§2.8#18 Ἐπεὶ δὲ φαίνεται καὶ τὰ ἄστρα μεθιστάμενα καὶ ὅλος ὁ οὐρανός, ἀναγκαῖον ἤτοι ἠρεμούντων ἀμφοτέρων γίγνεσθαι τὴν μεταβολήν, ἢ κινουμένων, ἢ τοῦ μὲν ἠρεμοῦντος τοῦ δὲ κινουμένου.
8 Since both the stars and the whole heaven appear to change their positions, it is necessary that this change occurs either with both at rest, or both in motion, or with one at rest and the other in motion.
ἀμφότερα μὲν τοίνυν ἠρεμεῖν ἀδύνατον ἠρεμούσης γε τῆς γῆς· οὐ γὰρ ἂν ἐγίγνετο τὰ φαινόμενα.
Now, it is impossible for both to be at rest while the earth is at rest; for the observed phenomena would not occur.
τὴν δὲ γῆν ὑποκείσθω ἠρεμεῖν.
And let it be assumed that the earth is at rest.
λείπεται δὴ ἢ ἀμφότερα κινεῖσθαι, τὸ μὲν κινεῖσθαι τὸ δʼ ἠρεμεῖν.
There remains, then, either that both are in motion, or that one is in motion and the other at rest.
εἰ μὲν οὖν ἀμφότερα κινήσεται, ἄλογον τὸ ταὐτὰ τάχη τῶν ἄστρων εἶναι καὶ τῶν κύκλων· ἕκαστον γὰρ δὴ ὁμοταχὲς ἔσται τῷ κύκλῳ καθʼ ὃν φέρεται.
If, then, both are to be in motion, it is unreasonable that the speeds of the stars and of their circles should be the same; for indeed each star will be of equal speed with the circle on which it is carried.
φαίνεται γὰρ ἅμα τοῖς κύκλοις καθιστάμενα πάλιν εἰς τὸ αὐτό.
For they appear to return to the same position again at the same time as their circles.
συμβαίνει οὖν ἅμα τό τε ἄστρον διεληλυθέναι τὸν κύκλον καὶ τὸν κύκλον ἐνηνέχθαι τὴν αὑτοῦ φοράν, διεληλυθότα τὴν αὑτοῦ περιφέρειαν.
It follows, then, that at one and the same time the star has traversed its circle and the circle has been carried through its own motion, having traversed its own circumference.
οὐκ ἔστι δʼ εὔλογον τὸ τὸν αὐτὸν λόγον ἔχειν τὰ τάχη τῶν ἄστρων καὶ τὰ μεγέθη τῶν κύκλων.
But it is not reasonable that the speeds of the stars and the sizes of the circles should have the same ratio.
τοὺς μὲν γὰρ κύκλους οὐθὲν ἄτοπον ἀλλʼ ἀναγκαῖον ἀνάλογον ἔχειν τὰ τάχη τοῖς μεγέθεσι, τῶν δʼ ἄστρων ἕκαστον τῶν ἐν τούτοις οὐδαμῶς εὔλογον·
For while there is nothing strange but rather a necessity for the circles to have their speeds proportional to their sizes, it is in no way reasonable for each of the stars in them to do so.
εἴτε γὰρ ἐξ ἀνάγκης τὸ τὸν μείζω κύκλον φερόμενον θᾶττον ἔσται, δῆλον ὅτι κἂν μετατεθῇ τὰ ἄστρα εἰς τοὺς ἀλλήλων κύκλους, τὸ μὲν ἔσται θᾶττον τὸ δὲ βραδύτερον· οὕτω δʼ οὐκ ἂν ἔχοιεν οἰκείαν κίνησιν, ἀλλὰ φέροιντʼ ἂν ὑπὸ τῶν κύκλων.
For if indeed by necessity the star carried on the larger circle is to be faster, it is clear that even if the stars were transposed into each other's circles, the one will be faster and the other slower; but in this way they would not have any motion of their own, but would be carried by the circles.
εἴτε ἀπὸ ταὐτομάτου συνέπεσεν, οὐδʼ οὕτως εὔλογον ὥστʼ ἐν ἅπασιν ἅμα τόν τε κύκλον εἶναι μείζω καὶ τὴν φορὰν θάττω τοῦ ἐν αὐτῷ ἄστρου· τὸ μὲν γὰρ ἓν ἢ δύο τοῦτον τὸν τρόπον ἔχειν οὐθὲν ἄτοπον, τὸ δὲ πάνθʼ ὁμοίως πλάσματι ἔοικεν.
Or if it happened by chance, even so it is not reasonable that in all cases at once the circle should be larger and the movement of the star in it faster; for while for one or two things to be in this state is nothing strange, for all of them to be so alike seems like a fiction.
ἄμα δὲ καὶ οὐκ ἔστιν ἐν τοῖς φύσει τὸ ὡς ἔτυχεν, οὐδὲ τὸ πανταχοῦ καὶ πᾶσιν ὑπάρχον τὸ ἀπὸ τύχης.
And at the same time, among things which exist by nature there is nothing which is random, nor is that which is everywhere and present to all things a matter of chance.
ἀλλὰ μὴν πάλιν εἰ οἱ μὲν κύκλοι μένουσιν, αὐτὰ δὲ τὰ ἄστρα κινεῖται, ταὕτα καὶ ὁμοίως ἔσται ἄλογα· συμβήσεται γὰρ θᾶττον κινεῖσθαι τὰ ἔξω, καὶ τὰ τάχη εἶναι κατὰ τὰ μεγέθη τῶν κύκλων.
But furthermore, if on the other hand the circles remain stationary and the stars themselves are in motion, the same and similar difficulties will follow; for it will result that the outer stars move faster, and that their speeds are in proportion to the sizes of their circles.
ἐπεὶ τοίνυν οὕτʼ ἀμφότερα κινεῖσθαι εὔλογον οὕτε τὸ ἄστρον μόνον, λείπεται τούς μὲν κύκλους κινεῖσθαι, τὰ δὲ ἄστρα ἠρεμεῖν καὶ ἐνδεδεμένα τοῖς κύκλοις φέρεσθαι· μόνως γὰρ οὕτως οὐθὲν ἄλογον συμβαίνει·
Since, then, it is reasonable neither that both should be in motion nor that the star alone should be, it remains that the circles are in motion, while the stars are at rest and are carried along being bound to the circles; for only in this way does nothing unreasonable follow.
τό τε γὰρ θᾶττον εἶναι τοῦ μείζονος κύκλου κλουτὸ τάχος εὔλογον περὶ τὸ αὐτὸ κέντρον ἐνδεδεμένων (ὥσπερ γὰρ ἐν τοῖς ἄλλοις τὸ μεῖζον σῶμα θᾶττον φέρεται τὴν οἰκείαν φοράν, οὕτως καὶ ἐν τοῖς ἐγκυκλίοις· μεῖζον γὰρ τῶν ἀφαιρουμένων ὑπὸ τῶν ἐκ τοῦ κέντρου τὸ τοῦ μείζονος κύκλου τμῆμα, ὥστʼ εὐλόγως ἐν τῷ ἴσῳ χρόνῳ ὁ μείζων περιοισθήσεται κύκλος), τό τε μὴ διασπᾶσθαι τὸν οὐρανὸν διά τε τοῦτο συμβήσεται καὶ ὅτι δέδεικται συνεχὲς ὄν τὸ ὅλον.
For that the speed of the larger circle should be faster is reasonable when they are bound about the same center (since just as among other bodies the larger body is carried more swiftly in its own proper motion, so it is also among circular bodies; for the segment of the larger circle is larger than the parts cut off by the radii, so that reasonably in an equal time the larger circle will be carried around), and that the heaven is not torn asunder will result both for this reason and because the whole has been shown to be continuous.