of the tenth [number]; the monad as being without parts, on account of the intelligible things that are without parts in respect to being and to activity, which is in rest and motionlessness; the dyad

περὶ τοῦ εἴδους, τῆς ὕλης καὶ τῆς αἰτίας, οἷον «τῶν οὐρανίων ὕλη οὐ τὰ τέτταρα στοιχεῖα, ἀλλὰ καὶ πέμπτον τι σφαιρικόν, ὡς πολυχωρητότατον ἢ διὰ τὸ πρεπῶδες τοῦ τοιούτου σχήματος, ὃ μήτε ἀρχὴν ἢ τέλος ἔχει· κύκλῳ κινεῖται κατὰ μίμησιν τῶν ὑπὲρ αὐτὸν νόων οἳ εἰς ἑαυτοὺς συννεύουσι· νοῦς γὰρ τὰ εἴδη ὁρῶν ἑαυτὸν ὁρᾷ καὶ ἀνάπαλιν· καὶ ὅτι ὁ νοῦς πανταχοῦ ἐστί». καὶ ταῦτα ὁ φυσικός· ἀποδώσει οὖν διὰ ταῦτα τὸν ὅρον ἐξ ὕλης καὶ εἴδους. ἡ μερικὴ τέχνη, ἤγουν ἰατρικὴ ἢ τεκτονική, ἧς διαφέρει φυσικὴ ὅτι αὐτὴ καὶ ἐκ τῶν πορρωτέρω αἰτίας ἀποδίδωσι. τυχὸν ἰατρὸς μὲν αἰτιᾶται τοὺς τέτταρας χυμοὺς ἢ τὰ τέτταρα στοιχεῖα, ὁ δὲ φυσικὸς καὶ τὴν ὕλην καὶ τὸ εἶδος. ἡ διαλεκτική, ἣ ἀποδώσει τοὺς ὁρισμοὺς ἐκ τῆς αἰτίας, περὶ ταῦτα καταγίνεται, καθὼς ὁρίζεται καὶ τὸν θυμὸν ὄρεξιν ἀντιλυπήσεως. ἡ μαθηματική, ἥτις ἀποδίδωσι τῶν καθ' αὑτὰ εἰδῶν ἐξ ἀφαιρέσεως τοὺς ὁρισμούς. ἡ πρώτη φιλοσοφία περὶ τῶν πάντῃ 38 χωριστῶν τῆς ὕλης εἰδῶν διαλέξεται. τί οὖν διαφέρει πρῶτος φιλόσοφος καὶ μαθηματικός; οἱ λόγοι τῶν εἰδῶν τῶν ἐν ὕλῃ εἰσὶ καὶ ἐν τῇ ἡμετέρᾳ ψυχῇ καὶ ἐν τῷ νῷ τῷ δημιουργικῷ. καὶ τῶν ἐν τῇ ψυχῇ οἱ μὲν διαστατοί, οἱ ἐν τῇ φαντασίᾳ, οἱ δὲ ἀμερεῖς καὶ ἀδιάστατοι, ὡς οἱ ἐν τῷ λογιστικῷ. ὁ μὲν οὖν γεωμέτρης περὶ τῶν ἐν φαντασίᾳ διαστατῶν εἰδῶν διαλέξεται· ὡς γὰρ ἀβακίῳ κέχρηται τῇ φαντασίᾳ μεριστῶς ἐνεργῶν καὶ διαστήματα ἀναμετρῶν καὶ τέμνων. ὁ δὲ πρῶτος φιλόσοφος περὶ τῶν εἰδῶν τῶν ἐν τῷ λογικῷ καὶ τῶν ἐν τῷ δημιουργικῷ διαλέξεται. οἱ μὲν οὖν ἐν τῷ λογικῷ εἰκόνες τῶν πρώτων, οἱ δὲ ἐν τῷ δημιουργικῷ νῷ ἀρχέτυποι καὶ ποιητικοί. περὶ ἐκείνων δὲ εἶπέν τις ὡς καθαρτικὸς παθῶν καὶ ἀγνοίας, περὶ δὲ τούτων ὡς θεωρητικός. ὁ ἐξ ὕλης καὶ εἴδους ὁρισμὸς τοῦ φυσικοῦ, ὁ ἐξ εἴδους τοῦ διαλεκτικοῦ, ὁ ἐξ ὕλης οὐδεμιᾶς· οὐδεμία γὰρ τέχνη περὶ ὕλην μόνην καταγίνεται. Τριττὸς ὁ θυμός· ὁ χωριστὸς παντὸς σώματος γεώδους ἀερίου, ὁ ἐν τῷ πνεύματι ὁ χωριστὸς μόνον τοῦ γεώδους, καὶ ὁ ἀχώριστος τοῦ σώματος, ἤγουν ἡ ζέσις τοῦ περὶ τὴν καρδίαν αἵματος. Λέγουσί τινες ὅτι οὔτε ἡ βῶλος κάτω κινεῖται κατὰ φύσιν· ἡ γὰρ γῆ τὸ μέσον χώραν ἔχει καὶ οὐ τὴν κάτω, οὔτε τὸ πῦρ τὴν ἄνω, ὅτι τὸ ὅλον τὴν κυκλικήν. λύσις· αἱ τοιαῦται κινήσεις οὐ κατὰ φύσιν, ἀλλ' ὁδοὶ ἐπὶ τὸ κατὰ φύσιν, ὡς λέγομεν τὴν ὑγίανσιν κατὰ φύσιν, παρὰ φύσιν δὲ τὴν οἷον νόσανσιν, ὅτι ἡ μὲν ἐπὶ τὸ κατὰ φύσιν ἄγει, ἡ δὲ ἐπὶ τὸ παρὰ φύσιν. Τὸ θεῖον ἑστὸς ἀκίνητον τὰ πάντα κινεῖ, τὰ δ' ἄλλα κινοῦντα κινοῦνται. τὸ κάλλος καὶ ἡ εἰκὼν κινοῦσι μὴ κινούμενα. Ῥυσμὸς κατὰ Ἀβδηρίτους τὸ σχῆμα, τροπὴ ἡ διάθεσις, διαθιγὴ ἡ τάξις. Αὐτοκίνητον λέγει τὴν ψυχὴν ὁ Πλάτων, οὐ διὰ τὴν κατὰ τόπον κίνησιν, ἀλλὰ τὴν κατὰ βούλησιν καὶ διάνοιαν. Πέντε τὰ γένη κατὰ Πλάτωνα, οὐσία, ταυτότης, ἑτερότης, κίνησις, στάσις, οὐχ ὡς τὰ παρὰ τοῖς φιλοσόφοις ὑπάλληλα, ἀλλ' ὡς πανταχοῦ διήκοντα. ἐν πᾶσι γὰρ οὐσία διὰ τὴν ὕπαρξιν, ταυτότης διὰ τὴν μίαν ἀρχήν, ἑτερότης ὅτι πλῆθός ἐσμεν, κίνησις (ἀλλ' οὐχ ἡ ἀτελής, ἀλλ' ἡ 39 ἐνέργεια τῶνδέ τινων, τοῦ θερμοῦ τὸ θερμαίνειν, ψυχροῦ τὸ ψύχειν), καὶ ἡ στάσις ἡ ἐν τοῖς οὖσι καὶ τοῖς ἀιδίοις. καὶ γὰρ καὶ ἐν τοῖς ἀεικινήτοις θεωρεῖται στάσις, οὐ διὰ τὸ ἵστασθαι τὸ ὅλον, ἀλλὰ καὶ τὸ ἀεικίνητον οἷον στάσιν ἔχει αὐτὸ τοῦτο. γνωρίζομεν πάντα ἢ ταυτότητι ὡς τὸ λευκὸν παραθέσει λευκοῦ (γνωρίζομεν γὰρ ὡς ὅμοιον), ἢ ἀνομοιότητι ὡς τὸ λευκὸν διὰ τοῦ μέλανος (γνωρίζομεν γὰρ ὡς ἕτερον). Ἔγραφε βιβλίον Ἀριστοτέλης περὶ τοῦ ἀγαθοῦ, εἰς ὃ τὰς ἀγράφους τοῦ Πλάτωνος δόξας κατατάττει. ἐτίμων οἱ Πυθαγορικοὶ μονάδα, δυάδα, τριάδα καὶ τετράδα· τὴν μὲν τετράδα ὅτι τέτταρα εἴδη ζῴων, οὐρανίων, ἀερίων, χθονίων, ἐνύδρων, καὶ ὅτι ἐν τοῖς αἰσθητοῖς σημεῖον, γραμμή, ἐπίπεδον, στερεόν, καὶ ὅτι πάντα ἐκ τῶν τεττάρων, καὶ ὅτι γεννητική ἐστι τοῦ δεκάτου· τὴν μονάδα ὡς ἀμερῆ διὰ τὰ νοητὰ τὰ ἀμερῆ κατ' οὐσίαν καὶ ἐνέργειαν τὴν ἐν στάσει καὶ ἀκινησίᾳ· τὴν δυάδα