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me； and the part of this infinite； E； cannot be so modified in the same time； since we assume that a less quantity makes the movement in a less time。 Let E then； when acted upon by A； complete the movement in the time D。 Then； as D is to CD； so is E to some finite part of B。 This part will necessarily be moved by A in the time CD。 For we suppose that the same agent produces a given effect on a greater and a smaller mass in longer and shorter times； the times and masses varying proportionately。 There is thus no finite time in which infinites can move one another。 Is their time then infinite？ No； for infinite time has no end； but the movement communicated has。 If therefore every perceptible body possesses the power of acting or of being acted upon； or both of these； it is impossible that an infinite body should be perceptible。 All bodies； however； that occupy place are perceptible。 There is therefore no infinite body beyond the heaven。 Nor again is there anything of limited extent beyond it。 And so beyond the heaven there is no body at all。 For if you suppose it an object of intelligence； it will be in a place…since place is what 'within' and 'beyond' denote…and therefore an object of perception。 But nothing that is not in a place is perceptible。 The question may also be examined in the light of more general considerations as follows。 The infinite； considered as a whole of similar parts； cannot； on the one hand； move in a circle。 For there is no centre of the infinite； and that which moves in a circle moves about the centre。 Nor again can the infinite move in a straight line。 For there would have to be another place infinite like itself to be the goal of its natural movement and another； equally great； for the goal of its unnatural movement。 Moreover； whether its rectilinear movement is natural or constrained； in either case the force which causes its motion will have to be infinite。 For infinite force is force of an infinite body； and of an infinite body the force is infinite。 So the motive body also will be infinite。 （The proof of this is given in our discussion of movement； where it is shown that no finite thing possesses infinite power； and no infinite thing finite power。） If then that which moves naturally can also move unnaturally； there will be two infinites； one which causes； and another which exhibits the latter motion。 Again； what is it that moves the infinite？ If it moves itself； it must be animate。 But how can it possibly be conceived as an infinite animal？ And if there is something else that moves it； there will be two infinites； that which moves and that which is moved； differing in their form and power。 If the whole is not continuous； but exists； as Democritus and Leucippus think； in the form of parts separated by void； there must necessarily be one movement of all the multitude。 They are distinguished； we are told； from one another by their figures； but their nature is one； like many pieces of gold separated from one another。 But each piece must； as we assert； have the same motion。 For a single clod moves to the same place as the whole mass of earth； and a spark to the same place as the whole mass of fire。 So that if it be weight that all possess； no body is； strictly speaking； light： and if lightness be universal； none is heavy。 Moreover； whatever possesses weight or lightness will have its place either at one of the extremes or in the middle region。 But this is impossible while the world is conceived as infinite。 And； generally； that which has no centre or extreme limit； no up or down； gives the bodies no place for their motion； and without that movement is impossible。 A thing must move either naturally or unnaturally； and the two movements are determined by the proper and alien places。 Again； a place in which a thing rests or to which it moves unnaturally； must be the natural place for some other body； as experience shows。 Necessarily； therefore； not everything possesses weight or lightness； but some things do and some do not。 From these arguments then it is clear that the body of the universe is not infinite。
8
We must now proceed to explain why there cannot be more than one heaven…the further question mentioned above。 For it may be thought that we have not proved universal of bodies that none whatever can exist outside our universe； and that our argument applied only to those of indeterminate extent。 Now all things rest and move naturally and by constraint。 A thing moves naturally to a place in which it rests without constraint； and rests naturally in a place to which it moves without constraint。 On the other hand； a thing moves by constraint to a place in which it rests by constraint； and rests by constraint in a place to which it moves by constraint。 Further； if a given movement is due to constraint； its contrary is natural。 If； then； it is by constraint that earth moves from a certain place to the centre here； its movement from here to there will be natural； and if earth from there rests here without constraint； its movement hither will be natural。 And the natural movement in each case is one。 Further； these worlds； being similar in nature to ours； must all be composed of the same bodies as it。 Moreover each of the bodies； fire； I mean； and earth and their intermediates； must have the same power as in our world。 For if these names are used equivocally； if the identity of name does not rest upon an identity of form in these elements and ours； then the whole to which they belong can only be called a world by equivocation。 Clearly； then； one of the bodies will move naturally away from the centre and another towards the centre； since fire must be identical with fire； earth with earth； and so on； as the fragments of each are identical in this world。 That this must be the case is evident from the principles laid down in our discussion of the movements； for these are limited in number； and the distinction of the elements depends upon the distinction of the movements。 Therefore； since the movements are the same； the elements must also be the same everywhere。 The particles of earth； then； in another world move naturally also to our centre and its fire to our circumference。 This； however； is impossible； since； if it were true； earth must； in its own world； move upwards； and fire to the centre； in the same way the earth of our world must move naturally away from the centre when it moves towards the centre of another universe。 This follows from the supposed juxtaposition of the worlds。 For either we must refuse to admit the identical nature of the simple bodies in the various universes； or； admitting this； we must make the centre and the extremity one as suggested。 This being so； it follows that there cannot be more worlds than one。 To postulate a difference of nature in the simple bodies according as they are more or less distant from their proper places is unreasonable。 For what difference can it make whether we say that a thing is this distance away or that？ One would have to suppose a difference proportionate to the distance and increasing with it； but the form is in fact the same。 Moreover； the bodies must have some movement； since the fact that they move is quite evident。 Are we to say then that all their movements； even those which are mutually contrary； are due to constraint？ No； for a body which has no natural movement at all cannot be moved by constraint。 If then the bodies have a natural movement； the movement of the particular instances of each form must necessarily have for goal a place numerically one； i。e。 a particular centre or a particular extremity。 If it be suggested that the goal in each case is one in form but numerically more than one； on the analogy of particulars which are many though each undifferentiated in form； we reply that the variety of goal cannot be limited to this portion or that but must extend to all alike。 For all are equally undifferentiated in form； but any one is different numerically from any other。 What I mean is this： if the portions in this world behave similarly both to one another and to those in another world； then the portion which is taken hence will not behave differently either from the portions in another world or from those in the same world； but similarly to them； since in form no portion differs from another。 The result is that we must either abandon our present assumption or assert that the centre and the extremity are each numerically one。 But this being so； the heaven； by the same evidence and the same necessary inferences； must be one only and no more。 A consideration of the other kinds of movement also makes it plain that there is some point to which earth and fire move naturally。 For in general that which is moved changes from something into something； the starting…point and the goal being different in form； and always it is a finite change。 For instance； to recover health is to change from disease to health； to increase is to change from smallness to greatness。 Locomotion must be similar： for it also has its goal and starting…pointand therefore the starting…point and the goal of the natural movement must differ in form…just as the movement of coming to health does not take any direction which chance or the wishes of