Authors/Aristotle/priora/Liber 1/C28

Chapter 28

Greek	Latin	English
	(PL 64 0670C) CAPUT XXIX. Medii syllogismorum inveniendi regulae.	28
43b39 Κατασκευάζειν μὲν οὖν βουλομένοις κατά τινος ὅλου τοῦ μὲν κατασκευαζομένου βλεπτέον εἰς τὰ ὑποκείμενα καθ᾽ ὧν αὐτὸ τυγχάνει λεγόμενον, οὗ δὲ δεῖ κατηγορεῖσθαι, ὅσα τούτωι ἕπεται· ἂν γάρ τι τούτων ἦι ταὐτόν, ἀνάγκη θάτερον θατέρωι ὑπάρχειν. ἢν δὲ μὴ ὅτι παντὶ ἀλλ᾽ ὅτι τινί, οἷς ἕπε ↵ ται ἑκάτερον· εἰ γάρ τι τούτων ταὐτόν, ἀνάγκη τινὶ ὑπάρχειν.	(0670D) Construere ergo volentibus aliquid de aliquo toto, eius quidem quod construitur, inspiciendum ad subiecta de quibus ipsum dicitur, de quo autem oportet praedicari quaecunque hoc sequuntur. Si enim aliquod horum sit idem, alterum alteri necesse est inesse. Si autem non quoniam omni, sed quoniam alicui, quae sequitur utrumque, si enim aliquod horum idem fuerit, necesse est alicui inesse.	If men wish to establish something about some whole, they must look to the subjects of that which is being established (the subjects of which it happens to be asserted), and the attributes which follow that of which it is to be predicated. For if any of these subjects is the same as any of these attributes, the attribute originally in question must belong to the subject originally in question. But if the purpose is to establish not a universal but a particular proposition, they must look for the terms of which the terms in question are predicable: for if any of these are identical, the attribute in question must belong to some of the subject in question.
ὅταν δὲ μηδενὶ δέηι ὑπάρχειν, ὧι μὲν οὐ δεῖ ὑπάρχειν, εἰς τὰ ἑπόμενα, ὁ δὲ δεῖ μὴ ὑπάρχειν, εἰς ἃ μὴ ἐνδέχεται αὐτῶι παρεῖναι· ἢ ἀνάπαλιν, ὧι μὲν δεῖ μὴ ὑπάρχειν, εἰς ἃ μὴ ἐνδέχεται αὐτῶι παρεῖναι, ὁ δὲ μὴ ὑπάρχειν, εἰς τὰ ἑπόμενα. τούτων γὰρ ὄντων τῶν αὐτῶν ὁποτερωνοῦν, οὐδενὶ ἐνδέχεται θατέρωι θάτερον ὑπάρχειν· γίνεται γὰρ ὁτὲ μὲν ὁ ἐν τῶι πρώτωι σχήματι συλλογισμός, ὁτὲ δ᾽ ὁ ἐν τῶι μέσωι.	Quando autem nulli oporteat inesse, cui quidem oportet non inesse, ad sequentia subiecti, quod autem oportet non inesse, inspiciendum ad ea quae non contingunt illi adesse. Aut conversim cui quidem oportet non inesse, ad ea quae non contingunt eidem adesse, quod vero non inesse, inspiciendum ad sequentia. Nam si haec sint eadem utrorumque, nulli contingi alteri alterum inesse, fit enim quandoque quidem in prima figura syllogismus, quandoque autem in media.	Whenever the one term has to belong to none of the other, one must look to the consequents of the subject, and to those attributes which cannot possibly be present in the predicate in question: or conversely to the attributes which cannot possibly be present in the subject, and to the consequents of the predicate. If any members of these groups are identical, one of the terms in question cannot possibly belong to any of the other. For sometimes a syllogism in the first figure results, sometimes a syllogism in the second.
ἐὰν δὲ τινὶ μὴ ὑπάρχειν, ὧι μὲν δεῖ μὴ ὑπάρχειν, οἷς ἕπεται, ὁ δὲ μὴ ὑπάρχειν, ἃ μὴ δυνατὸν αὐτῶι ὑπάρχειν· εἰ γάρ τι τούτων εἴη ταὐτόν, ἀνάγκη τινὶ μὴ ὑπάρχειν. Μᾶλλον δ᾽ ἴσως ὧδ᾽ ἔσται τῶν λεγομένων ἕκαστον φανερόν. ἔστω γὰρ τὰ μὲν ἑπόμενα τῶι Α ἐφ᾽ ὧν Β, οἷς δ᾽ αὐτὸ ἕπεται, ἐφ᾽ ὧν Γ, ἃ δὲ μὴ ἐνδέχεται αὐτῶι ὑπάρχειν, ἐφ᾽ ὧν Δ· πάλιν δὲ τῶι Ε τὰ μὲν ὑπάρχοντα, ἐφ᾽ οἷς Ζ, οἷς δ᾽ αὐτὸ ἕπεται, ἐφ᾽ οἷς Η, ἃ δὲ μὴ ἐνδέχεται αὐτῶι ὑπάρχειν, ἐφ᾽ οἷς Θ.	(0671A) Si autem alicui non inesse, cui quidem oportet non inesse, quae consequitur: quod vero non inesse, quae non possibile est illi inesse. Si enim aliquid horum sit idem, necesse est alicui non inesse. Magis autem fortasse erit sic, unumquodque eorum quae dicta sunt manifestum. Sint enim sequentia quidem A, in quibus B, quae autem ipsum sequitur, in quibus C, quae autem non contingunt ei inesse, in quibus D, rursum autem ipsi E quae quidem insunt, in quibus F, quae autem ipsum sequitur, in quibus G, quae autem non contingunt eidem inesse, in quibus H.	But if the object is to establish a particular negative proposition, we must find antecedents of the subject in question and attributes which cannot possibly belong to the predicate in question. If any members of these two groups are identical, it follows that one of the terms in question does not belong to some of the other. Perhaps each of these statements will become clearer in the following way. Suppose the consequents of A are designated by B, the antecedents of A by C, attributes which cannot possibly belong to A by D. Suppose again that the attributes of E are designated by F, the antecedents of E by G, and attributes which cannot belong to E by H.
εἰ μὲν οὖν ταὐτό τί ἐστι τῶν Γ τινὶ τῶν Ζ, ἀνάγκη τὸ Α παντὶ τῶι Ε ὑπάρχειν· τὸ μὲν γὰρ Ζ παντὶ τῶι Ε, τῶι δὲ Γ παντὶ τὸ Α, ὥστε παντὶ τῶι Ε τὸ Α. εἰ δὲ τὸ Γ καὶ τὸ Η ταὐτόν, ἀνάγκη τινὶ τῶι Ε τὸ Α ὑπάρχειν· τῶι μὲν γὰρ Γ τὸ Α, τῶι δὲ Η τὸ Ε παντὶ ἀκολουθεῖ. εἰ δὲ τὸ Ζ καὶ τὸ Δ ταὐτόν, οὐδενὶ τῶν Ε τὸ Α ὑπάρξει ἐκ προσυλλογισμοῦ· ἐπεὶ γὰρ ἀντιστρέφει τὸ στερητικὸν καὶ τὸ Ζ τῶι Δ ταὐτόν, οὐδενὶ τῶν Ζ ὑπάρξει τὸ Α, τὸ δὲ Ζ παντὶ τῶι Ε.	Si ergo eidem aliquid eorum quae sunt C, alicui eorum quae sunt F, necesse est A omni E inesse, nam F quidem omni E, C autem omni A, quare omni E inest. (0671B) Si autem C et G idem, necesse est alicui E inesse A, nam id quod est E A, id vero quod est G E, omne ei sequitur. Si autem F et D sint idem, nulli E inerit ex proprio syllogismo, quoniam enim convertitur privativa, et F ei quod est D idem, nulli F inerit A, F autem omni E.	If then one of the Cs should be identical with one of the Fs, A must belong to all E: for F belongs to all E, and A to all C, consequently A belongs to all E. If C and G are identical, A must belong to some of the Es: for A follows C, and E follows all G. If F and D are identical, A will belong to none of the Es by a prosyllogism: for since the negative proposition is convertible, and F is identical with D, A will belong to none of the Fs, but F belongs to all E.
πάλιν εἰ τὸ Β καὶ τὸ Θ ταὐτόν, οὐδενὶ τῶν Ε τὸ Α ὑπάρξει· τὸ γὰρ Β τῶι μὲν Α παντί, τῶι δ᾽ ἐφ᾽ ὧι τὸ Ε οὐδενὶ ὑπάρξει· ταὐτὸ γὰρ ἦν τῶι Θ, τὸ δὲ Θ οὐδενὶ τῶν Ε ὑπῆρχεν. εἰ δὲ τὸ Δ καὶ τὸ Η ταὐτόν, τὸ Α τινὶ τῶι Ε οὐχ ὑπάρξει· τῶι γὰρ Η οὐχ ὑπάρξει, ὅτι οὐδὲ τῶι Δ· τὸ δὲ Η ἐστὶν ὑπὸ τὸ Ε, ὥστε τινὶ τῶν Ε οὐχ ὑπάρξει. εἰ δὲ τῶι Η τὸ Β ταὐτόν, ἀντεστραμμένος ἔσται συλλογισμός· τὸ μὲν γὰρ Ε τῶι Α ὑπάρξει παντί – τὸ γὰρ Β τῶι Α, τὸ δὲ Ε τῶι Β (ταὐτὸ γὰρ ἦν τῶι Η) – τὸ δὲ Α τῶι Ε παντὶ μὲν οὐκ ἀνάγκη ὑπάρχειν, τινὶ δ᾽ ἀνάγκη διὰ τὸ ἀντιστρέφειν τὴν καθόλου κατη γορίαν τῆι κατὰ μέρος.	Rursus si B et H idem, nulli E inerit A, nam B A quidem omni, ei autem in quo E nulli inerit. Idem enim erat ei quod est H, B; H autem nulli E inerat. Si autem G et D idem, A alicui E non inerit, nam ei quod est G non inerit A, quoniam neque D, G autem sub E est, quare alicui E non inerit. (0671C) Si autem G et B idem, conversus erit syllogismus, nam G inerit omni A, nam B ei quod est A, E autem ei quod est B, idem enim erat ei quod est G, A autem ei quod est E, omni quidem non necessarium est inesse, alicui autem necessarium, eo quod convertatur universale praedicativum in particulare.	Again, if B and H are identical, A will belong to none of the Es: for B will belong to all A, but to no E: for it was assumed to be identical with H, and H belonged to none of the Es. If D and G are identical, A will not belong to some of the Es: for it will not belong to G, because it does not belong to D: but G falls under E: consequently A will not belong to some of the Es. If B is identical with G, there will be a converted syllogism: for E will belong to all A since B belongs to A and E to B (for B was found to be identical with G): but that A should belong to all E is not necessary, but it must belong to some E because it is possible to convert the universal statement into a particular.
Φανερὸν οὖν ὅτι εἰς τὰ προειρημένα βλεπτέον ἑκατέρου καθ᾽ ἕκαστον πρόβλημα· διὰ τούτων γὰρ ἅπαντες οἱ συλλογισμοί. δεῖ δὲ καὶ τῶν ἑπομένων, καὶ οἷς ἕπεται ἕκαστον, εἰς τὰ πρῶτα καὶ τὰ καθόλου μάλιστα βλέπειν, οἷον τοῦ μὲν Ε μᾶλλον εἰς τὸ Κ Ζ ἢ εἰς τὸ Ζ μόνον, τοῦ δὲ Α εἰς ↵ τὸ Κ Γ ἢ εἰς τὸ Γ μόνον. εἰ μὲν γὰρ τῶι Κ Ζ ὑπάρχει τὸ Α, καὶ τῶι Ζ καὶ τῶι Ε ὑπάρχει· εἰ δὲ τούτωι μὴ ἕπεται, ἐγχωρεῖ τῶι Ζ ἕπεσθαι. ὁμοίως δὲ καὶ ἐφ᾽ ὧν αὐτὸ ἀκολουθεῖ σκεπτέον· εἰ μὲν γὰρ τοῖς πρώτοις, καὶ τοῖς ὑπ᾽ ἐκεῖνα ἕπεται, εἰ δὲ μὴ τούτοις, ἀλλὰ τοῖς ὑπὸ ταῦτα ἐγχωρεῖ.	Manifestum ergo quoniam ad praedicta perspiciendum utrinque in unaquaque quaestione, per haec enim omnes syllogismi. Oportet autem et sequentium, et quibus sequitur singulum, ad prima et universalia maxime inspicere, ut E quidem magis ad k F quam ad F solum, A autem ad k C magis quam ad C solum. Si enim ei quod est k F inest A, et ei quod est F inest et ipsi E, si vero hoc non sequitur A, possibile est id quod est F sequi. Similiter autem et in quibus idem sequitur, considerandum, nam si primis, et iis quae sub ipsis sunt, sequitur; si autem non his, et iis quae sub ipsis sunt, possibile.	It is clear then that in every proposition which requires proof we must look to the aforesaid relations of the subject and predicate in question: for all syllogisms proceed through these. But if we are seeking consequents and antecedents we must look for those which are primary and most universal, e.g. in reference to E we must look to KF rather than to F alone, and in reference to A we must look to KC rather than to C alone. For if A belongs to KF, it belongs both to F and to E: but if it does not follow KF, it may yet follow F. Similarly we must consider the antecedents of A itself: for if a term follows the primary antecedents, it will follow those also which are subordinate, but if it does not follow the former, it may yet follow the latter.
Δῆλον δὲ καὶ ὅτι διὰ τῶν τριῶν ὅρων καὶ τῶν δύο προτάσεων ἡ σκέψις, καὶ διὰ τῶν προειρημένων σχημάτων οἱ συλλογισμοὶ πάντες. δείκνυται γὰρ ὑπάρχειν μὲν παντὶ τῶι Ε τὸ Α, ὅταν τῶν Γ καὶ Ζ ταὐτόν τι ληφθῆι. τοῦτο δ᾽ ἔσται μέσον, ἄκρα δὲ τὸ Α καὶ Ε· γίνεται οὖν τὸ πρῶτον σχῆμα.	(0671D) Palam autem quoniam per tres terminos et duas propositiones consideratio, et per praedictas figuras syllogismi omnes, monstratur enim omni quidem E inesse A, quando eorum quae sunt C F idem, quiddam sumitur, hoc autem erit medium, extremitates autem A et E, fit enim prima figura.	It is clear too that the inquiry proceeds through the three terms and the two premisses, and that all the syllogisms proceed through the aforesaid figures. For it is proved that A belongs to all E, whenever an identical term is found among the Cs and Fs. This will be the middle term; A and E will be the extremes. So the first figure is formed.
τινὶ δέ, ὅταν τὸ Γ καὶ τὸ Η ληφθῆι ταὐτόν. τοῦτο δὲ τὸ ἔσχατον σχῆμα· μέσον γὰρ τὸ Η γίνεται. μηδενὶ δέ, ὅταν τὸ Δ καὶ Ζ ταὐτόν. οὕτω δὲ καὶ τὸ πρῶτον σχῆμα καὶ τὸ μέσον, τὸ μὲν πρῶτον ὅτι οὐδενὶ τῶι Ζ ὑπάρχει τὸ Α (εἴπερ ἀντι- στρέφει τὸ στερητικόν), τὸ δὲ Ζ παντὶ τῶι Ε, τὸ δὲ μέσον ὅτι τὸ Δ τῶι μὲν Α οὐδενὶ τῶι δὲ Ε παντὶ ὑπάρχει. τινὶ δὲ μὴ ὑπάρχειν, ὅταν τὸ Δ καὶ Η ταὐτὸν ἦι. τοῦτο δὲ τὸ ἔσχατον σχῆμα· τὸ μὲν γὰρ Α οὐδενὶ τῶι Η ὑπάρξει, τὸ δὲ Ε παντὶ τῶι Η.	Alicui autem quando C et G sumitur idem, hoc autem postrema figura, medium enim fit G. Nulli vero quando D et F idem; sic autem et prima figura, et media: prima quidem, quoniam nulli F inest A, siquidem convertitur privativa, F autem omni E. Media autem quoniam D A quidem nulli, E autem omni inest. Alicui autem non inesse, quando D et G idem fuerit, haec autem postrema figura, nam A quidem nulli G inerit, E vero omni G;	And A will belong to some E, whenever C and G are apprehended to be the same. This is the last figure: for G becomes the middle term. And A will belong to no E, when D and F are identical. Thus we have both the first figure and the middle figure; the first, because A belongs to no F, since the negative statement is convertible, and F belongs to all E: the middle figure because D belongs to no A, and to all E. And A will not belong to some E, whenever D and G are identical. This is the last figure: for A will belong to no G, and E will belong to all G.
φανερὸν οὖν ὅτι διὰ τῶν προειρημένων σχη μάτων οἱ συλλογισμοὶ πάντες, καὶ ὅτι οὐκ ἐκλεκτέον ὅσα πᾶσιν ἕπεται, διὰ τὸ μηδένα γίγνεσθαι συλλογισμὸν ἐξ αὐτῶν. κατασκευάζειν μὲν γὰρ ὅλως οὐκ ἦν ἐκ τῶν ἑπομένων, ἀποστερεῖν δ᾽ οὐκ ἐνδέχεται διὰ τοῦ πᾶσιν ἑπομένου· δεῖ γὰρ τῶι μὲν ὑπάρχειν τῶι δὲ μὴ ὑπάρχειν.	manifestum igitur est quoniam per praedictas figuras omnes syllogismi. (0672A) Et quoniam non eligendum quaecunque omnibus sequuntur, eo quod nullus fiat syllogismus ex ipsis, nam construere quidem non omnino erat ex sequentibus, privare autem non contingit per ea quae omnibus sequuntur, oportet huic quidem inesse, illi vero non inesse.	Clearly then all syllogisms proceed through the aforesaid figures, and we must not select consequents of all the terms, because no syllogism is produced from them. For (as we saw) it is not possible at all to establish a proposition from consequents, and it is not possible to refute by means of a consequent of both the terms in question: for the middle term must belong to the one, and not belong to the other.
Φανερὸν δὲ καὶ ὅτι αἱ ἄλλαι σκέψεις τῶν κατὰ τὰς ἐκλογὰς ἄχρειοι πρὸς τὸ ποιεῖν συλλογισμόν, οἷον εἰ τὰ ἑπόμενα ἑκατέρωι ταὐτά ἐστιν, ἢ εἰ οἷς ἕπεται τὸ Α καὶ ἃ μὴ ἐνδέχεται τῶι Ε, ἢ ὅσα πάλιν μὴ ἐγχωρεῖ ἑκατέρωι ὑπάρχειν· οὐ γὰρ γίνεται συλλογισμὸς διὰ τούτων. εἰ μὲν γὰρ τὰ ἑπόμενα ταὐτά, οἷον τὸ Β καὶ τὸ Ζ, τὸ μέσον γίνεται σχῆμα κατηγορικὰς ἔχον τὰς προτάσεις· εἰ δ᾽ οἷς ἕπεται τὸ Α καὶ ἃ μὴ ἐνδέχεται τῶι Ε, οἷον τὸ Γ καὶ τὸ Θ, τὸ πρῶτον σχῆμα στερητικὴν ἔχον τὴν πρὸς τὸ ἔλαττον ἄκρον πρότασιν. εἰ δ᾽ ὅσα μὴ ἐνδέχεται ἑκατέρωι, οἷον τὸ Δ καὶ τὸ Θ, στερητικαὶ ἀμφότεραι αἱ προτάσεις, ἢ ἐν τῶι πρώτωι ἢ ἐν τῶι μέσωι σχήματι. οὕτως δ᾽ οὐδαμῶς συλλογισμός.	Manifestum autem quoniam et aliae considerationes quae secundum electiones, inutiles ad faciendum syllogismum. Ut si sequentia utrumque eadem sint, aut quae sequitur A, et quae non contingit E inesse, aut rursum quaecunque non possibile est utrique inesse, non enim fit syllogismus per haec. Nam si sequentia sunt eadem, ut B et F, media fit figura praedicativas habens utrasque propositiones. (0672B) Si autem ea quae sequitur A, et quae non contingit E, ut C, et H, prima erit figura privativam habens propositionem ad minorem extremitatem. Si autem quaecunque non contingunt utrique, ut D et H, privativae utraeque propositiones erunt vel in prima figura, vel in media, sic autem nullo modo erit syllogismus.	It is clear too that other methods of inquiry by selection of middle terms are useless to produce a syllogism, e.g. if the consequents of the terms in question are identical, or if the antecedents of A are identical with those attributes which cannot possibly belong to E, or if those attributes are identical which cannot belong to either term: for no syllogism is produced by means of these. For if the consequents are identical, e.g. B and F, we have the middle figure with both premisses affirmative: if the antecedents of A are identical with attributes which cannot belong to E, e.g. C with H, we have the first figure with its minor premiss negative. If attributes which cannot belong to either term are identical, e.g. C and H, both premisses are negative, either in the first or in the middle figure. But no syllogism is possible in this way.
Δῆλον δὲ καὶ ὅτι ὁποῖα ταὐτὰ ληπτέον τὰ κατὰ τὴν ἐπίσκεψιν, καὶ οὐχ ὁποῖα ἕτερα ἢ ἐναντία, πρῶτον μὲν ὅτι τοῦ μέσου χάριν ἡ ἐπίβλεψις, τὸ δὲ μέσον οὐχ ἕτερον ↵ ἀλλὰ ταὐτὸν δεῖ λαβεῖν. εἶτα ἐν ὅσοις καὶ συμβαίνει γίνεσθαι συλλογισμὸν τῶι ληφθῆναι ἐναντία ἢ μὴ ἐνδεχόμενα τῶι αὐτῶι ὑπάρχειν, εἰς τοὺς προειρημένους ἅπαντα ἀναχθήσεται τρόπους, οἷον εἰ τὸ Β καὶ τὸ Ζ ἐναντία ἢ μὴ ἐνδέχεται τῶι αὐτῶι ὑπάρχειν· ἔσται μὲν γὰρ τούτων ληφθέντων συλλογισμὸς ὅτι οὐδενὶ τῶν Ε τὸ Α ὑπάρχει, ἀλλ᾽ οὐκ ἐξ αὐτῶν ἀλλ᾽ ἐκ τοῦ προειρημένου τρόπου· τὸ γὰρ Β τῶι μὲν Α παντὶ τῶι δὲ Ε οὐδενὶ ὑπάρξει· ὥστ᾽ ἀνάγκη ταὐτὸ εἶναι τὸ Β τινὶ τῶι Θ. [πάλιν εἰ τὸ Β καὶ Η μὴ ἐγχωρεῖ τῶι αὐτῶι παρεῖναι, ὅτι τινὶ τῶι Ε οὐχ ὑπάρξει τὸ Α· καὶ γὰρ οὕτως τὸ μέσον ἔσται σχῆμα· τὸ γὰρ Β τῶι μὲν Α παντὶ τῶι δὲ Ε οὐδενὶ ὑπάρξει· ὥστ᾽ ἀνάγκη τὸ Β ταὐτόν τινι εἶναι τῶν Θ. τὸ γὰρ μὴ ἐνδέχεσθαι τὸ Β καὶ τὸ Η τῶι αὐτῶι ὑπάρχειν οὐδὲν διαφέρει ἢ τὸ Β τῶν Θ τινὶ ταὐ τὸν εἶναι· πάντα γὰρ εἴληπται τὰ μὴ ἐνδεχόμενα τῶι Ε ὑπάρχειν.]	Palam autem et quae eadem, sumendum secundum considerationem, et non quae diversa vel contraria, primum quidem quoniam medii gratia, inspectio, medium autem non diversum, sed idem oportet sumere. Deinde et in quibus accidit fieri syllogismum quod sumantur contraria, aut non contigentia eidem inesse, in praedictos omnia reducuntur modos. (0672C) Ut si B et F sint contraria, aut non contingant eidem inesse, erit enim his sumptis syllogismus, quoniam nulli E inest A, sed non ex ipsis, sed ex praedicto modo, nam B A quidem omni, E autem nulli inerit, quare necesse est B idem esse alicui eorum quae sunt H. Rursum si B et G non possint eidem adesse, erit quoniam alicui E non inerit A, nam et sic media erit figura, nam B A quidem omni, G vero nulli inerit, quare necesse est G idem esse alicui eorum quae sunt D, nam non contingere G et B eidem inesse nihil differt, aut G alicui D idem esse, omnia enim sumpta sunt in D, quae non contingunt A inesse.	It is evident too that we must find out which terms in this inquiry are identical, not which are different or contrary, first because the object of our investigation is the middle term, and the middle term must be not diverse but identical. Secondly, wherever it happens that a syllogism results from taking contraries or terms which cannot belong to the same thing, all arguments can be reduced to the aforesaid moods, e.g. if B and F are contraries or cannot belong to the same thing. For if these are taken, a syllogism will be formed to prove that A belongs to none of the Es, not however from the premisses taken but in the aforesaid mood. For B will belong to all A and to no E. Consequently B must be identical with one of the Hs. Again, if B and G cannot belong to the same thing, it follows that A will not belong to some of the Es: for then too we shall have the middle figure: for B will belong to all A and to no G. Consequently B must be identical with some of the Hs. For the fact that B and G cannot belong to the same thing differs in no way from the fact that B is identical with some of the Hs: for that includes everything which cannot belong to E.
Φανερὸν οὖν ὅτι ἐξ αὐτῶν μὲν τούτων τῶν ἐπιβλέψεων οὐδεὶς γίνεται συλλογισμός, ἀνάγκη δ᾽ εἰ τὸ Β καὶ τὸ Ζ ἐναντία, ταὐτόν τινι εἶναι τὸ Β τῶν Θ καὶ τὸν συλλογι σμὸν γίγνεσθαι διὰ τούτων. συμβαίνει δὴ τοῖς οὕτως ἐπισκοποῦσι προσεπιβλέπειν ἄλλην ὁδὸν τῆς ἀναγκαίας διὰ τὸ λανθάνειν τὴν ταὐτότητα τῶν Β καὶ τῶν Θ.	Manifestum ergo quoniam ex istis quidem inspectionibus nullus fit syllogismus, et si B et F sint contraria, idem esse B alicui H, et syllogismum semper fieri per haec. Accidit ergo sic inspicientibus considerare viam aliam necessariam, eo quod quandoque latet identitas horum quae sunt B et H.	It is clear then that from the inquiries taken by themselves no syllogism results; but if B and F are contraries B must be identical with one of the Hs, and the syllogism results through these terms. It turns out then that those who inquire in this manner are looking gratuitously for some other way than the necessary way because they have failed to observe the identity of the Bs with the Hs.