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g…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； and 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 and 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 in 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。 It 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 then； 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 slower 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 materials 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 acceleration。 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 is 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 could 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。 But 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 is 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； and further that its movement is regular； has now been sufficiently explained。
7
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； since； 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 and 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 so 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 themselves 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。
8
Since 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 is 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 in 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。 That 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 circles； 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 fall 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； and 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。 For； 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 the 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； inasmuch as we construct them out of the spherical body； and