on the heavens-第19节
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impossible。 And the same argument would fit the case of lightness。 Again； a body which is in motion but has neither weight nor lightness； must be moved by constraint； and must continue its constrained movement infinitely。 For there will be a force which moves it； and the smaller and lighter a body is the further will a given force move it。 Now let A； the weightless body； be moved the distance CE； and B； which has weight； be moved in the same time the distance CD。 Dividing the heavy body in the proportion CE：CD； we subtract from the heavy body a part which will in the same time move the distance CE； since the whole moved CD： for the relative speeds of the two bodies will be in inverse ratio to their respective sizes。 Thus the weightless body will move the same distance as the heavy in the same time。 But this is impossible。 Hence； since the motion of the weightless body will cover a greater distance than any that is suggested； it will continue infinitely。 It is therefore obvious that every body must have a definite weight or lightness。 But since 'nature' means a source of movement within the thing itself； while a force is a source of movement in something other than it or in itself qua other； and since movement is always due either to nature or to constraint； movement which is natural； as downward movement is to a stone； will be merely accelerated by an external force； while an unnatural movement will be due to the force alone。 In either case the air is as it were instrumental to the force。 For air is both light and heavy； and thus qua light produces upward motion； being propelled and set in motion by the force； and qua heavy produces a downward motion。 In either case the force transmits the movement to the body by first； as it were； impregnating the air。 That is why a body moved by constraint continues to move when that which gave the impulse ceases to accompany it。 Otherwise； i。e。 if the air were not endowed with this function； constrained movement would be impossible。 And the natural movement of a body may be helped on in the same way。 This discussion suffices to show （1） that all bodies are either light or heavy； and （2） how unnatural movement takes place。 From what has been said earlier it is plain that there cannot be generation either of everything or in an absolute sense of anything。 It is impossible that everything should be generated； unless an extra…corporeal void is possible。 For； assuming generation； the place which is to be occupied by that which is coming to be； must have been previously occupied by void in which no body was。 Now it is quite possible for one body to be generated out of another； air for instance out of fire； but in the absence of any pre…existing mass generation is impossible。 That which is potentially a certain kind of body may； it is true； become such in actuality； But if the potential body was not already in actuality some other kind of body； the existence of an extra…corporeal void must be admitted。
3
It remains to say what bodies are subject to generation； and why。 Since in every case knowledge depends on what is primary； and the elements are the primary constituents of bodies； we must ask which of such bodies are elements； and why； and after that what is their number and character。 The answer will be plain if we first explain what kind of substance an element is。 An element； we take it； is a body into which other bodies may be analysed； present in them potentially or in actuality （which of these； is still disputable）； and not itself divisible into bodies different in form。 That； or something like it； is what all men in every case mean by element。 Now if what we have described is an element； clearly there must be such bodies。 For flesh and wood and all other similar bodies contain potentially fire and earth； since one sees these elements exuded from them； and； on the other hand； neither in potentiality nor in actuality does fire contain flesh or wood； or it would exude them。 Similarly； even if there were only one elementary body； it would not contain them。 For though it will be either flesh or bone or something else； that does not at once show that it contained these in potentiality： the further question remains； in what manner it becomes them。 Now Anaxagoras opposes Empedocles' view of the elements。 Empedocles says that fire and earth and the related bodies are elementary bodies of which all things are composed； but this Anaxagoras denies。 His elements are the homoeomerous things； viz。 flesh； bone； and the like。 Earth and fire are mixtures； composed of them and all the other seeds； each consisting of a collection of all the homoeomerous bodies； separately invisible； and that explains why from these two bodies all others are generated。 （To him fire and aither are the same thing。） But since every natural body has it proper movement； and movements are either simple or mixed； mixed in mixed bodies and simple in simple； there must obviously be simple bodies； for there are simple movements。 It is plain； then； that there are elements； and why。
4
The next question to consider is whether the elements are finite or infinite in number； and； if finite； what their number is。 Let us first show reason or denying that their number is infinite； as some suppose。 We begin with the view of Anaxagoras that all the homoeomerous bodies are elements。 Any one who adopts this view misapprehends the meaning of element。 Observation shows that even mixed bodies are often divisible into homoeomerous parts； examples are flesh； bone； wood； and stone。 Since then the composite cannot be an element； not every homoeomerous body can be an element； only； as we said before； that which is not divisible into bodies different in form。 But even taking 'element' as they do； they need not assert an infinity of elements； since the hypothesis of a finite number will give identical results。 Indeed even two or three such bodies serve the purpose as well； as Empedocles' attempt shows。 Again； even on their view it turns out that all things are not composed of homocomerous bodies。 They do not pretend that a face is composed of faces； or that any other natural conformation is composed of parts like itself。 Obviously then it would be better to assume a finite number of principles。 They should； in fact； be as few as possible； consistently with proving what has to be proved。 This is the common demand of mathematicians； who always assume as principles things finite either in kind or in number。 Again； if body is distinguished from body by the appropriate qualitative difference； and there is a limit to the number of differences （for the difference lies in qualities apprehended by sense； which are in fact finite in number； though this requires proof）； then manifestly there is necessarily a limit to the number of elements。 There is； further； another view…that of Leucippus and Democritus of Abdera…the implications of which are also unacceptable。 The primary masses； according to them； are infinite in number and indivisible in mass： one cannot turn into many nor many into one； and all things are generated by their combination and involution。 Now this view in a sense makes things out to be numbers or composed of numbers。 The exposition is not clear； but this is its real meaning。 And further； they say that since the atomic bodies differ in shape； and there is an infinity of shapes； there is an infinity of simple bodies。 But they have never explained in detail the shapes of the various elements； except so far to allot the sphere to fire。 Air； water； and the rest they distinguished by the relative size of the atom； assuming that the atomic substance was a sort of master…seed for each and every element。 Now； in the first place； they make the mistake already noticed。 The principles which they assume are not limited in number； though such limitation would necessitate no other alteration in their theory。 Further； if the differences of bodies are not infinite； plainly the elements will not be an infinity。 Besides； a view which asserts atomic bodies must needs come into conflict with the mathematical sciences； in addition to invalidating many common opinions and apparent data of sense perception。 But of these things we have already spoken in our discussion of time and movement。 They are also bound to contradict themselves。 For if the elements are atomic； air； earth； and water cannot be differentiated by the relative sizes of their atoms； since then they could not be generated out of one another。 The extrusion of the largest atoms is a process that will in time exhaust the supply； and it is by such a process that they account for the generation of water； air； and earth from one another。 Again； even on their own presuppositions it does not seem as if the clements would be infinite in number。 The atoms differ in figure； and all figures are composed of pyramids； rectilinear the case of rectilinear figures； while the sphere has eight pyramidal parts。 The figures must have their principles； and； whether these are one or two or more； the simple bodies must be the same in number as they。 Again； if every element has its proper movement； and a simple body has a simple movement； and the number of simple
