§2.1010 Περὶ δὲ τῆς τάξεως αὐτῶν, ὃ μὲν τρόπον ἕκαστον κεῖται τῷ τὰ μὲν εἶναι πρότερα τὰ δʼ ὕστερα, καὶ πῶς ἔχει πρὸς ἄλληλα τοῖς ἀποστήμασιν, ἐκ τῶν περὶ ἀστρολογίαν θεωρείσθω· λέγεται γὰρ ἱκανῶς.
10 Concerning their order, in what manner each is situated by some being prior and others posterior, and how they are related to one another in their distances, let it be observed from the writings on astronomy; for it is sufficiently discussed.
συμβαίνει δὲ κατὰ λόγον γέγνεσθαι τὰς ἑκάστου κινήσεις τοῖς ἀποστήμασι τῷ τὰς μὲν εἶναι θάττους τὰς δὲ βραδυτέρας·
And it happens that the motions of each are in proportion to their distances by some being faster and others slower.
ἐπεὶ γὰρ ὑπόκειται τὴν μὲν ἐσχάτην τοῦ οὐρανοῦ περιφορὰν ἀπλῆν τʼ εἶναι καὶ ταχίστην, τὰς δὲ τῶν ἄλλων βραδυτέρας τε καὶ πλείους (ἕκακτον. γὰρ ἀντιφέρεται τῷ οὐρανῷ κατὰ τὸν αὑτοῦ κύκλον), εὔλογον ἤδῃ τὸ μὲν ἐγγυτάτω τῆς ἁπλῆς καὶ πρώτης περιφορᾶς ἐν πλείστῳ χρόνῳ διιέναι τὸν σὑτοῦ κύκλον, τὸ δὲ πορρωτάτω ἐν ἐλαχίστῳ, τῶν δʼ ἄλλων τὸ ἐγγύτερον ἀεὶ ἐν πλείονι, τὸ δὲ πορρώτερον ἐν ἐλάττονι.
For since it is assumed that the outermost revolution of the heaven is both simple and fastest, and those of the others are both slower and multiple (for each is carried in the opposite direction to the heaven along its own circle), it is then reasonable that that which is nearest to the simple and first revolution goes through its own circle in the longest time, and that which is furthest in the shortest [time], and of the others, that which is always nearer in a longer [time], and that which is further in a shorter [time].
τὸ μὲν γὰρ ἐγγυτάτω μάλιστα κρατεῖται, τὸ δὲ πορρωτάτω πάντων ἥκιστα διὰ τὴν ἀπόστασιν· τὰ δὲ μεταξὺ κατὰ λόγον ἤδη τῆς ἀποστάσεως, ὥσπερ καὶ δεικνύουσιν οἱ μαθηματιωοί.
For that which is nearest is dominated most, and that which is furthest of all least of all because of its distance; and the intermediate things then in proportion to their distance, just as the mathematicians also demonstrate.
§2.1111Τὸ δὲ σχῆμα τῶν ἄστρων ἑκάστου σφαιροειδὲς μάλιστʼ ἄν τις εὐλόγως ὑπολάβοι.
11 One might most reasonably assume that the shape of each of the stars is spherical.
ἐπεὶ γὰρ δέδεικται ὅτι οὐ πεφύκασι κινεῖσθαι διʼ ατῶν, ἡ δὲ φύσις οὐδὲν ἀλόγως οὐδὲ μάτην ποιεῖ, δῆλον ὅτι καὶ σχῆμα τοιοῦτον ἀπέδωκε τοῖς ἀκινήτοις ὃ ἥκιστά ἐστι κινητικόν.
For since it has been demonstrated that they are not by nature capable of moving by themselves, and nature does nothing unreasonable or in vain, it is clear that she also gave to the motionless things such a shape as is least capable of movement.
ἥκιστα δὲ κινητικὸν ἡ σφαῖρα διὰ τὸ μηδὲν ἔχειν ὄργανον πρὸς τὴν κίνησιν.
And the sphere is least capable of movement because of having no instrument for motion.
ὥστε δῆλον ὅτι σφαιροειδῆ ἂν εἴη τὸν ὄγκον.
So it is clear that they would be spherical in bulk.
ἔτι δʼ ὁμοίως μὲν ἅπαντα καὶ ἕν, ἡ δὲ σελήνη δείκνυται διὰ τῶν περὶ τὴν ὄψιν ὅτι σφαιροειδής· οὐ γὰρ ἂν ἐγίνετο αὐξανομένη καὶ φθίνουσα τὰ μὲν πλεῖστα μηνοειδὴς ἢ ἀμφίκυρτος ἅπαξ δὲ διχότομος. καὶ πάλιν διὰ τῶν ἀστρολογικῶν, ὅτι οὐκ ἂν ἦσαν αἱ τοῦ ἡλίου ἐκλείψεις μηνοειδεῖς.
Furthermore, all [stars] are alike and one [homogeneous sort], but the moon is shown through visual phenomena to be spherical; for [otherwise] in waxing and waning it would not become for the most part crescent-shaped or gibbous, and once dichotomous; and again through astronomical arguments, because the eclipses of the sun would not be crescent-shaped.
ὥστʼ εἴπερ ἓν τοιοῦτον, δῆλον ὅτι καὶ τἆλλα ἂν εἴη σφαιροειδῆ.
So if one is such, it is clear that the others also would be spherical.