§1.8#2τῶν γὰρ ἐν μέρει τι λεγομένων εἰδῶν ὑπῆρχεν ἂν αὐτῷ, τοῦτο δὲ ἀδύνατον μεμιγμένων γε πάντων· ἤδη γὰρ ἂν ἀπεκέκριτο, φησὶ δʼ εἶναι μεμιγμένα πάντα πλὴν τοῦ νοῦ, τοῦτον δὲ ἀμιγῆ μόνον καὶ καθαρόν.
For some of the forms that are spoken of as particular would have belonged to it, but this is impossible, at least if all things are mixed; for [if some form had belonged to it] it would already have been separated, but he says that all things are mixed except intellect, and this alone is unmixed and pure.
ἐκ δὴ τούτων συμβαίνει λέγειν αὐτῷ τὰς ἀρχὰς τό τε ἕν (τοῦτο γὰρ ἁπλοῦν καὶ ἀμιγές) καὶ θάτερον, οἷον τίθεμεν τὸ ἀόριστον πρὶν ὁρισθῆναι καὶ μετασχεῖν εἴδους τινός, ὥστε λέγει μὲν οὔτʼ ὀρθῶς οὔτε σαφῶς, βούλεται μέντοι τι παραπλήσιον τοῖς τε ὕστερον λέγουσι καὶ τοῖς νῦν φαινομένοις μᾶλλον. —ἀλλὰ γὰρ οὗτοι μὲν τοῖς περὶ γένεσιν λόγοις καὶ φθορὰν καὶ κίνησιν οἰκεῖοι τυγχάνουσι μόνον (σχεδὸν γὰρ περὶ τῆς τοιαύτης οὐσίας καὶ τὰς ἀρχὰς καὶ τὰς αἰτίας ζητοῦσι μόνης)· ὅσοι δὲ περὶ μὲν ἁπάντων τῶν ὄντων ποιοῦνται τὴν θεωρίαν, τῶν δʼ ὄντων τὰ μὲν αἰσθητὰ τὰ δʼ οὐκ αἰσθητὰ τιθέασι, δῆλον ὡς περὶ ἀμφοτέρων τῶν γενῶν ποιοῦνται τὴν ἐπίσκεψιν· διὸ μᾶλλον ἄν τις ἐνδιατρίψειε περὶ αὐτῶν, τί καλῶς ἢ μὴ καλῶς λέγουσιν εἰς τὴν τῶν νῦν ἡμῖν προκειμένων σκέψιν.
From these things, then, it follows that he speaks of the principles as both the One (for this is simple and unmixed) and the Other, such as we posit the indefinite before it is defined and participates in some form; so that he speaks neither correctly nor clearly, yet he wishes something close to what later thinkers say and what is now more apparent. — But indeed, these thinkers happen to be appropriate only to arguments concerning generation, destruction, and motion (for they seek the principles and causes of almost such substance alone); but those who make their inquiry concerning all existing things, and posit some existing things as sensible and others as non-sensible, clearly make their investigation concerning both genera; wherefore one might spend more time on them, to see what they say well or not well with respect to the investigation now before us.
οἱ μὲν οὖν καλούμενοι Πυθαγόρειοι ταῖς μὲν ἀρχαῖς καὶ τοῖς στοιχείοις ἐκτοπωτέροις χρῶνται τῶν φυσιολόγων (τὸ δʼ αἴτιον ὅτι παρέλαβον αὐτὰς οὐκ ἐξ αἰσθητῶν· τὰ γὰρ μαθηματικὰ τῶν ὄντων ἄνευ κινήσεώς ἐστιν ἔξω τῶν περὶ τὴν ἀστρολογίαν), διαλέγονται μέντοι καὶ πραγματεύονται περὶ φύσεως πάντα· γεννῶσί τε γὰρ τὸν οὐρανόν, καὶ περὶ τὰ τούτου μέρη καὶ τὰ πάθη καὶ τὰ ἔργα διατηροῦσι τὸ συμβαῖνον, καὶ τὰς ἀρχὰς καὶ τὰ αἴτια εἰς ταῦτα καταναλίσκουσιν, ὡς ὁμολογοῦντες τοῖς ἄλλοις φυσιολόγοις ὅτι τό γε ὂν τοῦτʼ ἐστὶν ὅσον αἰσθητόν ἐστι καὶ περιείληφεν ὁ καλούμενος οὐρανός.
Now, the so-called Pythagoreans use principles and elements more unusual than those of the natural philosophers (the reason being that they took them not from sensible things; for mathematical objects among existing things are without motion, except those concerning astronomy), yet they discuss and busy themselves about nature in all things; for they generate the heaven, and concerning its parts, attributes, and activities they observe what happens, and they spend their principles and causes on these, as if agreeing with the other natural philosophers that what exists is at least all that is sensible and is encompassed by the so-called heaven.
τὰς δʼ αἰτίας καὶ τὰς ἀρχάς, ὥσπερ εἴπομεν, ἱκανὰς λέγουσιν ἐπαναβῆναι καὶ ἐπὶ τὰ ἀνωτέρω τῶν ὄντων, καὶ μᾶλλον ἢ τοῖς περὶ φύσεως λόγοις ἁρμοττούσας.
But the causes and principles, as we said, they state to be sufficient to ascend even to the higher realm of existing things, and as fitting these rather than arguments about nature.
ἐκ τίνος μέντοι τρόπου κίνησις ἔσται πέρατος καὶ ἀπείρου μόνων ὑποκειμένων καὶ περιττοῦ καὶ ἀρτίου, οὐθὲν λέγουσιν, ἢ πῶς δυνατὸν ἄνευ κινήσεως καὶ μεταβολῆς γένεσιν εἶναι καὶ φθορὰν ἢ τὰ τῶν φερομένων ἔργα κατὰ τὸν οὐρανόν.
But in what way there will be motion, when only limit and the unlimited, and odd and even, are assumed as subjects, they say nothing, or how it is possible, without motion and change, for there to be generation and destruction, or the activities of the bodies moving through the heaven.
ἔτι δὲ εἴτε δοίη τις αὐτοῖς ἐκ τούτων εἶναι μέγεθος εἴτε δειχθείη τοῦτο, ὅμως τίνα τρόπον ἔσται τὰ μὲν κοῦφα τὰ δὲ βάρος ἔχοντα τῶν σωμάτων;
And further, whether one should grant them or it should be shown that magnitude is from these, yet in what way will some of the bodies be light and others have weight?
ἐξ ὧν γὰρ ὑποτίθενται καὶ λέγουσιν, οὐθὲν μᾶλλον περὶ τῶν μαθηματικῶν λέγουσι σωμάτων ἢ τῶν αἰσθητῶν· διὸ περὶ πυρὸς ἢ γῆς ἢ τῶν ἄλλων τῶν τοιούτων σωμάτων οὐδʼ ὁτιοῦν εἰρήκασιν, ἅτε οὐθὲν περὶ τῶν αἰσθητῶν οἶμαι λέγοντες ἴδιον.
For from what they assume and say, they speak no more of mathematical bodies than of sensible ones; wherefore they have said nothing whatever concerning fire or earth or other such bodies, since, I think, they say nothing peculiar about sensible things.
ἔτι δὲ πῶς δεῖ λαβεῖν αἴτια μὲν εἶναι τὰ τοῦ ἀριθμοῦ πάθη καὶ τὸν ἀριθμὸν τῶν κατὰ τὸν οὐρανὸν ὄντων καὶ γιγνομένων καὶ ἐξ ἀρχῆς καὶ νῦν, ἀριθμὸν δʼ ἄλλον μηθένα εἶναι παρὰ τὸν ἀριθμὸν τοῦτον ἐξ οὗ συνέστηκεν ὁ κόσμος;
And further, how must one understand that the attributes of number and number itself are the causes of what exists and is generated in the heaven, both from the beginning and now, while there is no other number than this very number out of which the world is constituted?
ὅταν γὰρ ἐν τῳδὶ μὲν τῷ μέρει δόξα καὶ καιρὸς αὐτοῖς ᾖ, μικρὸν δὲ ἄνωθεν ἢ κάτωθεν ἀδικία καὶ κρίσις ἢ μῖξις, ἀπόδειξιν δὲ λέγωσιν ὅτι τούτων μὲν ἕκαστον ἀριθμός ἐστι, συμβαίνει δὲ κατὰ τὸν τόπον τοῦτον ἤδη πλῆθος εἶναι τῶν συνισταμένων μεγεθῶν διὰ τὸ τὰ πάθη ταῦτα ἀκολουθεῖν τοῖς τόποις ἑκάστοις, πότερον οὗτος ὁ αὐτός ἐστιν ἀριθμός, ὁ ἐν τῷ οὐρανῷ, ὃν δεῖ λαβεῖν ὅτι τούτων ἕκαστόν ἐστιν, ἢ παρὰ τοῦτον ἄλλος;
For when in this part there is "opinion" and "opportunity" for them, and a little above or below "injustice" and "judgment" or "mixture", and they state as a proof that each of these is a number, and it happens that in this place there is already a multitude of constituted magnitudes because these attributes follow each of the places, is this number, the one in the heaven, which one must understand each of these to be, the very same, or is there another besides this?
ὁ μὲν γὰρ Πλάτων ἕτερον εἶναί φησιν· καίτοι κἀκεῖνος ἀριθμοὺς οἴεται καὶ ταῦτα εἶναι καὶ τὰς τούτων αἰτίας, ἀλλὰ τοὺς μὲν νοητοὺς αἰτίους τούτους δὲ αἰσθητούς.
For Plato says it is different; and yet he too thinks that both these things and their causes are numbers, but that the causal ones are intelligible and the others are sensible.