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The self-participations: He means participations, in which beings participate, such as being itself or life, or wisdom, or order, and the rest, which participations happen to be divine gifts, which he also called principles of beings.

§ 6. And it is from it and in it: It is to be understood thus; the self-super-goodness, being mind, and whole actuality, turned toward itself, is in actuality, not in potentiality, being previously folly, then becoming mind in actuality; whence also it is only pure mind, not having thought as something introduced from without, but in every way it thinks from itself. For if its substance is one thing, and the things it thinks are other than it, it itself will be mindless, that is, its substance; and if it has (14S_226> anything, it has it from itself, not from another; but if it thinks from itself and out of itself, it is itself what it thinks. Therefore, being mind, it truly thinks, being the things that are. If then, by thinking itself it thinks the things that are, it is itself the things that are; for it will either think them as being elsewhere, or in itself, as being its own; therefore it is not possible to think them as being elsewhere; for where are they, being in sensibles? for sensibles are not beings, since they are mutable, and come to be, and are destroyed. It thinks itself, therefore, and in itself. And since God is also the maker of beings, he will think them when they are not yet, but he himself is the archetype of this universe; and what he thinks, he does not receive as types from others, being himself the paradigm of beings; so that neither is he in a place, nor are the things in him as in a place, but he has them as having himself and being united to them, all things being together, and being in him without parts, but distinguished, in the partless partlessly. His thoughts, therefore, are the beings, and the beings are the forms. But thoughts must not be understood thus, that, because he thought this, this came to be, or is this; for this thought must be preceded by something thought, so that by thinking it, he might make it; but he thinks beings, since he thinks himself and is joined to the things within; for his very thinking is generation for beings. That which is within them, then, this is the form, and this is the idea; but he, being wholly mind, is wholly knowledge, and the minds from him and in him are like theorems of knowledge. And being many sciences together, they remain unconfused, and they operate outwardly one by one, when it is necessary; and the soul has all powers together in itself, by which it provides for the body, and yet puts them forth without confusion at the proper time, activating the natural (14S_228> power concerning the body, by which it nourishes it and makes it grow and makes it fit for generation, and it activates the sensitive power concerning the veins and arteries and the flesh and the nerves, by which power we perceive sensible things; and the opinative power, by which it judges sensible things; and the representational, by which it forms again; and the mnemonic, by which it remembers; and the appetitive, by which it desires and moves the living being according to place; and the imaginative, and the spirited, and the desiderative. For it has these powers, using the body in its irrational part. But after death, the mind alone will be active, while these are inactive.

And the things that are in any way by being: From the super-goodness of God, he says, which is the very being of God himself, the existence of beings and their continuance. Unitarily, he says, that is, according to some simple and comprehensive and unrelated cause of all things; for by no reason or thought or thing does the Divine have relation and communion with beings, but it is in every way and according to all things transcendent, touching them only by holding them together and providing for them, as one might say. But the following examples are confirmations of the argument that all things are from God, as the cause of their existence, he being other than these things and subsisting in himself, being other than these things.

And it has every number: For number increases to magnitude by the composition of many units; the unit, therefore, as the cause of numbers, has encompassed all the numbers in a unitary way; so also the center, that is, the point, contains the straight lines to the circle.

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Τάς αὐτομετοχάς: Μετοχάς φησιν, ὧν τά ὄντα μετέχουσιν, οἷον αὐτό τό εἶναι ἤ ζωή, ἤ σοφία, ἤ τάξις, καί τά λοιπά, αἵτινες μετοχαί θεῖαι τυγχάνουσι δωρεαί, ἅς καί ἀρχάς τῶν ὄντων ἐκάλεσε.

§ 6. Καί ἔστιν ἐξ αὐτῆς καί ἐν αὐτῇ: Οὕτω νοητέον· ἡ αὐτοϋπεραγαθότης, νοῦς οὖσα, καί ὅλη ἐνέργεια, εἰς ἑαυτήν ἐστραμμένη, ἐνεργείᾳ ἐστίν, οὐ δυνάμει, πρότερον οὖσα ἀφροσύνη, εἶτα νοῦς ἐνεργείᾳ γινομένη· ὅθεν καί ἐστι νοῦς μόνον καθαρός, οὐκ ἐπείσακτον ἔχων τό φρονεῖν, ἀλλά παρ' ἑαυτοῦ πάντως νοεῖ. Εἰ γάρ ἡ μέν οὐσία αὐτοῦ ἄλλη ἐστίν, ἅ δέ νοεῖ ἔτερα αὐτοῦ, αὐτός ἀνόητος ἔσται, ἤγουν ἡ οὐσία αὐτοῦ· εἴ τι δέ (14S_226> ἔχει, παρ' ἑαυτοῦ ἔχει, οὐ παρ' ἄλλου· εἰ δέ παρ' ἑαυτοῦ καί ἐξ αὐτοῦ νοεῖ, αὐτός ἐστιν ἅ νοεῖ. Οὐκοῦν νοῦς ὤν, ὄντως νοεῖ, τά ὄντα ὡς ὤν. Εἰ οὖν νοῶν ἑαυτόν τά ὄντα νοεῖ, αὐτός ἐστι τά ὄντα· ἤ γάρ ἑτέρωθι ὄντα αὐτά νοήσει, ἤ ἐν ἑαυτῷ, ὡς αὐτοῦ ὄντα· ἀλλαχοῦ μέν ὄντα οὖν οὐ δυνατόν νοῆσαι· ποῦ γάρ ὄντα ἐν αἰσθητοῖς; τά γάρ αἰσθητά οὔκ εἰσιν ὄντα, ἅτε τρεπτά ὄντα, καί γινόμενα, καί ἀπολλύμενα. Ἑαυτόν οὖν ἄρα καί ἐν ἑαυτῷ νοεῖ. Ἐπειδή δέ καί ποιητής τῶν ὄντων ἐστίν ὁ Θεός, ἐν τῷ μήπω ὄντι νοήσει αὐτά, ἀλλ' αὐτός ἀρχέτυπός ἐστι τούτου τοῦ παντός· καί ἅ νοεῖ, οὐ τύπους λαμβάνων ἀφ' ἑτέρων, αὐτός ὤν τῶν ὄντων παράδειγμα· ὥστε οὔτε αὐτός ἐν τόπῳ, οὔτε τά ἐν αὐτῷ ὡς ἐν τόπῳ, ἀλλ' ἔχει αὐτά ὡς ἑαυτόν ἔχων καί ἑνών αὐτοῖς, πάντων μέν ὁμοῦ ὄντων, καί ἐν ἀμερεῖ ὄντων ἐν αὐτῷ, διακεκριμένων δέ, ἐν τῷ ἀμερεῖ ἀμερῶς. Αἱ τοίνυν νοήσεις αὐτοῦ εἰσι τά ὄντα, τά δέ ὄντα εἰσί τά εἴδη. Νοήσεις δέ οὐχ οὕτως ἀκουστέον, ὅτι, ἐπειδή τόδε ἐνόησεν, ἐγένετο τόδε, ἤ ἐστί τόδε· ταύτης γάρ τῆς νοήσεως προηγεῖσθαι δεῖ νοούμενόν τι, ἵνα αὐτό νοήσας ποιήσῃ· ἀλλά νοεῖ τά ὄντα, ἅτε ἑαυτόν νοῶν καί τοῖς ἐνοῦσι συναπτόμενος· αὐτή γάρ αὐτῷ ἡ νόησις γένεσίς ἐστι τοῖς οὖσι. Τό οὖν ἐνόν ἐν αὐτοῖς, τοῦτό ἐστι τό εἴδος, καί τοῦτό ἐστιν ἡ ἰδέα· αὐτός δέ, νοῦς ὤν ὅλος, ὅλος ἐστίν ἐπιστήμη, τά δέ ἐξ αὐτοῦ καί ἐν αὐτῷ νόες ἐοικότες θεωρήμασι τῆς ἐπιστήμης. Εἰσί δέ ὁμοῦ πολλαί ἐπιστῆμαι οὖσαι, ἀσύγχυτοι μένουσι, καί ἐνεργοῦσι ἕξω κατά μίαν, ὅταν δέῃ· καί πάσας ὁμοῦ τάς δυνάμεις ἡ ψυχή ἐν ἑαυτῇ ἔχει, καθ' ἄς προνοεῖ τοῦ σώματος, καί ὅμως ἀσυγχύτως αὐτάς κατά καιρόν προβάλλει, τήν μέν φυσικήν (14S_228> ἐνεργοῦσα περί τό σῶμα δύναμιν, καθ' ἥν τρέφει τοῦτο καί αὕξει καί πρός γένναν ἐπιτήδειον ποιεῖ, τήν δέ αἰσθητικήν ἐνεργεῖ δύναμιν περί φλέβας καί ἀρτηρίας καί τήν σάρκα καί τά νεῦρα, καθ' ἥν δύναμιν τῶν αἰσθητῶν ἀντιλαμβανόμεθα· τήν δέ δοξαστικήν, καθ' ἥν κρίνει τά αἰσθητά· ἀναζωγραφικήν δέ, καθ' ἥν ἀναπλάττει· καί μνημονευτικήν, καθ' ἥν μέμνηται· ὀρεκτικήν δέ, καθ' ἥν ὀρέγεται καί κινεῖ τό ζῶν κατά τόπον· καί εἰκαστικήν, καί θυμοειδῆ, καί ἐπιθυμητικήν. Ταύτας γάρ ἔχει δυνάμεις σώματι χρωμένη ἐν τῷ ἀλόγῳ αὐτῆς μέρει. Μετά δέ θάνατον ὁ νοῦς μόνος ἔσται ἐνεργῶν, τοῦτων ἀργουσῶν.

Καί τά ὁπωσοῦν τῷ εἶναι: Ἐκ τῆς τοῦ Θεοῦ ὑπεραγαθότητός φησιν, ἥτις ἐστίν αὐτό τό εἶναι αὐτοῦ τοῦ Θεοῦ, ἡ ὕπαρξις τῶν ὄντων καί ἡ τούτων διαμονή. Ἑνιαίως φησίν, ἤγουν κατά ἁπλῆν τινα καί περιεκτικήν τῶν ὅλων αἰτίαν καί ἄσχετον· οὐδενί γάρ λόγῳ ἤ νοήματι καί πράγματι ἔχει τό Θεῖον τήν πρός τά ὄντα σχέσιν τε καί κοινωνίαν, ἀλλ' ἔστι πάντῃ καί κατά πάντα ὑπερηρμένον, μόνῳ τῷ συνέχειν καί προνοεῖσθαι τούτων ἐφαπτόμενον, ὡς ἄν τις εἴποι. Τά δέ ἑξῆς ὑποδείγματα πιστωτικά τοῦ λόγου τοῦ εἶναι πάντα ἐκ Θεοῦ, ὡς αἰτίου τῆς τούτων ὑπάρξεως, ἄλλο παρά ταῦτα ὑπάρχοντος καί ἐν ἑαυτῷ συνεστάναι ἄλλῳ παρά ταῦτα ὑπάρχοντι.

Καί ἔχει πάντα ἀριθμόν: Ὁ γάρ ἀριθμός ἐκ πολλῶν μονάδων συντιθεμένων εἰς μέγεθος παραύξει· ἡ οὖν μονάς, ὡς αἰτία ἀριθμῶν, ἑνοειδῶς τούς πάντας περιείληφεν ἀριθμούς· οὕτω καί τό κέντρον, ἤτοι σημεῖον, τάς ἐπί τόν κύκλον εὐθείας περιέχει.