§1.1.26Ἐπεὶ δʼ ἔχομεν περὶ ὧν οἱ συλλογισμοί, καὶ ποῖον ἐν ἑκάστῳ σχήματι καὶ ποσαχῶς δείκνυται, φανερόν ἡμῖν ἐστὶ καὶ ποῖον πρόβλημα χαλεπὸν καὶ ποῖον εὐεπιχείρητον·
Since we now have the subjects of syllogisms, and what sort of proposition is proven in each figure and in how many ways, it is also clear to us what sort of problem is difficult and what sort is easy to approach.
τὸ μὲν γὰρ ἐν πλείοσι σχήμασι καὶ διὰ πλειόνων πτώσεων περαινόμενον ῥᾷον, τὸ δʼ ἐν ἐλάττοσι καὶ διʼ ἐλαττόνων δυσεπιχειρητότερον.
For that which is concluded in more figures and through more inflections is easier, while that which is in fewer figures and through fewer inflections is more difficult to approach.
τὸ μὲν οὖν καταφατικὸν τὸ καθόλου διὰ τοῦ πρώτου σχήματος δείκνυται μόνου, καὶ διὰ τούτου μοναχῶς·
Now, the universal affirmative is proven through the first figure alone, and through this in only one way.
τὸ δὲ στερητικὸν διά τε τοῦ πρώτου καὶ διὰ τοῦ μέσου, καὶ διὰ μὲν τοῦ πρώτου μοναχῶς, διὰ δὲ τοῦ μέσου διχῶς·
The universal negative is proven through both the first and the middle figure, and through the first in only one way, but through the middle in two ways.
τὸ. δʼ ἐν μέρει καταφατικὸν διὰ τοῦ πρώτου καὶ διὰ τοῦ ἐσχάτου, μοναχῶς μὲν διὰ τοῦ πρώτου, τριχῶς δὲ διὰ τοῦ ἐσχάτου.
The particular affirmative is proven through the first and the last figure, in only one way through the first, but in three ways through the last.
τὸ δὲ στερητικόν τὸ κατὰ μέρος ἐν ἅπασι τοῖς σχήμασι δείκνυται, πλὴν ἐν μὲν τῷ πρώτῳ μοναχῶς, ἐν δὲ τῷ μέσῳ καὶ τῷ ἐσχάτῳ ἐν τῷ μὲν διχῶς ἐν τῷ δὲ τριχῶς.
The particular negative is proven in all the figures, except that in the first it is proven in only one way, while in the middle and the last, in one of them in two ways and in the other in three ways.
φανερὸν οὖν ὅτι τὸ καθόλου κατηγορικόν κατασκευάσαι μὲν χαλεπώτατον, ἀνασκευάσαι δὲ ῥᾷστον.
Thus it is clear that a universal affirmative is most difficult to establish, but easiest to refute.
ὅλως δʼ ἐστὶν ἀναιροῦντι μὲν τὰ καθόλου τῶν ἐν μέρει ῥᾴω·
In general, for one who is refuting, universal propositions are easier to refute than particular ones.
καὶ γὰρ ἢν μηδενὶ καὶ ἢν τινὶ μὴ ὑπάρχῃ, ἀνῄρηται·
For whether it belongs to none or not to some, the universal affirmative is refuted.
τούτων δὲ τὸ μὲν τινὶ μὴ ἐν ἅπασι τοῖς σχήμασι δείκνυται, τὸ δὲ μηδενὶ ἐν τοῖς δυσίν.
And of these, "not to some" is proven in all figures, while "to none" is proven in two figures.
τὸν αὐτὸν δὲ τρόπον κἀπὶ τῶν στερητικῶν· καὶ γὰρ εἰ παντὶ καὶ εἰ τινί, ἀνήρηται τὸ ἐξ ἀρχῆς·
The same way applies also to the negatives; for whether it belongs to all or to some, the original universal negative is refuted.
τοῦτο δʼ ἦν ἐν δύο σχήμασιν.
And this was in two figures.
ἐπὶ δὲ τῶν ἐν μέρει μοναχῶς, ἢ παντὶ ἢ μηδενὶ δείξαντα ὑπάρχειν.
But for particular propositions, the refutation is in only one way: by showing that it belongs either to all or to none.
κατασκευάζοντι δὲ ῥᾴω τὰ ἐν μέρει· καὶ γάρ ἐν πλείοσι σχήμασι καὶ διὰ πλειόνων τρόπων.
For one who is establishing, however, particular propositions are easier; for they are established in more figures and through more modes.
ὅλως τε οὐ δεῖ λανθάνειν ὅτι ἀνασκευάσαι μὲν διʼ ἀλλήλων ἔστι καὶ τὰ καθόλου διὰ τῶν ἐν μέρει καὶ ταῦτα διὰ τῶν καθόλου, κατασκευάσαι δʼ οὐκ ἔστι διὰ τῶν κατὰ μέρος τὰ καθόλου, διʼ ἐκείνων δὲ ταῦτʼ ἔστιν.
And in general, it must not escape our notice that it is possible to refute them through one another, both universals through particulars and particulars through universals, but it is not possible to establish universals through particulars, though it is possible to establish the latter through the former.
ἅμα δὲ δῆλον ὅτι καὶ τὸ ἀνασκευάζειν ἐστὶ τοῦ κατασκευάζειν ῥᾷον.
At the same time, it is clear that to refute is easier than to establish.
Πῶς μὲν οὖν γίνεται πᾶς συλλογισμὸς καὶ διὰ πόσων ὅρων καὶ προτάσεων, καὶ πῶς ἐχουσῶν πρὸς ἀλλήλας, ἔτι δὲ ποῖον πρόβλημα ἐν ἑκάστῳ σχήματι καὶ ποῖον ἐν πλείοσι καὶ ποῖον ἐν ἐλάττοσι δείκνυται, δῆλον ἐκ τῶν εἰρημένων.
How every syllogism comes about, therefore, and through how many terms and premises, and how they must be related to one another, and further, what sort of problem is proven in each figure, and what sort in more and what in fewer, is clear from what has been said.