§2.1.13#2εἰ γὰρ τοῦτο τοῦ μὴ ἀναπνεῖν αἴτιον, ἔδει τὸ ζῷον εἶναι αἴτιον τοῦ ἀναπνεῖν, οἷον εἰ ἡ ἀπόφασις αἰτία τοῦ μὴ ὑπάρχειν, ἡ κατάφασις τοῦ ὑπάρχειν, ὥσπερ εἰ τὸ ἀσύμμετρα εἶναι τὰ θερμὰ καὶ τὰ ψυχρὰ τοῦ μὴ ὑγιαίνειν, τὸ σύμμετρα εἶναι τοῦ ὑγιαίνειν,—ὁμοίως δὲ καὶ εἰ ἡ κατάφασις τοῦ ὑπάρχειν, ἡ ἀπόφασις τοῦ μὴ ὑπάρχειν.
For if this is the cause of not breathing, it would be necessary for being an animal to be the cause of breathing; as, if the negation is the cause of non-belonging, the affirmation is the cause of belonging, just as, if the lack of proportion between the hot and the cold is the cause of not being healthy, the proportion between them is the cause of being healthy; and similarly also if the affirmation is the cause of belonging, the negation is the cause of non-belonging.
ἐπὶ δὲ τῶν οὕτως ἀποδεδομένων οὐ συμβαίνει τὸ λεχθέν· οὐ γὰρ ἅπαν ἀναπνεῖ ζῷον.
But in the case of things thus rendered, what has been said does not occur; for not every animal breathes.
ὁ δὲ συλλογισμός γίνεται τῆς τοιαύτης αἰτίας ἐν τῷ μέσῳ σχήματι.
And the syllogism of this kind of cause comes about in the middle figure.
οἷον ἔστω τὸ Α ζῷον, ἐφʼ ᾧ Β τὸ ἀναπνεῖν, ἐφʼ ᾧ Γ τοίχος.
For example, let A be animal, B breathing, C wall.
τῷ μὲν οὖν Β παντὶ ὑπάρχει τὸ Α (πᾶν γὰρ τὸ ἀναπνέον ζῷον), τῷ δὲ Γ οὐθενί, ὥστε οὐδὲ τὸ Β τῷ Γ οὐθενί οὐκ ἄρα ἀναπνεῖ ὁ τοῖχος.
Thus, A belongs to all B (for everything that breathes is an animal), but to no C; so that B also belongs to no C; therefore, the wall does not breathe.
ἐοίκασι δʼ αἱ τοιαῦται τῶν αἰτιῶν τοῖς καθʼ ὑπερβολὴν εἰρημένοις· τοῦτο δʼ ἔστι τὸ πλέον ἀποστήσαντα τὸ μέσον εἰπεῖν, οἷον τὸ τοῦ Ἀναχάρσιος, ὅτι ἐν Σκύθαις οὐκ εἰσὶν αὐλητρίδες, οὐδὲ γὰρ ἄμπελοι.
But these kinds of causes resemble things said in exaggeration; and this is to state the middle term by removing it too far, such as the saying of Anacharsis, that there are no flute-girls among the Scythians, because indeed there are no vines.
Κατὰ μὲν δὴ τὴν αὐτὴν ἐπιστήμην καὶ κατὰ τὴν τῶν μέσων θέσιν αὗται διαφοραί εἰσι τοῦ ὅτι πρὸς τὸν τοῦ διότι συλλογισμόν· ἄλλον δὲ τρόπον διαφέρει τὸ διότι τοῦ ὅτι τῷ διʼ ἄλλης ἐπιστήμης ἑκάτερον θεωρεῖν.
Thus, within the same science and according to the position of the middle terms, these are the differences of the syllogism of the fact as against that of the reason why; but in another way the reason why differs from the fact, by each being contemplated through a different science.
τοιαῦτα δʼ ἐστίν· ὅσα οὕτως ἔχει πρὸς ἄλληλα ὥστ᾿ εἶναι θάτερον ὑπὸ θάτερον, οἷον τὰ ὀπτικά πρὸς γεωμετρίαν καὶ τὰ μηχανικά πρός στερεομετρίαν καὶ τὰ ἁρμονικὰ πρὸς ἀριθμητικὴν καὶ τὰ φαινόμενα πρὸς ἀστρολογικήν.
Such cases are those which are so related to one another that the one is under the other, as optics is to geometry, mechanics to stereometry, harmonics to arithmetic, and phenomena to astronomy.
σχεδὸν δὲ συνώνυμοί εἰσιν ἔνιαι τούτων τῶν ἐπιστημῶν, οἷον ἀστρολογία ἥ τε μαθηματικὴ καὶ ἡ ναυτική, καὶ ἁρμονικὴ ἥ τε μαθηματικὴ καὶ ἡ κατὰ τὴν ἀκοήν.
Some of these sciences are almost synonymous, as astronomy, both the mathematical and the nautical, and harmonics, both the mathematical and that based on hearing.
ἐνταῦθα γὰρ τὸ μὲν ὅτι τῶν αἰσθητικῶν εἰδέναι, τὸ δὲ διότι τῶν μαθηματικῶν· οὗτοι γὰρ ἔχουσι τῶν αἰτίων τὰς ἀποδείξεις, καὶ πολλάκις οὐκ ἴσασι τὸ ὅτι, καθάπερ οἱ τὸ καθόλου θεωροῦντες πολλάκις ἔνια τῶν καθʼ ἕκαστον οὐκ ἴσασι διʼ ἀνεπισκεψίαν.
For here, to know the fact belongs to the empirical scientists, but to know the reason why belongs to the mathematicians; for these possess the demonstrations of the causes, and often they do not know the fact, just as those who contemplate the universal often do not know some of the particulars through lack of observation.
ἔστι δὲ ταῦτα ὅσα ἕτερόν τι ὄντα τὴν οὐσίαν κέχρηται τοῖς εἴδεσιν.
And these are those things which, being something other in their essence, make use of forms.
τὰ γὰρ μαθήματα περὶ εἴδη ἐστίν· οὐ γὰρ καθʼ ὑποκειμένου τινός· εἰ γὰρ καὶ καθʼ ὑποκειμένου τινὸς τὰ γεωμετρικά ἐστιν, ἀλλʼ οὐχ ᾗ γε καθʼ ὑποκειμένου.
For mathematical objects are about forms; they are not of any underlying subject; for even if geometrical objects are of some underlying subject, yet they are not so insofar as they are of an underlying subject.
ἔχει δὲ καὶ πρὸς τὴν ὀπτικήν, ὡς αὕτη πρὸς τὴν γεωμετρίον, ἄλλη πρὸς ταύτην, οἷον τὸ περὶ τῆς ἴριδος· τὸ μὲν γὰρ ὅτι φυσικοῦ εἰδέναι, τὸ δὲ διότι ὀπτικοῦ, ἢ ἀπλῶς ἢ τοῦ κατὰ τὸ μάθημα.
And as optics is to geometry, so there is another science related to optics, for example, the study of the rainbow; for to know the fact belongs to the physicist, but to know the reason why belongs to the optician, either simply or to the mathematical optician.
πολλαὶ δὲ καὶ τῶν μὴ ὑπʼ ἀλλήλας ἐπιστημῶν ἔχουσιν οὕτως, οἷον ἰατρικὴ πρὸς γεωμετρίαν· ὅτι μὲν γὰρ τὰ ἕλκη τὰ περιφερῆ βραδύτερον ὑγιάζεται, τοῦ ἰατροῦ εἰδέναι, διότι δὲ τοῦ γεωμέτρου.
And many of the sciences not under one another are also related in this way, for example, medicine to geometry; for to know the fact that circular wounds heal more slowly belongs to the physician, but to know the reason why belongs to the geometer.