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assert and we may consistently admit； inasmuch 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； they 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 the 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 vision。 （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 absurdity 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。 This 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 unsuitable； 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 spherical…a shape which best suits the movement of the one and the immobility of the other。 9
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 of 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 and 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 very 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 be 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。 But 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； and 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 our 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 poop 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 bodies 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 nature 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。
10
With their order…I mean the position of each； as involving the priority of some and the 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。 It 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 leads 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 distance； which is least affected； the influence on the intermediate bodies varying； as the mathematicians show； with their distance。
11
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 which 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 part 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。
12
There are two difficulties； which may very reasonably here be raised； of which we 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 bodies； 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 near