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that which is turned, or changed, or lacking in form, cannot be perfect in itself. And that which is not perfect in itself, will certainly be in need of another, which provides it with perfection, and such a thing is perfect, but not perfect in itself, because it does not have perfection by nature, but by participation. But that which is in need of another for its perfection will be in much greater need for its very being. For if, as they say, substance is superior to form, and if that being which they wish to affirm was able to provide this for itself or simply to have it, how was it not sufficient to simply have or provide for itself the lesser thing, I mean the form? But if that being—which those who dare to attribute the unoriginated to things that are after God and from God wish to call either substance or matter (for we are not disputing about this)—was not sufficient to provide the lesser thing for itself, or simply to have it, how was it able to have the greater thing, I mean being itself, either simply or from itself, when it was unable to have the lesser? But if matter was in no way able to have the lesser thing from itself or simply, much more (1184) will it be unable to have being itself simply, or in any way from itself. Therefore, having proven weak with respect to having the lesser, I mean the form, as has been shown, it could never in any way be able to have the greater, I mean being itself. But if this is so, then both being and form have certainly been given by God to things that exist, since they do exist; and if every substance, both all matter and form, is from God, no one, unless entirely deprived of sound reasoning, would endure to say that matter is without beginning or unbegotten, knowing God to be the maker and creator of existing things.

A demonstration that everything that is moved, or that is co-contemplated from eternity with another that is different in substance, cannot be infinite, and that the dyad is neither a principle nor without principle, and that the monad alone is properly a principle and without principle.

And again, if matter was, as some say, it clearly has not come into being, and if it has not come into being, neither is it moved, and if it is not moved, it did not begin to be, and if it did not begin to be, it is certainly without beginning, and if without beginning, also infinite, and if infinite, certainly also unmoved (for the infinite is certainly unmoved, for that which is not defined has nowhere to be moved), and if this is so, there are certainly two infinites, without beginning and unmoved, God and matter, which is impossible. For a dyad will be able to be neither infinite, nor without beginning, nor unmoved, nor not a principle of anything at all, being circumscribed by union and division, by union, as having for its existence the composition of monads, by which it is contained as by parts and into which it can be cut as parts (and nothing divisible or divided, or composite or composed, by nature or by position or in any other conceivable way, nor even division or composition itself, simply so called, will be able to be infinite, because it is not also simple and alone, and not numerable or numbered or co-numbered, or simply free from any relation whatsoever; for all these things are considered in relation, but the infinite is without relation, for it has nothing at all joined to it by relation), and by division, as being moved by number, from which it began and by which it is contained, since it does not have its being by nature and without relation. For every dyad and every monad contributing to it as a part exists by number, according to which the monads within it deprive one another of the uncircumscribed. But no one who has any share whatsoever in reasoning would say that anything is infinite with which something different in substance is co-contemplated or co-observed from eternity, knowing that the argument concerning the infinite will certainly fall apart for one who thinks thus. For the infinite is infinite in every respect, reason, and manner, in substance, in power, in activity, in both

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τρεπόμενον, ἤ ἀλλοιούμενον, ἤ ἐλλιπές εἴδους, αὐτοτελές εἶναι οὐ δύναται. Τό δέ μή ὄν αὐτοτελές, ἑτέρου πάντως προσδεηθήσεται, τοῦ παρέχοντος αὐτῷ τήν τελειότητα, καί ἔστι τέλειον μέν τό τοιοῦτον, ἀλλ᾿ οὐκ αὐτοτελές, διά τό μή φύσει, μεθέξει δέ τό τέλειον ἔχειν. Τό δέ ἑτέρου προσδεόμενον πρός τελείωσιν καί πρός αὐτό τό εἶναι πολλῷ μᾶλλον προσδεηθήσεται. Εἰ γάρ εἴδους κρείττων, ὥς φασιν, ἡ οὐσία καθέστηκε, ταύτην δέ ἑαυτῷ παρασχεῖν ἤ ἁπλῶς ἔχειν δεδύνηται ἐκεῖνο τό ὄν, ὅπερ αὐτοί φάναι βούλονται, πῶς πρός τό ἔχειν ἁπλῶς ἤ παρασχεῖν ἑαυτῷ τό ἦττον, φημί δέ τό εἶδος, οὐκ ἐπήρκεσε; Εἰ δέ πρός τό παρασχεῖν ἑαυτῷ τό ἦττον, ἤ ἁπλῶς ἔχειν ἐκεῖνο τό ὄν, ὅπερ εἴ τε οὐσίαν, εἴ τε ὕλην καλεῖν βούλονται οἱ τό ἄναρχον τοῖς μετά Θεόν καί ἐκ Θεοῦ προσάπτειν τολμῶντες (οὐ γάρ περί τούτου διαφερόμεθα ) οὐκ ἐπήρκεσε, πῶς τό κρεῖττον, αὐτό τό εἶναί φημι, ἤ ἁπλῶς ἤ παρ᾿ ἑαυτοῦ ἔχειν δεδύνηται, τό πρός τό ἔχειν τό ἦττον ἀδυνατῆσαν; Εἰ δέ παρ᾿ ἑαυτῆς ἤ ἁπλῶς ἔχειν τό ἦττον οὐδαμῶς ἡ ὕλη δεδύνηται, πολλῷ μᾶλλον (1184) αὐτό τό εἶναι ἁπλῶς, ἤ πῶς παρ᾿ ἑαυτῆς ἔχειν οὐ δυνηθήσεται. Ἅρ᾿ οὖν ἡ πρός τό ἔχειν, ὡς δέδεικται, τό ἦττον, λέγω δέ τό εἶδος, ἀτονήσασα οὐδέ τό κρεῖττον, αὐτό τό εἶναί φημι, κἄν ὁπωσοῦν ἔχειν δυνηθείη ποτέ. Εἰ δέ τοῦτο, πάντως ἐκ Θεοῦ τό εἶναι τοῖς οὖσι καί τό εἶδος δεδώρηται, ἐπείπερ εἰσίν· εἰ δέ ἐκ Θεοῦ πᾶσα οὐσία, καί ὕλη καί εἶδος ἅπαν ἐστίν, οὐδείς ἄν μή πάντη σώφρονος λογισμοῦ ἐστερημένος εἰπεῖν ἀνάσχοιτο ἄναρχον ἤ ἀγένητον τήν ὕλην, Θεόν εἰδώς τῶν ὄντων ποιητήν καί δημιουργόν.

Ἀπόδειξις ὅτι πᾶν κινούμενον, ἤ ἄλλῳ διαφόρῳ κατά τήν οὐσίαν ἐξ ἀϊδίου συνθεωρούμενον, ἄπειρον εἶναι οὐ δύναται, καί ὅτι ἡ δυάς οὔτε ἀρχή ἐστιν, οὔτε ἄναρχος, καί ὅτι ἡ μονάς μόνη κυρίως ἀρχή καί ἄναρχος.

Καί πάλιν, εἰ ἦν, ὥς τινές φασιν, ἡ ὕλη, οὐ γέγονε δηλονότι, εἰ δέ μή γέγονεν, οὐδέ κινεῖται, εἰ δέ μή κινεῖται, οὔτε τοῦ εἶναι ἤρξατο, εἰ δέ τοῦ εἶναι μή ἤρξατο, πάντως ἄναρχον, εἰ δέ ἄναρχον, καί ἄπειρον, εἰ δέ ἄπειρον, πάντως καί ἀκίνητον (ἀκίνητον γάρ πάντως τό ἄπειρον, οὐ γάρ ἔχει ποῦ κινηθῆναι τό μή ὁριζόμενον), εἰ δέ τοῦτο, δύο πάντως τά ἄπειρα καί ἄναρχα καί ἀκίνητα, Θεός καί ὕλη, ὅπερ εἶναι ἀμήχανον. ∆υάς γάρ οὔτε ἄπειρος, οὔτε ἄναρχος, οὔτε ἀκίνητος, οὔτε μή ἀρχή καθόλου τινός εἶναι δυνήσεται, καθ᾿ ἕνωσίν τε καί διαίρεσιν περιγραφομένη, καθ᾿ ἕνωσιν μέν ὡς ὕπαρξιν ἔχουσα τῶν μονάδων τήν σύνθεσιν, ὑφ᾿ ὧν ὡς μερῶν περιέχεται καί εἰς ἅς ὡς μέρη τέμνεσθαι δύναται (οὐδέν δέ διαιρετόν ἤ διαιρούμενον, ἤ σύνθετον ἤ συντιθέμενον, κατά φύσιν ἤ θέσιν ἤ ἄλλον τινά ἐπινοηθῆναι δυνάμενον τρόπον, ἀλλ᾿ οὐδέ αὐτή ἡ ἁπλῶς λεγομένη διαίρεσις ἤ σύνθεσις, ἄπειρον εἶναι δυνήσεται, ὅτι μή καί ἁπλοῦν καί μόνον, καί μή ἀριθμητόν ἤ ἀριθμούμενον ἤ συναριθμούμενον, ἤ πάσης ἁπλῶς ἐλεύθερον τῆς οἱασδήποτε σχέσεως· πάντα γάρ ταῦτα ἐν σχέσει θεωρεῖται, τό δέ ἄπειρον ἄσχετον, οὐ γάρ ἔχει τι κατά σχέσιν συνημμένον παντάπασι), κατά διαίρεσιν δέ ὡς ἀριθμῷ κινουμένη, ἐξ οὗπερ ἤρξατό τε καί ὑφ᾿ οὗ περιέχεται, ἐπείπερ οὐ φύσει τό εἶναι καί ἄσχετον ἔχει. Ἀριθμῷ γάρ πᾶσα δυάς καί πᾶσα μονάς εἰς μέρος αὐτῆς συντελοῦσα εἶναι καθέστηκε, καθ᾿ ὅν ἀλλήλων αἱ κατ᾿ αὐτήν μονάδες, ἀφαιροῦνται τό ἀπερίγραφον. Οὐδείς δέ μεμοιραμένος καί ὁπωσοῦν τοῦ λογίζεσθαι εἴποι ἄν ἄπειρον εἶναι ᾧ ἐξ ἀϊδίου συνθεωρεῖταί τι ἤ συνεπιθεωρεῖται κατ᾿ οὐσίαν διάφορον, εἰδώς διαπεσεῖσθαι πάντως αὐτῷ τόν περί τοῦ ἀπείρου λόγον οὕτω φρονοῦντι. Τό γάρ ἄπειρον κατά πάντα καί λόγον καί τρόπον ἐστίν ἄπειρον, κατ᾿ οὐσίαν, κατά δύναμιν, κατ᾿ ἐνέργειαν, κατ᾿ ἄμφω