Name: On the Heavens, Book II
Author: Aristotle

Moraux (Budé, 1965) · Stocks (1922)

Stocks (1922)

Greek line numbers are exact. The translations carry no Bekker numbers of their own, so those beside the English are aligned to the Greek: upright = fixed (anchored to this point in the text), italic grey = approximate (interpolated estimate).

Book 2,Chapter 1 (283b26–284b5)

283b

Ὅτι μὲν οὖν οὔτε γέγονεν ὁ πᾶς οὐρανὸς οὔτ' ἐνδέχεται

φθαρῆναι, καθάπερ τινές φασιν αὐτόν, ἀλλ' ἔστιν εἷς καὶ

ἀΐδιος, ἀρχὴν μὲν καὶ τελευτὴν οὐκ ἔχων τοῦ παντὸς αἰῶνος,

ἔχων δὲ καὶ περιέχων ἐν αὑτῷ τὸν ἄπειρον χρόνον, ἔκ τε

30 τῶν εἰρημένων ἔξεστι λαμβάνειν τὴν πίστιν, καὶ διὰ τῆς δόξης

τῆς παρὰ τῶν ἄλλως λεγόντων καὶ γεννώντων αὐτόν· εἰ

γὰρ οὕτως μὲν ἔχειν ἐνδέχεται, καθ' ὃν δὲ τρόπον ἐκεῖνοι

γενέσθαι λέγουσιν οὐκ ἐνδέχεται, μεγάλην ἂν ἔχοι καὶ τοῦτο

That the heaven as a whole neither came into being nor admits of destruction, as some assert, but is one and eternal, with no end or beginning of its total duration, containing and embracing in itself the infinity of time, we may convince ourselves not only by the arguments already set forth but also by a consideration of the views 30of those who differ from us in providing for its generation. If our view is a possible one, and the manner of generation which they assert is impossible, this fact will have great weight in convincing us of the immortality and eternity of the world.

284a

1 ῥοπὴν εἰς πίστιν περὶ τῆς ἀθανασίας αὐτοῦ καὶ τῆς ἀϊδιότητος.

Διόπερ καλῶς ἔχει συμπείθειν ἑαυτὸν τοὺς ἀρχαίους

καὶ μάλιστα πατρίους ἡμῶν ἀληθεῖς εἶναι λόγους, ὡς ἔστιν

ἀθάνατόν τι καὶ θεῖον τῶν ἐχόντων μὲν κίνησιν, ἐχόντων

5 δὲ τοιαύτην ὥστε μηθὲν εἶναι πέρας αὐτῆς, ἀλλὰ μᾶλλον

ταύτην τῶν ἄλλων πέρας· τό τε γὰρ πέρας τῶν περιεχόντων

ἐστί, καὶ αὕτη τέλειος οὖσα περιέχει τὰς ἀτελεῖς καὶ

τὰς ἐχούσας πέρας καὶ παῦλαν, αὐτὴ μὲν οὐδεμίαν οὔτ'

ἀρχὴν ἔχουσα οὔτε τελευτήν, ἀλλ' ἄπαυστος οὖσα τὸν ἄπειρον

10 χρόνον, τῶν δ' ἄλλων τῶν μὲν αἰτία τῆς ἀρχῆς, τῶν

δὲ δεχομένη τὴν παῦλαν. Τὸν δ' οὐρανὸν καὶ τὸν ἄνω τόπον

οἱ μὲν ἀρχαῖοι τοῖς θεοῖς ἀπένειμαν ὡς ὄντα μόνον ἀθάνατον·

ὁ δὲ νῦν μαρτυρεῖ λόγος ὡς ἄφθαρτος καὶ ἀγένητος,

ἔτι δ' ἀπαθὴς πάσης θνητῆς δυσχερείας ἐστίν, πρὸς δὲ τούτοις

15 ἄπονος διὰ τὸ μηδεμιᾶς προσδεῖσθαι βιαίας ἀνάγκης, ἣ

κατέχει κωλύουσα φέρεσθαι πεφυκότα αὐτὸν ἄλλως· πᾶν

γὰρ τὸ τοιοῦτον ἐπίπονον, ὅσῳπερ ἂν ἀϊδιώτερον ᾖ, καὶ διαθέσεως

τῆς ἀρίστης ἄμοιρον. Διόπερ οὔτε κατὰ τὸν τῶν παλαιῶν

μῦθον ὑποληπτέον ἔχειν, οἵ φασιν Ἄτλαντός τινος

20 αὐτῷ προσδεῖσθαι τὴν σωτηρίαν· ἐοίκασι γὰρ καὶ τοῦτον οἱ

συστήσαντες τὸν λόγον τὴν αὐτὴν ἔχειν ὑπόληψιν τοῖς ὕστερον·

ὡς γὰρ περὶ βάρος ἐχόντων καὶ γεηρῶν ἁπάντων τῶν

ἄνω σωμάτων ὑπέστησαν αὐτῷ μυθικῶς ἀνάγκην ἔμψυχον.

Οὔτε δὴ τοῦτον τὸν τρόπον ὑποληπτέον, οὔτε διὰ τὴν δίνησιν

25 θάττονος τυγχάνοντα φορᾶς τῆς οἰκείας ῥοπῆς ἔτι

σώζεσθαι τοσοῦτον χρόνον, καθάπερ Ἐμπεδοκλῆς φησιν.

Ἀλλὰ μὴν οὐδ' ὑπὸ ψυχῆς εὔλογον ἀναγκαζούσης μένειν

ἀΐδιον· οὐδὲ γὰρ τῆς ψυχῆς οἷόν τ' εἶναι τὴν τοιαύτην ζωὴν

ἄλυπον καὶ μακαρίαν· ἀνάγκη γὰρ καὶ τὴν κίνησιν μετὰ βίας

30 οὖσαν, εἴπερ κινεῖ φέρεσθαι πεφυκότος τοῦ πρώτου σώματος

ἄλλως καὶ κινεῖ συνεχῶς, ἄσχολον εἶναι καὶ πάσης ἀπηλλαγμένην

ῥαστώνης ἔμφρονος, εἴ γε μηδ' ὥσπερ τῇ ψυχῇ τῇ

τῶν θνητῶν ζῴων ἐστὶν ἀνάπαυσις ἡ περὶ τὸν ὕπνον γινομένη

τοῦ σώματος ἄνεσις, ἀλλ' ἀναγκαῖον Ἰξίονός τινος μοῖραν

35 κατέχειν αὐτὴν ἀΐδιον καὶ ἄτρυτον. Εἰ δή, καθάπερ εἴπομεν,

1Hence it is well to persuade oneself of the truth of the ancient and truly traditional theories, that there is some immortal and divine thing which possesses movement, but movement such as has no limit and is rather itself the limit of all other movement. 5A limit is a thing which contains; and this motion, being perfect, contains those imperfect motions which have a limit and a goal, having itself no beginning or end, but unceasing through the infinity of time, and of other movements, to some the cause of their beginning, to others offering the goal. The ancients 10gave to the Gods the heaven or upper place, as being alone immortal; and our present argument testifies that it is indestructible and ungenerated. Further, it is unaffected by any mortal discomfort, and, in addition, effortless; for it needs no constraining necessity to keep it to its path, and prevent it from moving 15with some other movement more natural to itself. Such a constrained movement would necessarily involve effort the more so, the more eternal it were-and would be inconsistent with perfection. Hence we must not believe the old tale which says that the world needs some Atlas to keep it safe-a tale composed, it would 20seem, by men who, like later thinkers, conceived of all the upper bodies as earthy and endowed with weight, and therefore supported it in their fabulous way upon animate necessity. We must no more believe that than follow Empedocles when he says that the world, by being whirled round, received a movement quick 25enough to overpower its own downward tendency, and thus has been kept from destruction all this time. Nor, again, is it conceivable that it should persist eternally by the necessitation of a soul. For a soul could not live in such conditions painlessly or happily, since the movement involves constraint, being imposed 30on the first body, whose natural motion is different, and imposed continuously. It must therefore be uneasy and devoid of all rational satisfaction; for it could not even, like the soul of mortal animals, take recreation in the bodily relaxation of sleep. An Ixion's lot must needs possess it, without end or respite.

284b

1 ἐνδέχεται τὸν εἰρημένον ἔχειν τρόπον περὶ τῆς πρώτης

φορᾶς, οὐ μόνον αὐτοῦ περὶ τῆς ἀϊδιότητος οὕτως ὑπολαβεῖν

ἐμμελέστερον, ἀλλὰ καὶ τῇ μαντείᾳ τῇ περὶ τὸν θεὸν μόνως

ἂν ἔχοιμεν οὕτως ὁμολογουμένως ἀποφαίνεσθαι συμφώνους

5 λόγους. Ἀλλὰ τῶν μὲν τοιούτων λόγων ἅλις ἔστω τὸ νῦν.

1If then, as we said, the view already stated of the first motion is a possible one, it is not only more appropriate so to conceive of its eternity, but also on this hypothesis alone are we able to advance a theory consistent with popular divinations of the divine nature. 5But of this enough for the present.

Book 2,Chapter 2 (284b6–286a2)

Ἐπειδὴ δέ τινές εἰσιν οἵ φασιν εἶναί τι δεξιὸν καὶ ἀριστερὸν

τοῦ οὐρανοῦ, καθάπερ οἱ καλούμενοι Πυθαγόρειοι (ἐκείνων

γὰρ οὗτος ὁ λόγος ἐστίν), σκεπτέον πότερον τοῦτον ἔχει τὸν

τρόπον ὡς ἐκεῖνοι λέγουσιν, ἢ μᾶλλον ἑτέρως, εἴπερ δεῖ

10 προσάπτειν τῷ τοῦ παντὸς σώματι ταύτας τὰς ἀρχάς. Εὐθὺς

γὰρ πρῶτον, εἰ τὸ δεξιὸν ὑπάρχει καὶ τὸ ἀριστερόν, ἔτι

πρότερον τὰς προτέρας ὑποληπτέον ὑπάρχειν ἀρχὰς ἐν

αὐτῷ. Διώρισται μὲν οὖν περὶ τούτων ἐν τοῖς περὶ τὰς τῶν

ζῴων κινήσεις διὰ τὸ τῆς φύσεως οἰκεῖα τῆς ἐκείνων εἶναι·

15 φανερῶς γὰρ ἔν γε τοῖς ζῴοις ὑπάρχοντα φαίνεται τοῖς μὲν

πάντα τὰ τοιαῦτα μόρια, λέγω δ' οἷον τό τε δεξιὸν καὶ τὸ

ἀριστερόν, τοῖς δ' ἔνια, τοῖς δὲ φυτοῖς τὸ ἄνω καὶ τὸ κάτω

μόνον. Εἰ δὲ δεῖ καὶ τῷ οὐρανῷ προσάπτειν τι τῶν τοιούτων,

καὶ τὸ πρῶτον, καθάπερ εἴπομεν, ἐν τοῖς ζῴοις ὑπάρχον εὔλογον

20 ὑπάρχειν ἐν αὐτῷ· τριῶν γὰρ ὄντων ἕκαστον οἷον ἀρχή

τις ἐστίν. Λέγω δὲ τὰ τρία τὸ ἄνω καὶ τὸ κάτω, καὶ τὸ

πρόσθιον καὶ τὸ ἀντικείμενον, καὶ τὸ δεξιὸν καὶ τὸ ἀριστερόν·

ταύτας γὰρ τὰς διαστάσεις εὔλογον ὑπάρχειν τοῖς σώμασι

τοῖς τελείοις πάσας. Ἔστι δὲ τὸ μὲν ἄνω τοῦ μήκους ἀρχή, τὸ

25 δὲ δεξιὸν τοῦ πλάτους, τὸ δ' ἔμπροσθεν τοῦ βάθους. Ἔτι δ'

ἄλλως κατὰ τὰς κινήσεις· ἀρχὰς γὰρ ταύτας λέγω ὅθεν ἄρχονται

πρῶτον αἱ κινήσεις τοῖς ἔχουσιν. Ἔστι δὲ ἀπὸ μὲν τοῦ

ἄνω ἡ αὔξησις, ἀπὸ δὲ τῶν δεξιῶν ἡ κατὰ τόπον, ἀπὸ δὲ

τῶν ἔμπροσθεν ἡ κατὰ τὴν αἴσθησιν· ἔμπροσθεν γὰρ λέγω

30 ἐφ' ὃ αἱ αἰσθήσεις. Διὸ καὶ οὐκ ἐν ἅπαντι σώματι τὸ ἄνω

καὶ κάτω καὶ τὸ δεξιὸν καὶ ἀριστερὸν καὶ τὸ ἔμπροσθεν καὶ

ὄπισθεν ζητητέον, ἀλλ' ὅσα ἔχει κινήσεως ἀρχὴν ἐν αὑτοῖς

ἔμψυχα ὄντα· τῶν γὰρ ἀψύχων ἐν οὐθενὶ ὁρῶμεν ὅθεν ἡ

ἀρχὴ τῆς κινήσεως. Τὰ μὲν γὰρ ὅλως οὐ κινεῖται, τὰ δὲ κινεῖται

35 μὲν ἀλλ' οὐ πανταχόθεν ὁμοίως, οἷον τὸ πῦρ ἄνω μόνον

Since there are some who say that there is a right and a left in the heaven, with those who are known as Pythagoreans-to whom indeed the view really belongs-we must consider whether, if we are to apply these principles to the body of the universe, we should follow their statement of the matter or 10find a better way. At the start we may say that, if right and left are applicable, there are prior principles which must first be applied. These principles have been analysed in the discussion of the movements of animals, for the reason that they are proper to animal nature. For in some animals we find all such distinctions of parts as 15this of right and left clearly present, and in others some; but in plants we find only above and below. Now if we are to apply to the heaven such a distinction of parts, we must exect, as we have said, to find in it also the distinction which in animals is found first of them all. The distinctions are three, namely, above and below, front 20and its opposite, right and left-all these three oppositions we expect to find in the perfect body-and each may be called a principle. Above is the principle of length, right of breadth, front of depth. Or again we may connect them with the various movements, taking principle to mean that part, in a thing capable of movement, from which 25movement first begins. Growth starts from above, locomotion from the right, sensemovement from in front (for front is simply the part to which the senses are directed). Hence we must not look for above and below, right and left, front and back, in every kind of body, but only in those which, being animate, have a principle of movement 30within themselves. For in no inanimate thing do we observe a part from which movement originates. Some do not move at all, some move, but not indifferently in any direction; fire, for example, only upward, and earth only to the centre. It is true that we speak of above and below, right and left, in these bodies relatively to ourselves.

285a

1 καὶ ἡ γῆ ἐπὶ τὸ μέσον. Ἀλλ' ἐν μὲν τούτοις λέγομεν τὸ

ἄνω καὶ τὸ κάτω καὶ τὸ δεξιὸν καὶ τὸ ἀριστερὸν πρὸς ἡμᾶς ἐπαναφέροντες·

ἢ γὰρ κατὰ τὰ ἡμέτερα δεξιά, ὥσπερ οἱ μάντεις,

ἢ καθ' ὁμοιότητα τοῖς ἡμετέροις, ὥσπερ τὰ τοῦ ἀνδριάντος,

5 ἢ τὰ ἐναντίως ἔχοντα τῇ θέσει, δεξιὸν μὲν τὸ κατὰ τὸ

ἡμέτερον ἀριστερόν, ἀριστερὸν δὲ τὸ κατὰ τὸ ἡμέτερον δεξιόν,

[καὶ ὄπισθεν τὸ κατὰ τὸ ἡμέτερον ἔμπροσθεν]. Ἐν αὐτοῖς δὲ

τούτοις οὐδεμίαν ὁρῶμεν διαφοράν· ἐὰν γὰρ ἀνάπαλιν στραφῇ,

τὰ ἐναντία ἐροῦμεν δεξιὰ καὶ ἀριστερὰ καὶ ἄνω καὶ κάτω καὶ

10 ἔμπροσθεν καὶ ὄπισθεν. Διὸ καὶ τῶν Πυθαγορείων ἄν τις θαυμάσειεν

ὅτι δύο μόνας ταύτας ἀρχὰς ἔλεγον, τὸ δεξιὸν καὶ

τὸ ἀριστερόν, τὰς δὲ τέτταρας παρέλιπον οὐθὲν ἧττον κυρίας

οὔσας· οὐθὲν γὰρ ἐλάττω διαφορὰν ἔχει τὰ ἄνω πρὸς τὰ

κάτω καὶ τὰ ἔμπροσθεν πρὸς τὰ ὄπισθεν ἢ τὰ δεξιὰ πρὸς

15 τὰ ἀριστερὰ ἐν ἅπασι τοῖς ζῴοις. Τὰ μὲν γὰρ τῇ δυνάμει

διαφέρει μόνον, τὰ δὲ καὶ τοῖς σχήμασι, καὶ τὸ μὲν ἄνω

καὶ τὸ κάτω πᾶσι τοῖς ἐμψύχοις ἐστὶν ὁμοίως ζῴοις καὶ

φυτοῖς, τὸ δὲ δεξιὸν καὶ τὸ ἀριστερὸν οὐκ ἐνυπάρχει τοῖς φυτοῖς.

Ἔτι δ' ὡς τὸ μῆκος τοῦ πλάτους πρότερον, εἰ τὸ μὲν ἄνω

20 τοῦ μήκους ἀρχή, τὸ δὲ δεξιὸν τοῦ πλάτους, ἡ δὲ τοῦ προτέρου

ἀρχὴ προτέρα, πρότερον ἂν εἴη τὸ ἄνω τοῦ δεξιοῦ κατὰ γένεσιν,

ἐπειδὴ πολλαχῶς λέγεται τὸ πρότερον. Πρὸς δὲ τούτοις,

εἰ τὸ μὲν ἄνω ἐστὶ τὸ ὅθεν ἡ κίνησις, τὸ δὲ δεξιὸν

ἀφ' οὗ, τὸ δ' ἔμπροσθεν ἐφ' ὅ, κἂν οὕτως ἔχοι τινὰ δύναμιν

25 ἀρχῆς τὸ ἄνω πρὸς τὰς ἄλλας ἰδέας. Διά τε δὴ τὸ

παραλείπειν τὰς κυριωτέρας ἀρχὰς δίκαιον αὐτοῖς ἐπιτιμᾶν,

καὶ διότι ταύτας ἐν ἅπασιν ὁμοίως ἐνόμιζον ὑπάρχειν. Ἡμῖν

δ' ἐπεὶ διώρισται πρότερον ὅτι ἐν τοῖς ἔχουσιν ἀρχὴν κινήσεως

αἱ τοιαῦται δυνάμεις ἐνυπάρχουσιν, ὁ δ' οὐρανὸς ἔμψυχος

30 καὶ ἔχει κινήσεως ἀρχήν, δῆλον ὅτι ἔχει καὶ τὸ ἄνω καὶ

τὸ κάτω καὶ τὸ δεξιὸν καὶ τὸ ἀριστερόν. Οὐ δεῖ γὰρ ἀπορεῖν

διὰ τὸ σφαιροειδὲς εἶναι τὸ σχῆμα τοῦ παντός, ὅπως ἔσται

τούτου τὸ μὲν δεξιὸν τὸ δὲ ἀριστερὸν ὁμοίων γ' ὄντων τῶν μορίων

1The reference may be to our own right hands, as with the diviner, or to some similarity to our own members, such as the parts of a statue possess; or we may take the contrary spatial order, calling right that which is to our left, and left that which is to our right. We observe, 5however, in the things themselves none of these distinctions; indeed if they are turned round we proceed to speak of the opposite parts as right and left, a boy land below, front and back. Hence it is remarkable that the Pythagoreans should have spoken of these two principles, right and left, only, to the exclusion of the other four, which 10have as good a title as they. There is no less difference between above and below or front and back in animals generally than between right and left. The difference is sometimes only one of function, sometimes also one of shape; and while the distinction of above and below is characteristic of all animate things, whether plants or animals, 15that of right and left is not found in plants. Further, inasmuch as length is prior to breadth, if above is the principle of length, right of breadth, and if the principle of that which is prior is itself prior, then above will be prior to right, or let us say, since 'prior' is ambiguous, prior in order of generation. If, in addition, above is 20the region from which movement originates, right the region in which it starts, front the region to which it is directed, then on this ground too above has a certain original character as compared with the other forms of position. On these two grounds, then, they may fairly be criticized, first, for omitting the more fundamental principles, 25and secondly, for thinking that the two they mentioned were attributable equally to everything.
Since we have already determined that functions of this kind belong to things which possess, a principle of movement, and that the heaven is animate and possesses a principle of movement, clearly the heaven must also exhibit above and below, right 30and left. We need not be troubled by the question, arising from the spherical shape of the world, how there can be a distinction of right and left within it, all parts being alike and all for ever in motion.

285b

1 ἁπάντων καὶ κινουμένων τὸν ἅπαντα χρόνον, ἀλλὰ

νοεῖν ὥσπερ ἂν εἴ τις, ἐν οἷς ἔχει τὸ δεξιὸν πρὸς τὸ ἀριστερὸν διαφορὰν

καὶ τοῖς σχήμασιν, εἶτα περιθείη σφαῖραν· ἕξει μὲν

γὰρ τὴν δύναμιν διαφέρουσαν, δόξει δ' οὔ, διὰ τὴν ὁμοιότητα

5 τοῦ σχήματος. Τὸν αὐτὸν δὲ τρόπον καὶ περὶ τῆς ἀρχῆς τοῦ

κινεῖσθαι· καὶ γὰρ εἰ μηδέποτ' ἤρξατο, ὅμως ἔχειν ἀναγκαῖον

ἀρχήν, ὅθεν ἂν ἤρξατο, εἰ ἤρχετο κινούμενον, κἂν εἰ

σταίη, κινηθείη ἂν πάλιν. Λέγω δὲ μῆκος μὲν αὐτοῦ τὸ κατὰ

τοὺς πόλους διάστημα, καὶ τῶν πόλων τὸν μὲν ἄνω τὸν δὲ

10 κάτω· διαφορὰν γὰρ ἐν τούτοις μόνοις ὁρῶμεν τῶν ἡμισφαιρίων,

τῷ μὴ κινεῖσθαι τοὺς πόλους. Ἅμα δὲ καὶ εἰώθαμεν

λέγειν τὰ πλάγια ἐν τῷ κόσμῳ οὐ τὸ ἄνω καὶ τὸ κάτω,

ἀλλὰ τὸ παρὰ τοὺς πόλους, ὡς τούτου μήκους ὄντος· τὸ γὰρ εἰς

τὸ πλάγιόν ἐστι τὸ παρὰ τὸ ἄνω καὶ τὸ κάτω. Τῶν δὲ πόλων

15 ὁ μὲν ὑπὲρ ἡμᾶς φαινόμενος τὸ κάτω μέρος ἐστίν, ὁ δ' ἡμῖν

ἄδηλος τὸ ἄνω. Δεξιὸν γὰρ ἑκάστου λέγομεν, ὅθεν ἡ ἀρχὴ

τῆς κατὰ τόπον κινήσεως· τοῦ δ' οὐρανοῦ ἀρχὴ τῆς περιφορᾶς,

ὅθεν αἱ ἀνατολαὶ τῶν ἄστρων, ὥστε τοῦτ' ἂν εἴη δεξιόν,

οὗ δ' αἱ δύσεις, ἀριστερόν. Εἰ οὖν ἄρχεται ἀπὸ τῶν δεξιῶν

20 καὶ ἐπὶ τὰ δεξιὰ περιφέρεται, ἀνάγκη τὸ ἄνω εἶναι τὸν

ἀφανῆ πόλον· εἰ γὰρ ἔσται ὁ φανερός, ἐπ' ἀριστερὰ ἔσται ἡ

κίνησις, ὅπερ οὔ φαμεν. Δῆλον τοίνυν ὅτι ὁ ἀφανὴς πόλος

ἐστὶ τὸ ἄνω. Καὶ οἱ μὲν ἐκεῖ οἰκοῦντες ἐν τῷ ἄνω εἰσὶν ἡμισφαιρίῳ

καὶ πρὸς τοῖς δεξιοῖς, ἡμεῖς δ' ἐν τῷ κάτω καὶ

25 πρὸς τοῖς ἀριστεροῖς, ἐναντίως ἢ ὡς οἱ Πυθαγόρειοι λέγουσιν·

ἐκεῖνοι γὰρ ἡμᾶς ἄνω ποιοῦσι καὶ ἐν τῷ δεξιῷ μέρει, τοὺς

δ' ἐκεῖ κάτω καὶ ἐν τῷ ἀριστερῷ. Συμβαίνει δὲ τοὐναντίον.

Ἀλλὰ τῆς μὲν δευτέρας περιφορᾶς, οἷον τῆς τῶν πλανήτων,

ἡμεῖς μὲν ἐν τοῖς ἄνω καὶ ἐν τοῖς δεξιοῖς ἐσμεν, ἐκεῖνοι δὲ

30 ἐν τοῖς κάτω καὶ ἐν τοῖς ἀριστεροῖς· ἀνάπαλιν γὰρ τούτοις

ἡ ἀρχὴ τῆς κινήσεώς ἐστι διὰ τὸ ἐναντίας εἶναι τὰς φοράς,

ὥστε συμβαίνειν ἡμᾶς μὲν εἶναι πρὸς τῇ ἀρχῇ, ἐκείνους

δὲ πρὸς τῷ τέλει. Περὶ μὲν οὖν τῶν κατὰ τὰς διαστάσεις

1We must think of the world as of something in which right differs from left in shape as well as in other respects, which subsequently is included in a sphere. The difference of function will persist, but will appear not to by reason of the regularity of shape. In 5the same fashion must we conceive of the beginning of its movement. For even if it never began to move, yet it must possess a principle from which it would have begun to move if it had begun, and from which it would begin again if it came to a stand. Now by its length I mean the interval between its poles, one pole being above and 10the other below; for two hemispheres are specially distinguished from all others by the immobility of the poles. Further, by 'transverse' in the universe we commonly mean, not above and below, but a direction crossing the line of the poles, which, by implication, is length: for transverse motion is motion crossing motion up and down. 15Of the poles, that which we see above us is the lower region, and that which we do not see is the upper. For right in anything is, as we say, the region in which locomotion originates, and the rotation of the heaven originates in the region from which the stars rise. So this will be the right, and the region where they set the 20left. If then they begin from the right and move round to the right, the upper must be the unseen pole. For if it is the pole we see, the movement will be leftward, which we deny to be the fact. Clearly then the invisible pole is above. And those who live in the other hemisphere are above and to the right, while we are below and to 25the left. This is just the opposite of the view of the Pythagoreans, who make us above and on the right side and those in the other hemisphere below and on the left side; the fact being the exact opposite. Relatively, however, to the secondary revolution, I mean that of the planets, we are above and on the right and they are below 30and on the left. For the principle of their movement has the reverse position, since the movement itself is the contrary of the other: hence it follows that we are at its beginning and they at its end.

286a

1 τῶν μορίων καὶ τῶν κατὰ τόπον ὡρισμένων τοσαῦτα

εἰρήσθω.

1Here we may end our discussion of the distinctions of parts created by the three dimensions and of the consequent differences of position.

Book 2,Chapter 3 (286a3–286b9)

Ἐπεὶ δ' οὐκ ἔστιν ἐναντία κίνησις ἡ κύκλῳ τῇ κύκλῳ,

σκεπτέον διὰ τί πλείους εἰσὶ φοραί, καίπερ πόρρωθεν πειρωμένοις

5 ποιεῖσθαι τὴν ζήτησιν, πόρρω δ' οὐχ οὕτω τῷ τόπῳ,

πολὺ δὲ μᾶλλον τῷ τῶν συμβεβηκότων αὐτοῖς περὶ πάμπαν

ὀλίγων ἔχειν αἴσθησιν. Ὅμως δὲ λέγωμεν. Ἡ δ' αἰτία περὶ

αὐτῶν ἐνθένδε ληπτέα. Ἕκαστόν ἐστιν, ὧν ἐστιν ἔργον, ἕνεκα

τοῦ ἔργου. Θεοῦ δ' ἐνέργεια ἀθανασία· τοῦτο δ' ἐστὶ ζωὴ ἀΐδιος.

10 ὥστ' ἀνάγκη τῷ θεῷ κίνησιν ἀΐδιον ὑπάρχειν. Ἐπεὶ δ' ὁ οὐρανὸς

τοιοῦτος (σῶμα γάρ τι θεῖον), διὰ τοῦτο ἔχει τὸ ἐγκύκλιον

σῶμα, ὃ φύσει κινεῖται κύκλῳ ἀεί. Διὰ τί οὖν οὐχ

ὅλον τὸ σῶμα τοῦ οὐρανοῦ τοιοῦτον; ὅτι ἀνάγκη μένειν τι τοῦ

σώματος τοῦ φερομένου κύκλῳ, τὸ ἐπὶ τοῦ μέσου, τούτου δ' οὐθὲν

15 οἷόν τε μένειν μόριον, οὔθ' ὅλως οὔτ' ἐπὶ τοῦ μέσου. Καὶ

γὰρ ἂν ἡ κατὰ φύσιν κίνησις ἦν αὐτοῦ ἐπὶ τὸ μέσον· φύσει

δὲ κύκλῳ κινεῖται· οὐ γὰρ ἂν ἦν ἀΐδιος ἡ κίνησις· οὐθὲν

γὰρ παρὰ φύσιν ἀΐδιον. Ὕστερον δὲ τὸ παρὰ φύσιν τοῦ κατὰ

φύσιν, καὶ ἔκστασίς τίς ἐστιν ἐν τῇ γενέσει τὸ παρὰ φύσιν

20 τοῦ κατὰ φύσιν. Ἀνάγκη τοίνυν γῆν εἶναι· τοῦτο γὰρ ἠρεμεῖ

ἐπὶ τοῦ μέσου. Νῦν μὲν οὖν ὑποκείσθω τοῦτο, ὕστερον δὲ δειχθήσεται

περὶ αὐτοῦ. Ἀλλὰ μὴν εἰ γῆν, ἀνάγκη καὶ πῦρ εἶναι·

τῶν γὰρ ἐναντίων εἰ θάτερον φύσει, ἀνάγκη καὶ θάτερον εἶναι

φύσει, ἐάν περ ᾖ ἐναντίον, καὶ εἶναί τινα αὐτοῦ φύσιν·

25 ἡ γὰρ αὐτὴ ὕλη τῶν ἐναντίων, καὶ τῆς στερήσεως πρότερον

ἡ κατάφασις (λέγω δ' οἷον τὸ θερμὸν τοῦ ψυχροῦ), ἡ δ' ἠρεμία

καὶ τὸ βαρὺ λέγεται κατὰ στέρησιν κουφότητος καὶ

κινήσεως. Ἀλλὰ μὴν εἴπερ ἔστι πῦρ καὶ γῆ, ἀνάγκη καὶ τὰ

μεταξὺ αὐτῶν εἶναι σώματα· ἐναντίωσιν γὰρ ἔχει ἕκαστον

30 τῶν στοιχείσων πρὸς ἕκαστον. Ὑποκείσθω δὲ καὶ τοῦτο νῦν,

ὕστερον δὲ πειρατέον δεῖξαι. Τούτων δ' ὑπαρχόντων φανερὸν ὅτι

ἀνάγκη γένεσιν εἶναι διὰ τὸ μηδὲν οἷόν τ' αὐτῶν εἶναι ἀΐδιον·

πάσχει γὰρ καὶ ποιεῖ τἀναντία ὑπ' ἀλλήλων, καὶ φθαρτικὰ

ἀλλήλων ἐστίν. Ἔτι δ' οὐκ εὔλογον εἶναί τι κινητὸν ἀΐδιον,

35 οὗ μὴ ἐνδέχεται εἶναι κατὰ φύσιν τὴν κίνησιν ἀΐδιον·

Since circular motion is not the contrary of the reverse circular motion, we must consider why there is more than one motion, though we have to pursue 5our inquiries at a distance-a distance created not so much by our spatial position as by the fact that our senses enable us to perceive very few of the attributes of the heavenly bodies. But let not that deter us. The reason must be sought in the following facts. Everything which has a function exists for its function. The activity of God is immortality, i.e. eternal 10life. Therefore the movement of that which is divine must be eternal. But such is the heaven, viz. a divine body, and for that reason to it is given the circular body whose nature it is to move always in a circle. Why, then, is not the whole body of the heaven of the same character as that part? Because there must be something at rest at the centre of the 15revolving body; and of that body no part can be at rest, either elsewhere or at the centre. It could do so only if the body's natural movement were towards the centre. But the circular movement is natural, since otherwise it could not be eternal: for nothing unnatural is eternal. The unnatural is subsequent to the natural, being a derangement of the natural which 20occurs in the course of its generation. Earth then has to exist; for it is earth which is at rest at the centre. (At present we may take this for granted: it shall be explained later.) But if earth must exist, so must fire. For, if one of a pair of contraries naturally exists, the other, if it is really contrary, exists also naturally. In some form it must be present, 25since the matter of contraries is the same. Also, the positive is prior to its privation (warm, for instance, to cold), and rest and heaviness stand for the privation of lightness and movement. But further, if fire and earth exist, the intermediate bodies must exist also: each element stands in a contrary relation to every other. (This, again, we will here 30take for granted and try later to explain.) these four elements generation clearly is involved, since none of them can be eternal: for contraries interact with one another and destroy one another. Further, it is inconceivable that a movable body should be eternal, if its movement cannot be regarded as naturally eternal: and these bodies we know to possess movement.

286b

1 τούτων δ' ἔστι κίνησις. Ὅτι μὲν τοίνυν ἀναγκαῖον εἶναι

γένεσιν, ἐκ τούτων δῆλον. Εἰ δὲ γένεσιν, ἀναγκαῖον καὶ ἄλλην

εἶναι φοράν, ἢ μίαν ἢ πλείους· κατὰ γὰρ τὴν τοῦ ὅλου ὡσαύτως

ἀναγκαῖον ἔχειν τὰ στοιχεῖα τῶν σωμάτων πρὸς ἄλληλα.

5 Λεχθήσεται δὲ καὶ περὶ τούτου ἐν τοῖς ἑπομένοις σαφέστερον.

Νῦν δὲ τοσοῦτόν ἐστι δῆλον, διὰ τίνα αἰτίαν πλείω τὰ ἐγκύκλιά

ἐστι σώματα, ὅτι ἀνάγκη γένεσιν εἶναι, γένεσιν δ', εἴπερ

καὶ πῦρ, τοῦτο δὲ καὶ τἆλλα, εἴπερ καὶ γῆν· ταύτην

δ' ὅτι ἀνάγκη μένειν τι ἀεί, εἴπερ καὶ κινεῖσθαί τι ἀεί.

1Thus we see that generation is necessarily involved. But if so, there must be at least one other circular motion: for a single movement of the whole heaven would necessitate an identical relation of the elements of bodies to one another. This matter also shall be cleared up in what 5follows: but for the present so much is clear, that the reason why there is more than one circular body is the necessity of generation, which follows on the presence of fire, which, with that of the other bodies, follows on that of earth; and earth is required because eternal movement in one body necessitates eternal rest in another.

Book 2,Chapter 4 (286b10–287b21)

10 Σχῆμα δ' ἀνάγκη σφαιροειδὲς ἔχειν τὸν οὐρανόν· τοῦτο

γὰρ οἰκειότατόν τε τῇ οὐσίᾳ καὶ τῇ φύσει πρῶτον. Εἴπωμεν

δὲ καθόλου περὶ τῶν σχημάτων, τὸ ποῖόν ἐστι πρῶτον, καὶ

ἐν ἐπιπέδοις καὶ ἐν στερεοῖς. Ἅπαν δὴ σχῆμα ἐπίπεδον ἢ

εὐθύγραμμόν ἐστιν ἢ περιφερόγραμμον. Καὶ τὸ μὲν εὐθύγραμμον

15 ὑπὸ πλειόνων περιέχεται γραμμῶν, τὸ δὲ περιφερόγραμμον

ὑπὸ μιᾶς. Ἐπεὶ δὲ πρότερον [τῇ φύσει] ἐν ἑκάστῳ γένει

τὸ ἓν τῶν πολλῶν καὶ τὸ ἁπλοῦν τῶν συνθέτων, πρῶτον ἂν

εἴη τῶν ἐπιπέδων σχημάτων ὁ κύκλος. Ἔτι δὲ εἴπερ τέλειόν

ἐστιν οὗ μηδὲν ἔξω τῶν αὐτοῦ λαβεῖν δυνατόν, ὥσπερ ὥρισται

20 πρότερον, καὶ τῇ μὲν εὐθείᾳ πρόσθεσίς ἐστιν ἀεί, τῇ δὲ

τοῦ κύκλου οὐδέποτε, φανερὸν ὅτι τέλειος ἂν εἴη ἡ περιέχουσα

τὸν κύκλον· ὥστ' εἰ τὸ τέλειον πρότερον τοῦ ἀτελοῦς, καὶ διὰ

ταῦτα πρότερον ἂν εἴη τῶν σχημάτων ὁ κύκλος. Ὡσαύτως

δὲ καὶ ἡ σφαῖρα τῶν στερεῶν· μόνη γὰρ περιέχεται μιᾷ

25 ἐπιφανείᾳ, τὰ δ' εὐθύγραμμα πλείοσιν· ὡς γὰρ ἔχει ὁ

κύκλος ἐν τοῖς ἐπιπέδοις, οὕτως ἡ σφαῖρα ἐν τοῖς στερεοῖς.

Ἔτι δὲ καὶ οἱ διαιροῦντες εἰς ἐπίπεδα καὶ ἐξ ἐπιπέδων τὰ σώματα

γεννῶντες μεμαρτυρηκέναι φαίνονται τούτοις· μόνην γὰρ

τῶν στερεῶν οὐ διαιροῦσι τὴν σφαῖραν ὡς οὐκ ἔχουσαν πλείους

30 ἐπιφανείας ἢ μίαν· ἡ γὰρ εἰς τὰ ἐπίπεδα διαίρεσις οὐχ ὡς

ἂν τέμνων τις εἰς τὰ μέρη διέλοι τὸ ὅλον, τοῦτον διαιρεῖται

τὸν τρόπον, ἀλλ' ὡς εἰς ἕτερα τῷ εἴδει. Ὅτι μὲν οὖν πρῶτόν

ἐστιν ἡ σφαῖρα τῶν στερεῶν σχημάτων, δῆλον. Ἔστι δὲ καὶ

κατὰ τὸν ἀριθμὸν τὴν τάξιν ἀποδιδοῦσιν οὕτω τιθεμένοις εὐλογώτατον,

35 τὸν μὲν κύκλον κατὰ τὸ ἕν, τὸ δὲ τρίγωνον

The shape of the heaven 10is of necessity spherical; for that is the shape most appropriate to its substance and also by nature primary.
First, let us consider generally which shape is primary among planes and solids alike. Every plane figure must be either rectilinear or curvilinear. Now the rectilinear is bounded by more than one line, the curvilinear by one only. But since 15in any kind the one is naturally prior to the many and the simple to the complex, the circle will be the first of plane figures. Again, if by complete, as previously defined, we mean a thing outside which no part of itself can be found, and if addition is always possible to the straight line but never to the circular, clearly the line which embraces the 20circle is complete. If then the complete is prior to the incomplete, it follows on this ground also that the circle is primary among figures. And the sphere holds the same position among solids. For it alone is embraced by a single surface, while rectilinear solids have several. The sphere is among solids what the circle is among plane figures. Further, 25those who divide bodies into planes and generate them out of planes seem to bear witness to the truth of this. Alone among solids they leave the sphere undivided, as not possessing more than one surface: for the division into surfaces is not just dividing a whole by cutting it into its parts, but division of another fashion into parts different in form. 30It is clear, then, that the sphere is first of solid figures.
If, again, one orders figures according to their numbers, it is most natural to arrange them in this way. The circle corresponds to the number one, the triangle, being the sum of two right angles, to the number two. But if one is assigned to the triangle, the circle will not be a figure at all.

287a

1 κατὰ τὴν δυάδα, ἐπειδὴ ὀρθαὶ δύο. Ἐὰν δὲ τὸ ἓν κατὰ

τὸ τρίγωνον, ὁ κύκλος οὐκέτι ἔσται σχῆμα. Ἐπεὶ δὲ τὸ μὲν πρῶτον

σχῆμα τοῦ πρώτου σώματος, πρῶτον δὲ σῶμα τὸ ἐν τῇ

ἐσχάτῃ περιφορᾷ, σφαιροειδὲς ἂν εἴη τὸ τὴν κύκλῳ περιφερόμενον

5 φοράν. Καὶ τὸ συνεχὲς ἄρα ἐκείνῳ· τὸ γὰρ τῷ

σφαιροειδεῖ συνεχὲς σφαιροειδές. Ὡσαύτως δὲ καὶ τὰ πρὸς

τὸ μέσον τούτων· τὰ γὰρ ὑπὸ τοῦ σφαιροειδοῦς περιεχόμενα

καὶ ἁπτόμενα ὅλα σφαιροειδῆ ἀνάγκη εἶναι· τὰ δὲ κάτω

τῆς τῶν πλανήτων ἅπτεται τῆς ἐπάνω σφαίρας. Ὥστε σφαιροειδὴς

10 ἂν εἴη πᾶσα· πάντα γὰρ ἅπτεται καὶ συνεχῆ ἐστι

ταῖς σφαίραις. Ἔτι δὲ ἐπεὶ φαίνεται καὶ ὑπόκειται κύκλῳ

περιφέρεσθαι τὸ πᾶν, δέδεικται δ' ὅτι τῆς ἐσχάτης περιφορᾶς

οὔτε κενόν ἐστιν ἔξωθεν οὔτε τόπος, ἀνάγκη καὶ διὰ

ταῦτα σφαιροειδῆ εἶναι αὐτόν. Εἰ γὰρ ἔσται εὐθύγραμμος,

15 συμβήσεται καὶ τόπον εἶναι ἔξω καὶ σῶμα καὶ κενόν. Κύκλῳ

γὰρ στρεφόμενον τὸ εὐθέγραμμον οὐδέποτε τὴν αὐτὴν

ἐφέξει χώραν, ἀλλ' ὅπου πρότερον ἦν σῶμα, νῦν οὐκ ἔσται,

καὶ οὗ νῦν οὐκ ἔστι, πάλιν ἔσται, διὰ τὴν παράλλαξιν τῶν γωνιῶν.

Ὁμοίως δὲ κἂν εἴ τι ἄλλο σχῆμα γένοιτο μὴ ἴσας

20 ἔχον τὰς ἐκ τοῦ μέσου γραμμάς, οἷον φακοειδὲς ἢ ᾠοειδές·

ἐν ἅπασι γὰρ συμβήσεται καὶ τόπον ἔξω καὶ κενὸν εἶναι

τῆς φορᾶς, διὰ τὸ μὴ τὴν αὐτὴν χώραν κατέχειν τὸ ὅλον.

Ἔτι δ' εἰ τῶν μὲν κινήσεων τὸ μέτρον ἡ τοῦ οὐρανοῦ φορὰ διὰ

τὸ εἶναι μόνη συνεχὴς καὶ ὁμαλὴς καὶ ἀΐδιος, ἐν ἑκάστῳ δὲ

25 μέτρον τὸ ἐλάχιστον, ἐλαχίστη δὲ κίνησις ἡ ταχίστη, δῆλον

ὅτι ταχίστη ἂν εἴη πασῶν τῶν κινήσεων ἡ τοῦ οὐρανοῦ κίνησις.

Ἀλλὰ μὴν τῶν ἀφ' αὑτοῦ ἐφ' αὑτὸ ἐλαχίστη ἐστὶν ἡ

τοῦ κύκλου γραμμή· κατὰ δὲ τὴν ἐλαχίστην ταχίστη ἡ κίνησις·

ὥστ' εἰ ὁ οὐρανὸς κύκλῳ τε φέρεται καὶ τάχιστα κινεῖται,

30 σφαιροειδῆ αὐτὸν ἀνάγκη εἶναι. Λάβοι δ' ἄν τις καὶ

ἐκ τῶν περὶ τὸ μέσον ἱδρυμένων σωμάτων ταύτην τὴν πίστιν.

Εἰ γὰρ τὸ μὲν ὕδωρ ἐστὶ περὶ τὴν γῆν, ὁ δ' ἀὴρ περὶ τὸ

ὕδωρ, τὸ δὲ πῦρ περὶ τὸν ἀέρα, καὶ τὰ ἄνω σώματα κατὰ

τὸν αὐτὸν λόγον (συνεχῆ μὲν γὰρ οὐκ ἔστιν, ἅπτεται δὲ τούτων),

1Now the first figure belongs to the first body, and the first body is that at the farthest circumference. It follows that the body which revolves with a circular movement must be spherical. The same then will be true of the body continuous with it: for that which 5is continuous with the spherical is spherical. The same again holds of the bodies between these and the centre. Bodies which are bounded by the spherical and in contact with it must be, as wholes, spherical; and the bodies below the sphere of the planets are contiguous with the sphere above them. The sphere then will be spherical 10throughout; for every body within it is contiguous and continuous with spheres.
Again, since the whole revolves, palpably and by assumption, in a circle, and since it has been shown that outside the farthest circumference there is neither void nor place, from these grounds also it will follow necessarily that the heaven is 15spherical. For if it is to be rectilinear in shape, it will follow that there is place and body and void without it. For a rectilinear figure as it revolves never continues in the same room, but where formerly was body, is now none, and where now is none, body will be in a moment because of the projection at the corners. Similarly, 20if the world had some other figure with unequal radii, if, for instance, it were lentiform, or oviform, in every case we should have to admit space and void outside the moving body, because the whole body would not always occupy the same room.
Again, if the motion of the heaven is the measure of all movements whatever in virtue 25of being alone continuous and regular and eternal, and if, in each kind, the measure is the minimum, and the minimum movement is the swiftest, then, clearly, the movement of the heaven must be the swiftest of all movements. Now of lines which return upon themselves the line which bounds the circle is the shortest; and that 30movement is the swiftest which follows the shortest line. Therefore, if the heaven moves in a circle and moves more swiftly than anything else, it must necessarily be spherical.
Corroborative evidence may be drawn from the bodies whose position is about the centre.

287b

1 ἡ δὲ τοῦ ὕδατος ἐπιφάνεια σφαιροειδής ἐστιν, τὸ δὲ

τῷ σφαιροειδεῖ συνεχὲς ἢ κείμενον περὶ τὸ σφαιροειδὲς καὶ αὐτὸ

τοιοῦτον ἀναγκαῖον εἶναι· ὥστε κἂν διὰ τοῦτο φανερὸν εἴη ὅτι

σφαιροειδής ἐστιν ὁ οὐρανός. Ἀλλὰ μὴν ὅτι γε ἡ τοῦ ὕδατος

5 ἐπιφάνεια τοιαύτη φανερόν, ὑπόθεσιν λαμβάνουσιν ὅτι πέφυκεν

ἀεὶ συρρεῖν τὸ ὕδωρ εἰς τὸ κοιλότερον· κοιλότερον δέ ἐστι τὸ

τοῦ κέντρου ἐγγύτερον. Ἤχθωσαν οὖν ἐκ τοῦ κέντρου ἡ ΑΒ καὶ

ἡ ΑΓ, καὶ ἐπεζεύχθω ἐφ' ἧς ΒΓ. Ἡ οὖν ἀχθεῖσα ἐπὶ τὴν

βάσιν, ἐφ' ἧς ΑΔ, ἐλάττων ἐστὶ τῶν ἐκ τοῦ κέντρου· κοιλότερος

10 ἄρα ὁ τόπος. Ὥστε περιρρεύσεται τὸ ὕδωρ, ἕως ἂν ἰσασθῇ.

Ἴση δὲ ταῖς ἐκ τοῦ κέντρου ἡ ΑΕ. Ὥστ' ἀνάγκη πρὸς ταῖς

ἐκ τοῦ κέντρου εἶναι τὸ ὕδωρ· τότε γὰρ ἠρεμήσει. Ἡ δὲ τῶν

ἐκ τοῦ κέντρου ἁπτομένη περιφερής· σφαιροειδὴς ἄρα ἡ τοῦ

ὕδατος ἐπιφάνεια, ἐφ' ἧς ΒΕΓ. Ὅτι μὲν οὖν σφαιροειδής

15 ἐστιν ὁ κόσμος, δῆλον ἐκ τούτων, καὶ ὅτι κατ' ἀκρίβειαν ἔντορνος

οὕτως ὥστε μηθὲν μήτε χειρόκμητον ἔχειν παραπλησίως

μήτ' ἄλλο μηθὲν τῶν ἡμῖν ἐν ὀφθαλμοῖς φαινομένων.

Ἐξ ὧν γὰρ τὴν σύστασιν εἴληφεν, οὐδὲν οὕτω δυνατὸν

ὁμαλότητα δέξασθαι καὶ ἀκρίβειαν ὡς ἡ τοῦ πέριξ σώματος

20 φύσις· δῆλον γὰρ ὡς ἀνάλογον ἔχει, καθάπερ ὕδωρ

πρὸς γῆν, καὶ τὰ πλεῖον ἀεὶ ἀπέχοντα τῶν συστοίχων.

1If earth is enclosed by water, water by air, air by fire, and these similarly by the upper bodies-which while not continuous are yet contiguous with them-and if the surface of water is spherical, and that which is continuous with or embraces the spherical must itself be spherical, then on 5these grounds also it is clear that the heavens are spherical. But the surface of water is seen to be spherical if we take as our starting-point the fact that water naturally tends to collect in a hollow place-'hollow' meaning 'nearer the centre'. Draw from the centre the lines AB, AC, and let their extremities be joined by the straight line BC. The line AD, drawn to 10the base of the triangle, will be shorter than either of the radii. Therefore the place in which it terminates will be a hollow place. The water then will collect there until equality is established, that is until the line AE is equal to the two radii. Thus water forces its way to the ends of the radii, and there only will it rest: but the line which connects the 15extremities of the radii is circular: therefore the surface of the water BEC is spherical.
It is plain from the foregoing that the universe is spherical. It is plain, further, that it is turned (so to speak) with a finish which no manufactured thing nor anything else within the range of our observation can even approach. For the matter of which these are composed 20does not admit of anything like the same regularity and finish as the substance of the enveloping body; since with each step away from earth the matter manifestly becomes finer in the same proportion as water is finer than earth.

Book 2,Chapter 5 (287b22–288a12)

Ἐπεὶ δ' ἔστι διχῶς ἐπὶ τοῦ κύκλου κινηθῆναι, οἷον ἀπὸ

τοῦ Α τὴν μὲν ἐπὶ τὸ Β τὴν δ' ἐπὶ τὸ Γ, ὅτι μὲν οὖν οὐκ

εἰσὶν ἐναντίαι αὗται, πρότερον εἴρηται. Ἀλλ' εἰ μηδὲν ὡς

25 ἔτυχε μηδ' ἀπὸ ταὐτομάτου ἐνδέχεται ἐν τοῖς ἀϊδίοις εἶναι,

ὁ δ' οὐρανὸς ἀΐδιος καὶ ἡ κύκλῳ φορά, διὰ τίνα ποτ' αἰτίαν

ἐπὶ θάτερα φέρεται, ἀλλ' οὐκ ἐπὶ θάτερα; ἀνάγκη γὰρ καὶ

τοῦτο ἢ ἀρχὴν εἶναι ἢ εἶναι αὐτοῦ ἀρχήν. Ἴσως μὲν οὖν τὸ

περὶ ἐνίων ἀποφαίνεσθαί τι πειρᾶσθαι καὶ τὸ περὶ πάντων

30 καὶ τὸ παριέναι μηθὲν τάχ' ἂν δόξειεν εἶναι σημεῖον ἢ πολλῆς

εὐηθείας ἢ πολλῆς προθυμίας. Οὐ μὴν δίκαιόν γε πᾶσιν

ὁμοίως ἐπιτιμᾶν, ἀλλ' ὁρᾶν δεῖ τὴν αἰτίαν τοῦ λέγειν τίς

ἐστιν, ἔτι δὲ πῶς ἔχων τῷ πιστεύειν, πότερον ἀνθρωπίνως ἢ

καρτερώτερον. Τὰς μὲν οὖν ἀκριβεστέρας ἀνάγκας, ὅταν

Now there are two ways of moving along a circle, from A to B or from A to C, and we have already explained that these movements are not 25contrary to one another. But nothing which concerns the eternal can be a matter of chance or spontaneity, and the heaven and its circular motion are eternal. We must therefore ask why this motion takes one direction and not the other. Either this is itself an ultimate fact or there is an ultimate fact behind it. It may seem evidence of excessive folly or excessive 30zeal to try to provide an explanation of some things, or of everything, admitting no exception. The criticism, however, is not always just: one should first consider what reason there is for speaking, and also what kind of certainty is looked for, whether human merely or of a more cogent kind.

288a

1 τις ἐπιτύχῃ, τότε χάριν ἔχειν δεῖ τοῖς εὑρίσκουσι, νῦν δὲ τὸ

φαινόμενον ῥητέον. Εἰ γὰρ ἡ φύσις ἀεὶ ποιεῖ τῶν ἐνδεχομένων

τὸ βέλτιστον, ἔστι δὲ καθάπερ τῶν ἐπὶ τῆς εὐθείας φορῶν

ἡ πρὸς τὸν ἄνω τόπον τιμιωτέρα (θειότερος γὰρ τόπος ὁ

5 ἄνω τοῦ κάτω), τὸν αὐτὸν τρόπον καὶ ἡ εἰς τὸ πρόσθεν τῆς

εἰς τοὔπισθεν, ἔχει, εἴπερ καὶ τὸ δεξιὸν καὶ τὸ ἀριστερόν,

καθάπερ ἐλέχθη πρότερον, (καὶ μαρτυρεῖ δ' ἡ ῥηθεῖσα ἀπορία

ὅτι ἔχει) τὸ πρότερον καὶ ὕστερον· αὕτη γὰρ ἡ αἰτία

λύει τὴν ἀπορίαν. Εἰ γὰρ ἔχει ὡς ἐνδέχεται βέλτιστα,

10 αὕτη ἂν εἴη αἰτία καὶ τοῦ εἰρημένου· βέλτιστον γὰρ κινεῖσθαι

ἁπλῆν τε κίνησιν καὶ ἄπαυστον, καὶ ταύτην ἐπὶ τὸ

τιμιώτερον.

1When any one shall succeed in finding proofs of greater precision, gratitude will be due to him for the discovery, but at present we must be content with a probable solution. If nature always follows the best course possible, and, just as upward movement is the superior form of rectilinear 5movement, since the upper region is more divine than the lower, so forward movement is superior to backward, then front and back exhibits, like right and left, as we said before and as the difficulty just stated itself suggests, the distinction of prior and posterior, which provides a reason and so solves our difficulty. Supposing that nature is ordered in the best 10way possible, this may stand as the reason of the fact mentioned. For it is best to move with a movement simple and unceasing, and, further, in the superior of two possible directions.

Book 2,Chapter 6 (288a13–289a10)

Περὶ δὲ τῆς κινήσεως αὐτοῦ, ὅτι ὁμαλής ἐστι καὶ οὐκ

ἀνώμαλος, ἐφεξῆς ἂν εἴη τῶν εἰρημένων διελθεῖν. Λέγω δὲ

15 τοῦτο περὶ τοῦ πρώτου οὐρανοῦ καὶ περὶ τῆς πρώτης φορᾶς· ἐν

γὰρ τοῖς ὑποκάτω πλείους ἤδη αἱ φοραὶ συνεληλύθασιν εἰς

ἕν. Εἰ γὰρ ἀνωμάλως κινήσεται, δῆλον ὅτι ἐπίτασις ἔσται

καὶ ἀκμὴ καὶ ἄνεσις τῆς φορᾶς· ἅπασα γὰρ ἡ ἀνώμαλος

φορὰ καὶ ἄνεσιν ἔχει καὶ ἐπίτασιν καὶ ἀκμήν. Ἀκμὴ

20 δ' ἐστὶν ἢ ὅθεν φέρεται ἢ οἷ ἢ ἀνὰ μέσον, οἷον ἴσως τοῖς

μὲν κατὰ φύσιν οἷ φέρονται, τοῖς δὲ παρὰ φύσιν ὅθεν,

τοῖς δὲ ῥιπτουμένοις ἀνὰ μέσον. Τῆς δὲ κύκλῳ φορᾶς οὐκ

ἔστιν οὔτε ὅθεν οὔτε οἷ οὔτε μέσον· οὔτε γὰρ ἀρχὴ οὔτε πέρας

οὔτε μέσον ἐστὶν αὐτῆς ἁπλῶς· τῷ τε γὰρ χρόνῳ ἀΐδιος

25 καὶ τῷ μήκει συνηγμένη καὶ ἄκλαστος· ὥστ' εἰ μή ἐστιν ἀκμὴ

αὐτοῦ τῆς φορᾶς, οὐδ' ἂν ἀνωμαλία εἴη· ἡ γὰρ ἀνωμαλία

γίγνεται διὰ τὴν ἄνεσιν καὶ ἐπίτασιν. Ἔτι δ' ἐπεὶ πᾶν τὸ κινούμενον

ὑπό τινος κινεῖται, ἀνάγκη τὴν ἀνωμαλίαν γίγνεσθαι

τῆς κινήσεως ἢ διὰ τὸ κινοῦν ἢ διὰ τὸ κινούμενον ἢ

30 δι' ἄμφω· εἴτε γὰρ τὸ κινοῦν μὴ τῇ αὐτῇ δυνάμει κινοῖ,

εἴτε τὸ κινούμενον ἀλλοιοῖτο καὶ μὴ διαμένοι τὸ αὐτό, εἴτε

ἄμφω μεταβάλλοι, οὐθὲν κωλύει ἀνωμάλως κινεῖσθαι τὸ κινούμενον.

Οὐθὲν δὲ τούτων δυνατὸν περὶ τὸν οὐρανὸν γενέσθαι·

τὸ μὲν γὰρ κινούμενον δέδεικται ὅτι πρῶτον καὶ ἁπλοῦν καὶ

We have next to show that the movement of the heaven is regular and not irregular. This applies only to the first heaven and the first movement; for the lower spheres exhibit a 15composition of several movements into one. If the movement is uneven, clearly there will be acceleration, maximum speed, and retardation, since these appear in all irregular motions. The maximum may occur either at the starting-point or at the goal or between the two; and we expect natural motion to reach its maximum at the goal, unnatural motion at the starting-point, 20and missiles midway between the two. But circular movement, having no beginning or limit or middle in the direct sense of the words, has neither whence nor whither nor middle: for in time it is eternal, and in length it returns upon itself without a break. If then its movement has no maximum, it can have no irregularity, since irregularity is produced by retardation 25and acceleration. Further, since everything that is moved is moved by something, the cause of the irregularity of movement must lie either in the mover or in the moved or both. For if the mover moved not always with the same force, or if the moved were altered and did not remain the same, or if both were to change, the result might well be an irregular movement 30in the moved. But none of these possibilities can be conceived as actual in the case of the heavens. As to that which is moved, we have shown that it is primary and simple and ungenerated and indestructible and generally unchanging; and the mover has an even better right to these attributes.

288b

1 ἀγένητον καὶ ἄφθαρτον καὶ ὅλως ἀμετάβλητον, τὸ δὲ κινοῦν

πολὺ μᾶλλον εὔλογον εἶναι τοιοῦτον· τὸ γὰρ πρῶτον τοῦ

πρώτου καὶ τὸ ἁπλοῦν τοῦ ἁπλοῦ καὶ τὸ ἄφθαρτον καὶ ἀγένητον

τοῦ ἀφθάρτου καὶ ἀγενήτου κινητικόν. Ἐπεὶ οὖν τὸ κινούμενον

5 οὐ μεταβάλλει σῶμα ὄν, οὐδ' ἂν τὸ κινοῦν μεταβάλλοι

ἀσώματον ὄν. Ὥστε καὶ τὴν φορὰν ἀδύνατον ἀνώμαλον

εἶναι. Καὶ γὰρ εἰ γίνεται ἀνώμαλος, ἤτοι ὅλη μεταβάλλει

καὶ ὁτὲ μὲν γίνεται θάττων ὁτὲ δὲ βραδυτέρα πάλιν, ἢ τὰ

μέρη αὐτῆς. Τὰ μὲν οὖν μέρη ὅτι οὐκ ἔστιν ἀνώμαλα, φανερόν·

10 ἤδη γὰρ ἂν ἐγεγόνει διάστασις τῶν ἄστρων ἐν τῷ

ἀπείρῳ χρόνῳ, τοῦ μὲν θᾶττον κινουμένου τοῦ δὲ βραδύτερον.

Οὐ φαίνεται δ' οὐθὲν ἄλλως ἔχον τοῖς διαστήμασιν. Ἀλλὰ

μὴν οὐδὲ τὴν ὅλην ἐγχωρεῖ μεταβάλλειν· ἡ γὰρ ἄνεσις

ἑκάστου γίνεται δι' ἀδυναμίαν, ἡ δ' ἀδυναμία παρὰ φύσιν·

15 καὶ γὰρ αἱ ἐν τοῖς ζῴοις ἀδυναμίαι πᾶσαι παρὰ φύσιν

εἰσίν, οἷον γῆρας καὶ φθίσις. Ὅλη γὰρ ἴσως ἡ σύστασις τῶν

ζῴων ἐκ τοιούτων συνέστηκεν ἃ διαφέρει τοῖς οἰκείοις τόποις·

οὐθὲν γὰρ τῶν μερῶν ἔχει τὴν αὑτοῦ χώραν. Εἰ οὖν ἐν τοῖς

πρώτοις μή ἐστι τὸ παρὰ φύσιν (ἁπλᾶ γὰρ καὶ ἄμικτα

20 καὶ ἐν τῇ οἰκείᾳ χώρᾳ, καὶ οὐθὲν αὐτοῖς ἐναντίον), οὐδ' ἂν

ἀδυναμία εἴη, ὥστ' οὐδ' ἄνεσις οὐδ' ἐπίτασις· εἰ γὰρ ἐπίτασις,

καὶ ἄνεσις. Ἔτι δὲ καὶ ἄλογον ἄπειρον χρόνον ἀδύνατον εἶναι

τὸ κινοῦν, καὶ πάλιν ἄλλον ἄπειρον δυνατόν· οὐθὲν γὰρ

φαίνεται ὂν ἄπειρον χρόνον παρὰ φύσιν (ἡ δ' ἀδυναμία

25 παρὰ φύσιν), οὐδὲ τὸν ἴσον χρόνον παρὰ φύσιν καὶ κατὰ

φύσιν, οὐδ' ὅλως δυνατὸν καὶ ἀδύνατον· ἀνάγκη δ', εἰ ἀνίησιν

ἡ κίνησις, ἄπειρον ἀνιέναι χρόνον. Ἀλλὰ μὴν οὐδ' ἐπιτείνειν

ἀεὶ ἢ πάλιν ἀνιένται δυνατόν· ἄπειρος γὰρ ἂν εἴη καὶ

ἀόριστος ἡ κίνησις, ἅπασαν δέ φαμεν ἔκ τινος εἴς τι εἶναι

30 καὶ ὡρισμένην. Ἔτι δ' εἴ τις λάβοι εἶναί τινα χρόνον ἐλάχιστον,

οὗ οὐκ ἐνδέχεται ἐν ἐλάττονι κινηθῆναι τὸν οὐρανόν

(ὥσπερ γὰρ οὐδὲ κιθαρίσαι οὐδὲ βαδίσαι ἐν ὁτῳοῦν χρόνῳ δυνατόν,

ἀλλ' ἔστιν ἑκάστης πράξεως ὡρισμένος ὁ ἐλάχιστος χρόνος

κατὰ τὸ μὴ ὑπερβάλλειν, οὕτως οὐδὲ κινηθῆναι τὸν οὐρανὸν

1It is the primary that moves the primary, the simple the simple, the indestructible and ungenerated that which is indestructible and ungenerated. Since then that which is moved, being a body, is nevertheless unchanging, how should the mover, which is incorporeal, be changed?
It follows 5then, further, that the motion cannot be irregular. For if irregularity occurs, there must be change either in the movement as a whole, from fast to slow and slow to fast, or in its parts. That there is no irregularity in the parts is obvious, since, if there were, some divergence of the stars would have taken place before now in the infinity of time, as one moved 10slower and another faster: but no alteration of their intervals is ever observed. Nor again is a change in the movement as a whole admissible. Retardation is always due to incapacity, and incapacity is unnatural. The incapacities of animals, age, decay, and the like, are all unnatural, due, it seems, to the fact that the whole animal complex is made up of 15materials which differ in respect of their proper places, and no single part occupies its own place. If therefore that which is primary contains nothing unnatural, being simple and unmixed and in its proper place and having no contrary, then it has no place for incapacity, nor, consequently, for retardation or (since acceleration involves retardation) for 20acceleration. Again, it is inconceivable that the mover should first show incapacity for an infinite time, and capacity afterwards for another infinity. For clearly nothing which, like incapacity, unnatural ever continues for an infinity of time; nor does the unnatural endure as long as the natural, or any form of incapacity as long as the capacity. But if the movement 25is retarded it must necessarily be retarded for an infinite time. Equally impossible is perpetual acceleration or perpetual retardation. For such movement would be infinite and indefinite, but every movement, in our view, proceeds from one point to another and is definite in character. Again, suppose one assumes a minimum time in less than which the heaven 30could not complete its movement. For, as a given walk or a given exercise on the harp cannot take any and every time, but every performance has its definite minimum time which is unsurpassable, so, one might suppose, the movement of the heaven could not be completed in any and every time.

289a

1 ἐν ὁτῳοῦν χρόνῳ δυνατόν)· εἰ οὖν τοῦτ' ἀληθές, οὐκ ἂν εἴη

ἀεὶ ἐπίτασις τῆς φορᾶς (εἰ δὲ μὴ ἐπίτασις, οὐδ' ἄνεσις·

ὁμοίως γὰρ ἄμφω καὶ θάτερον), εἴπερ τῷ αὐτῷ τε ἐπιτείνει

τάχει ἢ μείζονι, καὶ ἄπειρον χρόνον. Λείπεται δὴ λέγειν

5 ἐναλλὰξ εἶναι τῇ κινήσει τὸ θᾶττον καὶ τὸ βραδύτερον·

τοῦτο δὲ παντελῶς ἄλογον καὶ πλάσματι ὅμοιον. Ἔτι δὲ καὶ

τὸ μὴ λανθάνειν ἐπὶ τούτων εὐλογώτερον· εὐαισθητότερα γὰρ

τὰ παρ' ἄλληλα τιθέμενα. Ὅτι μὲν οὖν εἷς τε μόνος ἐστὶν ὁ οὐρανός,

καὶ οὗτος ἀγένητος καὶ ἀΐδιος, ἔτι δὲ κινούμενος ὁμαλῶς,

10 ἐπὶ τοσοῦτον ἡμῖν εἰρήσθω.

1But in that case perpetual acceleration is impossible (and, equally, perpetual retardation: for the argument holds of both and each), if we may take acceleration to proceed by identical or increasing additions of speed and for an infinite time. The remaining alternative 5is to say that the movement exhibits an alternation of slower and faster: but this is a mere fiction and quite inconceivable. Further, irregularity of this kind would be particularly unlikely to pass unobserved, since contrast makes observation easy.
That there is one heaven, then, only, and that it is ungenerated and eternal, 10and further that its movement is regular, has now been sufficiently explained.

Book 2,Chapter 7 (289a11–35)

Περὶ δὲ τῶν καλουμένων ἄστρων ἑπόμενον ἂν εἴη λέγειν,

ἐκ τίνων τε συνεστᾶσι καὶ ἐν ποίοις σχήμασι καὶ τίνες

αἱ κινήσεις αὐτῶν. Εὐλογώτατον δὴ καὶ τοῖς εἰρημένοις ἑπόμενον

ἡμῖν τὸ ἕκαστον τῶν ἄστρων ποιεῖν ἐκ τούτου τοῦ σώματος

15 ἐν ᾧ τυγχάνει τὴν φορὰν ἔχον, ἐπειδὴ ἔφαμέν τι εἶναι

ὃ κύκλῳ φέρεσθαι πέφυκεν· ὥσπερ γὰρ οἱ πύρινα φάσκοντες

εἶναι διὰ τοῦτο λέγουσιν, ὅτι τὸ ἄνω σῶμα πῦρ εἶναί

φασιν, ὡς εὔλογον ὂν ἕκαστον συνεστάναι ἐκ τούτων ἐν οἷς

ἕκαστόν ἐστιν, ὁμοίως καὶ ἡμεῖς λέγομεν. Ἡ δὲ θερμότης ἀπ'

20 αὐτῶν καὶ τὸ φῶς γίνεται παρεκτριβομένου τοῦ ἀέρος ὑπὸ

τῆς ἐκείνων φορᾶς. Πέφυκε γὰρ ἡ κίνησις ἐκπυροῦν καὶ ξύλα

καὶ λίθους καὶ σίδηρον· εὐλογώτερον οὖν τὸ ἐγγύτερον τοῦ

πυρός, ἐγγύτερον δὲ ὁ ἀήρ· οἷον καὶ ἐπὶ τῶν φερομένων βελῶν·

ταῦτα γὰρ αὐτὰ ἐκπυροῦται οὕτως ὥστε τήκεσθαι τὰς

25 μολυβδίδας, καὶ ἐπείπερ αὐτὰ ἐκπυροῦται, ἀνάγκη καὶ τὸν

κύκλῳ αὐτῶν ἀέρα τὸ αὐτὸ τοῦτο πάσχειν. Ταῦτα μὲν οὖν

αὐτὰ ἐκθερμαίνεται διὰ τὸ ἐν ἀέρι φέρεσθαι, ὃς διὰ τὴν πληγὴν

τῇ κινήσει γίγνεται πῦρ. Τῶν δὲ ἄνω ἕκαστον ἐν τῇ

σφαίρᾳ φέρεται, ὥστ' αὐτὰ μὲν μὴ ἐκπυροῦσθαι, τοῦ δ' ἀέρος

30 ὑπὸ τὴν τοῦ κυκλικοῦ σώματος σφαῖραν ὄντος ἀνάγκη

φερομένης ἐκείνης ἐκθερμαίνεσθαι, καὶ ταύτῃ μάλιστα ᾗ ὁ

ἥλιος τετύχηκεν ἐνδεδεμένος· διὸ δὴ πλησιάζοντός τε αὐτοῦ

καὶ ἀνίσχοντος καὶ ὑπὲρ ἡμῶν ὄντος γίγνεται ἡ θερμότης.

Ὅτι μὲν οὖν οὔτε πύρινά ἐστιν οὔτ' ἐν πυρὶ φέρεται, ταῦθ'

35 ἡμῖν εἰρήσθω περὶ αὐτῶν.

We have next to speak of the stars, as they are called, of their composition, shape, and movements. It would be most natural and consequent upon what has been said that each of the stars should be composed of that substance in which their path lies, 15since, as we said, there is an element whose natural movement is circular. In so saying we are only following the same line of thought as those who say that the stars are fiery because they believe the upper body to be fire, the presumption being that a thing is composed of the same stuff as that in which it is situated. The warmth 20and light which proceed from them are caused by the friction set up in the air by their motion. Movement tends to create fire in wood, stone, and iron; and with even more reason should it have that effect on air, a substance which is closer to fire than these. An example is that of missiles, which as they move are themselves fired 25so strongly that leaden balls are melted; and if they are fired the surrounding air must be similarly affected. Now while the missiles are heated by reason of their motion in air, which is turned into fire by the agitation produced by their movement, the upper bodies are carried on a moving sphere, so that, though they are not 30themselves fired, yet the air underneath the sphere of the revolving body is necessarily heated by its motion, and particularly in that part where the sun is attached to it. Hence warmth increases as the sun gets nearer or higher or overhead. Of the fact, then, that the stars are neither fiery nor move in fire, enough has been said.

Book 2,Chapter 8 (289b1–290b11)

289b

1 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. Ἀμφότερα μὲν τοίνυν ἠρεμεῖν ἀδύνατον ἠρεμούσης

5 γε τῆς γῆς· οὐ γὰρ ἂν ἐγίγνετο τὰ φαινόμενα. Τὴν δὲ γῆν

ὑποκείσθω ἠρεμεῖν. Λείπεται δὴ ἀμφότερα κινεῖσθαι, ἢ

τὸ μὲν κινεῖσθαι τὸ δ' ἠρεμεῖν. Εἰ μὲν οὖν ἀμφότερα κινήσεται,

ἄλογον τὸ ταὐτὰ τάχη τῶν ἄστρων εἶναι καὶ τῶν κύκλων·

ἕκαστον γὰρ δὴ ὁμοταχὲς ἔσται τῷ κύκλῳ καθ' ὃν φέρεται.

10 Φαίνεται γὰρ ἅμα τοῖς κύκλοις καθιστάμενα πάλιν

εἰς τὸ αὐτό. Συμβαίνει οὖν ἅμα τό τε ἄστρον διεληλυθέναι

τὸν κύκλον καὶ τὸν κύκλον ἐνηνέχθαι τὴν αὑτοῦ φοράν, διεληλυθότα

τὴν περιφέρειαν. Οὐκ ἔστι δ' εὔλογον τὸ τὸν

αὐτὸν λόγον ἔχειν τὰ τάχη τῶν ἄστρων καὶ τὰ μεγέθη τῶν

15 κύκλων. Τοὺς μὲν γὰρ κύκλους οὐθὲν ἄτοπον ἀλλ' ἀναγκαῖον

ἀνάλογον ἔχειν τὰ τάχη τοῖς μεγέθεσι, τῶν δ' ἄστρων ἕκαστον

τῶν ἐν τούτοις οὐθαμῶς εὔλογον· εἴτε γὰρ ἐξ ἀνάγκης τὸ

τὸν μείζω κύκλον φερόμενον θᾶττον ἔσται, δῆλον ὅτι κἂν

μετατεθῇ τὰ ἄστρα εἰς τοὺς ἀλλήλων κύκλους, τὸ μὲν ἔσται

20 θᾶττον τὸ δὲ βραδύτερον (οὕτω δ' οὐκ ἂν ἔχοιεν οἰκείαν κίνησιν,

ἀλλὰ φέροιντ' ἂν ὑπὸ τῶν κύκλων), εἴτε ἀπὸ ταὐτομάτου

συνέπεσεν, οὐδ' οὕτως εὔλογον ὥστ' 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

25 ἄτοπον, τὸ δὲ πάνθ' ὁμοίως πλάσματι ἔοικεν. Ἅμα δὲ καὶ

οὐκ ἔστιν ἐν τοῖς φύσει τὸ ὡς ἔτυχεν, οὐδὲ τὸ πανταχοῦ καὶ

πᾶσιν ὑπάρχον τὸ ἀπὸ τύχης. Ἀλλὰ μὴν πάλιν εἰ οἱ μὲν

κύκλοι μένουσιν, αὐτὰ δὲ τὰ ἄστρα κινεῖται, τὰ αὐτὰ καὶ

ὁμοίως ἔσται ἄλογα· συμβήσεται γὰρ θᾶττον κινεῖσθαι τὰ

30 ἔξω, καὶ τὰ τάχη εἶναι κατὰ τὰ μεγέθη τῶν κύκλων. Ἐπεὶ

τοίνυν οὔτ' ἀμφότερα κινεῖσθαι εὔλογον οὔτε τὸ ἕτερον μόνον,

λείπεται τοὺς μὲν κύκλους κινεῖσθαι, τὰ δὲ ἄστρα ἠρεμεῖν

καὶ ἐνδεδεμένα τοῖς κύκλοις φέρεσθαι· μόνως γὰρ οὕτως οὐθὲν

ἄλογον συμβαίνει· τό τε γὰρ θᾶττον εἶναι τοῦ μείζονος κύκλου

35 τὸ τάχος εὔλογον περὶ τὸ αὐτὸ κέντρον ἐνδεδεμένων

1Since changes evidently occur not only in the position of the stars but also in that of the whole heaven, there are three possibilities. Either (1) both are at rest, or (2) both are in motion, or (3) the one is at rest and the other in motion.
(1) That both should be at rest is impossible; for, if the earth 5is at rest, the hypothesis does not account for the observations; and we take it as granted that the earth is at rest. It remains either that both are moved, or that the one is moved and the other at rest.
(2) On the view, first, that both are in motion, we have the absurdity that the stars and the circles move with the same speed, i.e. that the ace of every star is that of the circle 10in it moves. For star and circle are seen to come back to the same place at the same moment; from which it follows that the star has traversed the circle and the circle has completed its own movement, i.e. traversed its own circumference, at one and the same moment. But it is difficult to conceive that the pace of each star should be exactly proportioned to the size of its circle. 15That the pace of each circle should be proportionate to its size is not absurd but inevitable: but that the same should be true of the movement of the stars contained in the circles is quite incredible. For if, on the one and, we suppose that the star which moves on the greater circle is necessarily swifter, clearly we also admit that if stars shifted their position so as to exchange 20circles, the slower would become swifter and the swifter slower. But this would show that their movement was not their own, but due to the circles. If, on the other hand, the arrangement was a chance combination, the coincidence in every case of a greater circle with a swifter movement of the star contained in it is too much to believe. In one or two cases it might not inconceivably 25fall out so, but to imagine it in every case alike is a mere fiction. Besides, chance has no place in that which is natural, and what happens everywhere and in every case is no matter of chance.
(3) The same absurdity is equally plain if it is supposed that the circles stand still and that it is the stars themselves which move. For it will follow that the outer stars are the swifter, 30and that the pace of the stars corresponds to the size of their circles.
Since, then, we cannot reasonably suppose either that both are in motion or that the star alone moves, the remaining alternative is that the circles should move, while the stars are at rest and move with the circles to which they are attached. Only on this supposition are we involved in no absurd consequence.

290a

1 (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, ὥστ' εὐλόγως ἐν τῷ ἴσῳ χρόνῳ ὁ

5 μείζων περιοισθήσεται κύκλος), τό τε μὴ διασπᾶσθαι τὸν

οὐρανὸν διά τε τοῦτο συμβήσεται καὶ ὅτι δέδεικται συνεχὲς

ὂν τὸ ὅλον. Ἔτι δ' ἐπεὶ σφαιροειδῆ τὰ ἄστρα, καθάπερ οἵ

τ' ἄλλοι φασὶ καὶ ἡμῖν ὁμολογούμενον εἰπεῖν, ἐξ ἐκείνου γε

τοῦ σώματος γεννῶσιν, τοῦ δὲ σφαιροειδοῦς δύο κινήσεις εἰσὶ

10 καθ' αὑτό, κύλισις καὶ δίνησις, εἴπερ οὖν κινεῖται τὰ ἄστρα

δι' αὑτῶν, τὴν ἑτέραν ἂν κινοῖτο τούτων· ἀλλ' οὐδετέραν φαίνεται.

Δινούμενα μὲν γὰρ ἂν ἔμενεν ἐν ταὐτῷ καὶ οὐ μετέβαλλε

τὸν τόπον, ὅπερ φαίνεταί τε καὶ πάντες φασίν. Ἔτι

δὲ πάντα μὲν εὔλογον τὴν αὐτὴν κίνησιν κινεῖσθαι, μόνος δὲ

15 δοκεῖ τῶν ἄστρων ὁ ἥλιος τοῦτο δρᾶν ἀνατέλλων καὶ δύνων,

καὶ οὗτος οὐ δι' αὑτὸν ἀλλὰ διὰ τὴν ἀπόστασιν τῆς ἡμετέρας

ὄψεως· ἡ γὰρ ὄψις ἀποτεινομένη μακρὰν ἑλίσσεται

διὰ τὴν ἀσθένειαν. Ὅπερ αἴτιον ἴσως καὶ τοῦ στίλβειν φαίνεσθαι

τοὺς ἀστέρας τοὺς ἐνδεδεμένους, τοὺς δὲ πλάνητας μὴ

20 στίλβειν· οἱ μὲν γὰρ πλάνητες ἐγγύς εἰσιν, ὥστ' ἐγκρατὴς

οὖσα πρὸς αὐτοὺς ἀφικνεῖται ἡ ὄψις· πρὸς δὲ τοὺς μένοντας

κραδαίνεται διὰ τὸ μῆκος, ἀποτεινομένη πόρρω λίαν. Ὁ δὲ

τρόμος αὐτῆς ποιεῖ τοῦ ἄστρου δοκεῖν εἶναι τὴν κίνησιν· οὐθὲν

γὰρ διαφέρει κινεῖν τὴν ὄψιν ἢ τὸ ὁρώμενον. Ἀλλὰ μὴν

25 ὅτι οὐδὲ κυλίεται τὰ ἄστρα, φανερόν· τὸ μὲν γὰρ κυλιόμενον

στρέφεσθαι ἀνάγκη, τῆς δὲ σελήνης ἀεὶ δῆλόν ἐστι

τὸ καλούμενον πρόσωπον. Ὥστ' ἐπεὶ κινούμενα μὲν δι' αὑτῶν

τὰς οἰκείας κινεῖσθαι κινήσεις εὔλογον, ταύτας δ' οὐ φαίνεται

κινούμενα, δῆλον ὅτι οὐκ ἂν κινοῖτο δι' αὑτῶν. Πρὸς δὲ

30 τούτοις ἄλογον τὸ μηθὲν ὄργανον αὐτοῖς ἀποδοῦναι τὴν φύσιν

πρὸς τὴν κίνησιν (οὐθὲν γὰρ ὡς ἔτυχε ποιεῖ ἡ φύσις),

οὐδὲ τῶν μὲν ζῴων φροντίσαι, τῶν δ' οὕτω τιμίων ὑπεριδεῖν,

ἀλλ' ἔοικεν ὥσπερ ἐπίτηδες ἀφελεῖν πάντα δι' ὧν ἐνεδέχετο

προϊέναι καθ' αὑτά, καὶ ὅτι πλεῖστον ἀποστῆσαι τῶν ἐχόντων

35 ὄργανα πρὸς κίνησιν. Διὸ καὶ εὐλόγως ἂν δόξειεν ὅ τε

1For, in the first place, the quicker movement of the larger circle is natural when all the circles are attached to the same centre. Whenever bodies are moving with their proper motion, the larger moves quicker. It is the same here with the revolving bodies: for the are intercepted by two radii will be larger in 5the larger circle, and hence it is not surprising that the revolution of the larger circle should take the same time as that of the smaller. And secondly, the fact that the heavens do not break in pieces follows not only from this but also from the proof already given of the continuity of the whole.
Again, since the stars are spherical, as our opponents assert and we may consistently admit, 10inasmuch as we construct them out of the spherical body, and since the spherical body has two movements proper to itself, namely rolling and spinning, it follows that if the stars have a movement of their own, it will be one of these. But neither is observed. (1) Suppose them to spin. They would then stay where they were, and not change their place, as, by observation and general consent, 15they do. Further, one would expect them all to exhibit the same movement: but the only star which appears to possess this movement is the sun, at sunrise or sunset, and this appearance is due not to the sun itself but to the distance from which we observe it. The visual ray being excessively prolonged becomes weak and wavering. The same reason probably accounts for the apparent twinkling of 20the fixed stars and the absence of twinkling in the planets. The planets are near, so that the visual ray reaches them in its full vigour, but when it comes to the fixed stars it is quivering because of the distance and its excessive extension; and its tremor produces an appearance of movement in the star: for it makes no difference whether movement is set up in the ray or in the object of 25vision.
(2) On the other hand, it is also clear that the stars do not roll. For rolling involves rotation: but the 'face', as it is called, of the moon is always seen. Therefore, since any movement of their own which the stars possessed would presumably be one proper to themselves, and no such movement is observed in them, clearly they have no movement of their own.
There is, further, the 30absurdity that nature has bestowed upon them no organ appropriate to such movement. For nature leaves nothing to chance, and would not, while caring for animals, overlook things so precious. Indeed, nature seems deliberately to have stripped them of everything which makes selforiginated progression possible, and to have removed them as far as possible from things which have organs of movement.

290b

1 ὅλος οὐρανὸς σφαιροειδὴς εἶναι καὶ ἕκαστον τῶν ἄστρων.

Πρὸς μὲν γὰρ τὴν ἐν ἑαυτῷ κίνησιν ἡ σφαῖρα τῶν σχημάτων

χρησιμώτατον (οὕτω γὰρ ἂν καὶ τάχιστα κινοῖτο καὶ μάλιστα

κατέχοι τὸν αὐτὸν τόπον), πρὸς δὲ τὴν εἰς τὸ πρόσθεν

5 ἀχρηστότατον· ἥκιστα γὰρ ὅμοιον τοῖς δι' αὑτῶν κινητικοῖς·

οὐδὲν γὰρ ἀπηρτημένον ἔχει οὐδὲ προέχον, ὥσπερ τὸ

εὐθύγραμμον, ἀλλὰ πλεῖστον ἀφέστηκε τῷ σχήματι τῶν

πορευτικῶν σωμάτων. Ἐπεὶ οὖν δεῖ τὸν μὲν οὐρανὸν κινεῖσθαι

τὴν ἐν ἑαυτῷ κίνησιν, τὰ δ' ἄλλα [ἄστρα] μὴ προϊέναι δι' αὑτῶν,

10 εὐλόγως ἂν ἑκάτερον εἴη σφαιροειδές· οὕτω γὰρ μάλιστα

τὸ μὲν κινήσεται τὸ δ' ἠρεμήσει.

1This is just why it seems proper that the whole heaven and every star should be spherical. For while of all shapes the sphere is the most convenient for movement in one place, making possible, as it does, the swiftest and most selfcontained motion, for forward movement it is the most 5unsuitable, least of all resembling shapes which are self-moved, in that it has no dependent or projecting part, as a rectilinear figure has, and is in fact as far as possible removed in shape from ambulatory bodies. Since, therefore, the heavens have to move in one lace, and the stars are not required to move themselves forward, it is natural that both should be 10spherical-a shape which best suits the movement of the one and the immobility of the other.

Book 2,Chapter 9 (290b12–291a28)

Φανερὸν δ' ἐκ τούτων ὅτι καὶ τὸ φάναι γίνεσθαι φερομένων

ἁρμονίαν, ὡς συμφώνων γινομένων τῶν ψόφων,

κομψῶς μὲν εἴρηται καὶ περιττῶς ὑπὸ τῶν εἰπόντων, οὐ

15 μὴν οὕτως ἔχει τἀληθές. Δοκεῖ γάρ τισιν ἀναγκαῖον εἶναι

τηλικούτων φερομένων σωμάτων γίγνεσθαι ψόφον, ἐπεὶ καὶ

τῶν παρ' ἡμῖν οὔτε τοὺς ὄγκους ἐχόντων ἴσους οὔτε τοιούτῳ

τάχει φερομένων· ἡλίου δὲ καὶ σελήνης, ἔτι τε τοσούτων

τὸ πλῆθος ἄστρων καὶ τὸ μέγεθος φερομένων τῷ τάχει τοιαύτην

20 φορὰν ἀδύνατον μὴ γίγνεσθαι ψόφον ἀμήχανόν τινα

τὸ μέγεθος. Ὑποθέμενοι δὲ ταῦτα καὶ τὰς ταχυτῆτας ἐκ

τῶν ἀποστάσεων ἔχειν τοὺς τῶν συμφωνιῶν λόγους, ἐναρμόνιον

γίγνεσθαί φασι τὴν φωνὴν φερομένων κύκλῳ τῶν ἄστρων.

Ἐπεὶ δ' ἄλογον δοκεῖ τὸ μὴ συνακούειν ἡμᾶς τῆς φωνῆς

25 ταύτης, αἴτιον τούτου φασὶν εἶναι τὸ γιγνομένων εὐθὺς ὑπάρχειν

τὸν ψόφον, ὥστε μὴ διάδηλον εἶναι πρὸς τὴν ἐναντίαν

σιγήν· πρὸς ἄλληλα γὰρ φωνῆς καὶ σιγῆς εἶναι τὴν διάγνωσιν·

ὥστε καθάπερ τοῖς χαλκοτύποις διὰ συνήθειαν οὐθὲν

δοκεῖ διαφέρειν, καὶ τοῖς ἀνθρώποις ταὐτὸ συμβαίνειν.

30 Ταῦτα δή, καθάπερ εἴρηται πρότερον, ἐμμελῶς μὲν λέγεται

καὶ μουσικῶς, ἀδύνατον δὲ τοῦτον ἔχειν τὸν τρόπον. Οὐ

γὰρ μόνον τὸ μηθὲν ἀκούειν ἄτοπον, περὶ οὗ λέγειν ἐγχειροῦσι

τὴν αἰτίαν, ἀλλὰ καὶ τὸ μηδὲν πάσχειν χωρὶς αἰσθήσεως.

Οἱ γὰρ ὑπερβάλλοντες ψόφοι διακναίουσι καὶ τῶν ἀψύχων

35 σωμάτων τοὺς ὄγκους, οἷον ὁ τῆς βροντῆς διίστησι λίθους καὶ

From all this it is clear that the theory that the movement of the stars produces a harmony, i.e. that the sounds they make are concordant, in spite of the grace and originality with which it has been stated, is nevertheless untrue. Some thinkers suppose that the motion 15of bodies of that size must produce a noise, since on our earth the motion of bodies far inferior in size and in speed of movement has that effect. Also, when the sun and the moon, they say, and all the stars, so great in number and in size, are moving with so rapid a motion, how should they not produce a sound immensely great? Starting from this argument 20and from the observation that their speeds, as measured by their distances, are in the same ratios as musical concordances, they assert that the sound given forth by the circular movement of the stars is a harmony. Since, however, it appears unaccountable that we should not hear this music, they explain this by saying that the sound is in our ears from the 25very moment of birth and is thus indistinguishable from its contrary silence, since sound and silence are discriminated by mutual contrast. What happens to men, then, is just what happens to coppersmiths, who are so accustomed to the noise of the smithy that it makes no difference to them. But, as we said before, melodious and poetical as the theory is, it cannot 30be a true account of the facts. There is not only the absurdity of our hearing nothing, the ground of which they try to remove, but also the fact that no effect other than sensitive is produced upon us. Excessive noises, we know, shatter the solid bodies even of inanimate things: the noise of thunder, for instance, splits rocks and the strongest of bodies.

291a

1 τὰ καρτερώτατα τῶν σωμάτων. Τοσούτων δὲ φερομένων,

καὶ τοῦ ψόφου διιόντος πρὸς τὸ φερόμενον μέγεθος, πολλαπλάσιον

μέγεθος ἀναγκαῖον ἀφικνεῖσθαί τε δεῦρο καὶ τὴν ἰσχὺν

ἀμήχανον εἶναι τῆς βίας. Ἀλλ' εὐλόγως οὔτ' ἀκούομεν οὔτε

5 πάσχοντα φαίνεται τὰ σώματα βίαιον οὐδὲν πάθος, διὰ

τὸ μὴ ψοφεῖν. Ἅμα δ' ἐστὶ τό τ' αἴτιον τούτων δῆλον, καὶ

μαρτύριον τῶν εἰρημένων ἡμῖν λόγων, ὥς εἰσιν ἀληθεῖς· τὸ

γὰρ ἀπορηθὲν καὶ ποιῆσαν τοὺς Πυθαγορείους φάναι γίγνεσθαι

συμφωνίαν τῶν φερομένων ἡμῖν ἐστι τεκμήριον. Ὅσα

10 μὲν γὰρ αὐτὰ φέρεται, ποιεῖ ψόφον καὶ πληγήν· ὅσα δ'

ἐν φερομένῳ ἐνδέδεται ἢ ἐνυπάρχει, καθάπερ ἐν τῷ πλοίῳ

τὰ μόρια, οὐχ οἷόν τε ψοφεῖν, οὐδ' αὐτὸ τὸ πλοῖον, εἰ φέροιτο

ἐν ποταμῷ. Καίτοι τοὺς αὐτοὺς λόγους ἂν ἐξείη λέγειν,

ὡς ἄτοπον εἰ μὴ φερόμενος ὁ ἱστὸς καὶ ἡ πρύμνα

15 ποιεῖ ψόφον πολὺν τηλικαύτης νεώς, ἢ πάλιν αὐτὸ τὸ

πλοῖον κινούμενον. Τὸ δ' ἐν μὴ φερομένῳ φερόμενον ποιεῖ

ψόφον· ἐν φερομένῳ δὲ συνεχὲς καὶ μὴ ποιοῦν πληγὴν

ἀδύνατον ψοφεῖν. Ὥστ' ἐνταῦθα λεκτέον ὡς εἴπερ ἐφέρετο

τὰ σώματα τούτων εἴτ' ἐν ἀέρος πλήθει κεχυμένῳ κατὰ τὸ

20 πᾶν εἴτε πυρός, ὥσπερ πάντες φασίν, ἀναγκαῖον ποιεῖν

ὑπερφυᾶ τῷ μεγέθει τὸν ψόφον, τούτου δὲ γινομένου καὶ

δεῦρ' ἀφικνεῖσθαι καὶ διακναίειν. Ὥστ' ἐπείπερ οὐ φαίνεται

τοῦτο συμβαῖνον, οὔτ' ἂν ἔμψυχον οὔτε βίαιον φέροιτο φορὰν

οὐθὲν αὐτῶν, ὥσπερ τὸ μέλλον ἔσεσθαι προνοούσης τῆς φύσεως,

25 ὅτι μὴ τοῦτον τὸν τρόπον ἐχούσης τῆς κινήσεως οὐθὲν

ἂν ἦν τῶν περὶ τὸν δεῦρο τόπον ὁμοίως ἔχον. Ὅτι μὲν οὖν

σφαιροειδῆ τὰ ἄστρα καὶ ὅτι οὐ κινεῖται δι' αὑτῶν, εἴρηται.

1But if the moving bodies are so great, and the sound which penetrates to us is proportionate to their size, that sound must needs reach us in an intensity many times that of thunder, and the force of its action must be immense. Indeed the reason why we do not hear, 5and show in our bodies none of the effects of violent force, is easily given: it is that there is no noise. But not only is the explanation evident; it is also a corroboration of the truth of the views we have advanced. For the very difficulty which made the Pythagoreans say that the motion of the stars produces a concord corroborates 10our view. Bodies which are themselves in motion, produce noise and friction: but those which are attached or fixed to a moving body, as the parts to a ship, can no more create noise, than a ship on a river moving with the stream. Yet by the same argument one might say it was absurd that on a large vessel the motion of mast and 15poop should not make a great noise, and the like might be said of the movement of the vessel itself. But sound is caused when a moving body is enclosed in an unmoved body, and cannot be caused by one enclosed in, and continuous with, a moving body which creates no friction. We may say, then, in this matter that if the heavenly 20bodies moved in a generally diffused mass of air or fire, as every one supposes, their motion would necessarily cause a noise of tremendous strength and such a noise would necessarily reach and shatter us. Since, therefore, this effect is evidently not produced, it follows that none of them can move with the motion either of animate 25nature or of constraint. It is as though nature had foreseen the result, that if their movement were other than it is, nothing on this earth could maintain its character.
That the stars are spherical and are not selfmoved, has now been explained.

Book 2,Chapter 10 (291a29–291b10)

Περὶ δὲ τῆς τάξεως αὐτῶν, ὃν μὲν τρόπον ἕκαστα

30 κινεῖται τῷ τὰ μὲν εἶναι πρότερα τὰ δ' ὕστερα, καὶ πῶς

ἔχει πρὸς ἄλληλα τοῖς ἀποστήμασιν, ἐκ τῶν περὶ ἀστρολογίαν

θεωρείσθω· λέγεται γὰρ ἱκανῶς. Συμβαίνει δὲ κατὰ

λόγον γίγνεσθαι τὰς ἑκάστου κινήσεις τοῖς ἀποστήμασι τῷ

τὰς μὲν εἶναι θάττους τὰς δὲ βραδυτέρας· ἐπεὶ γὰρ ὑπόκειται

35 τὴν μὲν ἐσχάτην τοῦ οὐρανοῦ περιφορὰν ἁπλῆν τ' εἶναι

With their order-I mean the position of each, as involving the priority of some and 30the posteriority of others, and their respective distances from the extremity-with this astronomy may be left to deal, since the astronomical discussion is adequate. This discussion shows that the movements of the several stars depend, as regards the varieties of speed which they exhibit, on the distance of each from the extremity.

291b

1 καὶ ταχίστην, τὰς δὲ τῶν ἄλλων βραδυτέρας τε καὶ πλείους

(ἕκαστον γὰρ ἀντιφέρεται τῷ οὐρανῷ κατὰ τὸν αὑτοῦ κύκλον),

εὔλογον ἤδη τὸ μὲν ἐγγυτάτω τῆς ἁπλῆς καὶ πρώτης

περιφορᾶς ἐν πλείστῳ χρόνῳ διιέναι τὸν αὑτοῦ κύκλον,

5 τὸ δὲ πορρωτάτω ἐν ἐλαχίστῳ, τῶν δ' ἄλλων τὸ ἐγγύτερον

ἀεὶ ἐν πλείονι, τὸ δὲ πορρώτερον ἐν ἐλάττονι. 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 μαθηματικοί.

1It is established that the outermost revolution of the heavens is a simple movement and the swiftest of all, and that the movement of all other bodies is composite and relatively slow, for the reason that each is moving on its own circle with the reverse motion to that of the heavens. This at once 5leads us to expect that the body which is nearest to that first simple revolution should take the longest time to complete its circle, and that which is farthest from it the shortest, the others taking a longer time the nearer they are and a shorter time the farther away they are. For it is the nearest body which is most strongly influenced, and the most remote, by reason of its 10distance, which is least affected, the influence on the intermediate bodies varying, as the mathematicians show, with their distance.

Book 2,Chapter 11 (291b11–23)

Τὸ δὲ σχῆμα τῶν ἄστρων ἑκάστου σφαιροειδὲς μάλιστ'

ἄν τις εὐλόγως ὑπολάβοι. Ἐπεὶ γὰρ δέδεικται ὅτι οὐ

πεφύκασι κινεῖσθαι δι' αὑτῶν, ἡ δὲ φύσις οὐδὲν ἀλόγως

οὐδὲ μάτην ποιεῖ, δῆλον ὅτι καὶ σχῆμα τοιοῦτον ἀπέδωκε

15 τοῖς ἀκινήτοις ὃ ἥκιστά ἐστι κινητικόν. Ἥκιστα δὲ κινητικὸν

ἡ σφαῖρα διὰ τὸ μηδὲν ἔχειν ὄργανον πρὸς τὴν κίνησιν. Ὥστε

δῆλον ὅτι σφαιροειδῆ ἂν εἴη τὸν ὄγκον. Ἔτι δ' ὁμοίως μὲν

ἅπαντα καὶ ἕν, ἡ δὲ σελήνη δείκνυται διὰ τῶν περὶ τὴν

ὄψιν ὅτι σφαιροειδής· οὐ γὰρ ἂν ἐγίνετο αὐξανομένη καὶ

20 φθίνουσα τὰ μὲν πλεῖστα μηνοειδὴς ἢ ἀμφίκυρτος, ἅπαξ

δὲ διχότομος. Καὶ πάλιν διὰ τῶν ἀστρολογικῶν, ὅτι οὐκ ἂν

ἦσαν αἱ τοῦ ἡλίου ἐκλείψεις μηνοειδεῖς. Ὥστ' εἴπερ ἓν τοιοῦτον,

δῆλον ὅτι καὶ τἆλλα ἂν εἴη σφαιροειδῆ.

With regard to the shape of each star, the most reasonable view is that they are spherical. It has been shown that it is not in their nature to move themselves, and, since nature is no wanton or random creator, clearly she will have given things 15which possess no movement a shape particularly unadapted to movement. Such a shape is the sphere, since it possesses no instrument of movement. Clearly then their mass will have the form of a sphere. Again, what holds of one holds of all, and the evidence of our eyes shows us that the moon is spherical. For how else should the moon as it waxes and wanes show for the most 20part a crescent-shaped or gibbous figure, and only at one moment a half-moon? And astronomical arguments give further confirmation; for no other hypothesis accounts for the crescent shape of the sun's eclipses. One, then, of the heavenly bodies being spherical, clearly the rest will be spherical also.

Book 2,Chapter 12 (291b24–293a14)

Δυοῖν δ' ἀπορίαιν οὔσαιν, περὶ ὧν εἰκότως ἂν ὁστισοῦν

25 ἀπορήσειε, πειρατέον λέγειν τὸ φαινόμενον, αἰδοῦς ἀξίαν

εἶναι νομίζοντας τὴν προθυμίαν μᾶλλον ἢ θράσους, εἴ τις

διὰ τὸ φιλοσοφίας διψῆν καὶ μικρὰς εὐπορίας ἀγαπᾷ

περὶ ὧν τὰς μεγίστας ἔχομεν ἀπορίας. Ἔστι δὲ πολλῶν ὄντων

τοιούτων οὐχ ἥκιστα θαυμαστόν, διὰ τίνα ποτ' αἰτίαν οὐκ

30 ἀεὶ τὰ πλεῖον ἀπέχοντα τῆς πρώτης φορᾶς κινεῖται πλείους

κινήσεις, ἀλλὰ τὰ μεταξὺ πλείστας. Εὔλογον γὰρ ἂν δόξειεν

εἶναι τοῦ πρώτου σώματος μίαν κινουμένου φορὰν τὸ

πλησιαίτατον ἐλαχίστας κινεῖσθαι κινήσεις, οἷον δύο, τὸ δ'

ἐχόμενον τρεῖς ἤ τινα ἄλλην τοιαύτην τάξιν. Νῦν δὲ συμβαίνει

35 τοὐναντίον· ἐλάττους γὰρ ἥλιος καὶ σελήνη κινοῦνται

There are two difficulties, which may very reasonably here be raised, of which 25we must now attempt to state the probable solution: for we regard the zeal of one whose thirst after philosophy leads him to accept even slight indications where it is very difficult to see one's way, as a proof rather of modesty than of overconfidence.
Of many such problems one of the strangest is the problem why we find the greatest number of movements in the intermediate 30bodies, and not, rather, in each successive body a variety of movement proportionate to its distance from the primary motion. For we should expect, since the primary body shows one motion only, that the body which is nearest to it should move with the fewest movements, say two, and the one next after that with three, or some similar arrangement. But the opposite is the case.

292a

1 κινήσεις ἢ τῶν πλανωμένων ἄστρων ἔνια· καίτοι πορρώτερον

τοῦ μέσου καὶ πλησιαίτερον τοῦ πρώτου σώματός εἰσιν αὐτῶν.

Δῆλον δὲ τοῦτο περὶ ἐνίων καὶ τῇ ὄψει γέγονεν· τὴν

γὰρ σελήνην ἑωράκαμεν διχότομον μὲν οὖσαν, ὑπελθοῦσαν

5 δὲ τῶν ἀστέρων τὸν τοῦ Ἄρεος, καὶ ἀποκρυφέντα μὲν κατὰ τὸ

μέλαν αὐτῆς, ἐξελθόντα δὲ κατὰ τὸ φανὸν καὶ λαμπρόν.

Ὁμοίως δὲ καὶ περὶ τοὺς ἄλλους ἀστέρας λέγουσιν οἱ πάλαι

τετηρηκότες ἐκ πλείστων ἐτῶν Αἰγύπτιοι καὶ Βαβυλώνιοι,

παρ' ὧν πολλὰς πίστεις ἔχομεν περὶ ἑκάστου τῶν ἄστρων.

10 Τοῦτό τε δὴ δικαίως ἀπορήσειεν ἄν τις, καὶ διὰ τίνα ποτ'

αἰτίαν ἐν μὲν τῇ πρώτῃ φορᾷ τοσοῦτόν ἐστιν ἄστρων πλῆθος

ὥστε τῶν ἀναριθμήτων εἶναι δοκεῖν τὴν πᾶσαν τάξιν, τῶν δ'

ἄλλων ἓν χωρὶς ἕκαστον, δύο δ' ἢ πλείω οὐ φαίνεται ἐν τῇ

αὐτῇ ἐνδεδεμένα φορᾷ. Περὶ δὴ τούτων ζητεῖν μὲν καλῶς

15 ἔχει καὶ τὴν ἐπὶ πλεῖον σύνεσιν, καίπερ μικρὰς ἔχοντας

ἀφορμὰς καὶ τοσαύτην ἀπόστασιν ἀπέχοντας τῶν περὶ αὐτὰ

συμβαινόντων· ὅμως δ' ἐκ τῶν τοιούτων θεωροῦσιν οὐδὲν ἄλογον

ἂν δόξειεν εἶναι τὸ νῦν ἀπορούμενον. Ἀλλ' ἡμεῖς ὡς περὶ

σωμάτων αὐτῶν μόνον, καὶ μονάδων τάξιν μὲν ἐχόντων,

20 ἀψύχων δὲ πάμπαν, διανοούμεθα· δεῖ δ' ὡς μετεχόντων

ὑπολαμβάνειν πράξεως καὶ ζωῆς· οὕτω γὰρ οὐθὲν δόξει παράλογον

εἶναι τὸ συμβαῖνον. Ἔοικε γὰρ τῷ μὲν ἄριστα ἔχοντι

ὑπάρχειν τὸ εὖ ἄνευ πράξεως, τῷ δ' ἐγγύτατα διὰ ὀλίγης

καὶ μιᾶς, τοῖς δὲ πορρωτέρω διὰ πλειόνων, ὥσπερ ἐπὶ σώματος

25 τὸ μὲν οὐδὲ γυμναζόμενον εὖ ἔχει, τὸ δὲ μικρὰ περιπατῆσαν,

τῷ δὲ καὶ δρόμου δεῖ καὶ πάλης καὶ κονίσεως,

πάλιν δ' ἑτέρῳ οὐδ' ὁποσαοῦν πονοῦντι τοῦτό γ' ἂν ἔτι ὑπάρξαι

τἀγαθόν, ἀλλ' ἕτερόν τι. Ἔστι δὲ τὸ κατορθοῦν χαλεπὸν ἢ τὸ

πολλὰ ἢ τὸ πολλάκις, οἷον μυρίους ἀστραγάλους Χίους βαλεῖν

30 ἀμήχανον, ἀλλ' ἕνα ἢ δύο ῥᾷον. Καὶ πάλιν ὅταν τοδὶ μὲν δέῃ

τοῦδ' ἕνεκα ποιῆσαι, τοῦτο δ' ἄλλου καὶ τοῦτο ἑτέρου, ἐν μὲν

ἑνὶ ἢ δυσὶ ῥᾴδιον ἐπιτυχεῖν, ὅσῳ δ' ἂν διὰ πλειόνων, χαλεπώτερον.

1The movements of the sun and moon are fewer than those of some of the planets. Yet these planets are farther from the centre and thus nearer to the primary body than they, as observation has itself revealed. For we have seen the moon, half-full, pass beneath the planet Mars, which vanished on its 5shadow side and came forth by the bright and shining part. Similar accounts of other stars are given by the Egyptians and Babylonians, whose observations have been kept for very many years past, and from whom much of our evidence about particular stars is derived. A second difficulty which may with equal justice be raised is this. Why is it that the primary motion includes 10such a multitude of stars that their whole array seems to defy counting, while of the other stars each one is separated off, and in no case do we find two or more attached to the same motion?
On these questions, I say, it is well that we should seek to increase our understanding, though we have but little to go upon, and are placed at so great a distance from the facts 15in question. Nevertheless there are certain principles on which if we base our consideration we shall not find this difficulty by any means insoluble. We may object that we have been thinking of the stars as mere bodies, and as units with a serial order indeed but entirely inanimate; but should rather conceive them as enjoying life and action. On this view the facts cease 20to appear surprising. For it is natural that the best-conditioned of all things should have its good without action, that which is nearest to it should achieve it by little and simple action, and that which is farther removed by a complexity of actions, just as with men's bodies one is in good condition without exercise at all, another after a short walk, while another 25requires running and wrestling and hard training, and there are yet others who however hard they worked themselves could never secure this good, but only some substitute for it. To succeed often or in many things is difficult. For instance, to throw ten thousand Coan throws with the dice would be impossible, but to throw one or two is comparatively easy. In action, again, 30when A has to be done to get B, B to get C, and C to get D, one step or two present little difficulty, but as the series extends the difficulty grows.

292b

1 Διὸ δεῖ νομίζειν καὶ τὴν τῶν ἄστρων πρᾶξιν εἶναι

τοιαύτην οἵα περ ἡ τῶν ζῴων καὶ φυτῶν. Καὶ γὰρ ἐνταῦθα

αἱ τοῦ ἀνθρώπου πλεῖσται πράξεις· πολλῶν γὰρ τῶν εὖ δύναται

τυχεῖν, ὥστε πολλὰ πράττειν, καὶ ἄλλων ἕνεκα. (Τῷ

5 δ' ὡς ἄριστα ἔχοντι οὐθὲν δεῖ πράξεως· ἔστι γὰρ αὐτὸ τὸ οὗ

ἕνεκα, ἡ δὲ πρᾶξις ἀεί ἐστιν ἐν δυσίν, ὅταν καὶ οὗ ἕνεκα ᾖ

καὶ τὸ τούτου ἕνεκα). Τῶν δ' ἄλλων ζῴων ἐλάττους, τῶν δὲ

φυτῶν μικρά τις καὶ μία ἴσως· ἢ γὰρ ἕν τί ἐστιν οὗ τύχοι

ἄν, ὥσπερ καὶ ἄνθρωπος, ἢ καὶ τὰ πολλὰ πάντα πρὸ ὁδοῦ

10 ἐστι πρὸς τὸ ἄριστον. Τὸ μὲν οὖν ἔχει καὶ μετέχει τοῦ ἀρίστου,

τὸ δ' ἀφικνεῖται [ἐγγὺς] δι' ὀλίγων, τὸ δὲ διὰ πολλῶν, τὸ

δ' οὐδ' ἐγχειρεῖ, ἀλλ' ἱκανὸν εἰς τὸ ἐγγὺς τοῦ ἐσχάτου ἐλθεῖν·

οἷον εἰ ὑγίεια τέλος, τὸ μὲν δὴ ἀεὶ ὑγιαίνει, τὸ δ'

ἰσχνανθέν, τὸ δὲ δραμὸν καὶ ἰσχνανθέν, τὸ δὲ καὶ ἄλλο τι

15 πρᾶξαν τοῦ δραμεῖν ἕνεκα, ὥστε πλείους αἱ κινήσεις· ἕτερον

δ' ἀδυνατεῖ πρὸς τὸ ὑγιᾶναι ἐλθεῖν, ἀλλὰ πρὸς τὸ δραμεῖν

μόνον ἢ ἰσχνανθῆναι, καὶ τούτων θάτερον τέλος αὐτοῖς. Μάλιστα

μὲν γὰρ ἐκείνου τυχεῖν ἄριστον πᾶσι τοῦ τέλους· εἰ δὲ

μή, ἀεὶ ἄμεινόν ἐστιν ὅσῳ ἂν ἐγγύτερον ᾖ τοῦ ἀρίστου. Καὶ

20 διὰ τοῦτο ἡ μὲν γῆ ὅλως οὐ κινεῖται, τὰ δ' ἐγγὺς ὀλίγας

κινήσεις· οὐ γὰρ ἀφικνεῖται πρὸς τὸ ἔσχατον, ἀλλὰ μέχρι

ὅτου δύναται τυχεῖν τῆς θειοτάτης ἀρχῆς. Ὁ δὲ πρῶτος οὐρανὸς

εὐθὺς τυγχάνει διὰ μιᾶς κινήσεως. Τὰ δ' ἐν μέσῳ τοῦ

πρώτου καὶ τῶν ἐσχάτων ἀφικνεῖται μέν, διὰ πλειόνων δ'

25 ἀφικνεῖται κινήσεων. Περὶ δὲ τῆς ἀπορίας ὅτι κατὰ μὲν τὴν

πρώτην μίαν οὖσαν φορὰν πολὺ πλῆθος συνέστηκεν ἄστρων,

τῶν δ' ἄλλων χωρὶς ἕκαστον εἴληφεν ἰδίας κινήσεις, δι' ἓν

μὲν ἄν τις πρῶτον εὐλόγως οἰηθείη τοῦθ' ὑπάρχειν· νοῆσαι

γὰρ δεῖ τῆς ζωῆς καὶ τῆς ἀρχῆς ἑκάστης πολλὴν ὑπεροχὴν

30 εἶναι τῆς πρώτης πρὸς τὰς ἄλλας, εἴη δ' ἂν ἥδε συμβαίνουσα

κατὰ λόγον· ἡ μὲν γὰρ πρώτη μία οὖσα πολλὰ κινεῖ

τῶν σωμάτων τῶν θείων, αἱ δὲ πολλαὶ οὖσαι ἓν μόνον

1We must, then, think of the action of the lower stars as similar to that of animals and plants. For on our earth it is man that has the greatest variety of actions-for there are many goods that man can secure; hence his actions are various and directed to ends beyond them-while the perfectly 5conditioned has no need of action, since it is itself the end, and action always requires two terms, end and means. The lower animals have less variety of action than man; and plants perhaps have little action and of one kind only. For either they have but one attainable good (as indeed man has), or, if several, each contributes directly to their ultimate good. One thing then 10has and enjoys the ultimate good, other things attain to it, one immediately by few steps, another by many, while yet another does not even attempt to secure it but is satisfied to reach a point not far removed from that consummation. Thus, taking health as the end, there will be one thing that always possesses health, others that attain it, one by reducing flesh, another 15by running and thus reducing flesh, another by taking steps to enable himself to run, thus further increasing the number of movements, while another cannot attain health itself, but only running or reduction of flesh, so that one or other of these is for such a being the end. For while it is clearly best for any being to attain the real end, yet, if that cannot be, 20the nearer it is to the best the better will be its state. It is for this reason that the earth moves not at all and the bodies near to it with few movements. For they do not attain the final end, but only come as near to it as their share in the divine principle permits. But the first heaven finds it immediately with a single movement, and the bodies intermediate between 25the first and last heavens attain it indeed, but at the cost of a multiplicity of movement.
As to the difficulty that into the one primary motion is crowded a vast multitude of stars, while of the other stars each has been separately given special movements of its own, there is in the first place this reason for regarding the arrangement as a natural one. In thinking of 30the life and moving principle of the several heavens one must regard the first as far superior to the others. Such a superiority would be reasonable.

293a

1 ἑκάστη· τῶν γὰρ πλανωμένων ἓν ὁτιοῦν πλείους φέρεται

φοράς. Ταύτῃ τε οὖν ἀνισάζει ἡ φύσις καὶ ποιεῖ τινὰ τάξιν,

τῇ μὲν μιᾷ φορᾷ πολλὰ ἀποδοῦσα σώματα, τῷ δ' ἑνὶ

σώματι πολλὰς φοράς. Καὶ ἔτι διὰ τόδε ἓν ἔχουσι σῶμα

5 αἱ ἄλλαι φοραί, ὅτι πολλὰ σώματα κινοῦσιν αἱ πρὸ τῆς

τελευταίας καὶ τῆς ἓν ἄστρον ἐχούσης· ἐν πολλαῖς γὰρ

σφαίραις ἡ τελευταία σφαῖρα ἐνδεδεμένη φέρεται, ἑκάστη

δὲ σφαῖρα σῶμά τι τυγχάνει ὄν. Ἐκείνης ἂν οὖν κοινὸν εἴη τὸ

ἔργον· αὐτῇ μὲν γὰρ ἑκάστῃ ἡ ἴδιος φύσει φορά, αὕτη δὲ

10 οἷον πρόσκειται, παντὸς δὲ πεπερασμένου σώματος πρὸς πεπερασμένον

ἡ δύναμίς ἐστιν. Ἀλλὰ περὶ μὲν τῶν τὴν ἐγκύκλιον

φερομένων κίνησιν ἄστρων εἴρηται ποῖ' ἄττα κατά τε

τὴν οὐσίαν ἐστὶ καὶ κατὰ τὸ σχῆμα, περί τε τῆς φορᾶς

καὶ τῆς τάξεως αὐτῶν.

1For this single first motion has to move many of the divine bodies, while the numerous other motions move only one each, since each single planet moves with a variety of motions. Thus, then, nature makes matters equal and establishes a certain order, giving to the single motion many 5bodies and to the single body many motions. And there is a second reason why the other motions have each only one body, in that each of them except the last, i.e. that which contains the one star, is really moving many bodies. For this last sphere moves with many others, to which it is fixed, each sphere being actually a body; so that its movement will 10be a joint product. Each sphere, in fact, has its particular natural motion, to which the general movement is, as it were, added. But the force of any limited body is only adequate to moving a limited body.
The characteristics of the stars which move with a circular motion, in respect of substance and shape, movement and order, have now been sufficiently 15explained.

Book 2,Chapter 13 (293a15–296a23)

15 Λοιπὸν δὲ περὶ τῆς γῆς εἰπεῖν, οὗ τε τυγχάνει κειμένη,

καὶ πότερον τῶν ἠρεμούντων ἐστὶν ἢ τῶν κινουμένων, καὶ περὶ

τοῦ σχήματος αὐτῆς. Περὶ μὲν οὖν τῆς θέσεως οὐ τὴν αὐτὴν

ἅπαντες ἔχουσι δόξαν, ἀλλὰ τῶν πλείστων ἐπὶ τοῦ μέσου

κεῖσθαι λεγόντων, ὅσοι τὸν ὅλον οὐρανὸν πεπερασμένον εἶναί

20 φασιν, ἐναντίως οἱ περὶ τὴν Ἰταλίαν, καλούμενοι δὲ Πυθαγόρειοι

λέγουσιν· ἐπὶ μὲν γὰρ τοῦ μέσου πῦρ εἶναί φασι,

τὴν δὲ γῆν, ἓν τῶν ἄστρων οὖσαν, κύκλῳ φερομένην περὶ τὸ

μέσον νύκτα τε καὶ ἡμέραν ποιεῖν. Ἔτι δ' ἐναντίαν ἄλλην

ταύτῃ κατασκευάζουσι γῆν, ἣν ἀντίχθονα ὄνομα καλοῦσιν,

25 οὐ πρὸς τὰ φαινόμενα τοὺς λόγους καὶ τὰς αἰτίας ζητοῦντες,

ἀλλὰ πρός τινας λόγους καὶ δόξας αὑτῶν τὰ φαινόμενα

προσέλκοντες καὶ πειρώμενοι συγκοσμεῖν. Πολλοῖς δ' ἂν

καὶ ἑτέροις συνδόξειε μὴ δεῖν τῇ γῇ τὴν τοῦ μέσου χώραν

ἀποδιδόναι, τὸ πιστὸν οὐκ ἐκ τῶν φαινομένων ἀθροῦσιν ἀλλὰ

30 μᾶλλον ἐκ τῶν λόγων. Τῷ γὰρ τιμιωτάτῳ οἴονται προσήκειν

τὴν τιμιωτάτην ὑπάρχειν χώραν, εἶναι δὲ πῦρ μὲν γῆς

τιμιώτερον, τὸ δὲ πέρας τοῦ μεταξύ, τὸ δ' ἔσχατον καὶ

τὸ μέσον πέρας· ὥστ' ἐκ τούτων ἀναλογιζόμενοι οὐκ οἴονται

ἐπὶ τοῦ μέσου τῆς σφαίρας κεῖσθαι αὐτήν, ἀλλὰ μᾶλλον

It remains to speak of the earth, of its position, of the question whether it is at rest or in motion, and of its shape.
I. As to its position there is some difference of opinion. Most people-all, in fact, who regard the whole heaven as finite-say it lies at the centre. But the Italian philosophers known as Pythagoreans take the contrary 20view. At the centre, they say, is fire, and the earth is one of the stars, creating night and day by its circular motion about the centre. They further construct another earth in opposition to ours to which they give the name counterearth. In all this they are not seeking for theories and causes to account for observed facts, but rather forcing their 25observations and trying to accommodate them to certain theories and opinions of their own. But there are many others who would agree that it is wrong to give the earth the central position, looking for confirmation rather to theory than to the facts of observation. Their view is that the most precious place befits the most precious thing: but fire, 30they say, is more precious than earth, and the limit than the intermediate, and the circumference and the centre are limits. Reasoning on this basis they take the view that it is not earth that lies at the centre of the sphere, but rather fire. The Pythagoreans have a further reason.

293b

1 τὸ πῦρ. Ἔτι δ' οἵ γε Πυθαγόρειοι καὶ διὰ τὸ μάλιστα προςήκειν

φυλάττεσθαι τὸ κυριώτατον τοῦ παντός, τὸ δὲ μέσον

εἶναι τοιοῦτον, [ὃ] Διὸς φυλακὴν ὀνομάζουσι τὸ ταύτην ἔχον

τὴν χώραν πῦρ· ὥσπερ τὸ μέσον ἁπλῶς λεγόμενον, καὶ τὸ

5 τοῦ μεγέθους μέσον καὶ τοῦ πράγματος ὂν μέσον καὶ τῆς

φύσεως. Καίτοι καθάπερ ἐν τοῖς ζῴοις οὐ ταὐτὸν τοῦ ζῴου

καὶ τοῦ σώματος μέσον, οὕτως ὑποληπτέον μᾶλλον καὶ περὶ

τὸν ὅλον οὐρανόν. Διὰ μὲν οὖν ταύτην τὴν αἰτίαν οὐθὲν αὐτοὺς

δεῖ θορυβεῖσθαι περὶ τὸ πᾶν, οὐδ' εἰσάγειν φυλακὴν ἐπὶ τὸ

10 κέντρον, ἀλλ' ἐκεῖνο ζητεῖν τὸ μέσον, ποῖόν τι καὶ ποῦ πέφυκεν.

Ἐκεῖνο μὲν γὰρ ἀρχὴ τὸ μέσον καὶ τίμιον, τὸ δὲ τοῦ

τόπου μέσον ἔοικε τελευτῇ μᾶλλον ἢ ἀρχῇ· τὸ μὲν γὰρ

ὁριζόμενον τὸ μέσον, τὸ δ' ὁρίζον τὸ πέρας. Τιμιώτερον δὲ

τὸ περιέχον καὶ τὸ πέρας ἢ τὸ περαινόμενον· τὸ μὲν γὰρ

15 ὕλη, τὸ δ' οὐσία τῆς συστάσεώς ἐστιν. Περὶ μὲν οὖν τοῦ τόπου

τῆς γῆς ταύτην ἔχουσί τινες τὴν δόξαν, ὁμοίως δὲ καὶ περὶ

μονῆς καὶ κινήσεως· οὐ γὰρ τὸν αὐτὸν τρόπον ἅπαντες ὑπολαμβάνουσιν,

ἀλλ' ὅσοι μὲν μηδ' ἐπὶ τοῦ μέσου κεῖσθαί

φασιν αὐτήν, κινεῖσθαι κύκλῳ περὶ τὸ μέσον, οὐ μόνον δὲ

20 ταύτην, ἀλλὰ καὶ τὴν ἀντίχθονα, καθάπερ εἴπομεν πρότερον.

Ἐνίοις δὲ δοκεῖ καὶ πλείω σώματα τοιαῦτα ἐνδέχεσθαι

φέρεσθαι περὶ τὸ μέσον, ἡμῖν ἄδηλα διὰ τὴν ἐπιπρόσθησιν

τῆς γῆς. Διὸ καὶ τὰς τῆς σελήνης ἐκλείψεις πλείους ἢ

τὰς τοῦ ἡλίου γίγνεσθαί φασιν· τῶν γὰρ φερομένων ἕκαστον

25 ἀντιφράττειν αὐτήν, ἀλλ' οὐ μόνον τὴν γῆν. Ἐπεὶ γὰρ οὐκ ἔστιν

ἡ γῆ κέντρον, ἀλλ' ἀπέχει τὸ ἡμισφαίριον αὐτῆς ὅλον, οὐθὲν

κωλύειν οἴονται τὰ φαινόμενα συμβαίνειν ὁμοίως μὴ κατοικοῦσιν

ἡμῖν ἐπὶ τοῦ κέντρου, ὥσπερ κἂν εἰ ἐπὶ τοῦ μέσου

ἦν ἡ γῆ· οὐθὲν γὰρ οὐδὲ νῦν ποιεῖν ἐπίδηλον τὴν ἡμίσειαν

30 ἀπεχόντων τῆς διαμέτρου. Ἔνιοι δὲ καὶ κειμένην ἐπὶ τοῦ

κέντρου φασὶν αὐτὴν ἴλλεσθαι καὶ κινεῖσθαι περὶ τὸν διὰ παντὸς

τεταμένον πόλον, ὥσπερ ἐν τῷ Τιμαίῳ γέγραπται. Παραπλησίως

δὲ καὶ περὶ τοῦ σχήματος ἀμφισβητεῖται· τοῖς μὲν γὰρ δοκεῖ

εἶναι σφαιροειδής, τοῖς δὲ πλατεῖα καὶ τὸ σχῆμα τυμπανοειδής·

1They hold that the most important part of the world, which is the centre, should be most strictly guarded, and name it, or rather the fire which occupies that place, the 'Guardhouse of Zeus', as if the word 'centre' were quite unequivocal, and the centre of the mathematical figure were always the same 5with that of the thing or the natural centre. But it is better to conceive of the case of the whole heaven as analogous to that of animals, in which the centre of the animal and that of the body are different. For this reason they have no need to be so disturbed about the world, or to call in a guard for its centre: rather let them look for the centre in the other sense and 10tell us what it is like and where nature has set it. That centre will be something primary and precious; but to the mere position we should give the last place rather than the first. For the middle is what is defined, and what defines it is the limit, and that which contains or limits is more precious than that which is limited, see ing that the latter is the matter and the 15former the essence of the system.
II. As to the position of the earth, then, this is the view which some advance, and the views advanced concerning its rest or motion are similar. For here too there is no general agreement. All who deny that the earth lies at the centre think that it revolves about the centre, and not the earth only but, as we said before, the counter-earth as 20well. Some of them even consider it possible that there are several bodies so moving, which are invisible to us owing to the interposition of the earth. This, they say, accounts for the fact that eclipses of the moon are more frequent than eclipses of the sun: for in addition to the earth each of these moving bodies can obstruct it. Indeed, as in any case the surface of the 25earth is not actually a centre but distant from it a full hemisphere, there is no more difficulty, they think, in accounting for the observed facts on their view that we do not dwell at the centre, than on the common view that the earth is in the middle. Even as it is, there is nothing in the observations to suggest that we are removed from the centre by half the diameter of the 30earth. Others, again, say that the earth, which lies at the centre, is 'rolled', and thus in motion, about the axis of the whole heaven, So it stands written in the Timaeus.
III. There are similar disputes about the shape of the earth. Some think it is spherical, others that it is flat and drum-shaped.

294a

1 ποιοῦνται δὲ τεκμήριον ὅτι δύνων καὶ ἀνατέλλων ὁ

ἥλιος εὐθεῖαν ἀλλ' οὐ περιφερῆ τὴν ἀπόκρυψιν φαίνεται ποιούμενος

ὑπὸ τῆς γῆς, ὡς δέον, εἴπερ ἦν σφαιροειδής, περιφερῆ

γίνεσθαι τὴν ἀποτομήν, οὐ προσλογιζόμενοι τό τε ἀπόστημα

5 τοῦ ἡλίου πρὸς τὴν γῆν καὶ τὸ τῆς περιφερείας μέγεθος,

ὡς ἐν τοῖς φαινομένοις μικροῖς κύκλοις εὐθεῖα φαίνεται

πόρρωθεν. Διὰ μὲν οὖν ταύτην τὴν φαντασίαν οὐδὲν αὐτοὺς ἀπιστεῖν

δεῖ μὴ κυκλοτερῆ τὸν ὄγκον εἶναι τῆς γῆς· ἀλλ' ἔτι

προστιθέασι, καὶ φασὶ διὰ τὴν ἠρεμίαν ἀναγκαῖον τὸ σχῆμα

10 τοῦτ' ἔχειν αὐτήν. Καὶ γὰρ δὴ οἱ περὶ τῆς κινήσεως καὶ

τῆς μονῆς εἰρημένοι τρόποι πολλοὶ τυγχάνουσιν. Τὸ μὲν οὖν

ἀπορῆσαι πᾶσιν ἀναγκαῖον ἐπελθεῖν· τάχα γὰρ ἀλυποτέρας

διανοίας τὸ μὴ θαυμάζειν πῶς ποτε μικρὸν μὲν μόριον

τῆς γῆς, ἂν μετεωρισθὲν ἀφεθῇ, φέρεται καὶ μένειν οὐκ ἐθέλει,

15 καὶ τὸ πλεῖον ἀεὶ θᾶττον, πᾶσαν δὲ τὴν γῆν εἴ τις

ἀφείη μετεωρίσας, οὐκ ἂν φέροιτο. Νῦν δ' ἠρεμεῖ τοσοῦτον

βάρος. Ἀλλὰ μὴν κἂν εἴ τις τῶν φερομένων μορίων αὐτῆς,

πρὶν πεσεῖν, ὑφαιροίη τὴν γῆν, οἰσθήσεται κάτω μηθενὸς

ἀντερείσαντος. Ὥστε τὸ μὲν ἀπορεῖν εἰκότως ἐγένετο φιλοσόφημα

20 πᾶσιν· τὸ δὲ τὰς περὶ τούτου λύσεις μὴ μᾶλλον

ἀτόπους εἶναι δοκεῖν τῆς ἀπορίας, θαυμάσειεν ἄν τις. Οἱ μὲν

γὰρ διὰ ταῦτα ἄπειρον τὸ κάτω τῆς γῆς εἶναί φασιν, ἐπ'

ἄπειρον αὐτὴν ἐρριζῶσθαι λέγοντες, ὥσπερ Ξενοφάνης ὁ Κολοφώνιος,

ἵνα μὴ πράγματ' ἔχωσι ζητοῦντες τὴν αἰτίαν· διὸ

25 καὶ Ἐμπεδοκλῆς οὕτως ἐπέπληξεν, εἰπὼν ὡς

Οἱ δ' ἐφ' ὕδατος κεῖσθαι. Τοῦτον γὰρ ἀρχαιότατον

παρειλήφαμεν τὸν λόγον, ὅν φασιν εἰπεῖν Θαλῆν

30 τὸν Μιλήσιον, ὡς διὰ τὸ πλωτὴν εἶναι μένουσαν ὥσπερ

ξύλον ἤ τι τοιοῦτον ἕτερον (καὶ γὰρ τούτων ἐπ' ἀέρος μὲν οὐθὲν

πέφυκε μένειν, ἀλλ' ἐφ' ὕδατος), ὥσπερ οὐ τὸν αὐτὸν

λόγον ὄντα περὶ τῆς γῆς καὶ τοῦ ὕδατος τοῦ ὀχοῦντος τὴν γῆν·

οὐδὲ γὰρ τὸ ὕδωρ πέφυκε μένειν μετέωρον, ἀλλ' ἐπί τινός

1For evidence they bring the fact that, as the sun rises and sets, the part concealed by the earth shows a straight and not a curved edge, whereas if the earth were spherical the line of section would have to be circular. In this they leave out of account the great distance of the sun from 5the earth and the great size of the circumference, which, seen from a distance on these apparently small circles appears straight. Such an appearance ought not to make them doubt the circular shape of the earth. But they have another argument. They say that because it is at rest, the earth must necessarily have this shape. For there are many different ways in which 10the movement or rest of the earth has been conceived.
The difficulty must have occurred to every one. It would indeed be a complacent mind that felt no surprise that, while a little bit of earth, let loose in mid-air moves and will not stay still, and more there is of it the faster it moves, the whole earth, free in midair, should show no movement at all. Yet 15here is this great weight of earth, and it is at rest. And again, from beneath one of these moving fragments of earth, before it falls, take away the earth, and it will continue its downward movement with nothing to stop it. The difficulty then, has naturally passed into a common place of philosophy; and one may well wonder that the solutions offered are not seen 20to involve greater absurdities than the problem itself.
By these considerations some have been led to assert that the earth below us is infinite, saying, with Xenophanes of Colophon, that it has 'pushed its roots to infinity',-in order to save the trouble of seeking for the cause. Hence the sharp rebuke of Empedocles, in the words 'if the deeps of the earth 25are endless and endless the ample ether-such is the vain tale told by many a tongue, poured from the mouths of those who have seen but little of the whole. Others say the earth rests upon water. This, indeed, is the oldest theory that has been preserved, and is attributed to Thales of Miletus. It was supposed to stay still because it floated like wood and other 30similar substances, which are so constituted as to rest upon but not upon air. As if the same account had not to be given of the water which carries the earth as of the earth itself! It is not the nature of water, any more than of earth, to stay in mid-air: it must have something to rest upon.

294b

1 ἐστιν. Ἔτι δ' ὥσπερ ἀὴρ ὕδατος κουφότερον, καὶ γῆς ὕδωρ·

ὥστε πῶς οἷόν τε τὸ κουφότερον κατωτέρω κεῖσθαι τοῦ βαρυτέρου

τὴν φύσιν; Ἔτι δ' εἴπερ ὅλη πέφυκε μένειν ἐφ' ὕδατος,

δῆλον ὅτι καὶ τῶν μορίων ἕκαστον· νῦν δ' οὐ φαίνεται

5 τοῦτο γιγνόμενον, ἀλλὰ τὸ τυχὸν μόριον φέρεται εἰς

βυθόν, καὶ θᾶττον τὸ μεῖζον. Ἀλλ' ἐοίκασι μέχρι τινὸς ζητεῖν, ἀλλ'

οὐ μέχρι περ οὗ δυνατὸν τῆς ἀπορίας. Πᾶσι γὰρ ἡμῖν τοῦτο

σύνηθες, μὴ πρὸς τὸ πρᾶγμα ποιεῖσθαι τὴν ζήτησιν ἀλλὰ

πρὸς τὸν τἀναντία λέγοντα· καὶ γὰρ αὐτὸς ἐν αὑτῷ ζητεῖ

10 μέχρι περ ἂν οὗ μηκέτι ἔχῃ ἀντιλέγειν αὐτὸς αὑτῷ. Διὸ δεῖ

τὸν μέλλοντα καλῶς ζητήσειν ἐνστατικὸν εἶναι διὰ τῶν οἰκείων

ἐνστάσεων τῷ γένει, τοῦτο δ' ἐστὶν ἐκ τοῦ πάσας τεθεωρηκέναι

τὰς διαφοράς. Ἀναξιμένης δὲ καὶ Ἀναξαγόρας καὶ

Δημόκριτος τὸ πλάτος αἴτιον εἶναί φασι τοῦ μένειν αὐτήν.

15 Οὐ γὰρ τέμνειν ἀλλ' ἐπιπωμάζειν τὸν ἀέρα τὸν κάτωθεν,

ὅπερ φαίνεται τὰ πλάτος ἔχοντα τῶν σωμάτων ποιεῖν· ταῦτα

γὰρ καὶ πρὸς τοὺς ἀνέμους ἔχει δυσκινήτως διὰ τὴν ἀντέρεισιν.

Ταὐτὸ δὴ τοῦτο ποιεῖν τῷ πλάτει φασὶ τὴν γῆν πρὸς

τὸν ὑποκείμενον ἀέρα, (τὸν δ' οὐκ ἔχοντα μεταστῆναι τόπον

20 ἱκανὸν ἀθρόως [τῷ] κάτωθεν ἠρεμεῖν,) ὥσπερ τὸ ἐν ταῖς

κλεψύδραις ὕδωρ. Ὅτι δὲ δύναται πολὺ βάρος φέρειν ἀπολαμβανόμενος

καὶ μένων ὁ ἀήρ, τεκμήρια πολλὰ λέγουσιν.

Πρῶτον μὲν οὖν εἰ μὴ πλατὺ τὸ σχῆμα τῆς γῆς ἐστι,

διὰ τοῦτο μὲν οὐκ ἂν ἠρεμοῖ. Καίτοι τῆς μονῆς οὐ τὸ πλάτος

25 αἴτιον ἐξ ὧν λέγουσιν, ἀλλὰ τὸ μέγεθος μᾶλλον· διὰ

γὰρ τὴν στενοχωρίαν οὐκ ἔχων τὴν πάροδον ὁ ἀὴρ μένει διὰ

τὸ πλῆθος· πολὺς δ' ἐστὶ διὰ τὸ ὑπὸ μεγέθους πολλοῦ ἐναπολαμβάνεσθαι

τοῦ τῆς γῆς. Ὥστε τοῦτο μὲν ὑπάρξει, κἂν

σφαιροειδὴς μὲν ᾖ, τηλικαύτη δὲ τὸ μέγεθος· μενεῖ

30 γὰρ κατὰ τὸν ἐκείνων λόγον. Ὅλως δὲ πρὸς τοὺς οὕτω

λέγοντας περὶ τῆς κινήσεως οὐ περὶ μορίων ἐστὶν ἡ ἀμφιςβήτησις,

ἀλλὰ περὶ ὅλου τινὸς καὶ παντός. Ἐξ ἀρχῆς γὰρ

διοριστέον πότερόν ἐστί τις τοῖς σώμασι φύσει κίνησις ἢ οὐδεμία,

καὶ πότερον φύσει μὲν οὐκ ἔστι, βίᾳ δ' ἔστιν. Ἐπεὶ δὲ

1Again, as air is lighter than water, so is water than earth: how then can they think that the naturally lighter substance lies below the heavier? Again, if the earth as a whole is capable of floating upon water, that must obviously be the case with any part of it. But observation shows that this is 5not the case. Any piece of earth goes to the bottom, the quicker the larger it is. These thinkers seem to push their inquiries some way into the problem, but not so far as they might. It is what we are all inclined to do, to direct our inquiry not by the matter itself, but by the views of our opponents: and even when interrogating oneself one pushes the inquiry only to the point 10at which one can no longer offer any opposition. Hence a good inquirer will be one who is ready in bringing forward the objections proper to the genus, and that he will be when he has gained an understanding of all the differences.
Anaximenes and Anaxagoras and Democritus give the flatness of the earth as the cause of its staying still. Thus, they say, it does not cut, but 15covers like a lid, the air beneath it. This seems to be the way of flat-shaped bodies: for even the wind can scarcely move them because of their power of resistance. The same immobility, they say, is produced by the flatness of the surface which the earth presents to the air which underlies it; while the air, not having room enough to change its place because it is underneath 20the earth, stays there in a mass, like the water in the case of the water-clock. And they adduce an amount of evidence to prove that air, when cut off and at rest, can bear a considerable weight.
Now, first, if the shape of the earth is not flat, its flatness cannot be the cause of its immobility. But in their own account it is rather the size of the earth than its flatness 25that causes it to remain at rest. For the reason why the air is so closely confined that it cannot find a passage, and therefore stays where it is, is its great amount: and this amount great because the body which isolates it, the earth, is very large. This result, then, will follow, even if the earth is spherical, so long as it retains its size. So far as their arguments go, 30the earth will still be at rest.
In general, our quarrel with those who speak of movement in this way cannot be confined to the parts; it concerns the whole universe. One must decide at the outset whether bodies have a natural movement or not, whether there is no natural but only constrained movement.

295a

1 περὶ τούτων διώρισται πρότερον ὅσα κατὰ τὴν παροῦσαν

δύναμιν εἴχομεν, χρηστέον ὡς ὑπάρχουσιν. Εἰ γὰρ μηδεμία φύσει

κίνησίς ἐστιν αὐτῶν, οὐδὲ βίαιος ἔσται· εἰ δὲ μή ἐστι μήτε

φύσει μήτε βίᾳ, ὅλως οὐδὲν κινηθήσεται· περὶ γὰρ τούτων

5 ὅτι ἀναγκαῖον συμβαίνειν, διώρισται πρότερον, καὶ πρὸς τούτοις

ὅτι οὐδ' ἠρεμεῖν ἐνδέχεται· ὥσπερ γὰρ κίνησις ὑπάρχει

ἢ βίᾳ ἢ φύσει, οὕτω καὶ ἠρεμία. Ἀλλὰ μὴν εἴ γέ ἐστι κίνησίς

τις κατὰ φύσιν, οὐκ ἂν ἡ βίαιος εἴη φορὰ μόνον οὐδ'

ἠρέμησις· ὥστ' εἰ βίᾳ νῦν ἡ γῆ μένει, καὶ συνῆλθεν ἐπὶ τὸ

10 μέσον φερομένη διὰ τὴν δίνησιν· ταύτην γὰρ τὴν αἰτίαν πάντες

λέγουσιν ἐκ τῶν ἐν τοῖς ὑγροῖς καὶ περὶ τὸν ἀέρα συμβαινόντων·

ἐν τούτοις γὰρ ἀεὶ φέρεται τὰ μείζω καὶ βαρύτερα

πρὸς τὸ μέσον τῆς δίνης. Διὸ δὴ τὴν γῆν πάντες ὅσοι

τὸν οὐρανὸν γεννῶσιν, ἐπὶ τὸ μέσον συνελθεῖν φασίν· ὅτι δὲ

15 μένει, ζητοῦσι τὴν αἰτίαν, καὶ λέγουσιν οἱ μὲν τοῦτον τὸν

τρόπον, ὅτι τὸ πλάτος καὶ τὸ μέγεθος αὐτῆς αἴτιον, οἱ δ' ὥςπερ

Ἐμπεδοκλῆς, τὴν τοῦ οὐρανοῦ φορὰν κύκλῳ περιθέουσαν

καὶ θᾶττον φερομένην ἢ τὴν τῆς γῆς φορὰν κωλύειν, καθάπερ

τὸ ἐν τοῖς κυάθοις ὕδωρ· καὶ γὰρ τοῦτο κύκλῳ τοῦ κυάθου

20 φερομένου πολλάκις κάτω τοῦ χαλκοῦ γινόμενον ὅμως οὐ φέρεται

κάτω, πεφυκὸς φέρεσθαι, διὰ τὴν αὐτὴν αἰτίαν. Καίτοι

μήτε τῆς δίνης κωλυούσης μήτε τοῦ πλάτους, ἀλλ' ὑπείκοντος

τοῦ ἀέρος, ποῖ ποτ' οἰσθήσεται; Πρὸς μὲν γὰρ τὸ μέσον

βίᾳ, καὶ μένει βίᾳ· κατὰ φύσιν δέ γε ἀναγκαῖον εἶναί

25 τινα αὐτῆς φοράν. Αὕτη οὖν πότερον ἄνω ἢ κάτω, ἢ ποῦ

ἐστιν; Εἶναι μὲν γάρ τινα ἀναγκαῖον· εἰ δὲ μηδὲν μᾶλλον

κάτω ἢ ἄνω, ὁ δ' ἄνω ἀὴρ μὴ κωλύει τὴν ἄνω φοράν, οὐδ'

ἂν ὁ ὑπὸ τῇ γῇ κωλύοι τὴν κάτω· τὰ γὰρ αὐτὰ τῶν αὐτῶν

ἀναγκαῖον εἶναι αἴτια τοῖς αὐτοῖς. Ἔτι δὲ πρὸς Ἐμπεδοκλέα

30 κἂν ἐκεῖνό τις εἴπειεν. Ὅτε γὰρ τὰ στοιχεῖα διειστήκει

χωρὶς ὑπὸ τοῦ νείκους, τίς αἰτία τῇ γῇ τῆς μονῆς ἦν; Οὐ

γὰρ δὴ καὶ τότε αἰτιάσεται τὴν δίνην. Ἄτοπον δὲ καὶ τὸ μὴ

συννοεῖν ὅτι πρότερον μὲν διὰ τὴν δίνησιν ἐφέρετο τὰ μόρια

τῆς γῆς πρὸς τὸ μέσον· νῦν δὲ διὰ τίν' αἰτίαν πάντα τὰ βάρος

35 ἔχοντα φέρεται πρὸς αὐτήν; Οὐ γὰρ ἥ γε δίνη πλησιάζει

1Seeing, however, that we have already decided this matter to the best of our ability, we are entitled to treat our results as representing fact. Bodies, we say, which have no natural movement, have no constrained movement; and where there is no natural and no constrained movement there will be no movement 5at all. This is a conclusion, the necessity of which we have already decided, and we have seen further that rest also will be inconceivable, since rest, like movement, is either natural or constrained. But if there is any natural movement, constraint will not be the sole principle of motion or of rest. If, then, it is by constraint that the earth now keeps its place, the 10so-called 'whirling' movement by which its parts came together at the centre was also constrained. (The form of causation supposed they all borrow from observations of liquids and of air, in which the larger and heavier bodies always move to the centre of the whirl. This is thought by all those who try to generate the heavens to explain why the earth came together at the centre. 15They then seek a reason for its staying there; and some say, in the manner explained, that the reason is its size and flatness, others, with Empedocles, that the motion of the heavens, moving about it at a higher speed, prevents movement of the earth, as the water in a cup, when the cup is given a circular motion, though it is often underneath the bronze, is for this same reason 20prevented from moving with the downward movement which is natural to it.) But suppose both the 'whirl' and its flatness (the air beneath being withdrawn) cease to prevent the earth's motion, where will the earth move to then? Its movement to the centre was constrained, and its rest at the centre is due to constraint; but there must be some motion which is natural to it. Will 25this be upward motion or downward or what? It must have some motion; and if upward and downward motion are alike to it, and the air above the earth does not prevent upward movement, then no more could air below it prevent downward movement. For the same cause must necessarily have the same effect on the same thing.
Further, against Empedocles there is another point which might be 30made. When the elements were separated off by Hate, what caused the earth to keep its place? Surely the 'whirl' cannot have been then also the cause. It is absurd too not to perceive that, while the whirling movement may have been responsible for the original coming together of the art of earth at the centre, the question remains, why now do all heavy bodies move to the earth.

295b

1 πρὸς ἡμᾶς. Ἔτι δὲ καὶ τὸ πῦρ ἄνω φέρεται διὰ τίν' αἰτίαν;

Οὐ γὰρ διά γε τὴν δίνην. Εἰ δὲ τοῦτο φέρεσθαί που πέφυκεν,

δῆλον ὅτι καὶ τὴν γῆν οἰητέον. Ἀλλὰ μὴν οὐδὲ τῇ

δίνῃ γε τὸ βαρὺ καὶ κοῦφον ὥρισται, ἀλλὰ τῶν πρότερον

5 ὑπαρχόντων βαρέων καὶ κούφων τὰ μὲν εἰς τὸ μέσον ἔρχεται,

τὰ δ' ἐπιπολάζει διὰ τὴν κίνησιν. Ἦν ἄρα καὶ πρὶν γενέσθαι

τὴν δίνην τὸ μὲν βαρὺ τὸ δὲ κοῦφον, ἃ τίνι διώριστο καὶ

πῶς ἐπεφύκει φέρεσθαι ἢ ποῦ; ἀπείρου γὰρ ὄντος ἀδύνατον

εἶναι ἄνω ἢ κάτω, διώρισται δὲ τούτοις τὸ βαρὺ καὶ κοῦφον.

10 Οἱ μὲν οὖν πλεῖστοι περὶ τὰς αἰτίας ταύτας διατρίβουσιν·

εἰσὶ δέ τινες οἳ διὰ τὴν ὁμοιότητά φασιν αὐτὴν μένειν, ὥςπερ

τῶν ἀρχαίων Ἀναξίμανδρος· μᾶλλον μὲν γὰρ οὐθὲν ἄνω ἢ

κάτω ἢ εἰς τὰ πλάγια φέρεσθαι προσήκει τὸ ἐπὶ τοῦ μέσου

ἱδρυμένον καὶ ὁμοίως πρὸς τὰ ἔσχατα ἔχον· ἅμα δ' ἀδύνατον

15 εἰς τὸ ἐναντίον ποιεῖσθαι τὴν κίνησιν· ὥστ' ἐξ ἀνάγκης

μένειν. Τοῦτο δὲ λέγεται κομψῶς μέν, οὐκ ἀληθῶς δέ· κατὰ

γὰρ τοῦτον τὸν λόγον ἀναγκαῖον ἅπαν ὅ τι ἂν τεθῇ ἐπὶ τοῦ

μέσου, μένειν, ὥστε καὶ τὸ πῦρ ἠρεμήσει· τὸ γὰρ εἰρημένον

οὐκ ἴδιόν ἐστι τῆς γῆς. Ἀλλὰ μὴν οὐκ ἀναγκαῖον. Οὐ γὰρ μόνον

20 φαίνεται μένουσα ἐπὶ τοῦ μέσου, ἀλλὰ καὶ φερομένη

πρὸς τὸ μέσον. Ὅπου γὰρ ὁτιοῦν φέρεται μόριον αὐτῆς,

ἀναγκαῖον ἐνταῦθα φέρεσθαι καὶ τὴν ὅλην· οὗ δὲ φέρεται κατὰ

φύσιν, καὶ μένει ἐνταυθοῖ κατὰ φύσιν. Οὐκ ἄρα διὰ τὸ

ὁμοίως ἔχειν πρὸς τὰ ἔσχατα· τοῦτο μὲν γὰρ πᾶσι κοινόν,

25 τὸ δὲ φέρεσθαι πρὸς τὸ μέσον ἴδιον τῆς γῆς. Ἄτοπον δὲ καὶ

τοῦτο μὲν ζητεῖν, διὰ τί ποτε μένει ἡ γῆ ἐπὶ τοῦ μέσου, τὸ

δὲ πῦρ μὴ ζητεῖν διὰ τί ἐπὶ τοῦ ἐσχάτου. Εἰ μὲν γὰρ κἀκείνῳ

φύσει τόπος ὁ ἔσχατος, δῆλον ὅτι ἀναγκαῖον εἶναί

τινα καὶ τῇ γῇ φύσει τόπον· εἰ δὲ μὴ ταύτῃ οὗτος ὁ τόπος,

30 ἀλλὰ διὰ τὴν ἀνάγκην μένει τὴν τῆς ὁμοιότητος (ὥσπερ ὁ

περὶ τῆς τριχὸς λόγος τῆς ἰσχυρῶς μὲν ὁμοίως δὲ πάντῃ

τεινομένης, ὅτι οὐ διαρραγήσεται, καὶ τοῦ πεινῶντος καὶ διψῶντος

σφόδρα μέν, ὁμοίως δέ, καὶ τῶν ἐδωδίμων καὶ ποτῶν

ἴσον ἀπέχοντος· καὶ γὰρ τοῦτον ἠρεμεῖν ἀναγκαῖον), ζητητέον

35 αὐτοῖς περὶ τῆς τοῦ πυρὸς μονῆς ἐπὶ τῶν ἐσχάτων.

1For the whirl surely does not come near us. Why, again, does fire move upward? Not, surely, because of the whirl. But if fire is naturally such as to move in a certain direction, clearly the same may be supposed to hold of earth. Again, it cannot be the whirl which determines the heavy and the light. Rather 5that movement caused the pre-existent heavy and light things to go to the middle and stay on the surface respectively. Thus, before ever the whirl began, heavy and light existed; and what can have been the ground of their distinction, or the manner and direction of their natural movements? In the infinite chaos there can have been neither above nor below, and it is by these that 10heavy and light are determined.
It is to these causes that most writers pay attention: but there are some, Anaximander, for instance, among the ancients, who say that the earth keeps its place because of its indifference. Motion upward and downward and sideways were all, they thought, equally inappropriate to that which is set at the centre and indifferently related to every extreme 15point; and to move in contrary directions at the same time was impossible: so it must needs remain still. This view is ingenious but not true. The argument would prove that everything, whatever it be, which is put at the centre, must stay there. Fire, then, will rest at the centre: for the proof turns on no peculiar property of earth. But this does not follow. The observed facts about 20earth are not only that it remains at the centre, but also that it moves to the centre. The place to which any fragment of earth moves must necessarily be the place to which the whole moves; and in the place to which a thing naturally moves, it will naturally rest. The reason then is not in the fact that the earth is indifferently related to every extreme point: for this would apply 25to any body, whereas movement to the centre is peculiar to earth. Again it is absurd to look for a reason why the earth remains at the centre and not for a reason why fire remains at the extremity. If the extremity is the natural place of fire, clearly earth must also have a natural place. But suppose that the centre is not its place, and that the reason of its remaining there is 30this necessity of indifference-on the analogy of the hair which, it is said, however great the tension, will not break under it, if it be evenly distributed, or of the men who, though exceedingly hungry and thirsty, and both equally, yet being equidistant from food and drink, is therefore bound to stay where he is-even so, it still remains to explain why fire stays at the extremities.

296a

1 Θαυμαστὸν δὲ καὶ τὸ περὶ μὲν τῆς μονῆς ζητεῖν, περὶ δὲ

τῆς φορᾶς αὐτῶν μὴ ζητεῖν, διὰ τίν' αἰτίαν τὸ μὲν ἄνω φέρεται,

τὸ δ' ἐπὶ τὸ μέσον, μηδενὸς ἐμποδίζοντος. Ἀλλὰ μὴν οὐδ'

ἀληθές ἐστι τὸ λεγόμενον. Κατὰ συμβεβηκὸς μέντοι τοῦτό γ'

5 ἀληθές, ὡς ἀναγκαῖον μένειν ἐπὶ τοῦ μέσου πᾶν ᾧ μηθὲν

μᾶλλον δεῦρο ἢ δεῦρο κινεῖσθαι προσήκει. Ἀλλὰ διά γε

τοῦτον τὸν λόγον οὐ μενεῖ, ἀλλὰ κινηθήσεται, οὐ μέντοι ὅλον,

ἀλλὰ διεσπασμένον. Ὁ γὰρ αὐτὸς ἁρμόσει λόγος καὶ ἐπὶ

τοῦ πυρός· ἀνάγκη γὰρ τεθὲν μένειν ὁμοίως ὥσπερ τὴν γῆν·

10 ὁμοίως γὰρ ἕξει πρὸς τῶν σημείων τῶν ἐσχάτων ὁτιοῦν· ἀλλ'

ὅμως οἰσθήσεται ἀπὸ τοῦ μέσου, ὥσπερ καὶ φαίνεται φερόμενον,

ἂν μή τι κωλύῃ, πρὸς τὸ ἔσχατον· πλὴν οὐχ ὅλον

πρὸς ἓν σημεῖον (τοῦτο γὰρ ἀναγκαῖον μόνον συμβαίνειν ἐκ

τοῦ λόγου τοῦ περὶ τῆς ὁμοιότητος) ἀλλὰ τὸ ἀνάλογον μόριον

15 πρὸς τὸ ἀνάλογον τοῦ ἐσχάτου, λέγω δ' οἷον τὸ τέταρτον

μέρος πρὸς τὸ τέταρτον μέρος τοῦ περιέχοντος· οὐθὲν γὰρ

στιγμὴ τῶν σωμάτων ἐστίν. Ὥσπερ δὲ κἂν ἐκ μεγάλου συνέλθοι

πυκνούμενον εἰς ἐλάττω τόπον, οὕτω κἂν ἐξ ἐλάττονος εἰς

μείζω μανότερον γιγνόμενον· ὥστε κἂν ἡ γῆ τοῦτον τὸν τρόπον

20 ἐκινεῖτο ἀπὸ τοῦ μέσου διά γε τὸν τῆς ὁμοιότητος λόγον,

εἰ μὴ φύσει τῆς γῆς οὗτος ὁ τόπος ἦν. Ὅσα μὲν οὖν τυγχάνει

περί τε τοῦ σχήματος αὐτῆς ὑπολαμβανόμενα καὶ περὶ τόπου

καὶ μονῆς καὶ κινήσεως, σχεδὸν ταῦτ' ἐστίν.

1It is strange, too, to ask about things staying still but not about their motion,-why, I mean, one thing, if nothing stops it, moves up, and another thing to the centre. Again, their statements are not true. It happens, indeed, to be the case that a thing to which movement this way 5and that is equally inappropriate is obliged to remain at the centre. But so far as their argument goes, instead of remaining there, it will move, only not as a mass but in fragments. For the argument applies equally to fire. Fire, if set at the centre, should stay there, like earth, since it will be indifferently related to every point on the 10extremity. Nevertheless it will move, as in fact it always does move when nothing stops it, away from the centre to the extremity. It will not, however, move in a mass to a single point on the circumference-the only possible result on the lines of the indifference theory-but rather each corresponding portion of fire to the corresponding part of the extremity, 15each fourth part, for instance, to a fourth part of the circumference. For since no body is a point, it will have parts. The expansion, when the body increased the place occupied, would be on the same principle as the contraction, in which the place was diminished. Thus, for all the indifference theory shows to the contrary, earth also would have 20moved in this manner away from the centre, unless the centre had been its natural place.
We have now outlined the views held as to the shape, position, and rest or movement of the earth.

Book 2,Chapter 14 (296a24–298a20)

Ἡμεῖς δὲ λέγωμεν πρῶτον πότερον ἔχει κίνησιν ἢ μένει·

25 καθάπερ γὰρ εἴπομεν, οἱ μὲν αὐτὴν ἓν τῶν ἄστρων εἶναι ποιοῦσιν,

οἱ δ' ἐπὶ τοῦ μέσου θέντες ἴλλεσθαι καὶ κινεῖσθαί φασι

περὶ τὸν πόλον μέσον. Ὅτι δ' ἐστὶν ἀδύνατον, δῆλον λαβοῦσιν

ἀρχὴν ὡς εἴπερ φέρεται εἴτ' ἐκτὸς οὖσα τοῦ μέσου εἴτ'

ἐπὶ τοῦ μέσου, ἀναγκαῖον αὐτὴν βίᾳ κινεῖσθαι ταύτην τὴν

30 κίνησιν· οὐ γὰρ αὐτῆς γε τῆς γῆς ἐστιν· καὶ γὰρ ἂν τῶν

μορίων ἕκαστον ταύτην εἶχε τὴν φοράν· νῦν δ' ἐπ' εὐθείας

πάντα φέρεται πρὸς τὸ μέσον. Διόπερ οὐχ οἷόν τ' ἀΐδιον εἶναι,

βίαιόν γ' οὖσαν καὶ παρὰ φύσιν· ἡ δέ γε τοῦ κόσμου

τάξις ἀΐδιος. Ἔτι πάντα τὰ φερόμενα τὴν φορὰν τὴν

35 ἐγκύκλιον ὑπολειπόμενα φαίνεται καὶ κινούμενα πλείους

Let us first decide the question whether the earth moves or is at rest. For, as we said, there are some who make it one of the stars, and others who, setting it at 25the centre, suppose it to be 'rolled' and in motion about the pole as axis. That both views are untenable will be clear if we take as our starting-point the fact that the earth's motion, whether the earth be at the centre or away from it, must needs be a constrained motion. It cannot be the movement of the earth itself. If it were, any portion of it 30would have this movement; but in fact every part moves in a straight line to the centre. Being, then, constrained and unnatural, the movement could not be eternal. But the order of the universe is eternal. Again, everything that moves with the circular movement, except the first sphere, is observed to be passed, and to move with more than one motion.

296b

1 μιᾶς φορὰς ἔξω τῆς πρώτης, ὥστε καὶ τὴν γῆν

ἀναγκαῖον, εἴτε περὶ τὸ μέσον εἴτ' ἐπὶ τοῦ μέσου κειμένη

φέρεται, δύο κινεῖσθαι φοράς. Τούτου δὲ συμβαίνοντος ἀναγκαῖον

γίγνεσθαι πάροδον καὶ τροπὰς τῶν ἐνδεδεμένων ἄστρων.

5 Τοῦτο δ' οὐ φαίνεται γιγνόμενον, ἀλλ' ἀεὶ ταὐτὰ κατὰ τοὺς

αὐτοὺς ἀνατέλλει καὶ δύεται τόπους αὐτῆς. Ἔτι δ' ἡ φορὰ

τῶν μορίων καὶ ὅλης αὐτῆς ἡ κατὰ φύσιν ἐπὶ τὸ μέσον τοῦ

παντός ἐστιν· διὰ τοῦτο γὰρ καὶ τυγχάνει κειμένη νῦν ἐπὶ

τοῦ κέντρου· διαπορήσειε δ' ἄν τις, ἐπεὶ ταὐτὸν ἀμφοτέρων

10 ἐστὶ τὸ μέσον, πρὸς πότερον φέρεται τὰ βάρος ἔχοντα καὶ

τὰ μόρια τῆς γῆς κατὰ φύσιν· πότερον ὅτι τοῦ παντός ἐστι

μέσον, ἢ διότι τῆς γῆς. Ἀνάγκη δὴ πρὸς τὸ τοῦ παντός·

καὶ γὰρ τὰ κοῦφα καὶ τὸ πῦρ εἰς τοὐναντίον φερόμενα τοῖς

βάρεσι πρὸς τὸ ἔσχατον φέρεται τοῦ περιέχοντος τόπου

15 τὸ μέσον. Συμβέβηκε δὲ ταὐτὸ μέσον εἶναι τῆς γῆς καὶ τοῦ

παντός· φέρεται γὰρ καὶ ἐπὶ τὸ τῆς γῆς μέσον, ἀλλὰ

κατὰ συμβεβηκός, ᾗ τὸ μέσον ἔχει ἐν τῷ τοῦ παντὸς

μέσῳ. Ὅτι δὲ φέρεται καὶ πρὸς τὸ τῆς γῆς μέσον, σημεῖον

ὅτι τὰ φερόμενα βάρη ἐπὶ ταύτην οὐ παρ' ἄλληλα

20 φέρεται ἀλλὰ πρὸς ὁμοίας γωνίας, ὥστε πρὸς ἓν τὸ μέσον

φέρεται, καὶ τὸ τῆς γῆς. Φανερὸν τοίνυν ὅτι ἀνάγκη ἐπὶ

τοῦ μέσου εἶναι τὴν γῆν καὶ ἀκίνητον, διά τε τὰς εἰρημένας

αἰτίας, καὶ διότι τὰ βίᾳ ῥιπτούμενα ἄνω βάρη κατὰ

στάθμην πάλιν φέρεται εἰς ταὐτό, κἂν εἰς ἄπειρον ἡ δύναμις

25 ἐκριπτῇ. Ὅτι μὲν οὖν οὔτε κινεῖται οὔτ' ἐκτὸς κεῖται τοῦ

μέσου, φανερὸν ἐκ τούτων· πρὸς δὲ τούτοις δῆλον ἐκ τῶν

εἰρημένων τὸ αἴτιον τῆς μονῆς. Εἰ γὰρ φύσει πέφυκε φέρεσθαι

πάντοθεν πρὸς τὸ μέσον, ὥσπερ φαίνεται, καὶ τὸ

πῦρ ἀπὸ τοῦ μέσου πάλιν πρὸς τὸ ἔσχατον, ἀδύνατον ἐνεχθῆναι

30 ὁτιοῦν μόριον αὐτῆς ἀπὸ τοῦ μέσου μὴ βιασθέν· μία

γὰρ φορὰ τοῦ ἑνὸς καὶ ἁπλῆ τοῦ ἁπλοῦ, ἀλλ' οὐχ αἱ ἐναντίαι·

ἡ δ' ἀπὸ τοῦ μέσου τῇ ἐπὶ τὸ μέσον ἐναντία. Εἰ τοίνυν

ὁτιοῦν μόριον ἀδύνατον ἐνεχθῆναι ἀπὸ τοῦ μέσου, φανερὸν

ὅτι καὶ τὴν ὅλην ἔτι ἀδυνατώτερον· εἰς ὃ γὰρ τὸ μόριον

35 πέφυκε φέρεσθαι, καὶ τὸ ὅλον ἐνταῦθα πέφυκεν· ὥστ'

1The earth, then, also, whether it move about the centre or as stationary at it, must necessarily move with two motions. But if this were so, there would have to be passings and turnings of the fixed stars. Yet no such thing is observed. The same stars always rise and set in the same 5parts of the earth.
Further, the natural movement of the earth, part and whole alike, is the centre of the whole-whence the fact that it is now actually situated at the centre-but it might be questioned since both centres are the same, which centre it is that portions of earth and other heavy things move to. Is this their goal because it is the centre 10of the earth or because it is the centre of the whole? The goal, surely, must be the centre of the whole. For fire and other light things move to the extremity of the area which contains the centre. It happens, however, that the centre of the earth and of the whole is the same. Thus they do move to the centre of the earth, but accidentally, in virtue 15of the fact that the earth's centre lies at the centre of the whole. That the centre of the earth is the goal of their movement is indicated by the fact that heavy bodies moving towards the earth do not parallel but so as to make equal angles, and thus to a single centre, that of the earth. It is clear, then, that the earth must be at the centre and 20immovable, not only for the reasons already given, but also because heavy bodies forcibly thrown quite straight upward return to the point from which they started, even if they are thrown to an infinite distance. From these considerations then it is clear that the earth does not move and does not lie elsewhere than at the centre.
From what we have said 25the explanation of the earth's immobility is also apparent. If it is the nature of earth, as observation shows, to move from any point to the centre, as of fire contrariwise to move from the centre to the extremity, it is impossible that any portion of earth should move away from the centre except by constraint. For a single thing has a single movement, 30and a simple thing a simple: contrary movements cannot belong to the same thing, and movement away from the centre is the contrary of movement to it. If then no portion of earth can move away from the centre, obviously still less can the earth as a whole so move. For it is the nature of the whole to move to the point to which the part naturally moves.

297a

1 εἴπερ ἀδύνατον κινηθῆναι μὴ ὑπὸ κρείττονος ἰσχύος, ἀναγκαῖον

ἂν εἴη μένειν αὐτὴν ἐπὶ τοῦ μέσου. Μαρτυρεῖ δὲ τούτοις

καὶ τὰ παρὰ τῶν μαθηματικῶν λεγόμενα περὶ τὴν

ἀστρολογίαν· τὰ γὰρ φαινόμενα συμβαίνει μεταβαλλόντων

5 τῶν σχημάτων οἷς ὥρισται τῶν ἄστρων ἡ τάξις, ὡς ἐπὶ

τοῦ μέσου κειμένης τῆς γῆς. Περὶ μὲν οὖν τοῦ τόπου καὶ μονῆς

καὶ κινήσεως, ὃν τρόπον ἔχει, τοσαῦτα εἰρήσθω περὶ

αὐτῆς. Σχῆμα δ' ἔχειν σφαιροειδὲς ἀναγκαῖον αὐτήν· ἕκαστον

γὰρ τῶν μορίων βάρος ἔχει μέχρι πρὸς τὸ μέσον, καὶ

10 τὸ ἔλαττον ὑπὸ τοῦ μείζονος ὠθούμενον οὐχ οἷόν τε κυμαίνειν,

ἀλλὰ συμπιέζεσθαι μᾶλλον καὶ συγχωρεῖν ἕτερον

ἑτέρῳ, ἕως ἂν ἔλθῃ ἐπὶ τὸ μέσον. Δεῖ δὲ νοῆσαι τὸ λεγόμενον

ὥσπερ ἂν εἰ γιγνομένης τὸν τρόπον ὃν καὶ τῶν φυσιολόγων

λέγουσί τινες γενέσθαι. Πλὴν ἐκεῖνοι μὲν βίαν αἰτιῶνται

15 τῆς κάτω φορᾶς· βέλτιον δὲ τιθέναι τἀληθές, καὶ

φάναι τοῦτο συμβαίνειν διὰ τὸ φύσιν ἔχειν φέρεσθαι τὸ

βάρος ἔχον πρὸς τὸ μέσον. Ἐν δυνάμει οὖν ὄντος τοῦ μίγματος

τὰ διακρινόμενα ἐφέρετο ὁμοίως πάντοθεν πρὸς τὸ

μέσον. Εἴτ' οὖν ὁμοίως ἀπὸ τῶν ἐσχάτων διῃρημένα τὰ μόρια

20 συνήχθη πρὸς τὸ μέσον, εἴτ' ἄλλως ἔχοντα, ποιήσει

ταὐτόν. Ὅτι μὲν οὖν ὁμοίως γε πανταχόθεν ἀπὸ τῶν ἐσχάτων

φερομένων πρὸς ἓν μέσον ἀναγκαῖον ὅμοιον γίγνεσθαι

πάντῃ τὸν ὄγκον, φανερόν· ἴσου γὰρ πάντῃ προστιθεμένου

ἴσον ἀνάγκη ἀπέχειν τοῦ μέσου τὸ ἔσχατον· τοῦτο

25 δὲ τὸ σχῆμα σφαίρας ἐστίν. Οὐδὲν δὲ διοίσει πρὸς τὸν λόγον,

οὐδ' εἰ μὴ πανταχόθεν ὁμοίως συνέθει πρὸς τὸ μέσον

τὰ μόρια αὐτῆς. Τὸ γὰρ πλεῖον ἀεὶ τὸ πρὸ αὑτοῦ ἔλαττον

προωθεῖν ἀναγκαῖον μέχρι τοῦ μέσου τὴν ῥοπὴν ἐχόντων

ἀμφοῖν, καὶ τοῦ βαρυτέρου προωθοῦντος μέχρι τούτου τὸ

30 ἔλαττον βάρος. Ὃ γὰρ ἄν τις ἀπορήσειε, τὴν αὐτὴν ἔχει

τούτοις λύσιν· εἰ γὰρ οὔσης ἐπὶ τοῦ μέσου καὶ σφαιροειδοῦς

τῆς γῆς πολλαπλάσιον βάρος ἐπιγένοιτο πρὸς θάτερον ἡμισφαίριον,

οὐκ ἔσται τὸ αὐτὸ μέσον τοῦ ὅλου καὶ τὸ τῆς γῆς·

ὥστε ἢ οὐ μενεῖ ἐπὶ τοῦ μέσου, ἢ εἴπερ, ἠρεμήσει γε καὶ

1Since, then, it would require a force greater than itself to move it, it must needs stay at the centre. This view is further supported by the contributions of mathematicians to astronomy, since the observations made as the shapes change by which the order of the stars is determined, 5are fully accounted for on the hypothesis that the earth lies at the centre. Of the position of the earth and of the manner of its rest or movement, our discussion may here end.
Its shape must necessarily be spherical. For every portion of earth has weight until it reaches the centre, and the jostling of parts greater and smaller would bring about 10not a waved surface, but rather compression and convergence of part and part until the centre is reached. The process should be conceived by supposing the earth to come into being in the way that some of the natural philosophers describe. Only they attribute the downward movement to constraint, and it is better to keep to the truth and say that the 15reason of this motion is that a thing which possesses weight is naturally endowed with a centripetal movement. When the mixture, then, was merely potential, the things that were separated off moved similarly from every side towards the centre. Whether the parts which came together at the centre were distributed at the extremities evenly, or in some 20other way, makes no difference. If, on the one hand, there were a similar movement from each quarter of the extremity to the single centre, it is obvious that the resulting mass would be similar on every side. For if an equal amount is added on every side the extremity of the mass will be everywhere equidistant from its centre, i.e. the figure will be 25spherical. But neither will it in any way affect the argument if there is not a similar accession of concurrent fragments from every side. For the greater quantity, finding a lesser in front of it, must necessarily drive it on, both having an impulse whose goal is the centre, and the greater weight driving the lesser forward till this goal is reached. 30In this we have also the solution of a possible difficulty. The earth, it might be argued, is at the centre and spherical in shape: if, then, a weight many times that of the earth were added to one hemisphere, the centre of the earth and of the whole will no longer be coincident.

297b

1 μὴ τὸ μέσον ἔχουσα, ᾗ πέφυκε κινεῖσθαι καὶ νῦν. Τὸ μὲν οὖν

ἀπορούμενον τοῦτ' ἔστιν· ἰδεῖν δ' οὐ χαλεπὸν μικρὸν ἐπιτείναντας,

καὶ διελόντας πῶς ἀξιοῦμεν ὁποσονοῦν μέγεθος φέρεσθαι

πρὸς τὸ μέσον, βάρος ἔχον. Δῆλον γὰρ ὡς οὐχὶ μέχρι τοῦ

5 ἅψασθαι τοῦ κέντρου τὸ ἔσχατον, ἀλλὰ δεῖ κρατεῖν τὸ

πλέον ἕως ἂν λάβῃ τῷ αὑτοῦ μέσῳ τὸ μέσον· μέχρι τούτου

γὰρ ἔχει τὴν ῥοπήν. Οὐδὲν τοίνυν τοῦτο διαφέρει λέγειν ἐπὶ

βώλου καὶ μορίου τοῦ τυχόντος ἢ ἐπὶ ὅλης τῆς γῆς· οὐ γὰρ

διὰ μικρότητα ἢ μέγεθος εἴρηται τὸ συμβαῖνον, ἀλλὰ

10 κατὰ παντὸς τοῦ ῥοπὴν ἔχοντος ἐπὶ τὸ μέσον. Ὥστε εἴτε

ὅλη ποθὲν ἐφέρετο εἴτε κατὰ μέρος, ἀναγκαῖον μέχρι τούτου

φέρεσθαι ἕως ἂν πανταχόθεν ὁμοίως λάβῃ τὸ μέσον, ἀνισαζομένων

τῶν ἐλαττόνων ὑπὸ τῶν μειζόνων τῇ προώσει τῆς

ῥοπῆς. Εἴτ' οὖν ἐγένετο, τοῦτον ἀναγκαῖον γενέσθαι τὸν τρόπον,

15 ὥστε φανερὸν ὅτι σφαιροειδὴς ἡ γένεσις αὐτῆς, εἴτ' ἀγένητος

ἀεὶ διατελεῖ μένουσα, τὸν αὐτὸν τρόπον ἔχειν ὅνπερ κἂν εἰ γιγνομένη

τὸ πρῶτον ἐγένετο. Κατὰ τοῦτόν τε δὴ τὸν λόγον ἀναγκαῖον

εἶναι τὸ σχῆμα σφαιροειδὲς αὐτῆς, καὶ ὅτι πάντα φέρεται τὰ

βαρέα πρὸς ὁμοίας γωνίας, ἀλλ' οὐ παρ' ἄλληλα· τοῦτο δὲ

20 πέφυκε πρὸς τὸ φύσει σφαιροειδές. Ἢ οὖν ἐστι σφαιροειδής,

ἢ φύσει γε σφαιροειδής. Δεῖ δ' ἕκαστον λέγειν τοιοῦτον εἶναι

ὃ φύσει βούλεται εἶναι καὶ ὑπάρχειν, ἀλλὰ μὴ ὃ βίᾳ

καὶ παρὰ φύσιν. Ἔτι δὲ καὶ διὰ τῶν φαινομένων κατὰ τὴν

αἴσθησιν· οὔτε γὰρ ἂν αἱ τῆς σελήνης ἐκλείψεις τοιαύτας

25 ἂν εἶχον τὰς ἀποτομάς· νῦν γὰρ ἐν μὲν τοῖς κατὰ μῆνα

σχηματισμοῖς πάσας λαμβάνει τὰς διαιρέσεις (καὶ γὰρ

εὐθεῖα γίνεται καὶ ἀμφίκυρτος καὶ κοίλη), περὶ δὲ τὰς

ἐκλείψεις ἀεὶ κυρτὴν ἔχει τὴν ὁρίζουσαν γραμμήν, ὥστ'

ἐπείπερ ἐκλείπει διὰ τὴν τῆς γῆς ἐπιπρόσθησιν, ἡ τῆς γῆς

30 ἂν εἴη περιφέρεια τοῦ σχήματος αἰτία σφαιροειδὴς οὖσα. Ἔτι

δὲ διὰ τῆς τῶν ἄστρων φαντασίας οὐ μόνον φανερὸν ὅτι περιφερής,

ἀλλὰ καὶ τὸ μέγεθος οὐκ οὖσα μεγάλη· μικρᾶς

γὰρ γιγνομένης μεταστάσεως ἡμῖν πρὸς μεσημβρίαν καὶ

ἄρκτον ἐπιδήλως ἕτερος γίγνεται ὁ ὁρίζων κύκλος, ὥστε τὰ

1So that either the earth will not stay still at the centre, or if it does, it will be at rest without having its centre at the place to which it is still its nature to move. Such is the difficulty. A short consideration will give us an easy answer, if we first give precision to our 5postulate that any body endowed with weight, of whatever size, moves towards the centre. Clearly it will not stop when its edge touches the centre. The greater quantity must prevail until the body's centre occupies the centre. For that is the goal of its impulse. Now it makes no difference whether we apply this to a clod or common fragment of earth or to the 10earth as a whole. The fact indicated does not depend upon degrees of size but applies universally to everything that has the centripetal impulse. Therefore earth in motion, whether in a mass or in fragments, necessarily continues to move until it occupies the centre equally every way, the less being forced to equalize itself by the greater owing to the forward 15drive of the impulse.
If the earth was generated, then, it must have been formed in this way, and so clearly its generation was spherical; and if it is ungenerated and has remained so always, its character must be that which the initial generation, if it had occurred, would have given it. But the spherical shape, necessitated by this argument, follows also 20from the fact that the motions of heavy bodies always make equal angles, and are not parallel. This would be the natural form of movement towards what is naturally spherical. Either then the earth is spherical or it is at least naturally spherical. And it is right to call anything that which nature intends it to be, and which belongs to it, rather than that 25which it is by constraint and contrary to nature. The evidence of the senses further corroborates this. How else would eclipses of the moon show segments shaped as we see them? As it is, the shapes which the moon itself each month shows are of every kind straight, gibbous, and concave-but in eclipses the outline is always curved: and, since it is the 30interposition of the earth that makes the eclipse, the form of this line will be caused by the form of the earth's surface, which is therefore spherical. Again, our observations of the stars make it evident, not only that the earth is circular, but also that it is a circle of no great size.

298a

1 ὑπὲρ κεφαλῆς ἄστρα μεγάλην ἔχειν τὴν μεταβολήν, καὶ

μὴ ταὐτὰ φαίνεσθαι πρὸς ἄρκτον τε καὶ μεσημβρίαν μεταβαίνουσιν·

ἔνιοι γὰρ ἐν Αἰγύπτῳ μὲν ἀστέρες ὁρῶνται καὶ

περὶ Κύπρον, ἐν τοῖς πρὸς ἄρκτον δὲ χωρίοις οὐχ ὁρῶνται,

5 καὶ τὰ διὰ παντὸς ἐν τοῖς πρὸς ἄρκτον φαινόμενα τῶν

ἄστρων ἐν ἐκείνοις τοῖς τόποις ποιεῖται δύσιν. Ὥστ' οὐ μόνον ἐκ

τούτων δῆλον περιφερὲς ὂν τὸ σχῆμα τῆς γῆς, ἀλλὰ καὶ

σφαίρας οὐ μεγάλης· οὐ γὰρ ἂν οὕτω ταχὺ ἐπίδηλον ἐποίει

μεθισταμένοις οὕτω βραχύ. Διὸ τοὺς ὑπολαμβάνοντας συνάπτειν

10 τὸν περὶ τὰς Ἡρακλείας στήλας τόπον τῷ περὶ τὴν

Ἰνδικήν, καὶ τοῦτον τὸν τρόπον εἶναι τὴν θάλατταν μίαν, μὴ

λίαν ὑπολαμβάνειν ἄπιστα δοκεῖν· λέγουσι δὲ τεκμαιρόμενοι

καὶ τοῖς ἐλέφασιν, ὅτι περὶ ἀμφοτέρους τοὺς τόπους τοὺς

ἐσχάτους ὄντας τὸ γένος αὐτῶν ἐστιν, ὡς τῶν ἐσχάτων διὰ τὸ

15 συνάπτειν ἀλλήλοις τοῦτο πεπονθότων. Καὶ τῶν μαθηματικῶν

δὲ ὅσοι τὸ μέγεθος ἀναλογίζεσθαι πειρῶνται τῆς περιφερείας,

εἰς τετταράκοντα λέγουσιν εἶναι μυριάδας.

Ἐξ ὧν τεκμαιρομένοις οὐ μόνον σφαιροειδῆ τὸν ὄγκον ἀναγκαῖον

εἶναι τῆς γῆς, ἀλλὰ καὶ μὴ μέγαν πρὸς τὸ τῶν ἄλλων

20 ἄστρων μέγεθος.

1For quite a small change of position to south or north causes a manifest alteration of the horizon. There is much change, I mean, in the stars which are overhead, and the stars seen are different, as one moves northward or southward. Indeed there are some stars seen in Egypt and in the neighbourhood 5of Cyprus which are not seen in the northerly regions; and stars, which in the north are never beyond the range of observation, in those regions rise and set. All of which goes to show not only that the earth is circular in shape, but also that it is a sphere of no great size: for otherwise the effect of so slight a change of place would not be quickly apparent. Hence 10one should not be too sure of the incredibility of the view of those who conceive that there is continuity between the parts about the pillars of Hercules and the parts about India, and that in this way the ocean is one. As further evidence in favour of this they quote the case of elephants, a species occurring in each of these extreme regions, suggesting that the common 15characteristic of these extremes is explained by their continuity. Also, those mathematicians who try to calculate the size of the earth's circumference arrive at the figure 400,000 stades. This indicates not only that the earth's mass is spherical in shape, but also that as compared with the stars it is not of great size.
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