on the heavens-第12章
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。 Relatively； however； to the secondary revolution； I mean that of the planets； we are above and on the right and they are below and on the left。 For the principle of their movement has the reverse position； since the movement itself is the contrary of the other： hence it follows that we are at its beginning and they at its end。 Here we may end our discussion of the distinctions of parts created by the three dimensions and of the consequent differences of position。
3
Since circular motion is not the contrary of the reverse circular motion； we must consider why there is more than one motion； though we have to pursue our inquiries at a distance…a distance created not so much by our spatial position as by the fact that our senses enable us to perceive very few of the attributes of the heavenly bodies。 But let not that deter us。 The reason must be sought in the following facts。 Everything which has a function exists for its function。 The activity of God is immortality； i。e。 eternal life。 Therefore the movement of that which is divine must be eternal。 But such is the heaven； viz。 a divine body； and for that reason to it is given the circular body whose nature it is to move always in a circle。 Why； then； is not the whole body of the heaven of the same character as that part？ Because there must be something at rest at the centre of the revolving body； and of that body no part can be at rest； either elsewhere or at the centre。 It could do so only if the body's natural movement were towards the centre。 But the circular movement is natural； since otherwise it could not be eternal： for nothing unnatural is eternal。 The unnatural is subsequent to the natural； being a derangement of the natural which occurs in the course of its generation。 Earth then has to exist； for it is earth which is at rest at the centre。 （At present we may take this for granted： it shall be explained later。） But if earth must exist； so must fire。 For； if one of a pair of contraries naturally exists； the other； if it is really contrary； exists also naturally。 In some form it must be present； since the matter of contraries is the same。 Also； the positive is prior to its privation （warm； for instance； to cold）； and rest and heaviness stand for the privation of lightness and movement。 But further； if fire and earth exist； the intermediate bodies must exist also： each element stands in a contrary relation to every other。 （This； again； we will here take for granted and try later to explain。） these four elements generation clearly is involved； since none of them can be eternal： for contraries interact with one another and destroy one another。 Further； it is inconceivable that a movable body should be eternal； if its movement cannot be regarded as naturally eternal： and these bodies we know to possess movement。 Thus we see that generation is necessarily involved。 But if so； there must be at least one other circular motion： for a single movement of the whole heaven would necessitate an identical relation of the elements of bodies to one another。 This matter also shall be cleared up in what follows： but for the present so much is clear； that the reason why there is more than one circular body is the necessity of generation； which follows on the presence of fire； which； with that of the other bodies； follows on that of earth； and earth is required because eternal movement in one body necessitates eternal rest in another。
4
The shape of the heaven is of necessity spherical； for that is the shape most appropriate to its substance and also by nature primary。 First； let us consider generally which shape is primary among planes and solids alike。 Every plane figure must be either rectilinear or curvilinear。 Now the rectilinear is bounded by more than one line； the curvilinear by one only。 But since in any kind the one is naturally prior to the many and the simple to the complex； the circle will be the first of plane figures。 Again； if by complete； as previously defined； we mean a thing outside which no part of itself can be found； and if addition is always possible to the straight line but never to the circular； clearly the line which embraces the circle is complete。 If then the complete is prior to the incomplete； it follows on this ground also that the circle is primary among figures。 And the sphere holds the same position among solids。 For it alone is embraced by a single surface； while rectilinear solids have several。 The sphere is among solids what the circle is among plane figures。 Further； those who divide bodies into planes and generate them out of planes seem to bear witness to the truth of this。 Alone among solids they leave the sphere undivided； as not possessing more than one surface： for the division into surfaces is not just dividing a whole by cutting it into its parts； but division of another fashion into parts different in form。 It is clear； then； that the sphere is first of solid figures。 If； again； one orders figures according to their numbers； it is most natural to arrange them in this way。 The circle corresponds to the number one； the triangle； being the sum of two right angles； to the number two。 But if one is assigned to the triangle； the circle will not be a figure at all。 Now the first figure belongs to the first body； and the first body is that at the farthest circumference。 It follows that the body which revolves with a circular movement must be spherical。 The same then will be true of the body continuous with it： for that which is continuous with the spherical is spherical。 The same again holds of the bodies between these and the centre。 Bodies which are bounded by the spherical and in contact with it must be； as wholes； spherical； and the bodies below the sphere of the planets are contiguous with the sphere above them。 The sphere then will be spherical throughout； for every body within it is contiguous and continuous with spheres。 Again； since the whole revolves； palpably and by assumption； in a circle； and since it has been shown that outside the farthest circumference there is neither void nor place； from these grounds also it will follow necessarily that the heaven is spherical。 For if it is to be rectilinear in shape； it will follow that there is place and body and void without it。 For a rectilinear figure as it revolves never continues in the same room； but where formerly was body； is now none； and where now is none； body will be in a moment because of the projection at the corners。 Similarly； if the world had some other figure with unequal radii； if； for instance； it were lentiform； or oviform； in every case we should have to admit space and void outside the moving body； because the whole body would not always occupy the same room。 Again； if the motion of the heaven is the measure of all movements whatever in virtue of being alone continuous and regular and eternal； and if； in each kind； the measure is the minimum； and the minimum movement is the swiftest； then； clearly； the movement of the heaven must be the swiftest of all movements。 Now of lines which return upon themselves the line which bounds the circle is the shortest； and that movement is the swiftest which follows the shortest line。 Therefore； if the heaven moves in a circle and moves more swiftly than anything else； it must necessarily be spherical。 Corroborative evidence may be drawn from the bodies whose position is about the centre。 If earth is enclosed by water； water by air； air by fire； and these similarly by the upper bodies…which while not continuous are yet contiguous with them…and if the surface of water is spherical； and that which is continuous with or embraces the spherical must itself be spherical； then on these grounds also it is clear that the heavens are spherical。 But the surface of water is seen to be spherical if we take as our starting…point the fact that water naturally tends to collect in a hollow place…'hollow' meaning 'nearer the centre'。 Draw from the centre the lines AB； AC； and let their extremities be joined by the straight line BC。 The line AD； drawn to the base of the triangle； will be shorter than either of the radii。 Therefore the place in which it terminates will be a ho
