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A brief treatise on difference, through which is shown that the quantity according to essence of the united things is preserved.

If, therefore, after the union in Christ the difference according to essence of the parts from which He was composed with respect to one another is preserved, there is a clear proof for the pious that the quantity according to essence of the united things has remained undiminished after the union, preserving the unconfused definition and principle of the essence of each part with respect to the other in the whole composed from them. And if the hypostatic identity of the whole to its own parts, or rather, to speak more clearly, of the parts to one another in the composition of the whole from them, is preserved; it is clear that in no way do the parts, in the one hypostasis completed from them, differ completely from one another. And therefore, there is no argument able to show either the essentially different being confused, or the hypostatically single being divided.

A broader and more natural exposition concerning difference and quantity, and of the number that indicates them

Therefore, if we speak of a difference in Christ after the union, and with every difference quantity is by all means necessarily co-introduced by nature, of which we recognize number to be indicative, reasonably employing number for the sole indication of the difference of the differing things after the union, we do not by number divide the things signified at all, but we indicate the preserved existence of the united things; because every number is by nature indicative of quantity alone, and not divisive. For that which neither acts nor is acted upon, how could it be the cause of any relation whatsoever? since to act belongs to substance alone; just as to be acted upon belongs to accident, that is, to quality; from which being is, and from which, the practitioners of such arguments say, relations proceed. But to us who examine more precisely, relations are not the work of these things, I mean of substance and of accident, but of the productive cause and power of all things, which has placed in each of the created things a constitutive principle of being, and one that represents the natural affinity and alienation with respect to one another. And if relations do not properly have substance as their productive cause, much less would number; which, insofar as it is not a substance, cannot act at all; and insofar as it is not an accident, that is, a quality, it is not its nature to be acted upon. If then number is by nature neither to act nor to be acted upon, then it is a sign indicative of quantity, making no emphasis (564) of the relation in the quantity indicated; because it is not a genus, able to be predicated of others; but a sign, as I said, emphatic of the genus that is categorically predicated of others.

And if number has neither the capacity to act nor to be acted upon, it is clear that insofar as it does not act, it is not indicative of any relation whatsoever, that is, of union or of division; for this, as I said, belongs to another principle; and insofar as it is not its nature to be acted upon, it is not divided. For in itself every number is indivisible, not admitting motion according to alteration, which is proper to quality; nor contraction and expansion, which is proper to substance; nor indeed increase and decrease, which is proper to quantity. If then of quantity, but not of relation; for number is significant only of quantity spoken of simply, but not of quantity spoken of in a certain way; it is clear that number is by nature able to effect neither division nor union, but only the indication of quantity, so that we may conceive of it as existing. For to act, as I said, belongs to substance, and of accident, that is

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Περί διαφορᾶς διάληψις σύντομος, δι᾿ ἧς δείκνυται τό κατ᾿ οὐσίαν ποσόν τῶν ἡνωμένων σωζόμενον.

Εἰ τοίνυν σώζεται μετά τήν ἕνωσιν ἐν Χριστῷ τῶν ἐξ ὧν συνετέθη μερῶν ἡ πρός ἄλληλα κατά τήν οὐσίαν διαφορά, σαφής ὑπάρχει τοῖς εὐσεβοῦσιν ἀπόδειξις, ὡς τό κατ᾿ οὐσίαν ποσόν μεμένηκε τῶν ἡνωμένων ἀμείωτον μετά τήν ἕνωσιν, τόν ἑκατέρου μέρους πρός θάτερον ἐν τῷ κατά σύνθεσιν ἐξ αὐτῶν ὅλῳ διασῶζον τῆς οὐσίας ὅρον τε καί λόγον ἀσύμπτωτον. Εἰ δέ καί ἡ τοῦ ὅλου πρός τά οἰκεῖα μέρη, μᾶλλον δέ φάναι σαφέστερον, ἡ πρός ἄλληλα τῶν μερῶν κατά τήν ἐξ αὐτῶν ὅλου σύνθεσιν ὑποστατική διασώζεται ταυτότης· δῆλον ὡς οὐδενί τρόπῳ τά μέρη κατά τήν ἐξ αὐτῶν συμπληρουμένην μίαν ὑπόστασιν, πρός ἄλληλα παντελῶς διαφέρουσι. Καί λοιπόν οὐδείς ἐστι λόγος δεῖξαι δυνάμενος, ἤ τό κατ᾿ οὐσίαν διάφορον συγχεόμενον, ἤ τό καθ᾿ ὑπόστασιν μοναδικόν διαιρούμενον.

Κατασκευή πλατυτέρα τε καί φυσικωτέρα περί διαφορᾶς καί ποσότητος, καί τοῦ δηλοῦντος αὐτάς ἀριθμοῦ

Οὐκοῦν εἴπερ διαφοράν ἐπί Χριστοῦ μετά τήν ἕνωσιν λέγομεν, πάσῃ δέ πάντως ἐξ ἀνάγκης διαφορᾷ συνεισάγεσθαι πέφυκε ποσόν, οὗ δηλωτικόν τόν ἀριθμόν εἶναι γνωρίζομεν, εἰκότως πρός δήλωσιν μόνην τῆς τῶν διαφερόντων διαφορᾶς μετά τήν ἕνωσιν τόν ἀριθμόν παραλαμβάνοντες, οὐ διαιροῦμεν τῷ ἀριθμῷ τά σημαινόμενα παντελῶς, ἀλλά δηλοῦμεν σωζομένην τῶν ἡνωμένων τήν ὕπαρξιν· ὅτι καί μόνου ποσοῦ δηλωτικός πᾶς εἶναι πέφυκεν ἀριθμός, ἀλλ᾿ οὐ διαιρετικός. Τό γάρ μή ποιοῦν ἤ πάσχον, πῶς ἄν εἴη τῆς οἱανοῦν σχέσεως κύριον; ἐπειδή μόνης οὐσίας ἐστί τό μέν ποιεῖν· ὥσπερ καί τό πάσχειν συμβεβηκότος ἤγουν ποιότητος· ἀφ᾿ ὧν εἶναι, καί ἐξ ὧν τάς σχέσεις, οἱ τῶν τοιούτων γυμνασταί λόγων προϊέναι φασίν. Μᾶλλον δέ σκοποῦσιν ἡμῖν ἀκριβέστερον, οὐδέ τούτων, οὐσίας τέ φημι καί συμβεβηκότος, καθεστήκασιν ἔργον αἱ σχέσεις, ἀλλά τῆς πάντων ποιητικῆς αἰτίας τε καί δυνάμεως, καί λόγον ἐνθεμένης ἑκάστῳ τῶν γεγονότων τοῦ εἶναι συστατικόν, καί τῆς πρός ἄλληλα φυσικῆς παραστατικόν οἰκειώσεώς τε καί ἀλλοτριώσεως. Εἰ δέ κυρίως αἱ σχέσεις οὐκ ἔχουσιν αἰτίαν ποιητικήν ἑαυτῶν τήν οὐσίαν, σχολῇ γ᾿ ἄν τόν ἀριθμόν· ὅς καθό μέν οὐκ ἔστιν οὐσία, ποιεῖν οὐ δύναται παντελῶς· καθό δέ συμβεβηκός, ἤγουν ποιότης οὐκ ἔστιν, πάσχειν οὐ πέφηκεν. Εἰ δέ μήτε ποιεῖν, μήτε πάσχειν ὁ ἀριθμός πέφυκεν, ἄρα σημεῖόν ἐστι ποσοῦ δηλωτικόν, τῆς ἐν τῷ δηλουμένῳ ποσῷ σχέσεως οὐδεμίαν ποιούμενος (564) ἔμφασιν· ὅτι μή γένος ἐστίν, ἄλλων κατηγορεῖσθαι δυνάμενος· ἀλλά σημεῖον, ὡς ἔφην, τοῦ κατ᾿ ἄλλων κατηγορικῶς φερομένου γένους ἐμφατικόν.

Εἰ δέ μή τό τε ποιεῖν, μήτε πάσχειν ὁ ἀριθμός ἔχει, δῆλόν ἐστιν, ὅτι καθό μέν οὐ ποιεῖ, σχέσεως τῆς οἱασοῦν οὐκ ἔστι δηλωτικός, τουτέστιν ἑνώσεως ἤ διαιρέσεως· ἑτέρου γάρ, ὡς ἔφην, λόγου τοῦτο καθέστηκε· καθό δέ πάσχειν οὐ πέφυκεν, οὐ διαιρεῖται. Καθ᾿ ἑαυτόν γάρ ἀδιαίρετός ἐστι πᾶς ἀριθμός, τήν κατ᾿ ἀλλοίωσιν οὐκ ἐπιδεχόμενος κίνησιν, ὅπερ ἴδιον ὑπάρχει ποιότητος· οὔτε συστολήν καί διαστολήν, ὅπερ ἴδιον οὐσίας καθέστηκεν· οὔτε μήν αὔξησιν καί μείωσιν, ὅπερ ἴδιόν ἐστι ποσότητος. Εἰ δέ ποσότητος, ἀλλ᾿ οὐ σχέσεως· μόνης γάρ τῆς ἁπλῶς, ἀλλ᾿ οὐ τῆς πῶς λεγομένης ποσότητος, ὁ ἀριθμός ὑπάρχει σημαντικός· δῆλον ὡς οὔτε διαίρεσιν, οὔτε μήν ἕνωσν ὁ ἀριθμός ποιεῖν πέφυκεν, ἀλλά μόνην ποσότητος δήλωσιν, ὡς δ᾿ ἄν ταύτην ὑπάρχουσαν ἐννοήσωμεν. Οὐσίας γάρ, ὡς ἔφην, ἐστί τό ποιεῖν, καί συμβεβηκότος ἤγουν