§1.1.45#1Ὅσα δʼ ἐν πλείοσι σχήμασι δείκνυται τῶν προβλημάτων, ἢν ἐν θατέρῳ συλλογισθῇ, ἔστιν ἀναγαγεῖν τὸν συλλογισμὸν εἰς θάτερον, οἷον τὸν ἐν τῷ πρώτῳ στερητικὸν εἰς τὸ δεύτερον, καὶ τὸν ἐν τῷ μέσῳ εἰς τὸ πρῶτον, οὐχ ἅπαντας δὲ ἀλλʼ ἐνίους.
Of those problems that are demonstrated in more than one figure, if a syllogism is formed in one of them, it is possible to reduce the syllogism to the other, for example, the negative syllogism in the first figure to the second, and the one in the middle figure to the first, though not all of them but some.
ἔσται δὲ φανερὸν ἐν τοῖς ἑπομένοις.
This will be clear in what follows.
εἰ γὰρ τὸ Α μηδενὶ τῷ Β, τὸ δὲ Β παντὶ τῷ Γ, τὸ Α οὐδενὶ τῷ Γ. οὕτω μὲν οὖν τὸ πρῶτον·
For if A belongs to no B, and B to all C, A belongs to no C.
σχῆμα, ἐὰν δʼ ἀντιστραφῇ τὸ στερητικόν, τὸ μέσον ἔσται· τὸ γὰρ Β τῷ μὲν οὐδενί, τῷ δὲ Γ παντὶ ὑπάρχει.
This is the first figure; but if the negative premise is converted, there will be the middle figure, for B belongs to no A, and to all C.
ὁμοίως δὲ καὶ εἰ μὴ καθόλου ἀλλʼ ἐν μέρει ὁ συλλογισμός, οἷον εἰ τὸ μὲν Α μηδενὶ τῷ Β, τὸ δὲ Β τινὶ τῷ Γ· ἀντιστραφέντος γὰρ τοῦ στερητικοῦ τὸ μέσον ἔσται σχῆμα.
Similarly also if the syllogism is not universal but particular, as for example if A belongs to no B, and B to some C; for when the negative is converted there will be the middle figure.
Τῶν δʼ ἐν τῷ δευτέρῳ συλλογισμῶν οἱ μὲν καθόλου ἀναχθήσονται εἰς τὸ πρῶτον, τῶν δʼ ἐν μέρει ἅτερος μόνος.
Of the syllogisms in the second figure, the universal ones will be reduced to the first, but of the particular ones only one of the two.
ἔστω γὰρ τὸ τῷ μὲν Β μηδενὶ τῷ δὲ Γ παντὶ ὑπάρχονἀν.
For let A belong to no B and to all C.
τιστραφέντος οὖν τοῦ στερητικοῦ τὸ πρῶτον ἔσται σχῆμα· τὸ μὲν γὰρ Β οὐδενὶ τῷ Α, τὸ δὲ Α παντὶ τῷ Γ ὑπάρξει.
When the negative is converted, then, there will be the first figure; for B will belong to no A, and A to all C.
ἐὰν δὲ τὸ κατηγορικὸν ᾖ πρὸς τῷ Β, τὸ δὲ στερητικὸν πρὸς τῷ πρῶτον ὅρον θετέον τὸ Γ· τοῦτο γὰρ οὐδενὶ τῷ Α, τὸ δὲ Α παντὶ τῷ Β ὥστʼ οὐδενὶ τῷ Β τὸ Γ. οὐδ᾿ ἄρα τὸ Β τῷ Γ οὐδενί·
But if the affirmative is at B, and the negative at C, we must posit C as the first term; for this belongs to no A, and A to all B, so that C belongs to no B.
ἀντιστρέφει γὰρ τὸ στερητικόν.
Therefore neither does B belong to any C; for the negative converts.
ἐὰν δʼ ἐν μέρει ᾖ ὁ συλλογισμός, ὅταν μὲν ᾖ τὸ στερητικὸν πρὸς τῷ μείζονι ἄκρῳ, ἀναχθήσεται εἰς τὸ πρῶτον, οἷον εἰ τὸ Α μηδενὶ τῷ Β, τῷ δὲ Γ τινί· ἀντιστραφέντος γὰρ τοῦ στερητικοῦ τὸ πρῶτον ἔσται σχῆμα· τὸ μὲν γὰρ Β οὐδενὶ τῷ Α, τὸ δὲ Α τινὶ τῷ Γ. ὅταν δὲ τὸ κατηγορικόν, οὐκ ἀναλυθήσεται, οἷον εἰ τὸ Α τῷ μὲν Β παντί, τῷ δὲ Γ οὐ παντί· οὔτε γὰρ δέχεται ἀντιστροφὴν τὸ Β, οὔτε γενομένης ἔσται συλλογισμός.
But if the syllogism is particular, when the negative is at the major extreme, it will be reduced to the first figure, for example, if A belongs to no B, and to some C; for when the negative is converted there will be the first figure; for B belongs to no A, and A to some C. But when the affirmative is at the major extreme, it will not be analyzed, as for example if A belongs to all B, and not to all C; for neither does B admit of conversion, nor if it did would there be a syllogism.
Πάλιν οἱ μὲν ἐν τῷ τρίτῳ σχήματι οὐκ ἀναλυθήσονται πάντες εἰς τὸ πρῶτον, οἱ δʼ ἐν τῷ πρώτῳ πάντες εἰς τὸ τρίτον.
Again, the syllogisms in the third figure will not all be analyzed into the first, but those in the first will all be analyzed into the third.
ὑπαρχέτω γὰρ τὸ Α παντὶ τῷ Β, τὸ δὲ Β τινὶ τῷ Γ. οὐκοῦν ἐπειδὴ ἀντιστρέφει τὸ ἐν μέρει κατηγορικόν, ὑπάρξει τὸ Γ τινὶ τῷ Β· τὸ δὲ Α παντὶ ὑπῆρχεν, ὥστε γίνεται τὸ τρίτον σχῆμα.
For let A belong to all B, and B to some C. Since, then, the particular affirmative converts, C will belong to some B; and A belonged to all B, so that the third figure is produced.
καὶ εἰ στερητικὸς ὁ συλλογισμός, ὡσαύτως· ἀντιστρέφει γὰρ τὸ ἐν μέρει κατηγορικόν, ὥστε τὸ μὲν Α οὐδενὶ τῷ Β, τὸ δὲ Γ τινὶ ὑπάρξει.
And if the syllogism is negative, it is likewise; for the particular affirmative converts, so that A will belong to no B, and C to some B.