§1.5#1ἐν δὲ τούτοις καὶ πρὸ τούτων οἱ καλούμενοι Πυθαγόρειοι τῶν μαθημάτων ἁψάμενοι πρῶτοι ταῦτά τε προήγαγον, καὶ ἐντραφέντες ἐν αὐτοῖς τὰς τούτων ἀρχὰς τῶν ὄντων ἀρχὰς ᾠήθησαν εἶναι πάντων.
During the time of these thinkers and before them, the so-called Pythagoreans, having applied themselves to mathematics, were the first to advance this study, and having been brought up in it, they thought that its principles were the principles of all existing things.
ἐπεὶ δὲ τούτων οἱ ἀριθμοὶ φύσει πρῶτοι, ἐν δὲ τούτοις ἐδόκουν θεωρεῖν ὁμοιώματα πολλὰ τοῖς οὖσι καὶ γιγνομένοις, μᾶλλον ἢ ἐν πυρὶ καὶ γῇ καὶ ὕδατι, ὅτι τὸ μὲν τοιονδὶ τῶν ἀριθμῶν πάθος δικαιοσύνη τὸ δὲ τοιονδὶ ψυχή τε καὶ νοῦς ἕτερον δὲ καιρὸς καὶ τῶν ἄλλων ὡς εἰπεῖν ἕκαστον ὁμοίως, ἔτι δὲ τῶν ἁρμονιῶν ἐν ἀριθμοῖς ὁρῶντες τὰ πάθη καὶ τοὺς λόγους,—ἐπεὶ δὴ τὰ μὲν ἄλλα τοῖς ἀριθμοῖς ἐφαίνοντο τὴν φύσιν ἀφωμοιῶσθαι πᾶσαν, οἱ δʼ ἀριθμοὶ πάσης τῆς φύσεως πρῶτοι, τὰ τῶν ἀριθμῶν στοιχεῖα τῶν ὄντων στοιχεῖα πάντων ὑπέλαβον εἶναι, καὶ τὸν ὅλον οὐρανὸν ἁρμονίαν εἶναι καὶ ἀριθμόν·
And since numbers are by nature first among these, and in numbers they seemed to observe many likenesses to things that exist and come to be, more than in fire, earth, and water—for instance, that such-and-such a modification of numbers is justice, and another is soul and intellect, and another is opportunity, and similarly almost each of the other things—and further, seeing that the attributes and ratios of musical scales are in numbers,—since, indeed, all other things seemed in their whole nature to be modeled after numbers, and numbers were the first things in the whole of nature, they supposed the elements of numbers to be the elements of all existing things, and the whole heaven to be a harmony and a number.
καὶ ὅσα εἶχον ὁμολογούμενα ἔν τε τοῖς ἀριθμοῖς καὶ ταῖς ἁρμονίαις πρὸς τὰ τοῦ οὐρανοῦ πάθη καὶ μέρη καὶ πρὸς τὴν ὅλην διακόσμησιν, ταῦτα συνάγοντες ἐφήρμοττον.
And whatever they could show to be in agreement in numbers and harmonies with the attributes, parts, and whole ordering of the heaven, they collected and fitted together.
κἂν εἴ τί που διέλειπε, προσεγλίχοντο τοῦ συνειρομένην πᾶσαν αὐτοῖς εἶναι τὴν πραγματείαν·
And if anything was lacking anywhere, they eagerly strove to make their whole system coherent with them.
λέγω δʼ οἷον, ἐπειδὴ τέλειον ἡ δεκὰς εἶναι δοκεῖ καὶ πᾶσαν περιειληφέναι τὴν τῶν ἀριθμῶν φύσιν, καὶ τὰ φερόμενα κατὰ τὸν οὐρανὸν δέκα μὲν εἶναί φασιν, ὄντων δὲ ἐννέα μόνον τῶν φανερῶν διὰ τοῦτο δεκάτην τὴν ἀντίχθονα ποιοῦσιν.
I mean, for example, since the decad is thought to be perfect and to comprise the whole nature of numbers, they say that the bodies moving in the heaven are also ten, and as only nine are visible, for this reason they invent the tenth, the 'counter-earth'.
διώρισται δὲ περὶ τούτων ἐν ἑτέροις ἡμῖν ἀκριβέστερον.
But we have defined these matters more accurately elsewhere.
ἀλλʼ οὗ δὴ χάριν ἐπερχόμεθα, τοῦτό ἐστιν ὅπως λάβωμεν καὶ παρὰ τούτων τίνας εἶναι τιθέασι τὰς ἀρχὰς καὶ πῶς εἰς τὰς εἰρημένας ἐμπίπτουσιν αἰτίας.
But the purpose for which we are reviewing this is that we may grasp from these thinkers as well what they posit as principles, and how these fall under the causes we have mentioned.
φαίνονται δὴ καὶ οὗτοι τὸν ἀριθμὸν νομίζοντες ἀρχὴν εἶναι καὶ ὡς ὕλην τοῖς οὖσι καὶ ὡς πάθη τε καὶ ἕξεις, τοῦ δὲ ἀριθμοῦ στοιχεῖα τό τε ἄρτιον καὶ τὸ περιττόν, τούτων δὲ τὸ μὲν πεπερασμένον τὸ δὲ ἄπειρον, τὸ δʼ ἓν ἐξ ἀμφοτέρων εἶναι τούτων (καὶ γὰρ ἄρτιον εἶναι καὶ περιττόν), τὸν δʼ ἀριθμὸν ἐκ τοῦ ἑνός, ἀριθμοὺς δέ, καθάπερ εἴρηται, τὸν ὅλον οὐρανόν. —ἕτεροι δὲ τῶν αὐτῶν τούτων τὰς ἀρχὰς δέκα λέγουσιν εἶναι τὰς κατὰ συστοιχίαν λεγομένας, πέρας ἄπειρον, περιττὸν ἄρτιον, ἓν πλῆθος, δεξιὸν ἀριστερόν, ἄρρεν θῆλυ, ἠρεμοῦν κινούμενον, εὐθὺ καμπύλον, φῶς σκότος, ἀγαθὸν κακόν, τετράγωνον ἑτερόμηκες·
Indeed, these thinkers too appear to believe that number is the principle, both as matter for existing things and as their attributes and states; and that the elements of number are the even and the odd, and of these the former is unlimited and the latter limited; and the one is composed of both of these (for it is both even and odd), and number is derived from the one, and the whole heaven, as has been said, consists of numbers. — But others of these same thinkers say that the principles are ten, which are spoken of according to the parallel alignment: limit and unlimited, odd and even, one and plurality, right and left, male and female, resting and moving, straight and curved, light and darkness, good and bad, square and oblong.
ὅνπερ τρόπον ἔοικε καὶ Ἀλκμαίων ὁ Κροτωνιάτης ὑπολαβεῖν, καὶ ἤτοι οὗτος παρʼ ἐκείνων ἢ ἐκεῖνοι παρὰ τούτου παρέλαβον τὸν λόγον τοῦτον·
In the same way Alcmaeon of Croton also seems to have conceived it, and either he took this theory from them or they from him.
καὶ γὰρ Ἀλκμαίων ἀπεφήνατο παραπλησίως τούτοις· φησὶ γὰρ εἶναι δύο τὰ πολλὰ τῶν ἀνθρωπίνων, λέγων τὰς ἐναντιότητας οὐχ ὥσπερ οὗτοι διωρισμένας ἀλλὰ τὰς τυχούσας, οἷον λευκὸν μέλαν, γλυκὺ πικρόν, ἀγαθὸν κακόν, μέγα μικρόν.
For Alcmaeon declared in a similar way to them; for he says that most human affairs are two, meaning the contraries, not defined as these thinkers did, but any chance ones, such as white and black, sweet and bitter, good and bad, great and small.
οὗτος μὲν οὖν ἀδιορίστως ἀπέρριψε περὶ τῶν λοιπῶν, οἱ δὲ Πυθαγόρειοι καὶ πόσαι καὶ τίνες αἱ ἐναντιώσεις ἀπεφήναντο.
This thinker, then, threw out suggestions about the other contraries in an undefined way, but the Pythagoreans declared both how many and what the contraries are.
παρὰ μὲν οὖν τούτων ἀμφοῖν τοσοῦτον ἔστι λαβεῖν, ὅτι τἀναντία ἀρχαὶ τῶν ὄντων· τὸ δʼ ὅσαι παρὰ τῶν ἑτέρων, καὶ τίνες αὗταί εἰσιν.
From both of these, then, so much can be gathered: that contraries are the principles of existing things; and how many they are and what they are, from the latter group.
πῶς μέντοι πρὸς τὰς εἰρημένας αἰτίας ἐνδέχεται συνάγειν, σαφῶς μὲν οὐ διήρθρωται παρʼ ἐκείνων, ἐοίκασι δʼ ὡς ἐν ὕλης εἴδει τὰ στοιχεῖα τάττειν· ἐκ τούτων γὰρ ὡς ἐνυπαρχόντων συνεστάναι καὶ πεπλάσθαι φασὶ τὴν οὐσίαν. —τῶν μὲν οὖν παλαιῶν καὶ πλείω λεγόντων τὰ στοιχεῖα τῆς φύσεως ἐκ τούτων ἱκανόν ἐστι θεωρῆσαι τὴν διάνοιαν·
How, however, it is possible to bring these into relation with the causes we have mentioned, has not been clearly articulated by them, but they seem to arrange the elements as in the form of matter; for they say that substance is composed and fashioned out of these as being immanent in it. — From these thinkers, then, both the ancients and those who speak of more than one element of nature, it is sufficient to observe their thought.
εἰσὶ δέ τινες οἳ περὶ τοῦ παντὸς ὡς μιᾶς οὔσης φύσεως ἀπεφήναντο, τρόπον δὲ οὐ τὸν αὐτὸν πάντες οὔτε τοῦ καλῶς οὔτε τοῦ κατὰ τὴν φύσιν.
But there are some who declared concerning the universe as being a single nature, yet not all in the same way, neither with respect to excellence nor according to nature.