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infinite； then； cannot revolve in a circle； nor could the world； if it were infinite。 （3） That the infinite cannot move may also be shown as follows。 Let A be a finite line moving past the finite line； B。 Of necessity A will pass clear of B and B of A at the same moment； for each overlaps the other to precisely the same extent。 Now if the two were both moving； and moving in contrary directions； they would pass clear of one another more rapidly； if one were still and the other moving past it； less rapidly； provided that the speed of the latter were the same in both cases。 This； however； is clear： that it is impossible to traverse an infinite line in a finite time。 Infinite time； then； would be required。 （This we demonstrated above in the discussion of movement。） And it makes no difference whether a finite is passing by an infinite or an infinite by a finite。 For when A is passing B； then B overlaps A and it makes no difference whether B is moved or unmoved； except that； if both move； they pass clear of one another more quickly。 It is； however； quite possible that a moving line should in certain cases pass one which is stationary quicker than it passes one moving in an opposite direction。 One has only to imagine the movement to be slow where both move and much faster where one is stationary。 To suppose one line stationary； then； makes no difficulty for our argument； since it is quite possible for A to pass B at a slower rate when both are moving than when only one is。 If； therefore； the time which the finite moving line takes to pass the other is infinite； then necessarily the time occupied by the motion of the infinite past the finite is also infinite。 For the infinite to move at all is thus absolutely impossible； since the very smallest movement conceivable must take an infinity of time。 Moreover the heavens certainly revolve； and they complete their circular orbit in a finite time； so that they pass round the whole extent of any line within their orbit； such as the finite line AB。 The revolving body； therefore； cannot be infinite。 （4） Again； as a line which has a limit cannot be infinite； or； if it is infinite； is so only in length； so a surface cannot be infinite in that respect in which it has a limit； or； indeed； if it is completely determinate； in any respect whatever。 Whether it be a square or a circle or a sphere； it cannot be infinite； any more than a foot…rule can。 There is then no such thing as an infinite sphere or square or circle； and where there is no circle there can be no circular movement； and similarly where there is no infinite at all there can be no infinite movement； and from this it follows that； an infinite circle being itself an impossibility； there can be no circular motion of an infinite body。 （5） Again； take a centre C； an infinite line； AB； another infinite line at right angles to it； E； and a moving radius； CD。 CD will never cease contact with E； but the position will always be something like CE； CD cutting E at F。 The infinite line； therefore； refuses to complete the circle。 （6） Again； if the heaven is infinite and moves in a circle； we shall have to admit that in a finite time it has traversed the infinite。 For suppose the fixed heaven infinite； and that which moves within it equal to it。 It results that when the infinite body has completed its revolution； it has traversed an infinite equal to itself in a finite time。 But that we know to be impossible。 （7） It can also be shown； conversely； that if the time of revolution is finite； the area traversed must also be finite； but the area traversed was equal to itself； therefore； it is itself finite。 We have now shown that the body which moves in a circle is not endless or infinite； but has its limit。
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Further； neither that which moves towards nor that which moves away from the centre can be infinite。 For the upward and downward motions are contraries and are therefore motions towards contrary places。 But if one of a pair of contraries is determinate； the other must be determinate also。 Now the centre is determined； for； from whatever point the body which sinks to the bottom starts its downward motion； it cannot go farther than the centre。 The centre； therefore； being determinate； the upper place must also be determinate。 But if these two places are determined and finite； the corresponding bodies must also be finite。 Further； if up and down are determinate； the intermediate place is also necessarily determinate。 For； if it is indeterminate； the movement within it will be infinite； and that we have already shown to be an impossibility。 The middle region then is determinate； and consequently any body which either is in it； or might be in it； is determinate。 But the bodies which move up and down may be in it； since the one moves naturally away from the centre and the other towards it。 From this alone it is clear that an infinite body is an impossibility； but there is a further point。 If there is no such thing as infinite weight； then it follows that none of these bodies can be infinite。 For the supposed infinite body would have to be infinite in weight。 （The same argument applies to lightness： for as the one supposition involves infinite weight； so the infinity of the body which rises to the surface involves infinite lightness。） This is proved as follows。 Assume the weight to be finite； and take an infinite body； AB； of the weight C。 Subtract from the infinite body a finite mass； BD； the weight of which shall be E。 E then is less than C； since it is the weight of a lesser mass。 Suppose then that the smaller goes into the greater a certain number of times； and take BF bearing the same proportion to BD which the greater weight bears to the smaller。 For you may subtract as much as you please from an infinite。 If now the masses are proportionate to the weights； and the lesser weight is that of the lesser mass； the greater must be that of the greater。 The weights； therefore； of the finite and of the infinite body are equal。 Again； if the weight of a greater body is greater than that of a less； the weight of GB will be greater than that of FB； and thus the weight of the finite body is greater than that of the infinite。 And； further； the weight of unequal masses will be the same； since the infinite and the finite cannot be equal。 It does not matter whether the weights are commensurable or not。 If （a） they are incommensurable the same reasoning holds。 For instance； suppose E multiplied by three is rather more than C： the weight of three masses of the full size of BD will be greater than C。 We thus arrive at the same impossibility as before。 Again （b） we may assume weights which are commensurate； for it makes no difference whether we begin with the weight or with the mass。 For example； assume the weight E to be commensurate with C； and take from the infinite mass a part BD of weight E。 Then let a mass BF be taken having the same proportion to BD which the two weights have to one another。 （For the mass being infinite you may subtract from it as much as you please。） These assumed bodies will be commensurate in mass and in weight alike。 Nor again does it make any difference to our demonstration whether the total ma