§2.1.9Ἐπεὶ δὲ φανερὸν ὅτι ἕκαστον ἀποδείξαι οὐκ ἔστιν ἀλλʼ ἢ ἐκ τῶν ἑκάστου ἀρχῶν, ἂν τὸ δεικνύμενον ὑπάρχῃ ἧ ἐκεῖνο, οὐκ ἔστι τὸ ἐπίστασθαι τοῦτο, ἂν ἐξ ἀληθῶν καὶ ἀναποδείκτων δειχθῇ καὶ ἀμέσων.
Since it is clear that it is not possible to prove each thing except from the proper principles of each, that is, if the thing demonstrated belongs to it insofar as it is that thing, then knowing this is not achieved even if it is demonstrated from premises that are true, indemonstrable, and immediate.
ἔστι γὰρ οὕτω δεῖξαι, ὥσπερ Βρύσων τὸν τετραγωνισμόν.
For it is possible to demonstrate in this way, just as Bryson demonstrated the quadrature of the circle.
κατά κοινόν τε γὰρ δεικνύουσιν οἱ τοιοῦτοι λόγοι, ὃ καὶ ἑτέρῳ ὑπάρξει διὸ καὶ ἐπ᾿ ἄλλων ἐφαρμόττουσιν οἱ λόγοι οὐ συγγενῶν.
For such arguments demonstrate on the basis of something common, which will also belong to another subject; therefore, these arguments also apply to other things that are not akin.
οὐκοῦν οὐχ ᾗ ἐκεῖνο ἐπίσταται, ἀλλὰ κατὰ συμβεβηκός· οὐ γὰρ ἂν ἐφήρμοττεν ἡ ἀπόδειξις καὶ ἐπʼ ἄλλο γένος.
Consequently, one does not know the thing insofar as it is that thing, but only accidentally; for otherwise the demonstration would not have applied to another genus.
Ἕκαστον δʼ ἐπιστάμεθα μὴ κατὰ συμβεβηκός, ὅταν κατʼ ἐκεῖνο γινώσκωμεν καθʼ ὃ ὑπάρχει, ἐκ τῶν ἀρχῶν τῶν ἐκείνου ᾗ ἐκεῖνο, οἷον τὸ δυσὶν ὀρθαῖς ἴσας ἔχειν, ὧ ὑπάρχει καθʼ αὐτὸ τὸ εἰρημένον, ἐκ τῶν ἀρχῶν τῶν τούτου.
And we know each thing non-accidentally when we recognize it according to that subject in virtue of which the attribute belongs to it, from the principles of that subject insofar as it is that subject—for instance, as having angles equal to two right angles, for the subject to which this mentioned attribute belongs in itself, from the principles of this subject.
ὥστʼ εἰ καθʼ αὐτὸ κἀκεῖνο ὑπάρχει ᾧ ὑπάρχει, ἀνάγκη τὸ μέσον ἐν τῇ αὐτῇ συγγενείᾳ εἶναι.
Thus, if that attribute also belongs in itself to that subject to which it belongs, the middle term must be in the same family.
εἰ δὲ μή, ἀλλʼ ὡς τὰ ἁρμονικὰ διʼ ἀριθμητικῆς.
Otherwise, they belong as harmonic properties are demonstrated through arithmetic.
τὰ δὲ τοιαῦτα δείκνυται μὲν ὡσαύτως, διαφέρει δέ· τὸ μὲν γὰρ ὅτι ἑτέρας ἐπιστήμης (τὸ γὰρ ὑποκείμενον γένος ἕτερον), τὸ δὲ διότι τῆς ἄνω, ἧς καθʼ αὐτὰ τὰ πάθη ἐστίν.
Such properties are demonstrated in the same way, but they differ: for the fact (the 'that') belongs to another science (for the underlying genus is different), but the reason (the 'why') belongs to the higher science, to which the properties belong in themselves.
ὥστε καὶ ἐκ τούτων φανερὸν ὅτι οὐκ ἔστιν ἀποδεῖξαι ἕκαστον ἀπλῶς ἄλλʼ ἢ ἐκ τῶν ἑκάστου ἀρχῶν.
Consequently, from these considerations too it is clear that it is not possible to demonstrate each thing simply, except from the proper principles of each.
ἀλλὰ τούτων αἱ ἀρχαὶ ἔχουσι τὸ κοινόν.
But the principles of these sciences share something in common.
Εἱ δὲ φανερὸν τοῦτο, φανερὸν καὶ ὅτι οὐκ ἔστι τὰς ἑκάστου ἰδίας ἀρχὰς ἀποδεῖξαι· ἔσονται γὰρ ἐκεῖναι ἀπάντων ἀρχαί, καὶ ἐπιστήμη ἡ ἐκείνων κυρία πάντων.
And if this is clear, it is also clear that it is not possible to demonstrate the proper principles of each science; for those would then be the principles of all things, and the science of those principles would be sovereign over all.
καὶ γὰρ ἐπίσταται μᾶλλον ὁ ἐκ τῶν ἀνώτερον αἰτίων εἰδώς· ἐκ τῶν προτέρων γὰρ οἶδεν, ὅταν ἐκ μὴ αἰτιατῶν εἰδῇ αἰτίων.
For a person knows more when he knows from higher causes; for he knows from prior things when he knows from causes that are themselves uncaused.
ὥστʼ εἰ μᾶλλον οἶδε καὶ μάλιστα, κἂν ἐπιστήμη ἐκείνη εἴη καὶ μᾶλλον καὶ μάλιστα.
Thus, if he knows more and knows most, that science too would be a science both in a higher degree and in the highest degree.
ἡ δʼ ἀπόδειξις οὐκ ἐφαρμόττει ἐπʼ ἄλλο γένος, ἀλλʼ ἢ ὡς εἴρηται αἱ γεωμετρικαὶ ἐπὶ τὰς μηχανικὰς ἢ ὀπτικὰς καὶ αἱ ἀριθμητικαὶ ἐπὶ τὰς ἁρμονικάς.
But demonstration does not apply to another genus, except, as has been said, geometrical demonstrations to mechanical or optical sciences, and arithmetic demonstrations to harmonics.
Χαλεπὸν δʼ ἐστὶ τὸ γνῶναι εἰ οἶδεν ἢ μή.
But it is difficult to determine whether one knows or not.
χαλεπὸνs γὰρ τὸ γνῶναι εἰ ἐκ τῶν ἑκάστου ἀρχῶν ἴσμεν ἢ μή· ὅπερ ἐστὶ τὸ εἰδέναι.
For it is difficult to determine whether we know from the proper principles of each thing or not—which is what knowing actually is.
οἰόμεθα δʼ, ἂν ἔχωμεν ἐξ ἀληθινῶν τινῶν συλλογισμὸν καὶ πρώτων, ἐπίστασθαι.
We think, however, that if we have a syllogism from some premises that are true and primary, we know.
τὸ δʼ οὐκ ἔστιν, ἀλλὰ συγγενῆ δεῖ εἶναι τοῖς πρώτοις.
But this is not so, but [the terms] must be akin to the primary things.