§1.2.22Ὅταν δʼ ἀντιστρέφῃ τὰ ἄκρα, ἀνάγκη καὶ τὸ μέσον ἀντιστρέφειν πρὸς ἄμφω.
When the extremes convert, it is necessary that the middle also converts with respect to both.
εἰ γὰρ τὸ Α κατὰ τοῦ Γ διὰ τοῦ Β ὑπάρχει, εἰ ἀντιστρέφει καὶ ὑπάρχει, ὧ τὸ Α, παντὶ τὸ Γ, καὶ τὸ Β τῷ ἀντιστρέψει καὶ ὑπάρξει, ὧ τὸ Α, παντὶ τὸ Β διὰ μέσου τοῦ Γ·
For if A belongs to Γ through B, if they convert and Γ belongs to everything to which A belongs, then B also will convert with [A], and B will belong to everything to which A belongs, through Γ as middle; and Γ will convert with B through A as middle.
καὶ τὸ Γ τῷ Β ἀντιστρέψει διὰ μέσου τοῦ Α. καὶ ἐπὶ τοῦ μὴ ὑπάρχειν ὡσαύτως, οἷον εἰ τὸ Β τῷ Γ ὑπάρχει, τῷ δὲ Β τὸ οὐχ ὑπάρχει, οὐδὲ τὸ τῷ Γ οὐχ ὑπάρξει.
And similarly in the case of not belonging, as for instance if B belongs to Γ, but [A] does not belong to B, neither will [A] belong to Γ.
εἰ δὴ τὸ Β τῷ ἀντιστρέφει, καὶ τὸ Γ τῷ Α ἀντιστρέψει.
So if B converts with [A], Γ also will convert with A.
ἔστω γὰρ τὸ Β μὴ ὑπάρχον· τῷ Α· οὐδʼ ἄρα τὸ Γ·
For let B not belong to A; then neither will Γ belong to it; for B belonged to every Γ.
παντὶ γὰρ τῷ Γ τὸ Β ὑπῆρχει καὶ εἰ τῷ Β τὸ Γ ἀντιστρέφει, καὶ τὸ Α ἀντιστρέψει·
And if Γ converts with B, A also will convert; for to whatever B belongs, Γ also belongs.
καθʼ οὗ γὰρ ἅπαντος τὸ Β, καὶ τὸ Γ. καί εἰ τὸ Γ καὶ πρὸς τὸ ἀντιστρέφει, καὶ τὸ Β ἀντιστρέφει.
And if Γ also converts with [A], B also converts.
ὧ γὰρ τὸ Β, τὸ ᾧ δὲ τὸ Α, τὸ Γ οὐχ ὑπάρχει.
For to whatever B belongs, [Γ] belongs; and to whatever A belongs, Γ does not belong.
καὶ μόνον τοῦτο ἀπὸ τοῦ συμπεράσματος ἄρχεται, τὰ δʼ ἄλλα οὐχ ὁμοίως καὶ ἐπὶ τοῦ κατηγορικοῦ συλλογισμοῦ.
And only this starts from the conclusion, while the others are not in the same way as in the case of the affirmative syllogism.
Πάλιν εἰ τὸ καὶ τὸ Β ἀντιστρέφει, καὶ τὸ Γ καὶ τὸ Δ ὡσαύτως, ἀπόντι δʼ ἀνάγκη τὸ ἢ τὸ Γ ὑπάρχειν, καὶ τὸ Β καὶ Δ οὕτως ἔξει ὥστε παντὶ θάτερον ὑπάρχειν.
Again, if [A] and B convert, and Γ and Δ likewise, and if in everything [A] or Γ must belong, then B and Δ also will be so related that one of them belongs to everything.
ἐπεὶ γὰρ ᾧ τὸ Α, τὸ Β, καὶ ᾧ τὸ Γ, τὸ Δ, παντὶ δὲ τὸ ἢ τὸ Γ καὶ οὐχ ἅμα, φανερὸν ὅτι καὶ τὸ Β ἢ τὸ Δ παντὶ καὶ οὐχ ἅμα· δύο γάρ συλλογισμοὶ σύγκεινται.
For since B belongs to whatever A belongs, and Δ to whatever Γ belongs, and either [A] or Γ belongs to everything (and not both together), it is clear that either B or Δ belongs to everything (and not both together); for two syllogisms are combined.
πάλιν εἰ παντὶ μὲν τὸ Α ἢ τὸ Β καὶ τὸ Γ ἢ τὸ Δ, ἅμα δὲ μὴ ὑπάρχει, εἰ ἀντιστρέφει τὸ καὶ τὸ Γ, καὶ τὸ Β καὶ τὸ Δ ἀντιστρέφει.
Again, if either A or B belongs to everything, and either Γ or Δ likewise, but they do not belong together, and if [A] and Γ convert, then B and Δ also convert.
εἰ γὰρ τινὶ μὴ ὑπάρχει τὸ Β, ᾧ τὸ Δ, δῆλον ὅτι τὸ Α ὑπάρχει.
For if B does not belong to something to which Δ belongs, it is clear that A belongs to it.
εἰ δὲ τὸ Α, καὶ τὸ Γ·
But if A belongs, Γ also belongs; for they convert.
ἀντιστρέφει γάρ. ὥστε ἅμα τὸ Γ καὶ τὸ Δ. τοῦτο δʼ ἀδύνατον.
Thus Γ and Δ will belong together; but this is impossible.
οἶον εἰ τὸ ἀγένητον ἄφθαρτον καὶ τὸ ἄφθαρτον ἀγένητον, ἀνάγκη τὸ γένομενον φθαρτὸν καὶ τὸ φθαρτόν γεγονέναι.
As, for example, if the ungenerated is incorruptible and the incorruptible is ungenerated, it is necessary that the generated is corruptible and the corruptible is generated.
Ὅταν δὲ τὸ Α ὅλῳ τῷ Β καὶ τῷ Γ ὑπάρχῃ καὶ μηδενὸς ἄλλου κατηγορῆται, ὑπάρχῃ δὲ καὶ τὸ Β παντὶ τῷ Γ, ἀνάγκη τὸ καὶ Β ἀντιστρέφειν·
But when A belongs to the whole of B and of Γ, and is predicated of nothing else, and B also belongs to every Γ, it is necessary that [A] and B convert.
ἐπεὶ γὰρ κατὰ μόνων τῶν Β Γ λέγεται τὸ Α, κατηγορεῖται δὲ τὸ Β καὶ αὐτὸ αὑτοῦ καὶ τοῦ Γ, φανερὸν ὅτι καθʼ ὧν τὸ Α, καὶ τὸ Β λεχθήσεται πάντων πλὴν αὐτοῦ τοῦ Α. πάλιν ὅταν τὸ Α καὶ τὸ Β ὅλῳ τῷ Γ ὑπάρχῃ, ἀντιστρέφῃ δὲ τὸ Γ τῷ Β, ἀνάγκη τὸ Α παντὶ τῷ Β ὑπάρχειν·
For since A is said of B and Γ alone, and B is predicated both of itself and of Γ, it is clear that of whatever A is said, B also will be said, of all of them except A itself. Again, when A and B belong to the whole of Γ, and Γ converts with B, it is necessary that A belongs to every B.
ἐπεὶ γὰρ παντὶ τῷ Γ τὸ Α, τὸ δὲ Γ τῷ Β διὰ τὸ ἀντιστρέφειν, καὶ τὸ παντὶ τῷ Β.
Ὅταν δὲ δυοῖν ὄντοιν τὸ Α τοῦ Β αἱρετώτερον ᾖ, ὄντων ἀντικειμένων, καὶ τὸ Δ τοῦ Γ ὡσαύτως, εἰ αἱρετώτερα τὰ Α Γ γῶν Β Δ, τὸ Α τοῦ Δ αἱρετώτερον.
For since A belongs to every Γ, and Γ to B because they convert, [A] also belongs to every B. But when, there being two things, A is more desirable than B (they being opposites), and Δ likewise than Γ, if A and Γ are more desirable than B and Δ, A is more desirable than Δ.
ὁμοίως γὰρ διωκτὸν τὸ Α καὶ φευκτὸν τὸ Β (ἀντικείμενα γάρ), καὶ τὸ Γ τῷ Δ (καὶ γὰρ ταῦτα ἀντίκειται).
For A is to be pursued in the same way as B is to be avoided (for they are opposites), and Γ likewise to Δ (for these too are opposites).
εἰ οὖν τὸ Α τῷ Δ ὁμοίως αἱρετόν, καὶ τὸ Β τῷ Γ φευκτόν· ἑκάτερον γὰρ ἑκατέρῳ ὁμοίως, φευκτὸν διωκτῷ.
If therefore A is equally desirable to Δ, B is also equally to be avoided to Γ; for each is similarly related to each, the to-be-avoided to the to-be-pursued.
ὥστε καὶ τὰ ἄμφω τὰ Γ τοῖς Β Δ. ἐπεὶ δὲ μᾶλλον, οὐχ οἷόν τε ὁμοίως·
So that both [A] and Γ would be similarly related to B and Δ.
καὶ γὰρ ἄν τὰ Β Δ ὁμοίως ἦσαν.
But since they are more desirable, they cannot be equally so; for then B and Δ would also be equal.
εἰ δὲ τὸ Δ τοῦ αἱρετώτερον, καὶ τὸ Β τοῦ Γ ἧττον φευκτόν· τὸ γὰρ ἔλαττον τῷ ἐλάττονι ἀντίκειται.
And if Δ is more desirable than [A], B is also less to be avoided than Γ; for the lesser is opposite to the lesser.
αἱρετώτερον δὲ τὸ μεῖζον ἀγαθὸν καὶ ἔλαττον κακὸν ἢ τὸ ἔλαττον ἀγαθὸν καὶ μεῖζον κακόν· καὶ τὸ ἅπαν ἄρα, τὸ Β Δ, αἱρετώτερον τοῦ Α Γ νῦν δʼ οὐκ ἔστιν.
But the greater good and lesser evil is more desirable than the lesser good and greater evil; therefore the whole, B and Δ, would be more desirable than A and Γ; but in fact it is not.
τὸ Α ἄρα αἱρετώτερον τοῦ Δ, καὶ τὸ Γ ἄρα τοῦ Β ἧττον φευκτόν.
Therefore A is more desirable than Δ, and Γ is therefore less to be avoided than B.
εἰ δὴ ἕλοιτο πᾶς ὁ ἐρῶν κατὰ τὸν ἔρωτα τὸ Α τὸ οὕτως ἔχειν ὥστε χαρίζεσθαι, καὶ τὸ μὴ χαρίζεσθαι τὸ ἐφʼ οὗ Γ, ἢ τὸ χαρίζεσθαι τὸ ἐφʼ οὗ Δ, καὶ τὸ μὴ τοιοῦτον εἶναι οἷον χαρίζεσθαι τὸ ἐφʼ οὗ Β, δῆλον ὅτι τὸ Α τὸ τοιοῦτον εἶναι αἱρετίώτερόν ἐστιν ἢ τὸ χαρίζεσθαι.
If then indeed every lover, according to his love, would choose A, namely, to be of such a character as to be granted favors, and [prefer] A to Γ, which is not being granted favors, or Δ, which is granting favors, to B, which is not being of such a character as to grant favors, it is clear that A, being of such a character, is more desirable than granting favors.
τὸ ἄρα φιλεῖσθαι τῆς συνουσίας αἱρετώτερον κατὰ τὸν ἔρωτα.
Therefore, in love, being loved is more desirable than sexual association.
μᾶλλον ἄρα ὁ ἔρως ἐστὶ τῆς φιλίας ἢ τοῦ συνεῖναι.
Love, therefore, is more a matter of friendship than of being together.
εἰ δὲ μάλιστα τούτου, καὶ τέλος τοῦτο.
And if it is most of all of this, then this is also the end.
τὸ ἄρα συνεῖναι ἢ οὐκ ἔστιν ὅλως ἢ τοῦ φιλεῖσθαι ἕνεκεν· καὶ γὰρ αἱ ἄλλαι ἐπιθυμίαι καὶ τέχναι οὕτως.
Therefore, being together either does not exist at all or is for the sake of being loved; for indeed other desires and arts are so.