thematical 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 movements is not infinite； because the simple motions are only two and the number of places is not infinite； on these grounds also we should have to deny that the number of elements is infinite。
5
Since the number of the elements must be limited； it remains to inquire whether there is more than one element。 Some assume one only； which is according to some water； to others air； to others fire； to others again something finer than water and denser than air； an infinite body…so they say…bracing all the heavens。 Now those who decide for a single element； which is either water or air or a body finer than water and denser than air； and proceed to generate other things out of it by use of the attributes density and rarity； all alike fail to observe the fact that they are depriving the element of its priority。 Generation out of the elements is； as they say； synthesis； and generation into the elements is analysis； so that the body with the finer parts must have priority in the order of nature。 But they say that fire is of all bodies the finest。 Hence fire will be first in the natural order。 And whether the finest body is fire or not makes no difference； anyhow it must be one of the other bodies that is primary and not that which is intermediate。 Again； density and rarity； as instruments of generation； are equivalent to fineness and coarseness； since the fine is rare； and coarse in their use means dense。 But fineness and coarseness； again； are equivalent to greatness and smallness； since a thing with small parts is fine and a thing with large parts coarse。 For that which spreads itself out widely is fine； and a thing composed of small parts is so spread out。 In the end； then； they distinguish the various other substances from the element by the greatness and smallness of their parts。 This method of distinction makes all judgement relative。 There will be no absolute distinction between fire； water； and air； but one and the same body will be relatively to this fire； relatively to something else air。 The same difficulty is involved equally in the view elements and distinguishes them by their greatness and smallness。 The principle of distinction between bodies being quantity； the various sizes will be in a definite ratio； and whatever bodies are in this ratio to one another must be air； fire； earth； and water respectively。 For the ratios of smaller bodies may be repeated among greater bodies。 Those who start from fire as the single element； while avoiding this difficulty； involve themselves in many others。 Some of them give fire a particular shape； like those who make it a pyramid； and this on one of two grounds。 The reason given may be…more crudely…that the pyramid is the most piercing of figures as fire is of bodies； or…more ingeniously…the position may be supported by the following argument。 As all bodies are composed of that which has the finest parts； so all solid figures are composed of pryamids： but the finest body is fire； while among figures the pyramid is primary and has the smallest parts； and the primary body must have the primary figure： therefore fire will be a pyramid。 Others； again； express no opinion on the subject of its figure； but simply regard it as the of the finest parts； which in combination will form other bodies； as the fusing of gold…dust produces solid gold。 Both of these views involve the same difficulties。 For （1） if； on the one hand； they make the primary body an atom； the view will be open to the objections already advanced
against the atomic theory。 And further the theory is inconsistent with a regard for the facts of nature。 For if all bodies are quantitatively commensurable； and the relative size of the various homoeomerous masses and of their several elements are in the same ratio； so that the total mass of water； for instance； is related to the total mass of air as the elements of each are to one another； and so on； and if there is more air than water and； generally； more of the finer body than of the coarser； obviously the element of water will be smaller than that of air。 But the lesser quantity is contained in the greater。 Therefore the air element is divisible。 And the same could be shown of fire and of all bodies whose parts are relatively fine。 （2） If； on the other hand； the primary body is divisible； then （a） those who give fire a special shape will have to say that a part of fire is not fire； because a pyramid is not composed of pyramids； and also that not every body is either an element or composed of elements； since a part of fire will be neither fire nor any other element。 And （b） those whose ground of distinction is size will have to recognize an element prior to the element； a regress which continues infinitely； since every body is divisible and that which has the smallest parts is the element。 Further； they too will have to say that the same body is relatively to this fire and relatively to that air； to others again water and earth。 The common error of all views which assume a single element is that they allow only one natural movement； which is the same for every body。 For it is a matter of observation that a natural body possesses a principle of movement。 If then all bodies are one； all will have one movement。 With this motion the greater their quantity the more they will move； just as fire； in proportion as its quantity is greater； moves faster with the upward motion which belongs to it。 But the fact is that increase of quantity makes many things move the faster downward。 For these reasons； then； as well as from the distinction already established of a plurality of natural movements； it is impossible that there should be only one element。 But if the elements are not an infinity and not reducible to one； they must be several and finite in number。
6
First we must inquire whether the elements are eternal or subject to generation and destruction； for when this question has been answered their number and character will be manifest。 In the first place； they cannot be eternal。 It is a matter of observation that fire； water； and every simple body undergo a process of analysis； which must either continue infinitely or stop somewhere。 （1） Suppose it infinite。 Then the time occupied by the process will be infinite； and also that occupied by the reverse process of synthesis。 For the processes of analysis and synthesis succeed one another in the various parts。 It will follow that there are two infinite times which are mutually exclusive； the time occupied by the synthesis； which is infinite； being preceded by the period of analysis。 There are thus two mutually exclusive infinites； which is impossible。 （2） Suppose； on the other hand； that the analysis stops somewhere。 Then the body at which it stops will be either atomic or； as Empedocles seems to have intended； a divisible body which will yet never be divided。 The foregoing arguments show that it cannot be an atom； but neither can it be a divisible body which analysis will never reach。 For a smaller body is more easily destroyed than a larger； and a destructive process which succeeds in destroying； that is； in resolving into smaller bodies； a body of some size； cannot reasonably be expected to fail with the smaller body。 Now in fire we observe a destruction of two kinds： it is destroyed by its contrary when it is quenched； and by itself when it dies out。 But the effect is produced by a greater quantity upon a lesser； and the more quickly the smaller it is。 The elements of bodies must therefore be subject to destruction and generation。 Since they are generated； they must be generated either from something incorporeal or from a body； and if from a body； either from one another or from something else。 The theory which generates them from something incorporeal requires an extra…corporeal void。 For everything that comes to be comes to be in something； and that in which the generation takes place must either be incorporeal or possess body； and if it has body； there will be two bodies in the same place at the same time； viz。 that which is coming to be and that which was previously there； while if it is incorporeal； there must be an extra…corporeal void。 But we have already shown that this is impossible。 But； on the other hand； it is equally impossible that the elements should be generated from some kind of body。 That would involve a body distinct from the elements and prior to them。 But if this body possesses weight or lightness； it will be one of the elements； and if it has no tendency to movement； it will be an immovable or mathematical entity； and therefore not in a place at all。 A place in which a thing is at rest is a place in which it might move； either by constraint； i。e。 unnaturally； or in the absence of constraint； i。e。 naturally。 If； then； it is in a place and somewhere； it will be one of the elements； and if it is not in a place； nothing can come from it； since that which comes into being and that out of which it comes must needs be together。 The elements therefore cannot be generated from something incorporeal nor from a body which is not an element； and the only r