ot 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 the mover may select。 Thus； too； fire and earth move not to infinity but to opposite points； and since the opposition in place is between above and below； these will be the limits of their movement。 （Even in circular movement there is a sort of opposition between the ends of the diameter； though the movement as a whole has no contrary： so that here too the movement has in a sense an opposed and finite goal。） There must therefore be some end to locomotion： it cannot continue to infinity。 This conclusion that local movement is not continued to infinity is corroborated by the fact that earth moves more quickly the nearer it is to the centre； and fire the nearer it is to the upper place。 But if movement were infinite speed would be infinite also； and if speed then weight and lightness。 For as superior speed in downward movement implies superior weight； so infinite increase of weight necessitates infinite increase of speed。 Further； it is not the action of another body that makes one of these bodies move up and the other down； nor is it constraint； like the 'extrusion' of some writers。 For in that case the larger the mass of fire or earth the slower would be the upward or downward movement； but the fact is the reverse： the greater the mass of fire or earth the quicker always is its movement towards its own place。 Again； the speed of the movement would not increase towards the end if it were due to constraint or extrusion； for a constrained movement always diminishes in speed as the source of constraint becomes more distant； and a body moves without constraint to the place whence it was moved by constraint。 A consideration of these points； then； gives adequate assurance of the truth of our contentions。 The same could also be shown with the aid of the discussions which fall under First Philosophy； as well as from the nature of the circular movement； which must be eternal both here and in the other worlds。 It is plain； too； from the following considerations that the universe must be one。 The bodily elements are three； and therefore the places of the elements will be three also； the place； first； of the body which sinks to the bottom； namely the region about the centre； the place； secondly； of the revolving body； namely the outermost place； and thirdly； the intermediate place； belonging to the intermediate body。 Here in this third place will be the body which rises to the surface； since； if not here； it will be elsewhere； and it cannot be elsewhere： for we have two bodies； one weightless； one endowed with weight； and below is place of the body endowed with weight； since the region about the centre has been given to the heavy body。 And its position cannot be unnatural to it； for it would have to be natural to something else； and there is nothing else。 It must then occupy the intermediate place。 What distinctions there are within the intermediate itself we will explain later on。 We have now said enough to make plain the character and number of the bodily elements； the place of each； and further； in general； how many in number the various places are。
9
We must show not only that the heaven is one； but also that more than one heaven is and； further； that； as exempt from decay and generation； the heaven is eternal。 We may begin by raising a difficulty。 From one point of view it might seem impossible that the heaven should be one and unique； since in all formations and products whether of nature or of art we can distinguish the shape in itself and the shape in combination with matter。 For instance the form of the sphere is one thing and the gold or bronze sphere another； the shape of the circle again is one thing； the bronze or wooden circle another。 For when we state the essential nature of the sphere or circle we do not include in the formula gold or bronze； because they do not belong to the essence； but if we are speaking of the copper or gold sphere we do include them。 We still make the distinction even if we cannot conceive or apprehend any other example beside the particular thing。 This may； of course； sometimes be the case： it might be； for instance； that only one circle could be found； yet none the less the difference will remain between the being of circle and of this particular circle； the one being form； the other form in matter； i。e。 a particular thing。 Now since the universe is perceptible it must be regarded as a particular； for everything that is perceptible subsists； as we know； in matter。 But if it is a particular； there will be a distinction between the being of 'this universe' and of 'universe' unqualified。 There is a difference； then； between 'this universe' and simple 'universe'； the second is form and shape； the first form in combination with matter； and any shape or form has； or may have； more than one particular instance。 On the supposition of Forms such as some assert； this must be the case； and equally on the view that no such entity has a separate existence。 For in every case in which the essence is in matter it is a fact of observation that the particulars of