§1.1.24Ἔτι τε ἐν ἅπαντι δεῖ κατηγορικόν τινα τῶν ὅρων εἶναι καὶ τὸ καθόλου ὑπάρχειν·
Furthermore, in every [syllogism] some of the terms (or premises) must be affirmative, and the universal must belong.
ἄνευ γὰρ τοῦ καθόλου ἢ οὐκ ἔσται συλλογισμὸς ἢ οὐ πρὸς τὸ κείμενον, ἢ τὸ ἐξ ἀρχῆς αἰτήσεται.
For without the universal, either there will be no syllogism, or it will not be in relation to the proposed question, or it will assume the original point.
κείσθω γὰρ τὴν μουσικὴν ἡδονὴν εἶναι σπουδαίαν.
Let it be assumed, for instance, that musical pleasure is good.
εἰ μὲν οὖν ἀξιώσειεν ἡδονὴν εἶναι σπουδαίαν μὴ προσθεὶς τὸ πᾶσαν, οὐκ ἔσται συλλογισμός·
If, then, someone should claim that pleasure is good, without adding 'every', there will be no syllogism.
εἰ δὲ τινὰ ἡδονήν, εἰ μέν ἄλλην, οὐδὲν πρὸς τὸ κείμενον, εἰ δʼ αὐτὴν ταύτην, τὸ ἐξ ἀρχῆς λαμβάνει.
But if they should claim 'some pleasure', then if it is another pleasure, it is not at all in relation to the proposed question, and if it is this very pleasure, they assume the original point.
μᾶλλον δὲ γίνεται φανερὸν ἐν τοῖς διαγράμμασιν, οἷον ὅτι τοῦ ἰσοσκελοῦς ἴσαι αἱ πρὸς τῇ βάσει.
But this becomes more manifest in diagrams, as for example, that the angles at the base of an isosceles triangle are equal.
ἔστωσαν εἰς τὸ κέντρον ἠγμέναι αἱ Α Β. εἰ οὖν ἴσην λαμβάνοι τὴν Α Γ γωνίαν τῇ Β Δ μὴ ὅλως ἀξιώσας ἴσας τὰς τῶν ἡμικυκλίων, καὶ πάλιν τὴν Γ τῇ Δ μὴ πᾶσαν προσλαβὼν τὴν τοῦ τμήματος, ἔτι δʼ ἀπʼ ἴσων οὐσῶν τῶν ὅλων γωνιῶν καὶ ἴσων ἀφῃρημένων ἴσας εἶναι τὰς λοιπὰς τὰς Ε Ζ, τὸ ἐξ ἀρχῆς αἰτήσεται, ἐὰν μὴ λάβῃ ἀπὸ τῶν ἴσων ἴσων ἀφαιρουμένων ἴσα λείπεσθαι.
Let the lines A and B be drawn to the center. If, then, one should take the angle A to be equal to B without overall claiming that those of semicircles are equal, and again Γ to be equal to Δ without assuming every angle of a segment, and furthermore, when the whole angles are equal and equal angles are subtracted, that the remaining angles E and Z are equal, they will assume the original point, unless they assume that if equals are subtracted from equals, equals remain.
φανερὸν οὖν ὅτι ἐν ἅπαντι δεῖ τὸ καθόλου ὑπάρχειν, καὶ ὅτι τὸ μὲν καθόλου ἐξ ἀπάντων τῶν ὅρων καθόλου δείκνυται, τὸ δʼ ἐν μέρει καὶ οὕτως κἀκείνως, ὥστʼ ἐὰν μὲν ᾖ τὸ συμπέρασμα καθόλου, καὶ τοὺς ὅρους ἀνάγκη καθόλου εἶναι, ἐὰν δʼ οἱ ὅροι καθόλου, ἐνδέχεται τὸ συμπέρασμα μὴ εἶναι καθόλου.
It is manifest, then, that the universal must belong in every [syllogism], and that while the universal is proved from all terms being universal, the particular is proved both in this way and in that; so that if the conclusion is universal, the terms must also be universal, but if the terms are universal, the conclusion may not be universal.
δῆλον δὲ καὶ ὅτι ἐν ἅπαντι συλλογισμῷ ἢ ἀμφοτέρας ἢ τὴν ἑτέραν πρότασιν ὁμοίαν ἀνάγκη γίνεσθαι τῷ συμπεράσματι.
It is also clear that in every syllogism, either both premises or one of them must become similar to the conclusion.
λέγω δʼ οὐ μόνον τῷ καταφατικὴν εἶναι ἢ στερητικήν, ἀλλὰ καὶ τῷ ἀναγκαίαν ἢ ὑπάρχουσαν ἢ ἐνδεχομένην.
By similar, I mean not only in being affirmative or negative, but also in being necessary, assertoric (actual), or contingent.
ἐπισκέψασθαι δὲ δεῖ καὶ τὰς ἄλλας κατηγορίας.
One must also investigate the other predications (or categories).
Φανερὸν δὲ καὶ ἀπλῶς πότʼ ἔσται καὶ πότʼ οὐκ ἔσται συλλογισμός, καὶ πότε δυνατὸς καὶ πότε τέλειος, καὶ ὅτι συλλογισμοῦ ὄντος ἀναγκαῖον ἔχειν τοὺς ὅρους κατά τινα τῶν εἰρημένων τρόπων.
It is also manifest, simply, when there will be a syllogism and when there will not, and when it is possible and when complete, and that if there is a syllogism, the terms must necessarily be related in some of the aforementioned ways.