Greco-Christian stream·Corpus Aristotelicum (Complete Works of Aristotle)·On the Heavens (De Caelo)

Source context

Theme

cosmological structure of the heavens, elemental spheres, and celestial motion

Soul-faculty

Intellectual Soul

Steiner

not engaged in the GA corpus

Cross-tradition

• Ptolemaic-Neoplatonic cosmologyAristotle's concentric spherical cosmos of four sub-lunar elements plus the fifth aether became the structural framework adopted and spiritualised by Neoplatonic commentators, who mapped the heavenly spheres onto hierarchies of divine intellects.
• Vedic / Samkhya cosmologyCross-tradition congruence appears in Samkhya's hierarchical ordering of subtle and gross elements (tanmatras / mahabhutas) as a structured descent from the unmanifest toward gross material existence, paralleling Aristotle's elemental stratification from ether to earth.
• Kabbalistic Sephirothic cosmologyCross-tradition congruence exists between Aristotle's bounded, spherically ordered cosmos and the Kabbalistic tree of emanation, where each Sephirah corresponds to a distinct ontological and spatial register between the infinite and the material world.

On the Heavens

Περὶ Οὐρανοῦ · De Caelo · physics

[268a.1] science which has to do with nature clearly concerns itself for the most part with bodies and magnitudes and their properties and movements, but also with the principles of this sort of substance, as many as they may be. For of

[268a.5] things constituted by nature some are bodies and magni- tudes, some possess body and magnitude,! and some are principles of things which possess these.2- Now a continuum is that which is divisible into parts always capable of sub- division, and a body is that which is every way divisible. A magnitude if divisible one way is a line, if two ways a surface, and if three a body. Beyond these there is no other magnitude, because the three dimensions are all that to there are, and that which is divisible in three directions is divisible in all. For, as the Pythagoreans say, the world and all that is in it is determined by the number three, since beginning and middle and end give the number of an ‘all’, and the number they give is the triad. And so, having taken these three* from nature as (so to speak) laws of it, we make further use of the number three in the worship of the Gods Further, we use the terms in practice in this way. Of two things, or men, we say ‘both’, but not ‘all’: three is the first number to which the term ‘all’ has been appropriated.® And in this, as we have said, we do but follow the lead which nature gives. Therefore, since ‘every’ and ‘all’ and ‘complete’ do not differ from one another in respect of form, but only, if at all,® in their “ 5 te ° ! i.e. animate things, such as plants and animals. 2 e.g. matter and form, movement, or, in the case of living things, soul. $ Viz, beginning, middle, and end. * Oaths, for instance, usually appeal to three Gods, as in the Homeric appeal to Zeus, Athene, and Apollo (Prantl). ae ’ Reading «/Ajgayev with E and Prantl. The other MSS. have gbapév (FLM) or xarapapev (HJ).

[269a.1] simple movement is of a simple body (for if it is movement sof a compound it will be in virtue of a prevailing simple element), then there must necessarily be some simple body which revolves naturally and in virtue of its own nature’ with a circular movement. By constraint, of course, it may be brought to move with the motion of something else different from itself, but it cannot so move naturally, since there is one sort of movement natural to each of the simple bodies. Again, if the unnatural movement is the contrary ro of the natural and a thing can have no more than one con- trary, it will follow that circular movement, being a simple motion, must be unnatural, if it is not natural, to the body moved. If then (1) the body, whose movement is circular, is fire or some other element, its natural motion must be the contrary of the circular motion. But a single thing has a single contrary; and upward and downward motion are

[269a.15] the contraries of one another.2 If, on the other hand, (2) the body moving with this circular motion which is unnatural to it is something differént from the elements, there will be some other motion which is natural to it. But this cannot be. For if the natural motion is upward, it will be fire or air, and if downward, water or earth. Further, this circular motion is necessarily primary. For the

[269a.20] perfect is naturally prior to the imperfect, and the circle is a perfect thing. This cannot be said of any straight line: —not of an infinite. line; for, if it were perfect, it would have a limit and an end: nor of any finite line; for in every case there is something beyond it,® since any finite line can be extended. And so, since the prior movement

[269a.25] belongs to the body which is naturally prior, and circular movement is prior to straight, and movement in a straight line belongs to simple bodies—fire moving straight upward and earthy bodies straight downward towards the centre— since this is so, it follows that circular movement also must " Reading éavrod with all MSS. except E. ® Therefore neither of these can be a/so the contrary of circular sae Thus there is 0 simple motion opposed as contrary to the circular, 3 Md - , > , , at Me Reading racy yap éori ti exrds (eoti is omitted by E alone). BOOK I. 2 269° be the movement of some simple body.! For the move- ment of composite bodies is, as we said, determined by that

[269a.30] simple body which preponderates in the composition. These premises clearly give the conclusion that there is in nature some bodily substance other than the formations we know, prior to them all and more divine than they. But it may also be proved as follows. We may take it that all movement is either natural or unnatural, and that the movement which is unnatural to one body is natural to another—as, for instance, is the case with the upward and

[269a.35] downward movements, which are natural and unnatural to fire and earth respectively. It necessarily follows that 269” circular movement, being unnatural to these bodies, is the natural movement of some other. Further, if, on the one hand, circular movement is zatural to something, it must surely be some simple and primary body which is ordained to move with a natural circular motion, as fire is ordained 5 to fly up and earth down. If, on the other hand, the movement of the rotating bodies about the centre is unnatural, it would be remarkable and indeed quite in- conceivable that this movement alone should be continuous and eternal, being nevertheless contrary to nature. At any rate the evidence of all other cases goes to show that it is the unnatural which quickest passes away. And so, if, as some say, the body so moved is fire, this movement is just as unnatural to it as downward movement ; for any one can see that fire moves in a straight line away from the centre. On all these grounds, therefore, we may infer with con- fidence that there is something beyond the bodies that are about us on this earth, different and separate from them ; and that the superior glory of its nature is proportionate to its distance from this world of ours.’ — ° = o merely that circular movement is the movement of a simple body, but also that it is the movement of a simple body’prior to the other simple bodies. Prantl therefore inserts mporépov after tkvds and appeals to Simplicius’s paraphrase for corroboration. Simplicius, however, not : only does not corroborate the conjecture but actually points out that this part of the conclusion is suppressed (drep ws cages mapyxe). The insertion of mporépov does not really make the argument any clearer. In consequence of what has been said, in part by way of 3 assumption and in part by way of proof, it is clear that not 20 every body either possesses lightness or heaviness. As 30 35

[270a.1] a preliminary we must explain in what sense we are using the words ‘heavy’ and ‘light’, sufficiently, at least, for our present purpose :! we can examine the terms more closely later, when we come to consider their essential nature.” Let us then apply the term ‘heavy’ to that which naturally moves towards the centre, and ‘light’ to that which moves naturally away from the centre. The heaviest thing will be s that which sinks to the bottom of all things that move downward, and the lightest that which rises to the surface of everything that moves upward. Now, necessarily,® every- thing which moves either up or down possesses lightness or heaviness or both—but not both relatively to the same thing: for things are heavy and light relatively to one another ; air, for instance, is light relatively to water, and water light relatively to earth. The body, then, which moves in a circle cannot possibly possess either heaviness or lightness. For neither naturally nor unnaturally can it move either towards or away from the centre. Movement in a straight line certainly does not belong to it naturally, since one sort of movement is, as we saw, appropriate to each simple body, and so we should be compelled to identify it with one of the bodies which move imthis way. Suppose, then, that the movement is z#szzatural. In that case, if it is the downward movement which is unnatural, the upward movement will be natural; and if it is the upward which is unnatural, the downward will be natural. For we decided that of contrary movements, if the one is unnatural to any- thing, the other will be natural to it. But since the natural movement of the whole and of its part—of earth, for in- stance, as a whole and of a small clod—have one and the same direction, it results, in the first place, that this body can possess no lightness or heaviness at all (for that would mean that it could move by its own nature either from or * Reading ixavds os mpds (as is omitted by E alone). ? Below, Bk. IV, ce. i-iv. * Reading avayxn 67 (8€ is in F alone).

[270a.3] BOOK I. towards the centre, which, as we know, is impossible); and, secondly, that it cannot possibly move in the way of locomotion by being forced violently aside in an upward or downward direction. For neither naturally nor un- naturally can it move with any other motion but its own, either itself or any part of it, since the reasoning which applies to the whole applies also to the part. It is equally reasonable to assume that this body will be ungenerated and indestructible and exempt from increase and alteration, since everything that comes to be comes into being from its contrary and in some substrate, and passes away likewise in a substrate by the action of the contrary into the contrary, as we explained in our opening discussions.? Now the motions of contraries are contrary. If then this body can have no contrary, because there can be no con- trary motion to the circular, nature seems justly to have exempted from contraries the body which was to be un- generated and indestructible. For it is in contraries that generation and decay subsist. Again, that which is subject to increase increases upon contact with a kindred body, which is resolved into its matter. But there is nothing out of which this body can have been generated.* And if it is exempt from increase and diminution,‘ the same reasoning leads us to suppose that it is also unalterable. For altera- tion is movement in respect of quality; and qualitative states and dispositions, such as health and disease, do not come into being without changes of properties, But all 15 20

[270a.30] natural bodies which change their properties we see to be subject without exception to increase and diminution. This is the case, for instance, with the bodies of animals and 1 Phys. I. vii-ix. For the phrase, cf. 311% 12. three representative MSS. (EFJ), are not referred to by Simplicius or Themistius, and are an awkward intrusion in the sentence since what follows applies only to increase. For the doctrine, cf. De Gen. et Corr. I. v. 3 Increase is effected by generation of one kindred body out of another. This body has no contrary out of which it can be generated. Therefore it cannot increase. * Reading dp@:rov with H (so Prantl). All other MSS. have apOaprov ; but the rare dpé:rov would be easily altered to the commoner word. Simplicius has é@@aprov, but explains that Péious is a kind of pOopa and so apOaprov may be used for apéirov. their parts and with vegetable bodies, and similarly also with those of the elements. And so, if the body which moves with a circular motion cannot admit of increase

[270a.35] or diminution, it is reasonable to suppose that it is also unalterable. 270° The reasons why the primary body is eternal and not sub- ject to increase or diminution, but unaging and unalterable and unmodified, will be clear from what has been said to any one who believes in our assumptions. Our theory seems to 5 confirm experience and to be confirmed by it. For all men have some conception of the nature of the gods, and all who believe in the existence of gods at all, whether barbarian or Greek, agree in allotting the highest place to the deity, surely because they suppose that immortal is linked with immortal and regard any other supposition as inconceivable. 10 If then there is, as there certainly is, anything divine, what we have just said about the primary bodily substance was well said. The mere evidence of the senses is enough to convince us of this, at least with human certainty. For in the whole range of time past, so far as our inherited records 15 reach,’ no change appears to have taken place either in the whole scheme of the outermost heaven or in any of its proper parts. The common name, too, which has been handed down from our distant ancestors even to our own day, seems to show that they conceived of it in the fashion which we have been expressing. The same ideas, one must 20 believe, recur in men’s minds not once or twice but again and again. And so, implying that the primary body is something else beyond earth, fire, air, and water, they gave the highest place a name of its own, azther, derived from the fact that it ‘runs always’? for an eternity of time. Anaxa- 25 goras, however, scandalously misuses this name, taking aither as equivalent to fire.® It is also clear from what has been said why the number * Simplicius says he ‘has been told’ that there are written astro- nomical records (aorp@as tnpjoes dvaypdnrous) in Egypt for the past 630,000 years and in Babylon for the past 1,440,000 years. * i.e. al@np from dei Oe. The derivation was suggested by Plato (Cratylus, 410 B). * i.e. deriving ai@yp from aidew. Cf. Bk. II], 302 4. a y BOOK I. 3 270° of what we call simple bodies cannot be greater than it is. The motion of a simple body must itself be simple, and we assert that there are only these two simple motions, the circular and the straight, the latter being subdivided into motion away from and motion towards the centre. oo w 4 That there is no other form of motion opposed as contrary to the circular may be proved in various ways. In the first place, there is an obvious tendency to oppose the straight line to the circular. For concave and convex 35

[271a.1] only regarded as opposed to one another, but they are also coupled together and treated as a unity in oppo- sition to the straight. And so, if there is a contrary to circular motion, motion in a straight line must be re- cognized as having the best claim to that name. But the two forms of rectilinear motion are opposed to one another

[271a.5] by reason of their places; for up and down is a difference and a contrary opposition in place.t Secondly, it may be thought that the same reasoning which holds good of the rectilinear path applies also to the circular, movement from A to B being opposed as contrary to movement from B to A. But what is meant is still rectilinear motion. For that is limited to a single path, while the circular paths which pass to through the same two points are infinite in number.” Even if we are confined to the single semicircle and the opposition is between movement from C to D and from PD to C along ; that semicircle, the case is no better. For the motion is the same as that along the diameter, since we invariably regard the distance between two points as the length of the straight line which joins them. It is no more satisfactory to con- struct a circle and treat motion along one semicircle as contrary to motion along the other. For example, taking 5 generally admitted case of contrary opposition (viz. that of upward and downward motion) rests on a contrary opposition of places (viz. above and below), no such ground can be suggested for the opposition of circular to rectilinear motion. o FiG#is hig i. ah; 2 ° 30 DE-CAELO a complete circle, motion from £ to F on the semicircle G may be opposed to motion from F to £ on the semicircle H. But even supposing these are contraries, it in no way follows that the reverse motions on the complete cir- cumference are contraries. Nor again can motion along the circle from A to B be regarded as the contrary of motion from A to C:! for the motion goes from the same point towards the same point, and contrary motion was distinguished as motion from a contrary to its contrary.” And even if the motion round a circle is the contrary of the reverse motion, one of the two would be ineffective: for both move to the same point, because that which moves in a circle, at whatever point it begins, must necessarily pass through all the contrary places alike. (By contrarieties of place I mean up and down, back and front, and right and left; and the contrary oppositions of movements are determined by those of places.) One of the motions, then, would be ineffective, for if the two motions were of equal strength, there would be no movement either way, and if one of the two were preponderant, the other would be inoperative. So that if both bodies were there, one of them, inasmuch as it would not be moving with its own movement, would be useless, in the sense in which a shoe is useless when it is not worn. But God and nature create nothing that has not its use.° PS TGeel Ute IT PHYS. Va, e29> 2 Ne * Reading ér: for the ér of our MSS. after Simplicius, who had both readings before him. * Prantl’s alteration of yap into dp’ is not needed. The ydp refers back to the remark ‘one of the two would be ineffective’. That remark is therefore repeated in the text. ° The bearing of this argument is clear if it is remembered that the assertion of the existence of a certain movement necessarily involves for Aristotle the assertion of the existence of a body which naturally exhibits the movement. Similarly the assertion that a movement is inoperative involves the assertion that a body is inoperative. BOOK I. 5 which remain. First, is there an infinite body, as the majority of the ancient philosophers thought, or is this an impossibility? The decision of this question, either way, is not unimportant, but rather all-important, to our search for the truth.’ It is this problem which has practically always been the source of the differences of those who have written about nature as a whole. So it has been and so it must be; since the least initial deviation from the truth is multiplied later a thousandfold. Admit, for instance, the existence of a minimum magnitude, and you will find that the minimum which you have introduced, small as it is, causes the greatest truths of mathematics to totter. The reason is that a principle is great rather in power than in extent; hence that which was small at the start turns out a giant at the end. Now the conception of the infinite possesses this power of principles, and indeed in the sphere of quantity possesses it in a higher degree than any other conception ; so that it is in no way absurd or unreasonable that the assump- tion that an infinite body exists should be of peculiar moment to our inquiry. The infinite, then, we must now discuss, opening the whole matter from the beginning. Every body is necessarily to be classed either as simple or as composite ;* the infinite body, therefore, will be either simple or composite. But it is clear, further, that if the simple : bodies are finite, the composite must also be finite, since that which is composed of bodies finite both in number and in magnitude is itself finite in respect of number and magnitude: its quantity is in fact the same as that of the bodies which compose it. What remains for us to consider, then, is whether any of the simple bodies can be infinite in magnitude, or whether this is impossible. Let us try the 2 primary body first, and then go on to consider the others. The body which moves in a circle must necessarily be finite in every respect, for the following reasons. (1) If the body so moving is infinite, the radii drawn from the centre in Jet. 993% 30. mn ° to ° 3o will be infinite.1 But the space between infinite radii is infinite: and by the space between the radii I mean the area outside which no magnitude which is in contact with the two lines can be conceived as falling.? This, I say, will be infinite: first, because in the case of finite radii it is always

[272a.1] because in it one can always go on to a width greater than any given width; thus the reasoning which forces us to believe in infinite number, because there is no maximum, applies also to the space between the radii. Now the infinite cannot be traversed, and if the body is infinite the interval between the radii is necessarily infinite:

[272a.5] circular motion therefore is an impossibility. Yet our eyes tell us that the heavens revolve in a circle,and by argument also we have determined that there is something to which circular movement belongs. (2) Again, if from a finite time a finite time be subtracted, what remains must be finite and have a beginning. And if ro the time of a journey has a beginning, there must be a beginning also of the movement, and consequently also of the distance traversed. This applies universally. Take a line, ACE, infinite in one direction, £, and another line, BB, infinite in both directions. Let ACE describe a circle, 1 “The centre’, when not in any way qualified, means the centre of the earth, which is taken by Aristotle to be also the centre of all the revolutions of the heavenly bodies. He cannot here mean the centre of the supposed infinite body, since to that no shape has yet been given. understood by Prantl. A comparison of this passage with others in which what is practically the same phrase occurs (esp. Jez. 1021” 12, 1055°12) shows (a) that od is governed by éé@ (‘ outside which’), and (6) that the phrase is roughly equivalent to réActov. The point here is that by dtaornua he means, not a straight line spanning the interval between the radii, but the whole area enclosed between the two radii and the portion of the circumference which connects their extremities. In I. 30 read, after Sudornpa, dé rather than ydp, which is in E alone. * Reading ér with the MSS.; Prantl’s éwed seems to have nothing to recommend it. It will then be necessary to put a full-stop after dvaotyparos in 1, 3. This sentence gives, of course, a second reason for taking the Suiornua to be infinite. SedetGwnl Vs BOOK I. 5 272°

[272a.15] revolving upon C as centre. In its movement it will cut BB continuously for a certain time. This will be a finite time, since the total time is finite in which the heavens complete their circular orbit, and consequently the time subtracted from it, during which the one line in its motion cuts the other, is also finite. Therefore there will be a point at which ACE began for the first time to cut BA. This, however, is impossible. The infinite, then, cannot

[272a.20] 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 bea finite line moving past the finite line, B. Of necessity A will pass clear of Band 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

[272a.30] ; time. Infinite time, then, would be required. (This we - demonstrated above in the discussion of movement.*) And ve ~~ 7 er is) 5 rat baie % | be fe 7," ' ~ =e es” 1 In this argument the ascertained fact that the revolution of the heavens occupies a limited time is used to prove the finitude of its path and consequently also of the body itself. A&B represents an infinite line drawn within the infinite body and therefore ‘traversed’ by that body in its revolution. But there can be no point at which the contact of ACE with PA either begins or ends, while there is a time within which the revolution is completed. Therefore the revolving body is not infinite.—Possibly the centre of the movement of ACE should be A (as in F and Simpl.) rather than C: 2 Movement of the ‘world’ (kédapos) is here used for movement of the ‘heaven’ (ovpavds), Either kéopos stands for the hgavenly body, as in ic. Eth. 1141"1, or the movement and the infinity are treated for the moment as attributes of the whole. 8 Aristotle refers to the Piyszcs, here and elsewhere, as continuous with the De Cae/o. Different parts of the Physics are referred to by different names. Simplicius (p. 226, 19) observes that P/ys. I-IV are cited as ‘the discussion of principles’ (epi apyav) and Phys. V-VIII as ‘the discussion of movement’ (epi xivnoews). In PAys. VIII, 257% 34, Aristotle refers back to an earlier passage as occurring év rois xaOdXov rois rept Pioews ; and Simplicius, commenting on this (Comm, in Phys. p. 1233, 30), ‘infers’ that Phys. I-V are the mepi picews and Phys. VI-VIII the epi xwnoews. But his inference is false. The r reference is not, as he thought, to V. iv. The principle had been asserted earlier, viz. in III.i. The ‘general considerations concerning nature’ may therefore be identified with the ‘discussion of principles’, and the PAysics may be divided in the middle, i.e. at the end of Book 1V.—The reference in this passage is to PAys. VI. vii. 5 10 15 DE CAEEO it makes no difference whether a finite is passing by an infinite or an infinite by a finite. For when J 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 42. 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 to mapaddartret, map’, rests upon the sole authority of E: for L has mapadXatr. lap’ is intolerable, since it must stand for @éperae mapa and thus attributes movement to 4, of which in the same sentence it is said that it may be unmoved. to the possession of zépas (‘limit’) than a denial of infinity; in which case GAN’ elrep, emt pjkos means ‘or if a finite line is infinite, it is so in length’. The antecedent thus appears to contradict both itself and the consequent. Simplicius preserves a variant for emi pijKos, émt @darepa. (‘A finite line can only be infinite, if at all, in one direction ’.) —Perhaps, however, the text is correct. The sentence may be para- phrased as follows. A limited line cannot be infinite: lines, in fact, can only be infinite, if at all, in that respect in which they are un- limited: byt there is nothing in the nature of ‘line’ to determine the length of any given line: consequently, it is only in respect to length that infinity is ever ascribed to lines. (Mr. Ross suggests that 7 should be read instead of fs in 1.17. ‘A line cannot be infinite in that respect in which it is a limit.’ The line is the limit of the plane, i.e. a limit in respect of breadth. Similarly the plane is the limit in respect of depth. This correction has support from the translation of Argyropylus (‘ex ea parte qua finis est’), and is probably right.) BOOK I. 5 272° 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 20 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, AZ, another infinite line at right angles to it, Z, and a moving radius, CD.’ CD will never cease contact with £, but the position will always be something like CZ, 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, 30 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 2733 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; ws G3 1 Also, of course, infinite. SrIGe Vs complete the circle owing to its inability to extricate its outer extremity from that of the other infinite, “. The MSS. vary between kixdat (EL), xkixdk@ (M), and xixdoy (HFJ: the last, however, has wm supra- scriptum). In FMJ mepieox follows instead of preceding kvxdov (xuxhw M). Perhaps xvxAov meplecow should be read with FJ, though either reading will give the sense required.

[273a.1] but the area traversed was equal to itself; therefore, it is itself finite.+ 5; We have now shown that the body which moves in a circle is not endless or infinite, but has its limit.

[273a.6] 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 there- fore motions towards contrary places. But if one of a pair

[273a.10] 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 down- ward motion, it cannot go farther than the centre. The centre, therefore, being determinate, the upper place must also bedeterminate. But if these two places are determined 1g 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 indeter- minate, the movement within it will be infinite?; and that we have already shown to be an impossibility.2 .The middle region then is determinate, and consequently any body which either is in it, or might be in it, is determinate.

[273a.20] 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 argu- ment 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 2 nr infinite body and show the difficulties involved in the consequent assumption of an infinite path and in the infinite time needed for its completion. The converse argument starts from known finite time of revolution and argues from that to the finitude of the path traversed and of the body which traverses it. ® Reading etn") Kivnots with FHMJ Simpl. 8 Phys. VIII. viii. BOOK I. 6 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 Z. £ 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 propor- tionate 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 zxzcom- mensurable the same reasoning holds. For instance, suppose £ 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 (4) we may assume weights which are com- mensurate; for it makes no difference whether we begin with the weight or with the mass. For example, assume the weight Z to be commensurate with C, and take from the infinite mass a part BD of weight &. 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 mass has its weight equally or unequally distributed. For it must always be possible to take from the infinite mass a body of equal PL BIG, Vis A G F D B = C 3° 5 ° 25 3°

[274a.1] weight to BD by diminishing or increasing the size of the section to the necessary extent.t From what we have said, then, it is clear that the weight of the infinite body cannot be finite. It must then be infinite. We have therefore only to show this to be im- possible in order to prove an infinite body impossible. But the impossibility of infinite weight can be shown in the following way. A given weight moves a given distance in a given time; a weight which is as great and more moves the same distance in a less time, the times being in inverse proportion to the weights. For instance, if one weight is twice another, it will take half as long over a given, move- ment. Further,a finite weight traverses any finite distance in a finite time. It necessarily follows from this that infinite weight, if there is such a thing, being, on the one hand, as great and more than as great as the finite,’ will move accordingly, but being, on the other hand, compelled to move in a time inversely proportionate to its greatness, cannot move at all. The time should be less in proportion as the weight is greater. But there is no proportion be- tween the infinite and the finite: proportion can only hold between a less and a greater finite time. And though you may say that the time of the movement can be continually diminished, yet there is no minimum. Nor, if there were, 1 Delete comma after BA. ? There can be no doubt that the comma should follow, not precede, kat ére (1. 5). The phrase rowdySe dcoy 1rd memepacpevoy xai Ere is parallel to the roaotroy kai ére of 273%31. Bonitz (Jad. 2917) takes cai érx in this way, but appears to interpret the phrase as indicating the distance moved, which is impossible—For the use of xat ért cf. Met. 1021 6, S Because, as explained in the following sentences, there is no time for ittomovein. The argument is: the infinite may (uév) be regarded loosely as something exceedingly great, in which case it follows simply that it moves exceedingly fast: so far there is no difficulty: but (8é) as soon as you begin to specify Aow great it is and ow fast it moves the difficulties become insuperable. * GA’ del ev eXarrove is probably an opponent's objection. It is an application of the argument mentioned in 27281. We talk of number as infinite, A. says there, because there is no maximum. Similarly the advocate of infinite weight says, ‘At any rate the weight can be increased andthe time proportionately diminished ad infinitum’. But the motion of the infinite, to be conceivable, must according to Aristotle occupy @ time; and any time, however small, will be a time in which the given movement could be effected by a finite body. ee bl BOOK I. 6 274° would it help us. For some finite body could have been found greater than the given finite in the same proportion which is supposed to hold between the infinite and the given finite ;* so that an infinite and a finite weight must have traversed an equal distance in equal time. But that is impossible. Again, whatever the time, so long as it is finite, in which the infinite performs the motion, a finite 1; weight must necessarily move a certain finite distance in that same time. Infinite weight is therefore impossible, and the same reasoning applies also to infinite lightness. Bodies then of infinite weight and of infinite lightness are equally impossible. That there is no infinite body may be shown, as we have

[274a.20] shown it, by a detailed consideration of the various cases. But it may also be shown universally, not only by such reasoning as we advanced in our discussion of principles ?- (though in that passage we have already determined univer- sally the sense in which the existence of an infinite is to be asserted or denied), but also suitably to our present purpose in the following way. That will lead us to a further question. Even if the total mass is not infinite, it may 2; yet be great enough to admit a plurality of universes, The question might possibly be raised whether there is any obstacle to our believing that there are other universes composed on the pattern of our own, more than one, though stopping short of infinity. First, however, let us treat of the infinite universally. 1 What difficulty there is in this sentence is due to the elliptical expression and to the tacit inference from a proportion between the times to a proportion between the bodies. What is known is the ratio between the imaginary minimum time assigned to the infinite body and some other finite time. A. speaks of this known ratio as a ratio between the infinite body and another body. The argument is: take any other finite body (érepov): its ratio to the infinite may be deter- mined by their respective times: but another finite body (dAdo re merrepagpévorv) could be found in the same ratio (on the basis of a comparison of times) to the first. Thus a finite body will cover the same distance as the infinite body in the same time, which is absurd.— The comma after Ady@ in 1. 11 should be deleted. jei{ov belongs to the predicate both of the relative clause and of the main sentence. Neither Simplicius nor Alexander (as reported by Simplicius) seems to have interpreted the words quite correctly. 2 Phys. ILL. iv-viii (see n. on 272% 30). Read eipyyevous with FM,

[274a.30] Every body must necessarily be either finite or infinite, 7 and if infinite, either of similar or of dissimilar parts. If its parts are dissimilar, they must represent either a finite or an infinite number of kinds. That the kinds cannot be infinite is evident, if our original presuppositions remain 274° unchallenged. For the primary movements being finite in number, the kinds of simple body are necessarily also finite, since the movement of a simple body is simple, and the simple movements are finite, and every natural body must 5 always have its proper motion. Now if! the infinite body is to be composed of a fizzte number of kinds, then each of its parts must necessarily be infinite in quantity, that is to say, the water, fire, &c., which compose it. But this is impossible, because, as we have already shown, infinite weight and lightness do not exist. Moreover it would be necessary also that their places should be infinite in extent, ro so that the movements too of all these bodies would be in- finite. But this ts not possible, if we are to hold to the truth of our original presuppositions and to the view that neither that which moves downward, nor, by the same reasoning, that which moves upward, can prolong its move- ment to infinity. For it is true in regard to quality, quantity, and place alike that any process of change is 15 impossible which can have no end. I mean that if it is im- possible for a thing to have come to be white, or a cubit long, or in Egypt, it is also impossible for it to be in process of coming to be any of these. It is thus impossible for a thing to be moving to a place at which in its motion it can never by any possibility arrive. Again, suppose the body to exist in dispersion, it may be maintained none the less that the total of all these scattered particles, say, of fire, is 20 infinite. But body we saw to be that which has exten- sion every way. How can there be several dissimilar ele- ments, each infinite? Each would have to be infinitely extended every way. It is no more conceivable, again, that the infinite should exist as a whole of szmzlar parts. For, in the first place, ? Reading elye with FHMJ. * “As Anaxagoras seems to have supposed’ (Simpl.). ld, ee Bs BOOK I. 7 274° there is no other (straight) movement beyond those men- tioned: we must therefore give it one of them. And if so, we shall have to admit either infinite weight or infinite 25 lightness. Nor, secondly, could the body whose movement is circular be infinite, since it is impossible for the infinite to move in a circle. This, indeed, would be as good as saying that the heavens are infinite, which we have shown to be impossible. Moreover, in general, it is impossible that the infinite 30 should move at all. If it did, it would move either natur- ally or by constraint: and if by constraint, it possesses also a natural motion, that is to say, there is another place, infinite like itself, to which it will move. But that is impossible.! That in general it is impossible for the infinite to be acted upon by the finite or to act upon it may be shown as follows.

[275a.1] The infinite cannot be acted upon by the finite.) Let A be an infinite, 2 a finite, C the time of a given movement produced by one in the other. Suppose, then, that A was heated, or impelled, or modified in any way, or caused to undergo any sort of movement whatever, by B in the time C. Let D be less than 8; and, assuming that a lesser agent moves a lesser patient in an equal time, call the quan- tity thus modified by D, &. Then, as D is to B,so is £ to some finite quantum. We assume that the alteration of equal by equal takes equal time, and the alteration of less by less or of greater by greater takes the same time, if the quantity of the patient is such as to keep the proportion which obtains between the agents, greater and less. If so, 0 no movement can be caused in the infinite* by any finite agent in any time whatever. For a less agent will produce that movement in a less patient in an equal time, and the proportionate equivalent of that patient will be a finite uo 1 Because an infinite place cannot exclude, or be ‘other’ than, any finite place. This argument applies to natural as well as unnatural movement : for a body moves naturally in the effort to reach its place. —Read rémos ddXos toos with EL, confirmed by Simplicius (rémos ioos G)Xos, 239, 24). ' 275° DE -CAELO quantity, since no proportion holds between finite and infinite. (2. The infinite cannot act upon the finite.) Nor, again, can

[275a.15] the infinite produce a movement in the finite in any time whatever. Let 4 be an infinite, B! a finite, C the time of action. In the time C, D will produce that motion in a patient less than B,say /. Then take £, bearing the same proportion to D as the whole BF bears to F. £ will pro- duce the motion in BF in the time C. Thus the finite and ao the infinite effect the same alteration in equal times. But this is impossible; for the assumption is that the greater effects it in a shorter time. It will be the same with any time that can be taken, so that there will be no time in which the infinite can effect this movement. And, as to infinite time, in that nothing can move another or be moved by it. For such time has no limit, while the action and reaction have. (3. There 1§ no interaction between infinites.) Nor can a5 infinite be acted upon in any way by infinite. Let A and B be infinites, CD being the time of the action of A upon B. Now the whole & was modified in a certain time, and the part of this infinite, £, cannot be so modified in the same time, since we assume that a less quantity makes the move- ment in a less time. Let & then, when acted upon by 4,

[275a.30] complete the movement in the time D. Then, as D is to CD, so is & to some finite part of B. This part will neces- sarily be moved by 4 in the time CD. For we suppose that the same agent produces a given effect on a greater 275° and a smaller mass in longer and shorter times, the times and masses varying proportionately. There is thus no finite time in which infinites can move one another. Is their time then infinite? No, for infinite time has no end, but the movement communicated has. 5 If therefore every perceptible body possesses the power of acting or of being acted upon, or both of these, it is im- possible that an infinite body should be perceptible. All bodies, however, that occupy place are perceptible. There is therefore no infinite body beyond the heaven. Nor again is there anything of limited extent beyond it. And so 1 Called BF a few lines below. ee BOOK I. 7 beyond the heaven there is no body at all. For if you suppose it an object of intelligence, it will be in a place— since place is what ‘within’ and ‘beyond’ denote—and therefore an object of perception. But nothing that is not in a place is perceptible. The question may also be examined in the light of more general considerations as follows. The infinite, considered as a whole of similar parts, cannot, on the one hand, move in acircle. For there is no centre of the infinite, and that which moves in a circle moves about the centre. Nor again can the infinite move in a straight line. For there would have to be another place infinite like itself to be the goal of its natural movement and another, equally great, for the goal of its unnatural movement. Moreover, whether its rectilinear movement is natural or constrained, in either case the force which causes its motion will have to be infinite. or infinite force is force of an infinite body, and of an infinite body the force is infinite. So the motive body also will be infinite. (The proof of this is given in our dis- cussion of movement,’ where it is shown that no finite thing possesses infinite power, and no infinite thing finite power.) If then that which moves naturally can also move unnatur- ally, there will be two infinites, one which causes, and another which exhibits the latter motion. Again, what is it that moves the infinite? If it moves itself, it must be animate. But how can it possibly be conceived as an infinite animal? And if there is something else that moves it, there will be two infinites, that which moves and that which is moved, differing in their form and power.® notes than a finished argument. The final remark seems inconsequent. We should expect: ‘but what is not perceptible cannot occupy a place’; so that the hypothesis that the body beyond the heaven is voyrév contradicts itself. The main point, however, is that all these connected attributes are inapplicable to an object of intelligence like the Platonic e/dos. 2 Phys. Ville x repetition of the preceding. The preceding sentence shows that an infinite disturbing force is needed to account for any unnatural move- ment of an infinite body. Finally, it is suggested that even the natural or normal movement of such a body would presuppose an independent infinite force. Again, the foregoing argument applied only to rectilinear If the whole is not continuous, but exists, as Democritus and Leucippus think, in the form of parts separated by void, there must necessarily be one movement of all the multitude. They are distinguished, we are told, from one

[276a.1] another by their figures; but their nature is one, like many pieces of gold separated from one another. But each piece must, as we assert, have the same motion. For a single clod moves to the same place as the whole mass of earth, and a spark to the same place as the whole mass of fire. So that if it be weight that all possess, no body is, strictly

[276a.5] speaking, light; and if lightness' be universal, none is heavy. Moreover, whatever possesses weight or ligntness will have its place either at one of the extremes or in the middle region. But this is impossible while the world is conceived as infinite. And, generally, that which has no centre or extreme limit, no up or down, gives the bodies no to place for their motion; and without that movement is impossible. A thing must move either naturally or un- naturally, and the two movements are determined by the proper and alien places. Again, a place in which a thing rests or to which it moves unnaturally, must be the natural

[276a.15] place for some other body, as experience shows. Neces- sarily, therefore, not everything possesses weight or lightness, but some things do and some do not. From these argu- ments then it is clear that the body of the universe is not infinite. We must now proceed to explain why there cannot be g more than one heaven—the further question mentioned above.” For it may be thought that we have not proved ao universally of bodies that none whatever can exist outside ° movement, since unnatural circular movement has been shown to be impossible: but the last argument would apply equally to circular movement. The remark ‘if it moves itself, it must be animate’ implies that it is incorrect to think of the natural movement of the elements as self-movement. It is only movement uninfluenced by any sublunary body. That self-movement is impossible Aristotle has already shown in PAys, VII. ? Prantl misprints «2 for e2, * In lL. 18 Prantl’s \€¢youey seems to be a misprint for \éyouer.— ‘Heaven’ here stands of course for world (odpards = xéopos).—The reference is to c. vi (274 24). BOOK I. 8 276% our universe, and that our argument applied only to those of indeterminate extent. Now all things rest and move naturally and by con- straint. A thing moves naturally to a place in which it rests without constraint, and rests naturally in a place to

[276a.25] 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 duc to constraint, its contrary is natural. If, then, it is by con- straint 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 move-

[276a.30] ment 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 276° our world. For if these names are used equivocally, if the identity of name does not rest upon an identity of form in those 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 5 centre and another towards the centre, since fire must be identical with fire, earth with earth, and so on, as the frag- ments 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 10 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 15 fire to the centre; in the same way the earth of our world and Simpl. is misleading and suggests an argument where there is none. The principle is simply stated for future use. 2 Above, cc. ii-iv. U 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 20 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? 25 One would have to suppose a difference proportionate to 3 ° 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, 1 In 1. 17 the comma which Prantl places after @vaw should be placed instead after péoor. It is needed in this place in order to show that the following clause (d:a ro... dAAnAovs) is explanatory of the avaykn of 1. 14, not of déperOa in |. 16. ® If there is one centre and one extremity, there is only one heaven or world. (Read rovrov 8 dvros, advvatoy xrd. Prantl’s arémov is found only in F and J, and in both it is preceded by rod, which shows that it is an adscript intended to explain the meaning of rovrov.)—The argument of the chapter down to this point is a single reductio ad absurdum. Simplicius tries unsuccessfully to interpret it as a series of reductions. The remainder of the chapter reasserts the conclusion here drawn by closing up various pathways of escape. In truth there is only one way of escape, as Aristotle here says, viz. to deny the identity of the fire and earth in the other worlds with that in our own; but the contention takes a variety of forms—(1) ‘distance makes a difference’; (2) ‘they have no movement, or only move by con- straint’; (3) ‘the goal of their movement is only the same z# 4imd as that of the corresponding elements here’. These suggestions are refuted in what follows. * Throughout this paragraph when Aristotle speaks of ‘the bodies’ he is thinking of the fire, earth, &c., supposed to constitute another xdgpos. He is not proving over again the proposition that the four elements have each a natural motion, but considering what would be their motion in another world existing beside our own. The empirical evidence of movement here appealed to must be that of the fire and earth of this world; but a thing that did not move would not be a body at all. 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 sug- gested that the goal in each case is one in form but

[277a.1] 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

[277a.5] 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

[277a.10] present assumptions 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

[277a.15] 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-point—and therefore the starting-point and the goal,of the natural movement must differ in form—just as the movement of

[277a.20] coming to health does not take any direction which chance none but a ‘numerical’ difference can be postulated between the portions (e.g. of earth) in this world and those in another, and since a difference of goal can only be justified by a difference in the body, we should have to suppose a distinct goal for every single portion of earth; which is absurd. "2 A full-stop, rather than a comma, is needed after peraBoAy in |. 16. Three principles are laid down and all are illustrated in the case of locomotion. But the instances of health and increase are used only to illustrate the first. ; 25 30 Pye? or the wishes of the mover may select.1_ 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 light- ness. For as superior speed in downward movement implies superior weight, so infinite increase of weight neces- sitates 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 1 }]. 18-19, the full-stop after wot should be deleted, and the words det dpa. . . pepecOat should be marked as a parenthesis. Locomotion, like healing, has a determinate direction, and that involves a difference of form between its two terms. ? The remarks which follow concerning circular motion are a kind of footnote and would be best marked as a parenthesis. ° In l. 29 it is tempting to read e/ & eis detpov jw for ei 8° darecpov Fr, but no evidence of such a reading survives. The sense of the para- graph is plain. We observe an increase of speed in a falling body as it approaches the earth. The explanation, on our view, is the proximity of the goal. But if there is no goal, the movement, and with it the increase of speed, is capable of continuing to infinity. But infinite speed means infinite weight, which has already (c. vi) been proved impossible. ‘The Greek of the last sentence is puzzling and may be corrupt. Accepting the text of Bekker and Prantl, we must translate as follows: ‘as that which by reason of speed is lower than another body would be presumed speedy by reason of weight, so if there were infinite increase of weight there would also be infinite increase of speed.’ (The alteration of an accent is required: Bdpe for Bapet in 1. 32.) The sentence is clumsy, but it gives the required sense. Simplicius seems to have interpreted the passage as above. In]. 31 érepov is found in F alone, all the other MSS. giving érepo»; but €répov must be right. * The atomists, Leucippus and Democritus. BOOK I. 8 ayy? is the reverse: the greater the mass of fire or earth the quicker always is its movement towards its own place. s 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 10 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 con- siderations 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 15 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 the place of the body endowed with 20 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 fur-

[277a.25] ther, in general, how many in number the various places are. Ve ee ~*~. g We must show not only that the heaven is one,’ but also that more than one heaven is impossible, and, further, 1 j,e. Metaphysics. Cf. Met. A. 8. 2 Prantl misprints els for «fs. For otpav’s read 6 ovpavds with M. J, like EHL, omits the word odpavds altogether. that, as exempt from decay and generation, the heaven is eternal. We may begin by raising a difficulty. From 3c 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. 278° 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, 5 because they do not belong to the essence, but if we are speaking of the copper or gold sphere we do in- clude 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 Jess the difference will remain between the being of circle and of this particular circle, the one being form, the other form in matter, 10 i.e. a particular thing. Now since the universe is per- ceptible it must be regarded as a particular; for every- thing 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 15 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 like form are several or infinite in 20 number. Hence there either are, or may be, more heavens * More correctly: that the heaven should be ecessarily one and unique. The argument here set out only attempts to prove the possibility of more than one world, and Aristotle replies by proving the impossibility of more than one. Alexander (cited by Simpl.) points out this defect in the statement. i it ae

[278a.1] than one.! On these grounds, then, it might be inferred either that there are or that there might be several heavens. We must, however, return and ask how much of this argu- ment is correct and how much not. Now it is quite right to say that the formula of the shape apart from the matter must be different from that

[278a.25] of the shape in the matter, and we may allow this to be true. We are not, however, therefore compelled to assert a plurality of worlds. Such a plurality is in fact impossible if this world contains the entirety of matter, as in fact it does. But perhaps our contention can be made clearer in this way. Suppose ‘aquilinity’ to be curvature in the

[278a.30] nose or flesh, and flesh to be the matter of aquilinity. Suppose, further, that all flesh came together into a single whole of flesh endowed with this aquiline quality. Then neither would there be, nor could there arise, any other thing that was aquiline. Similarly, suppose flesh and bones to be the matter of man, and suppose a man to be created

[278a.35] of all flesh and all bones in indissoluble union. The possibility of another man would be removed. Whatever case you took it would be the same. The general rule 278° is this: a thing whose essence resides in a substratum of matter can never come into being in the absence of all matter.2, Now the universe is certainly a particular and a material thing: if however it is composed not of a part but of the whole of matter, then though the being 5 of ‘universe’ and of ‘this universe’ are still distinct, yet there is no other universe, and no possibility of others being made, because all the matter is already included in this. It remains, then, only to prove that it is composed of all natural perceptible body. First, however, we must explain what we mean by ‘heaven’ 10 and in how many senses we use the word, in order to make clearer the object of our inquiry. (a) In one sense, then, we call J has it. But the article does not seem to be required here. In corresponding passages in this chapter it is omitted. All the other MSS., as well as Simpl., have ruv’s dAns, and E is full of small omissions. ‘heaven’ the substance of the extreme circumference of the whole, or that natural body whose place is at the extreme circumference. We recognize habitually a special right to 15 the name ‘ heaven’ in the extremity or upper region, which we take to be the seat of all that is divine.’ (6) In another sense, we use this name for the body continuous with the extreme circumference, which contains the moon, the sun, and some of the stars; these we say are ‘in the heaven’. (c) In yet another sense we give the name to all body 20 included within the extreme circumference, since we habi- tually call the whole or totality ‘the heaven’. The word, then, is used in three senses. Now the whole included within the extreme circumference must be composed of a// physical and sensible body, because there neither is, nor can come into being, any body outside 25 the heaven. For if there is a natural body outside the extreme circumference it must be either a simple or a com- posite body, and its position must be either natural or unnatural. But it cannot be any of the simple bodies. For, first, it has been shown? that that which moves in a circle 30 cannot change its place. And, secondly, it cannot be that which moves from the centre or that which lies lowest. Naturally they could not be there, since their proper places are elsewhere; and if these are there unnaturally, the exterior place will be natural to some other body, since a place which is unnatural to one body must be natural to another: but we saw that there is no other body besides 35 these.* Then it is not possible that any simple body should

[279a.1] be outside the heaven. But, if no simple body, neither can any mixed body be there: for the presence of the simple body is involved in the presence of the mixture. Further neither can any body come into that place: for it will do so either naturally or unnaturally, and will be either simple

[279a.5] or composite; so that the same argument will apply, since it makes no difference whether the question is ‘does A UVIEXES. * Read 16 pev yap. The pév is wanted, and is omitted by E alone. The reference is to cc. ii and iii above. “ c. 11 above. BOOK I. 9 279" exist?’ or ‘could A come to exist?’ From our arguments then it is evident not only that there is not, but also that there could never come to be, any bodily mass whatever outside the circumference. The world asa whole, therefore, includes all its appropriate matter, which is, as we saw, natural perceptible body. So that neither are there now, nor have

[279a.10] r there ever been, nor can there ever be formed more heavens than one, but this heaven of ours is one and unique and complete. It is therefore evident that there is also no place or void or time outside the heaven. For in every place body can be present ; and void is said to be that in which the presence

[279a.15] of body, though not actual, is possible; and time is the number of movement. But in the absence of natural body there is no movement, and outside the heaven, as we have shown, body neither exists nor can come to exist. It is clear then that there is neither place, nor void, nor time, outside the heaven. Hence whatever is there, is of such a nature as not to occupy any place, nor does time age it;

[279a.20] nor is there any change in any of the things which lie beyond the outermost motion; they continue through their entire duration unalterable and unmodified, living the best and most self-sufficient of lives. As a matter of fact, this word ‘duration’ possessed a divine significance for the ancients, for the fulfilment which includes the period of life of any creature, outside of which no natural development can fall,

[279a.25] has been called its duration. On the same principle the fulfilment of the whole heaven, the fulfilment which includes all time and infinity, is ‘duration’—a name based upon the fact that it zs always'—duration immortal and divine. From it derive the being and life which other things,

[279a.30] some more or less articulately but others feebly, enjoy. So, too, in its discussions concerning the divine, popular philosophy? often propounds the view that whatever is - F i b 9 2 Aristotle refers apparently under this name to elementary hand- books of philosophy current among his audience. It is usual to identify them with the ééwrepixol Adyor, as Simpl. does in his com- mentary on this passage. See Bonitz, /md, Ar, S.v. "ApiororeAns, 105° 27. divine, whatever is primary and supreme, is necessarily unchangeable. This fact confirms what we have said. For there is nothing else stronger than it to move it—

[279a.35] since that would mean more divine—and it has no defect 279° and lacks none of its proper excellences. Its unceasing movement, then, is also reasonable, since everything ceases to move when it comes to its proper place, but the body whose path is the circle has one and the same place for starting-point and goal. Having established these distinctions, we may now pro- IO 5 ceed to the question whether the heaven is ungenerated or generated, indestructible or destructible. Let us start with a review of the theories of other thinkers; for the proofs of a theory are difficulties for the contrary theory.* Besides, those who have first heard the pleas of our, adversaries will be more likely to credit the assertions 1o which we are going to make. We shall be less open to the charge of procuring judgement by default. To give a satisfactory decision as to the truth it is necessary to be rather an arbitrator than a party to the dispute. That the world was generated all are agreed, but, genera- tion over, some say that it is eternal, others say that it is destructible like any other natural formation.2 Others 15 again, with Empedocles of Acragas and Heraclitus of Ephesus, believe that there is alternation in the destructive process, which takes now this direction, now that, and continues without end.® 1 Prantl misprints riv evavriwy for rav evavriwy in |. 6. * The former view, according to Alexander (af. Simpl.), is that of Orpheus (i.e. of Orphic cosmogony), Hesiod, and Plato, while the latter is that of Democritus and his school. * Cf. Burnet, E.G.P.° p. 157 (§ 77). Heraclitus“and Empedocles are agreed in believing in periodic changes in the constitution of our world as a whole. For both, the world exists, as it were, in a succession of lives (below, 280814); and the view is a kind of compromise between that which regards it as eternal and that which gives it a single life ended by annihilation. The phrase ‘alternation in the destructive process’ is somewhat inaccurate, since the alternation may be described as between generation and destruction (Empedocles’ Love and Strife, Stoic diaxdopnois and exmipwcis). But it is intelligible. Aristotle is here classing the theory for convenience with those that hold to a destructible world, and the antithesis is between destruction dm\@s and destruction with alternation. Later he explains that this BOOK I. to 279° Now to assert that it was generated and yet is eternal is to assert the impossible ; for we cannot reasonably attribute to anything any characteristics but those which observation detects in many or all instances. But in this case the facts 20 point the other way: generated things are seen always to be destroyed. Further, a thing whose present state had no beginning and which could not have been other than it was at any previous moment throughout its entire duration, cannot possibly be changed.! For there will have to be some cause of change, and if this had been present earlier it would have made possible another condition of that to which any other condition was impossible. Suppose that the world was formed out of elements which were formerly otherwise conditioned than as they are now. Then (1) if their condition was always so and could not have been otherwise, the world could never have come into being.? And (2) if the world did come into being, then, clearly, their condition must have been capable of change and not eternal: after combination therefore they will be dispersed, just as in the past after dispersion they came into combination, and this process either has been, or could have been, indefinitely repeated. But if this is so, 30 the world cannot be indestructible, and it does not matter whether the change of condition has actually occurred or remains a possibility. Some of those who hold that the world, though in- destructible, was yet generated, try to support their case by a parallel which is illusory. They say that in their statements about its generation they are doing what geometricians do when they construct their figures, not 35 implying that the universe really had a beginning, but , bw alternation is not @Oopa at all. Lurnet in his first edition proposed to excise POeipdpevov, but the suggestion is now tacitly retracted. In his later editions Burnet wrongly states that what is here in question is the eternity of the first heaven. That has already been proved in c. iii, and the first heaven would not be referred to as 6 KOopos, 1 A comma is required after aléva in 1. 22, unless the comma after éxew in the preceding line is deleted. demands a comma, rather than a full-stop, after éyévero. $ Simpl. refers the following argument to Xenocrates and the Platonists.

[280a.1] for didactic reasons facilitating understanding by exhibiting 5 the object, like the figure, as in course of formation. The two cases, as we said, are not parallel; for, in the construc- tion of the figure, when the various steps are completed the required figure forthwith results; but in these other demonstrations what results is not that which was required.! Indeed it cannot be so; for antecedent and consequent, as assumed, are in contradiction. The ordered, it is said,? arose out of the unordered; and the same thing cannot be at the same time both ordered and unordered; there must be a process and a lapse of time separating the two

[280a.10] states. In the figure, on the other hand, there is no temporal separation.? It is clear then that the universe cannot be at once eternal and generated. To say that the universe alternately combines and dissolves is no more paradoxical than to make it eternal but vary- ing in shape. It is as if one were to think that there was now

[280a.15] destruction and now existence when from a child a man is 2 ° generated, and froma manachild. For it is clear that when the elements come together the result is not a chance system and combination, but the very same as before—especially on the view of those who hold this theory, since they say that the contrary is the cause of each state. So that if the totality of body, which is a continuum, is now in this order or disposition and now in that, and if the combination of the whole is a world or heaven, then it will not be the world that comes into being and is destroyed, but only its dispositions. If the world is believed to be one, it is impossible to construction, but these cosmogonists cannot. The figure, or world, constructed should be ‘the same’ (ré airé) as that demanded in the UndGeots. 2 Cp. Plato, Ztmaeus 30 A. * The construction of the cosmogonist cannot be a mere didactic device like that of the geometrician; for the attributes successively assumed in the construction of the world cannot exist simultaneously iis those assumed by the geometrician do. * Here Aristotle clearly refers to Empedocles, rather than to Heraclitus. The two causes of Empedocles are Love and Strife (fsXia and veixos), and since these are two it follows, Aristotle argues, that the world would merely oscillate between two arrangements or dispositions. a BOOK I. 10 i. ew II suppose that it should be, as a whole, first generated and then destroyed, never to reappear; since before it came into being there was always present the combination prior to it, and that, we hold, could never change if it was never generated. If, on the other hand, the worlds are infinite in number the view is more plausible. But whether this is, or is not, impossible will be clear from what follows. For there are some who think it possible both for the ungenerated to be destroyed and for the generated to persist undestroyed.t (This is held in the Zimaeus,? where Plato says that the heaven, though it was generated, will none the less exist to eternity.) So far as the heaven is concerned we have answered this view with arguments appropriate to the nature of the heaven: on the general question we shall attain clearness when we examine the matter universally. i or We must first distinguish the senses in which we use the 280° words ‘ungenerated’ and ‘generated’, ‘destructible’ and ‘indestructible .4 These have many meanings, and though 1 In ]. 29 Prantl misprints xpi for kai. ? A colon instead of a full-stop is needed after Tiwaiw. The reference is to Plato, Zzmaeus 31. Plato is quoted as authority for the in- destructible-generated not for the ungenerated-destructible, as the context shows. ‘ungenerated ’, ‘ destructible’, ‘indestructible’, which have so far been considered only in their application to the heaven. The terms are discussed universally, i.e. apart from any special application, in cc. xiand xii. The combination attributed to Plato is refuted at the end of that discussion (2831 ff.). Simplicius found the argument of the last paragraph of this chapter (Il. 23 ff.) somewhat obscure. It deals, provisionally and subject to further investigation, with the view that the world is subject both to generation and to destruction in the sense in which the man Socrates is. Simpl. is probably right in supposing that under this head Aristotle is thinking of the atomists. Their infinite worlds were successive, if also co-existent. Aristotle here argues that if that out of which the world was formed had the capacity to give birth to a world, then that into which the world is destroyed will have the same capacity. Thus the theory of world- annihilation is dismissed as absurd, while the infinite succession of destructible worlds is left open. But the refutation even of the first of these views, and therefore a fortiori of the second, cannot be regarded as complete until the whole problem of generation and destruction has been examined. similar grammatical forms as the Greek yevnrés and Oaprds are. But from the analysis given by Aristotle it will be seen that in meaning the Greek verbal adjective tends to approximate to the past it may make no difference to the argument, yet some con- fusion of mind must result from treating as uniform in its suse a word which has several distinct applications. The character which is the ground of the predication will always remain obscure. The word ‘ungenerated’ then is used (a) in one sense whenever something now is. which formerly was not, no process of becoming or change being involved. Such is the case, according to some, with contact and motion, since there is no process of coming to be in contact or in motion. (2) It is used in another sense, when something which is 10 capable of coming to be, with or without process, does not exist; such a thing is ungenerated in the sense that its generation is not a fact but a possibility. (c) It is also applied where there is general impossibility of any generation such that the thing now is which then was not. And ‘im- possibility’ has two uses: first, where it is untrue to say that the thing can ever come into being, and secondly, where it cannot do so easily, quickly, or well. In the 1g same way the word ‘generated’ is used, (a) first, where what formerly was not afterwards is, whether a process of becoming was or was not involved, so long as that which then was not, now is; (4) secondly, of anything capable of existing, ‘capable’ being defined with reference either to truth or to facility ; (c) thirdly, of anything to which the passage from not being to being belongs,! whether already actual, if its existence is due to a past process of becoming,

[280a.20] or not yet actual but only possible. The uses of the words ‘destructible’ and ‘indestructible’ are similar. ‘ Destruc- tible’ is applied (a2) to that which formerly was and after- wards either is not or might not be, whether a period of being destroyed and changed intervenes or not ;* and (6) participle, and therefore it is not worth while to insist on ‘generable’, ‘ungenerable’ for yevnrds, ayévnros. 1 For éeav 4 yéveows read éav 9 yeveots. (M has 9 4, but all other MSS. have 7.) The correction was suggested by Hayduck (Greifs- wald Gymnasium Program, 1871, p. 11). * The evidence afforded by Simpl. and the MSS., together with the difficulty of establishing a precise correspondence between this defini- tion of @aprév and the parallel uses of ‘ungenerated’ (4) and ‘generated’ (a), might lead one to doubt the soundness of the text - this point; but it is guaranteed by Aristotle’s own citation at 281) 27, BOOK Lu 280° Sometimes we apply the word to that which a process of destruction may cause not to be; and also (c) in a third

[280a.25] sense, to that which is easily destructible, to the ‘easily- destroyed’, so to speak.! Of the indestructible the same account holds good. It is either (2) that which now is and now is not, without any process of destruction, like contact, which without being destroyed afterwards is not, though formerly it was; or () that which is but might not be, or which will at some time not be, though it now is.2, For you

[280a.30] exist now and so does the contact ; yet both are destructible, because a time will come when it will not be true of you that you exist, nor of these things that they are in contact. Thirdly (c) in its most proper use, it is that which is, but is incapable of any destruction such that the thing which now is later ceases to be or might cease to be; or again, that which has not yet been destroyed, but in the future may

[281a.1] cease to be. For indestructible is also used of that which is destroyed with difficulty. 1 Aristotle carelessly omits to mention the other and more exact kind of possibility. Cf. ‘ungenerated’ (c) and ‘generated’ (4). ? The third # (in ]. 29) is not coordinate with the two which precede it (ll. 26, 28), and it would be well to mark this by putting a colon instead of a comma after «iaiy in 1.28. Simplicius read # kal ovx in 1. 29, and the addition of xai would be an improvement. which Prantl’s note attributes to Simplicius is found only in one inferior MS. and is not printed in Heiberg’s text of the commentary. J also has no word between ¢Péappévoy and évdexcpevov, nor had Alexander. * Read Aéyerat yap for d€éyerat 8¢, and place a colon instead of a full- stop before Aéyerat. This alteration is conjectural, but it is preferable to Hayduck’s excision of # kal... elva: (Il. 33, 34), and without some alteration the Greek will not give a satisfactory sense. The account given of ‘indestructible’ is closely parallel to that given of ‘un- generated’ above. Sense (a) of ‘indestructible’ (Il. 26-28) turns on the absence of process, like sense (a) of ‘ ungenerated’, even repeating the same instance, touch. In sense (4) (ll. 28-31) ‘indestructible’ covers all that has not been destroyed, as ‘ungenerated’ in sense (4) covers what has not yet come into being: as ‘ungenerated’ includes all possible existents which are now non-existent, so ‘indestructible’ includes all possible non-existents which are now existent. There remains the third and proper sense, viz. potentiality or possibility, subdivided in the case of ‘ungenerated’, according to an ambiguity in the word possible, into (i) strict and final impossibility (r@ adnbes eva eimeiv), (ii) popular or ‘practical’ impossibility (re 47 padios pnde tax 4 xadds). The third sense of ‘indestructible’ is introduced by ro 8€ padtora xvpiws in |. 31, and its subdivision a is effected by # xai in 1. 33. The words before #) xai assert the final 5 10 15 20 This being so, we must ask what we mean by ‘ possible’ and ‘impossible’. For in its most proper use the predicate ‘indestructible’ is given because it is impossible that the thing should be destroyed, i.e. exist at one time and not at another. And ‘ungenerated’ also involves impossibility when used for that which cannot be generated, in such fashion that, while formerly it was not, later it is. An in- stance is a commensurable diagonal. Now when we speak of a power! to move? or to lift weights, we refer always to the maximum. We speak, for instance, of a power to lift a hundred talents or walk a hundred stades—though a power to effect the maximum is also a power to effect any part of the maximum—-since we feel obliged in defining the power to give the limit or maximum. A thing, then, which is capable of a certain amount as maximum must also be capable of that which lies within it. If, for example, a man can lift a hundred talents, he can also lift two, and if he can walk a hundred stades, he can also walk two. But the power is of the maximum, and a thing said, with reference to its maximum,® to be incapable of so much is also in- capable of any greater amount. It is, for instance, clear that a person who cannot walk a thousand stades will also be unable to walk a thousand and one. This point need not trouble us, for we may take it as settled that what is, in the strict sense, possible is determined by a limiting maxi- mum. Now perhaps the objection might be raised that removal of the possibility of non-existence, and the following clause relaxes the requirement as popular use demands. Even if the possi- bility of destruction has not been finally removed, a thing may be called ‘indestructible’ in this sense if it has not been destroyed. By calling this the proper sense, whether in its stricter or more popular use, Aristotle must mean that the verbal adjective in -ros should not in precise speech be allowed to approximate, as it often does, to a past participle passive. (Simplicius’s interpretation of this passage is quite inadmissible, but he was confused by faulty MSS.) 1 Power’ (Svvauis) must be taken throughout as the noun corre- sponding to the adiective ‘ possible’ (Svvurdy). * The MSS. have xun@nvac orddia éxatéy (‘to move a hundred stades’). The translation omits the reference to distance, which seems clearly out of place. The words orddia éxarév, which occur more than once in the context, probably got their place in this clause through a copyist’s mistake: * Prantl misprints brepBadny for imepBorjv. BOOK I. 1 281° there is no necessity in this, since he who sees a stade need 2; not see the smaller measures contained in it, while, on the contrary, he who can see a dot or hear a small sound will perceive what is greater. This, however, does not touch our argument. The maximum may be determined either in the power or in its object.1. The application of this is plain. Superior sight is sight of the smaller body, but superior speed is that of the greater body. I2 Having established these distinctions we can now proceed to the sequel. If there are things capable both of being and of not being, there must be some definite maximum

[281a.30] time of their being and not being ; a time, I mean, during which continued existence is possible to them and a time during which continued non-existence is possible. And this is true in every category, whether the thing is, for ex- ample, ‘ man’, or ‘ white’, or ‘three cubits long’, or whatever it may be. For if the time is not definite in quantity, but longer than any that can be suggested and shorter than none, then it will be possible for one and the same thing to 281° exist for infinite time and not to exist for another infinity. This, however, is impossible. Let us take our start from this point. The impossible and the false have not the same significance. One use of ‘impossible’ and ‘ possible’, and ‘ false’ and ‘true’, is hypo- 5 thetical. It is impossible, for instance, on a certain hypothesis that the triangle should have its angles equal to two right angles, and on another the diagonal is commen- surable. But there are also things possible and impossible, false and true, absolutely. Now it is one thing to be abso- lutely false, and another thing to be absolutely impossible. To say that you are standing when you are not standing is to assert a falsehood, but not an impossibility. Similarly ° 1 j,e. sometimes the maximum is an actual maximum (determined ‘in the object’, éi 100 mpdyparos), e.g. in the case of weight-lifting, where the largest weight lifted serves to define the power; sometimes it is an actual minimum, determined as maximum ‘in the power’ (¢mi rns duvduews), e.g. in the case of vision, where the smallest object seen serves to define the capacity. Cf the distinction between the pecoy Tov mpdyparos (or xara rd mpaypa) and the péoov mpds jas in Eth. Nic. 11068 26 ff. x to say that a man who is playing the harp, but not singing, is singing, is to say what is false but not impossible. To say, however, that you are at once standing and sitting, or that the diagonal is commensurable, is to say what is not only false but also impossible. Thus it is not the same thing to make a false and to make an impossible hypothesis ; 15 and from the impossible hypothesis impossible results follow. 2 3 fo} om ° A man has, it is true, the capacity at once of sitting and of standing, because when he possesses the one he also possesses the other; but it does not follow that he can at once sit and stand, only that at another time he can do the other also. But? if a thing has for infinite time more than one capacity, another time is impossible and the times must coincide. Thus if anything which exists for infinite time is destructible, it will have the capacity of not being. Now if it exists for infinite time let this capacity be actualized ; and it will be in actuality at once existent and non-existent. Thus a false conclusion would follow because a false assump- tion was made, but if what was assumed had not been impossible its consequence would not have been- im- possible.* Anything then which always exists is absolutely im- perishable. It is also ungenerated, since if it was generated it will have the power for some time of not being. For as that which formerly was, but now is not, or is capable at some future time of not being, is destructible, so that which is capable of formerly not having been is generated.6 But in the case of that which always is, there is no time for such a capacity of not being, whether the supposed time is finite Cf. Anal. Prior. 34°1 ff. for this distinction. There should be a colon rather than a full-stop after @dvvarov. The production of like consequences is of course not peculiar to the impossible hypothesis : it applies equally to the false hypothesis. See Zoc. cit. ? Read ef d€ with FHMJ for «i 57. There is- no semblance of inference. Simplicius makes the connexion antithetical. * For éora read éorw with all MSS. (except E) and Simpl. The py elvat Which follows dvvarae in FHMJ must have been a copyist’s mistake. ° The words are taken in their ‘most proper ’ sense, as the qualifica- tion ‘absolutely’ in 1. 25 suggests; viz. as conveying a strict and demonstrable possibility or impossibility. See foregoing chapter. BOOK I. 12 281” or infinite ; for its capacity of being must include the finite time since it covers infinite time. It is therefore impossible that one and the same thing _ should be capable of always existing and of always not- existing? And ‘not always existing’, the contradictory, is also excluded. Thus it is impossible for a thing always to

[282a.1] exist and yet to be destructible. Nor, similarly, can it be _ generated. For of two attributes if B cannot be present without A, the impossibility of A proves the impossibility of B. What always is, then, since it is incapable of ever not being, cannot possibly be generated. But since the

[282a.5] contradictory of ‘ that which is always capable of being’ is ‘that which is not always capable of being’; while ‘that which is always capable of not being’ is the contrary, whose contradictory in turn is ‘that which is not always capable of not being’, it is necessary that the contradictories of both terms should be predicable of one and the same thing, and thus that, intermediate between what always is and what always is not, there should be that to which being

[282a.10] and not-being are both possible; for the contradictory of each will at times be true of it unless it always exists, Hence that which not always is not will sometimes be and sometimes not be; and it is clear that this is true also of that which cannot always be but sometimes is and therefore sometimes is not. One thing, then, will have the power of being and of not being, and will thus be intermediate _ between the other two. Expressed universally our argument is as follows. Let there be two attributes, A and J&, not capable of being present in any one thing together, while either A or C and j 4 a 5 1 In 1. 29 after jy) eva a full-stop is required instead of a comma. The construction of the following clauses is difficult. The translation given above proceeds on the hypothesis that no stop is required after det dv (1. 30) and that duvardv... dore pu) elva is equivalent to duvardy py eva. I cannot find another case of dvvardv Sore, but similar uses of Scare are fairly common in Aristotle (see Bonitz, /md. Ar., p. 873° 20). ovr’ tiretpov obre memepacpévoy (SC. ypdvov) is a loose epexegesis of ovK gorw év & xpdve, and perhaps should be preceded by a comma. 2 Kal del pt elva is the reading of FJ Simpl. Since the omission of dei in the other MSS. is easily accounted for, it seems best to accept this. (J at the first attempt omitted the kai.) 20 2 or [e} either B or D are capable of being present in everything. Then C and D must be predicated of everything of which neither A nor B is predicated. Let £ lie between A and B; for that which is neither of two contraries is a mean between them. In £ both C and D must be present, for either A or C is present everywhere and therefore in £. Since then A is impossible, C must be present, and the same argument holds of D.! Neither that which always is, therefore, nor that which always is not is either generated or destructible. And clearly whatever is generated or destructible is not eternal. Ifit were, it would be at once capable of always being and capable of not always being, but it has already been shown ® that this is impossible. Surely then whatever is ungenerated and in being must be eternal, and whatever is indestructible and in being must equally be so. (I use the words ‘ungen- erated’ and ‘indestructible’ in their proper sense, ‘un- generated’ for that which now is and could not at any previous time have been truly said not to be; ‘indestruc- tible’ for that which now is and cannot at any future time be truly said not to be.*) If, again, the two terms are coincident,° if the ungenerated is indestructible, and the in- destructible ungenerated, then each of them is coincident which is always capable of being’ = ‘what always is’, B is its contrary, ‘that which is always capable of not being’= ‘ what always is not’, C is its contradictory, ‘that which is not always capable of being’, and D is the contradictory of 2, ‘that which is not always capable of not being’. Cand JY might also be described by the terms ‘what not always is’ and ‘what not always is not’ respectively. * 28118 ff. * The question-mark should come at the end of the line after dy dé, preceded by a comma at eirat. * i.e. each term has its third sense as defined in chapter xi (280) 11, 31). ° The term ‘coincidence’ is used in this passage to express the mutual involution (called by later writers dvraxodovbia) of predicates. This mutual involution is here described by Aristotle in terms which mean that the two terms ‘follow’ or ‘accompany’ one another. But later on (e.g. in 282 10, 27, 32) he frequently says simply that one predicate ‘follows’ another when he means that the two terms are mutually involved. To avoid confusion I have expressed the relation in terms of coincidence throughout.—The # following the parenthesis introduces an alternative proof to the same effect as that which preceded the parenthesis. BOOK I. 12 282° with ‘eternal’; anything ungenerated is eternal and anything 282° indestructible is eternal. This is clear too from the defini- tion of the terms. Whatever is destructible must be generated ; for it is either ungenerated or generated, but, if ungenerated, it is by hypothesis! indestructible. Whatever, _ further, is generated must be destructible. For it is either _ destructible or indestructible, but, if indestructible, it is by 5 hypothesis ' ungenerated. If, however, ‘indestructible’ and ‘ungenerated’ are not coincident, there is no necessity that either the ungenerated or the indestructible should be eternal. But they must be coincident, for the following reasons. The terms ‘ gener- ated’ and ‘destructible’ are coincident; this is obvious from our former remarks, since between what always is and 10 what always is not there 1s an intermediate which is neither, and that intermediate is the generated and destructible. For whatever is either of these is capable both of being and of not being for a definite time: in either case, I mean, there is a certain period of time during which the thing is and another during which it is not. Anything therefore

[282a.15] which is generated or destructible must be intermediate. Now let A be that which always is and ZB that which always is not, C the generated, and YP the destructible. Then C must be intermediate between A and &. For in their case there is no time in the direction of either limit,? in which either A is not or # is. But for the generated 1 281>25 ff. But Aristotle proceeds to give a proof of the mutual involution of these terms. If the destructible is generated and the generated is destructible, it follows that the ungenerated is eternal and the indestructible is eternal, and this is the thesis set out for proof in 28225. But the proof here given of the antecedent depends on the assumption that ‘ungenerated’ and ‘indestructible’ are coincident, which assumption is now proved. Aristotle’s procedure, however, is needlessly complicated. Having proved the coincidence of ‘ generated’ and ‘destructible’ by assuming the coincidence of ‘ungenerated’ and ‘indestructible’, he now proves the coincidence of the latter by proving (on other lines) the coincidence of the former. 2 ij, e., in effect, ‘neither in the past nor in the future’. But time, of course, has no limit. The notion of limit is transferred to the in- destructible-ungenerated from the destructible-generated. The being of the latter class is necessarily limited in both directions, by birth on one side and death on the other, and the same terms limit its not- being. These two limits of finite existence are used to describe the two directions of infinite existence.

[282a.20] there must be such a time either actually or potentially, though not for A and B in either way. C then will be, and also not be, for a limited length of time, and this is true also of D, the destructible. Therefore each is both generated and destructible. Therefore ‘generated’ and ‘ destruc- tible’ are coincident. Now let & stand for the ungenerated,

[282a.25] F for the generated, G for the indestructible, and H for the destructible. As for F and H, it has been shown that they are coincident. But when terms stand to one another as these do, F and H coincident, £ and F never predicated of the same thing but one or other of everything, and G and H \ikewise, then & and G must needs be coincident. For suppose that £& is not coincident with G, then F will be, since either £ or F is predicable of everything. But of that of which F is predicated #7 will be predicable also. A will

[283a.1] then be coincident with G, but this we saw to be impossible. And the same argument shows that G is coincident with £. Now the relation of the ungenerated (£) to the generated (F) is the same as that of the indestructible (G) to the de- structible (47). To say then that there is no reason why anything should not be generated and yet indestructible or ungenerated and yet destroyed, to imagine that in the one case generation and in the other case destruction occurs once for all, is to destroy part of the data.’ For (1) every- thing is capable of acting or being acted upon, of being or not being, either for an infinite, or for a definitely limited space of time; and the infinite time is only a possible alter- native because it is after a fashion defined, as a length of time which cannot be exceeded. But infinity in one direction is neither infinite nor finite, (2) Further, why, after always existing, was the thing destroyed, why, after an infinity of not being, was it generated, at one moment rather than another? If every moment is alike and the moments are infinite in number, it is clear that a generated or destructible thing existed for an infinite time. It has ° 3 om ° ’ Aristotle now proceeds to apply h's results to the refutation of the view attributed in 280% 30 to Plato’s Zimaeus. He there promised to give a clearer demonstration of its absurdity when the terms ‘generated’, ‘ungenerated’, &c. should be investigated on their own account and apart from the special case of the heaven.

[283a.12] BOOK I, _ therefore for an infinite time the capacity of not being ; ‘ i q , (since the capacity of being and the capacity of not being , will be present together), if destructible, in the time before destruction, if generated, in the time after generation. If then we assume the two capacities to be actualized, oppo- sites will be present together.2 (3) Further, this second capacity will be present like the first at every moment, so that the thing will have for an infinite time the capacity both of being and of not being; but this has been shown to be impossible. (4) Again, if the capacity is present prior to the activity, it will be present for all time, even while the thing was as yet ungenerated and non-existent, throughout the infinite time in which it was capable of being generated. At the time, then, when it was not, at that same time it had the capacity of being, both of being then and of being there- after, and therefore for an infinity of time. It is clear also on other grounds that it is impossible that the destructible should not at some time be destroyed. For otherwise it will always be at once destructible and in actuality indestructible,°® so that it will be at the same time ro pev, ro 6€ which follow explain the clause which precedes them. They should be enclosed in brackets and the colon after xpévoyr deleted. follows: & 8tvaras FM Simpl., 4 dvvavrac EL, adivara HJ. Bekker prints the last, though attested by only one of his MSS. arrives at an adsurdum by actualizing the capacity, while the third points out that the co-presence of two such capacities has already been admitted to be impossible. Cf. 28245, ‘that which is always capable of being’ is the contrary of ‘that which is always capable of not being’. Alexander seems to have maintained that our third argu- ment was not a distinct argument at all; but the short account of his view given by Simpl. is not convincing. 4 A colon is required after Uorepov. Aristotle is proving that the capacity was present for infinite time, which in argument (3) he assumed as evident without proof. 5 Prantl’s note as to the reading in 1. 26 is inaccurate. ‘The words kat dpOaproy (not cai POaprdv) were lacking in the MSS. used both by Alexander and by Simpl.; and they interpreted the sentence without those words to mean—‘it will be at once eternal and in actuality destructible’; but ‘in actuality destructible’ means ‘destroyed’, and therefore the assertion is not justified by the context. Alex., how- ever, suggested the insertion of the words xai dp@aprov, and Simpl. says he ‘has come across’ a manuscript in which the words are found. kai 4pOaproy seems to have been added to E upon revision, but all our other MSS. have the words, and it is best to retain them in the text. 15 we or capable of always existing and of not always existing. Thus the destructible is at some time actually destroyed. The generable, similarly, has been generated, for it is capable of having been generated and thus also of not always existing.’

[283a.30] We may also see in the following way how impossible it is either for a thing which is generated to be thenceforward indestructible, or for a thing which is ungenerated and has always hitherto existed to be destroyed. Nothing thatis by chance can be indestructible or ungenerated, since the pro- 283” ducts of chance and fortune are opposed to what is, or comes to be, always or usually, while anything which exists for a time infinite either absolutely or in one direction, is in exist- ence either always or usually. That which is by chance, then, is by nature such as to exist at one time and not at another. But in things of that character the contradictory states 5 proceed from one and the same capacity, the matter of the thing being the cause equally of its existence and of its non- existence. Hence contradictories would be present together in actuality.” statement of the parallel argument with regard to generation. If this is so we require a full-stop instead of a comma after @Oaprév. rd @Oaprov can hardly be the subject of yéyorey, as Prantl’s stopping suggests. The last words, cai pi det dpa eiva, are unsatisfactory, since, though they draw a true consequence, it is one more directly appropriate to @éopa than to yéveors. It is tempting to read xai jy det dpa jy eivat. We should then have the relevant consequence and a more precise parallelism between the two arguments.—The point of the paragraph as a whole is to remove the possibility of an escape, by means of a doctrine of unrealized possibilities, from the conclusion already drawn that what is generated is also destructible. (Simpl. appositely quotes Z77zaews 41 A, B, where the permanence of the world- order depends on the will and promise of the Demiurge.) Aristotle always maintains that an unrealized possibility in this sense is inconceivable. * For Prantl’s xat dua read Gua. The xai is omitted by FMJ Simpl.— The notions of ‘chance’ (rd avréuarov) and ‘fortune’ (rvyn) are fully discussed in PAys. II. iv—vi, the exclusion of the ‘necessary’ and the ‘usual’ (283 32) being explained in II. v._ It is there plainly implied that chance had actually been suggested by earlier writers as the generative cause of the world (196% 33, 198810). The reason why they had recourse to this notion would be that chance means a cause quite external to the nature of the thing considered; and thus the chance generation or destruction of the world would not involve the consequence that in general and as such the world was either generated or destructible. Aristotle’s reply to the suggestion is simply that chance necessarily implies intermittent being, so that a chance- BOOK I. 12 ‘Further, it cannot truly be said of a thing now that it exists last year, nor could it be said last year that it exists now.’ It is therefore impossible for what once did not exist later to be eternal. For in its later state it will possess the capacity of not existing, only? not of not existing at a time when it exists—since then it exists in actuality—but of not existing last year or in the past. Now suppose it to be in actuality what it is capable of being. It will then be true to say now that it does not exist last year. But this is impossible. No capacity relates to being in the past, but always to being in the present or future. It is the same with the notion of an eternity of existence followed later by non-existence. In the later state the capacity will be present for that which is not there inactuality.? Actualize, then, the capacity. It will be true to say now that this exists last year or in the past generally. Considerations also not general like these but proper to the subject show it to be impossible that what was formerly eternal should later be destroyed or that what formerly was not should later be eternal. Whatever is destructible or generated is always alterable. Now alteration is due to contraries, and the things which compose the natural body are the very same that destroy it.* eternal is a contradiction in terms. (‘ Fortune’ is a name for chance within the sphere of conduct; and anything which can be caused by chance could also, according to Aristotle, be caused either by intelli- gence, as in the case of conduct, or by nature, as here. See PAys. 1. c.) introduced very abruptly, by a formula which shows that in Aristotle’s mind the suggestion here criticized is only another form of the appeal to chance just dealt with. The suggestion: is that a capacity may be limited in respect of time of fulfilment. Aristotle refutes it by assuming that its authors admit (a) that the Possession of the capacity is not limited in time, and (4) that any capacity may be actualized. 2 Before r\nv a comma is required instead of Prantl’s full-stop. 3 o§ must be taken to stand for éxeivov 6, as in Simpl.'s paraphrase.— The meaning is that after the thing has ceased to be it still retains its capacity of existing at any time previous to that event. A comma is required after évavyrios and, for ovviorarat, ovviorarat. Io ~ 5 BOOK II 283°:6 THAT the heaven as a whole neither came into being1 nor admits of destruction, as some assert, but is one and eternal, with no end or beginning of its total duration, con- 3o taining and embracing in itself the infinity of time, we may convince ourselves not only by the arguments already set forth but also by a consideration of the views of those who differ from us in providing for its generation. If our-view is a possible one, and the manner of generation which they

[284a.1] assert is impossible, this fact will have great weight in con- vincing us of the immortality and eternity of the world. Hence it is well to persuade oneself of the truth of the ancient and truly traditional theories, that there is some immortal and divine thing which possesses movement, but s movement such as has no limit and is rather itself the limit of all other movement. A limit is a thing which contains; and this motion’, being perfect, contains those imperfect motions which have a limit and a goal, having itself no beginning or end, but unceasing through the infinity of

[284a.10] time, and of other movements, to some the cause of their beginning, to others offering the goal. The ancients gave to the Gods the heaven or upper place, as being alone im- mortal ; and our present argument testifies that it is inde- structible and ungenerated. Further, it is unaffected by

[284a.15] any mortal discomfort, and, in addition, effortless; for it needs no constraining necessity to keep it to its path, and prevent it from moving with some other movement more natural to itself. Such a constrained movement would necessarily involve effort—the more so, the more eternal it were—and would be inconsistent with perfection. Hence we must not believe the old tale which says that the world ao needs some Atlas to keep it safe—a tale composed, it would seem, by men who, like later thinkers, conceived of all the * Omit # kuxAopopia, The words are found only in L, and though harmless are quite superfluous. There is no reference to xvxdopopia in Simpl.’s paraphrase. BOOK II. 1 284" upper bodies as earthy and endowed with weight, and therefore supported it in their fabulous way upon animate necessity. We must no more believe that than follow Em- pedocles when he says that the world, by being whirled

[284a.25] round, received a movement quick enough to overpower its own downward tendency, and thus has been kept from destruction all this time. Nor, again, is it conceivable that it should persist eternally by the necessitation of a soul.1 For a soul could not live in such conditions painlessly or

[284a.30] happily, since the movement involves constraint, being im- posed on the first body, whose natural motion is different, and imposed continuously.2_ It must therefore be uneasy and devoid of all rational satisfaction ; for it could not even, like the soul of mortal animals, take recreation in the bodily

[284a.35] relaxation of sleep. An Ixion’s lot must needs possess it, without end or respite. If then, as we said, the view already 284° stated of the first motion is a possible one, it is not only more appropriate so to conceive of its eternity, but also on this hypothesis alone are we able to advance a theory con- sistent with popular divinations of the divine nature.? But 5 of this enough for the present. 2 Since there are some who say that there is a right and a left in the heaven, with those who are known as Pythago- reans—to whom indeed the view really belongs—we must consider whether, if we are to apply these principles to the body of the universe, we should follow their statement of 10 the matter or find a better way. At the start we may say body of the cosmos by a world-soul as the human soul imposes move- ment on the human body. Such a notion necessarily implies constraint on the part ‘of the body and effort on the part of the’soul, and there- fore the movement could not be eternal. Aristotle has in mind, no doubt, the world-soul of the Z7maeus. with all MSS. except E. Simpl.’s paraphrase supports this reading. — The remarks which follow as to the absence of ‘ rational satisfaction ’ recall verbally Plato, Zimaeus 36 E Ociav dpxiv fpEaro [) Wuxn—the world-soul] dmavorov kai Euppovos Biov mpos Tov gupmayta xpivov. ‘ 8 By ‘ divination’ (uavreia) Aristotle means, not any religious practice of prophecy or the like, but simply the inspired guesses of common sense—riv Kowny ravtny evvovay fy €xopev mepi THs amrovias Kal pakapto- tyros tov Oeiov (Simpl.). 284 15 2 ° cs} on [e) 3 35

[285a.1] tuat, if right and left are applicable, there are prior princi- ples which must first be applied. These principles have been analysed in the discussion of the movements of animals,! for the reason that they are proper to animal nature. For in some animals we find all such distinctions of parts as this of right and left clearly present, and in others some; but in plants we find only above and below. Now if we are to apply to the heaven such a distinction of parts, we must expect, as we have said, to find in it also that distinction which in animals is found first of them all. The distinctions are three,? namely, above and below, front and its opposite, right and left—all these three oppositions we expect to find in the perfect body—and each may be called a principle. Above is the principle of length, right of breadth, front of depth. Or again we may connect them with the various movements, taking principle to mean that part, in a thing capable of movement, from which move- ment first begins. Growth starts from above, locomotion from the right, sense-movement from in front (for front is simply the part to which the senses are directed). Hence we must not look for above and below, right and left, front and back, in every kind of body, but only in those which, being animate, have a principle of movement within them- selves. For in no inanimate thing do we observe a part from which movement originates. Some do not meve at all, some move, but not indifferently in any direction : fire, for example, only upward, and earth only to the centre. It is true that we speak of above and below, right and left, in these bodies relatively to ourselves. The reference may be to our own right hands, as with the diviner, or to some similarity to our own members, such as the parts of a statue possess; or we may take the contrary spatial order, calling right that which is to our left, and ieft that which is to our right.2 We observe, however, in the things 1 De Incessu Anim., cc. iv, v. * Prantl misprints yay for ydp. * Bekker and Prantl are probably right in regarding the words which follow deétdv (viz. kai. . . EumpooOev) as spurious, though they are a in all MSS. except E. There is no trace of them in Simpl. or Them, BOOK II. 2 285° themselves none of these distinctions; indeed if they are turned round we proceed to speak of the opposite parts as

[285a.10] right and left, above and below, front and back. Hence it is remarkable that the Pythagoreans should have spoken of these two principles, right and left, only, to the exclusion of the other four, which have as good a title as they. There is no less difference between above and below or front and

[285a.15] back in animals generally than between right and left. The difference is sometimes only one of function,! some- times also one of shape; and while the distinction of above and below is characteristic of all animate things, whether plants or animals, that of right and left is not found in plants. Further, inasmuch as length is prior to breadth, if

[285a.20] above is the principle of length, right of breadth, and if the principle of that which is prior is itself prior, then above will be prior to right, or let us say, since ‘ prior’ is am- biguous, prior in order of generation.” If, in addition, above is the region from which movement originates, right the region in which it starts, front the region to which it is

[285a.25] directed, then on this ground too above has a certain original character as compared with the other forms of position. On these two grounds, then, they may fairly be criticized, first, for omitting the more fundamental principles, and secondly, for thinking that the two they mentioned were attributable equally to everything. Since we have already determined that functions of this kind belong to things which possess a principle of move- ment,* and that the heaven is animate and possesses a prin- 3° ciple of movement,‘ clearly the heaven must also exhibit in shape. It is implied that the difference of function underlies all the oppositions and determines the differences of shape where these occur. The differences of function are summarized above, 284» 25-30. * For the four main kinds of ‘priority’, see Cav. ch. xii (14% 26 ff.). Additional distinctions are made in Jer. A, ch. xi. 3 j,e. to animals. This is laid down at the beginning of the present chapter, 283” 13, where reference is made to the De /ncessu Animalium. Cf. also PAys. VIII. 4, 254” 7. 4 Bk. I, 279928, where it is stated to be the source of all life and movement. The term ‘animate’ (éuWuxos) has not hitherto been applied to it. The notion that the stars are ‘inanimate’ is rejected below, 292° 20. above and below, right and left. We need not be troubled by the question, arising from the spherical shape of the world, how there can be a distinction of right and left 285° within it, all parts being alike and all for ever in motion. 5 To I 2 2 mn ° on We must think of the world as of something in which right differs from left in shape as well as in other respects, which subsequently is included in a sphere. The difference of function will persist, but will appear not to by reason of the regularity of shape. In the same fashion must we conceive of the beginning of its movement. For even if it never began to move, yet it must possess a prin- ciple from which it would have begun to move if it had begun, and from which it would begin again if it came to a stand. Now by its length I mean the interval between its poles, one pole being above and the other below; for two hemispheres are specially distinguished from all others by the immobility of the poles. Further, by ‘transverse’ in the universe we commonly mean, not above and below, but a direction crossing the line of the poles, which, by implication, is length: for transverse motion is motion crossing motion up and down. Of the poles, that which we see above us is the lower region, and that which we do not see is the upper. For right in anything is, as we say, the region in which locomotion originates, and the rotation of the heaven originates in the region from which the stars rise. So this will be the right, and the region where they set the left. If then they begin from the right and move round to the right, the upper must be the unseen pole. For if it is the pole we see, the movement will be leftward, which we deny to be the fact. Clearly then the invisible pole is above. And those who live in the other hemisphere are above and to the right, while we are below and to the left. This is just the opposite of the view of the Pythago- reans, who make us above and on the right side and those in the other hemisphere below and on the left side; the fact ’ The unmoving poles mark out one among the infinite possible bisections of the sphere as natural and intelligible. We thus arrive, as explained in what follows, at an ‘upper’ and a ‘lower’ hemi- sphere. i BOOK II. 2 285° being the exact opposite.! Relatively, however, to the secondary revolution, I mean that of the planets, we are

[285a.30] above and on the right and they are below and on the left. For the principle of their movement has the reverse posi- tion, 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 286 of parts created by the three dimensions and of the conse- quent differences of position. * > 4 4 h. 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 5 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 follows: ‘“Right’’ is the place from which motion in space starts; and the motion of the heaven starts from the side where the stars rise, i.e. the east; therefore the east is “right” and the west “left”. If now (1) you suppose yourself to be lying along the world’s axis with your head towards the worth pole, your feet towards the south pole, and your right hand towards the east, then clearly the apparent motion of the stars from east to west is over your Jack from your right side towards your left; this motion, Aristotle maintains, cannot be called motion “to the right”, and therefore our hypothesis does not fit the assumption from which we start, namely that the daily rotation “ begins from the right and is carried round towards the right (emt ra deftd)”. We must therefore alter the hypothesis and suppose (2) that you are lying with your head towards the south pole and your feet towards the north pole. If then your right hand is to the east, the daily motion begins at your right hand and proceeds over the front of your body from your right hand to your left.’ Heath points out that to us this still gives a wrong result: the motion across your front will still be from right to left ; but he accepts Simpl.’s explanation that movement to the front is regarded as rightward and motion to the back as left- ward—i yap emi befia maivras eis ro eumpoobey éort. If this is true, Heath’s account is satisfactory. It is curious that the notion of right- ward movement also gives trouble in the cosmology of Plato. Heath has an entirely different solution of that difficulty, in which the ordinary sense of ‘to the right” is preserved (pp. 160-3). In view of the solution of the present passage quoted above, perhaps there is something after all to be said for the assertion of Proclus (J Timaeum 220 E), quoted by Heath only to be dismissed, that émi did does not mean éis rd defidy but is confined to circular motion and means ‘the direction of a movement imparted by the right hand’ (¢p’ & rd defy xwei), The discrimination of right and left in circular motions is peculiarly difficult and ambiguous, as every child knows ; and some such use of emi defud may have been the Greek solution of the termino- logical problem.

[286a.1] 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.

[286a.10] 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

[286a.15] body no part can be at rest, either elsewhere or at the centre. It could do so only if the body’s natural moyement were towards the centre. But the circular movement 1s natural, since otherwise it could not be eternal: for nothing unnatural is eternal. The unnatural is subse- quent to the natural, being a derangement of the natural a0 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 ex- plained 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

[286a.25] must be present, since the matter of contraries is the same. Also, the positive is prior to its privation (warm, for in- stance, to cold), and rest and heaviness stand for the priva- body has motion. Therefore the notion of a divine body necessarily involves the notion of an eternal movement.—Simpl. says wrongly that 6eds here stands for Oeiov cdpa. * The nature of the circular motion, and the reasons why it alone is compatible with immutability and the other divine attributes, have been explained in Bk. I, chaps. iii and iv.—The adjective ‘circular’ (éyxvxAtos) here and in several other passages of this book is trans- ferred from the motion to the body endowed with it. * The body which is at the centre cannot be of the same nature, and endowed with the same motion, as that which is at the extremity ; for the actual position and movement of one or the other would in that case be unnatural. There must therefore be a body whose natural position is at the centre and whose natural movement is towards the centre. * All change involves ‘derangement’ (éxoraois), Phys. 22216: cf. Phys. 241%2. exoraots is opposed to tedeiwors (‘fulfilment’, or movement of a thing towards its ideal nature), Phys. 246° 17, 2, 247° 3. > See ch, xiv. : BOOK II. 3 286° tion of lightness and movement. But further, if fire and ; earth exist, the intermediate bodies! must exist also: for

[286a.30] _ each element stands in a contrary relation to every other. (This, again, we will here take for granted and try later to explain.*) With 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,

[286a.35] if its movement cannot be regarded as naturally eternal: and these bodies we know to possess movement.? Thus we 286? see that generation is necessarily involved. But if so, there must be at least one other circular motion : fora single move- ment of the whole heaven would necessitate an identical re- lation of the elements of bodies tooneanother. 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. w ~ that is the shape most appropriate to its substance and also by nature primary. 1 viz. air and water. ? See De Gen. et Corr. 11. iii, iv. 5 Retaining the MSS. reading, which is confirmed by Simpl. and Them., rovrwy 8 €or xivnors. If these words are taken to mean ratra 8 éott xwnrda, the argument, though summarily stated, is complete and Prantl’s conjecture is unnecessary. If it is granted that the sublunary elements move, generation is admitted, unless it can be shown that their movement is such as to be naturally eternal. But it has already been shown (/Ays. 261% 31 ff.) that the rectilinear movements must be intermittent. of the planets. ‘If’, he argues, ‘there were only the movement of the fixed stars, and sun and moon were set in it and carried along with it, the varieties of summer and winter and the other seasons would disappear and the daily interchange would not follow its accustomed course. For if the sun were set in Cancer, we should have perpetual summer, and if it were set in Capricorn, perpetual winter: there would be no generation or destruction, not even the varied phases of the moon’ (Simpl.). The further discussion promised here is to be found in De Gen. et Corr. II. x. First, let us consider generally which shape is primary among planes and solids alike. Every plane figure must 15 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 a0 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 25 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 30 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, 35 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. 1S) io,2) “I p 1 Phys. II]. 20788. For the terms of the definition cf. sup. 271 31. This notion of ‘ perfect’ (or ‘ complete’) is presupposed in the opening chapter of this treatise—In 1. 19 read ray avrod: the réy is omitted only in E and F. * Cf. PAys. VI. 1 and inf. Bk. III, ch. i for further criticisms of these theories. The theory criticized is that expressed by Timaeus the Pythagorean in Plato’s dialogue of that name. (So Simpl. on 298? 33.) * Prantl’s pdvy is a misprint for povny. * Both sphere and circle can of course be divided into parts, but they cannot be geometrically analysed into constituents not themselves spherical or circular, The geometrical analysis requires that the constituent or ‘part’ shall be different in form from the whole.

[287a.1] 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

[287a.5] 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

[287a.10] 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 !5 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 2° 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 75 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; of the axis of revolution. In the case of a perfect sphere alone the position of the axis is immaterial. , MSS. The rod and ré in Prantl's text are conjectural insertions. J has aq’ atrod eq’ airé. 2872 DE CAELO and that movement is the swiftest which follows the shortest linet Therefore, if the heaven moves in a circle 30and 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 287” 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 5 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 4B, 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.® to Therefore the place in which it terminates will be a hollow place. The water then will collect there until equality is established, that is until the line AZ is equal to the two radii. Thus water forces its way to the ends of the radii, and there only will it rest: but the line which connects the extremities of the radii is circular: therefore the surface of the water BEC is spherical.

[287a.15] It is plain from the foregoing that the universe is spherical. It is plain, further, that it is turned (so to speak) with a finish which no manufactured thing nor anything postulated. In a word, the underlying notion is rather the compara- tive economy than the comparative swzftwess of movements.—For the origin of this argument Simpl. refers to 7777. 33 B. * ‘Continuous’, ‘contiguous’, and the related terms are defined in Phys. V. iil. If these bodies were continuous with the heavenly body they would have to move with the same motion as it. : B Ls, BOOK II. 4 287° ais else within the range of our observation can even approach. For the matter of which these are composed does not admit of anything like the same regularity and finish as

[287a.20] the substance of the enveloping body ; since with each step away from earth the matter manifestly becomes finer in the same proportion as water is finer than earth. 5 Now there are two ways of moving along a circle, from A to B or from A to C}! and we have already explained? that these movements are not contrary to ohe another. But

[287a.25] nothing which concerns the eternal can be a matter of _ chance or spontaneity, and the heaven and its circular motion are eternal. We must therefore ask why this motion takes one direction and not the other. Either this is itself an ultimate fact or there is an ultimate fact behind it. It may seem evidence of excessive folly or excessive zeal to try to provide an explanation of some things, or of every- 3° thing, admitting no exception. The criticism, however, is not always just: one should first consider what reason there is for speaking, and also what kind of certainty is looked for, whether human merely or of a more cogent kind.’ When

[288a.1] any one shall succeed in finding proofs of greater precision, gratitude will be due to him for the discovery, but at present we must be content with a probable solution.‘ If nature always follows the best course possible, and, just as upward movement is the superior form of rectilinear move-

[288a.5] + ment, since the upper region is more divine than the lower, so forward movement is superior to backward, then front and back exhibits, like right and left.as we said before’ and , towards C? Probably, answers Aristotle, because movement towards / is ‘forward’ and movement towards C ‘backward’ motion. : If A is the ‘right from which movement starts, iS; why should the movement be towards / rather than Cc Slee ye all other MSS. It is difficult to imagine why. There is good Platonic parallel for the use of xaprepés in this connexion (Phaedo 77 A, Theaet. 169 B): aA similar caution is repeated at the beginning of ch. xii, 291” 25. For this use of hatvdpevoy cf, Bonitz, Jad. Ar, 809% 24. _ . as the difficulty just stated itself suggests, the distinction of prior and posterior, which provides a reason and so solves our difficulty. Supposing: that nature is ordered in the

[288a.10] best way possible, this may stand as the reason of the fact mentioned. For it is best to move with a movement simple and unceasing, and, further, in the superior of two possible directions. We have next to show that the movement of the heaven 6 1s is regular and not irregular. This applies only to the first heaven and the first movement; for the lower spheres exhibit a composition of several movements into one. Ifthe movement is uneven, clearly there will be acceleration, maximum speed, and retardation, since these appear in all

[288a.20] irregular motions. The maximum may occur either at the starting-point or at the goal or between the two; and we expect natural motion to reach its maximum at the goal, unnatural motion at the starting-point,and missiles midway between the two.! But circular movement, having no be- The passage as punctuated by Bekker is untranslatable. The apo- dosis undoubtedly begins at the word €xa. EL give éyer dé cizep, the remaining MSS. éye eirep.—The existence of a ‘front’ and ‘back’ in the world was asserted in ch. ii. The priority of ‘up’, ‘right’, and ‘front’ over ‘down’, ‘left’, and ‘back’ is assumed in the same chapter, 284% 24.—The gist of the present rather involved and hesita- ting statement is that the only way to account for the direction of the heavenly movements is by means of these oppositions and the priority commonly attributed in each to one term over the other. shooting stars come under the notion of ‘ missiles’ or ‘ things thrown’. Their motion is compared to that of the stone of a fruit when it is made to fly through the air by being squeezed out from between the fingers. Ordinary throwing, e. g. of a stone or javelin, would of course also be included.—Simpl. and, by his report, Alexander are much puzzled by the statement in the text. Simpl. makes the wild sugges- tion that A. here regards animal movements as ‘missile’ motion, in that they are neither upward nor downward but horizontal. Alex. suggests that ‘ missile” movements may be said to have their maximum between goal and starting-point, because every earthly body has its goal either up or down, and the whole of the ‘missile’ movement from beginning to end, takes place in the middle region. Alex. is probably right. It is to be remembered that all movement is either natural or unnatural, and that ‘missile’ movement can only be distinguished in principle as a mixture of the two; further that the body thrown must be composed of one or more of the four elementary bodies. ‘Throwing’ is thought of as a forced horizontal motion put upon one of these bodies, each of which has a ‘goal’, down (or up) and a ‘starting-point’, up (or down). In such a motion the maximum BOOK II. 6 288" ginning or limit or middle in the direct sense of the words, has neither whence nor whither nor middle: for in time it is eternal, and in length it returns upon itself without a break. If then its movement has no maximum, it can have no irregularity, since irregularity is produced by re- tardation and acceleration. Further, since everything that is moved is moved by something, the cause of the irregu- larity of movement must lie either in the mover or in the

[288a.30] moved or in both. For if the mover moved not always with the same force, or if the moved were altered and did not remain the same, or if both were to change, the result might well be an irregular movement in the moved. But none of these possibilities can be conceived as actual in the case of the heavens. As to that which is moved, we have shown that it is primary and simple and ungencrated and 288° indestructible and generally unchanging; and the mover has an even better right to these attributes. It is the _. primary that moves the primary, the simple the simple, the.indestructible and ungenerated that which is indestruc- tible and ungenerated. Since then that which is moved, being a body, is nevertheless unchanging, how should the mover, which is incorporeal, be changed ? It follows then, further, that the motion cannot be irregular. For if irregularity occurs, there must be change either in the movement as a whole, from fast to slow and slow to fast, or in its parts. That there is no irregularity in the parts is obvious, since, if there were, some divergence 10 of the stars would have taken place! before now in the infinity of time, as one moved slower and another faster : but no alteration of their intervals is ever observed. Nor again is a change in the movement as a whole admissible. Retardation is always due to incapacity, and incapacity is unnatural. The incapacities of animals, age, decay, and the like, are all unnatural, due, it seems, to the fact that the wn 5 or ur cannot be said to be attained at either terminus, since neither terminus is involved, but only ‘between the two’. This means that in the case of natural motion ‘goal’ must be taken to be the natural place of the body, which is also the ‘starting-point’ of unnatural motion in the same body. In ‘throwing’, therefore, there is neither starting-point nor goal, but all is in the intermediate region. 1 For yeydve read eyeydvee with FHLMJ. whole animal complex is made up of materials which differ 20 25

[289a.1] in respect of their proper places, and no single part occupies its own place. If therefore that which is primary contains nothing unnatural, being simple and unmixed and in its proper place and having no contrary, then it has no place for incapacity, nor, consequently, for retardation or (since acceleration involves retardation) for acceleration. Again, it is inconceivable that the mover should first show in- capacity for an infinite time, and capacity afterwards for another infinity. For clearly nothing which, like incapacity, is unnatural ever continues for an infinity of time; nor does the unnatural endure as long as the natural, or any form of incapacity as long as the capacity.' But if the movement is retarded it must necessarily be retarded for an infinite time.2 Equally impossible is perpetual acceleration or perpetual retardation. For such movement would be in- finite and indefinite,* but every movement, in our view, proceeds from one point to another and is definite in character. Again, suppose one assumes a minimum time in less than which the heaven could not complete its move- ment. For, as a given walk or a given exercise on the harp cannot take any and every time, but every performance has its definite minimum time which is unsurpassable, so, one might suppose, the movement of the heaven could not be completed in any and every time. But in that case per- petual acceleration is impossible (and, equally, perpetual retardation: for the argument holds of both and each),‘ in reading ovd’ GAws.—The effect of d\Xes is to make the unnatural one species or department within the general notion of incapacity. é6\ws has much more varied uses and enables one to avoid this implication. * i.e. equality of duration must be supposed between the incapacity (retardation) and the preceding capacity, as assumed in the foregoing argument, in which infinity (sc. in ove direction) is attributed to each. For if the speed of movement has been everlastingly increasing, and now begins to decrease, it is impossible to suppose anything else but that it will decrease everlastingly. * viz, in respect of its speed. The hypothesis now considered is retardation or acceleration not balanced by its opposite but having neither beginning nor end, i.e. infinite in d0¢% directions. * Prantl’s stopping needs correction. The words ei d€ yu). . . Odérepov should be enclosed within brackets, rene BOOK II. 6 289° if we may take acceleration to proceed by identical or in- creasing additions of speed and for an infinite time. The

[289a.5] remaining alternative is to say that the movement exhibits an alternation of slower and faster: but this is a mere fiction-and quite inconceivable. Further, irregularity of this kind would be particularly unlikely to pass unobserved, since contrast makes observation easy. That there is one heaven, then, only, and that it is un- generated and eternal, and further that its movement is regular, has now been sufficiently explained. Io 7 We have next to speak of the stars, as they are called, of their composition, shape, and movements. It would be most natural and consequent upon what has been said that

[289a.15] each of the stars should be composed of that substance in whick their path lies,! since, as we said, there is an element whose natural movement is circular. In so saying we are only following the same line of thought as those who say that the stars are fiery because they believe the upper body to be fire, the presumption being that a thing is composed of the same stuff as that in which it is situated. The warmth

[289a.20] and light which proceed from them are caused by the friction set up in the air by their motion. Movement tends to create fire in wood, stone, and iron; and with even more reason should it have that effect on air, a substance which is closer to fire than these. An example is that of missiles, which as they move are themselves fired so strongly that

[289a.25] leaden balls are melted ; and if they are fired the surround- ing air must be similarly affected. Now while the missiles are heated by reason of their motion in air, which is turned into fire by the agitation produced by their movement,’ the upper bodies are carried on a moving sphere, so that,

[289a.30] though they are not themselves fired, yet the air underneath the sphere of the revolving body is necessarily heated by its 1 i,e. of the same substance as the spheres to which their motion is due. 2 A colon is required after the word dyp in 1. 23. 3’ Any seems to stand here for the continuous beating of the missile upon the air rather than for a single blow. Cf. Simpl. 439. 25 ind tis... mAnyns Kat maparpiyews, The same use recurs below, 2g1* 17. motion, and particularly in that part where the sun is attached to it.1 Hence warmth increases as the sun gets nearer or higher or overhead. Of the fact, then, that the

[289a.35] stars are neither fiery nor move in fire, enough has been said. 289° Since changes evidently occur not only in the position of 8 the stars but also in that of the whole heaven, there are three possibilities. Either (1) both are at rest, or (2) both are in motion, or (3) the one is at rest and the other in motion. (1) That both should be at rest is impossible; for, if the g earth is at rest, the hypothesis does not account for the observations ; and we take it as granted that the earth is at rest. It remains either that both are moved, or that the one is moved and the other at rest. (2) On the view, first, that both are in motion, we have the absurdity that the stars and the circles move with the same speed, i.e. that the pace of every star is that of the circle in to which it moves. For star and circle are seen to come back to the same place at the same moment; from which it follows that the star has traversed the circle and the circle has completed its own movement, i.e. traversed its own circumference, at one and the same moment. But it is difficult to conceive that the pace of each star should be 15 exactly proportioned to the size of its circle. That the pace of each circle should be proportionate to its size is not absurd but inevitable: but that the same should be true of the movement of the stars contained in the circles is quite which they are composed cannot be transmuted into any other as fire, air, and the other sublunary substances can. It is, however, legitimate to object to the above account that fire, not air, is the substance in contact with the spheres, and that only with the innermost. How, then, is air ignited by the movement of the spheres? Alex. and Simpl. agree that ‘ air’ must in some sense include fire (or Uréxkavya, the ‘fuel of fire’ which occupies the outer place); but that, evén if true, will not solve the difficulties. The view here advanced is nowhere fully worked out; but some further suggestions are made in Meteor. I. iii and iv. Cf. Heath, Aristarchus, pp. 241-2. It seems certain that what Aristotle meant was that the ‘fire’ which is in contact with the spheres is ignited and agitated by their motion and the air beneath by it (341% 2-3 and 30-31). BOOK II. 8 289? incredible. For if, on the one hand, we suppose that the star which moves on the greater circle is necessarily swifter, clearly we also admit that if stars shifted their position so as to exchange circles, the slower would become swifter and 20 the swifter slower. But this would show that their move- ment was not their own, but due to the circles. If, on the other hand, the arrangement was a chance combination, the coincidence in every case of a greater circle with a swifter movement of the star contained in it is too much to believe. In one or two cases it might not inconceivably fall out so, but to imagine it in every case alike-is a mere fiction. Besides, chance has no place in that which is natural, and what happens everywhere and in every case is no matter of chance. (3) The same absurdity is equally plain? if it is supposed that the circles stand still and that it is the stars them- selves which move. For it will follow that the outer stars are the swifter, and that the pace of the stars corresponds to 3° the size of their circles. Since, then, we cannot reasonably suppose either that both are in motion or that the star alone moves, the remain- ing alternative is that the circles should move, while the stars are at rest and move with the circles to which they are attached. Only on this supposition are we involved in no absurd consequence. For, in the first place, the quicker movement of the larger circle is natural when all the circles 35

[290a.1] are attached to the same centre. Whenever bodies are moving with their proper motion, the larger moves quicker. It is the same here with the revolving bodies: for the arc intercepted by two radii will be larger in the larger circle, and hence it is not surprising that the

[290a.5] revolution of the larger circle should take the same time as that of the smaller. And secondly, the fact that the heavens do not break in pieces follows not only from this » 5 reading of all MSS. and of Simpl. The alteration is unnecessary. The difficulty is the same as that pointed out in the preceding argu- ment—an unaccountable correspondence between the size of the circle and the speed of the star’s movement. 2907 DE CAELO but also from the proof already given! of the continuity of the whole. Again, since the stars are spherical, as our opponents assert and we may consistently admit, inasmuch as we construct them out of the spherical body, and since the

[290a.10] spherical body has two movements proper to itself, namely rolling and spinning,’ it follows that if the stars have a movement of their own, it will be one of these. But neither is observed. (1) Suppose them to spix. They would then stay where they were, and not change their place, as, by ob- servation and general consent, they do. Further, one would expect them all to exhibit the same movement: but the 1s only star which appears to possess this movement is the sun, at sunrise or sunset, and this appearance is due not to the sun itself but to the distance from which we observe it. The visual ray being excessively prolonged becomes weak and wavering.’ The same reason probably accounts for the apparent twinkling of the fixed stars and the absence of

[290a.20] twinkling in the planets. The planets are near, so that the visual ray reaches them in its full vigour, but when it comes to the fixed stars it is quivering because of the dis- tance and its excessive extension ; and its tremor produces an appearance of movement in the star: for it makes no difference whether movement is set up in the ray or in the object of vision. a5 (2) On the other hand, it is also clear that the stars do not vo//. For rolling involves rotation: but the ‘face’, ‘Cf. c. iv. But there is no attempt to prove continuity in the De Caelo. ? By ‘spinning’ is meant rotation on a stationary axis, by ‘rolling’ a forward movement in which a body turns completely round in a distance equal to its own circumference. See Heath, Aristarchus, Pp: 233-5. * The term 6ys (= visual ray) belongs to pre-Aristotelian psychology. Cf. Plato, eno, 76c-D. Aristotle’s use of it here and elsewhere (e.g. Meteor, III. iv, 3732) seems to commit him ‘to the view that the eye sees by rays issuing from a native fire within it’ (Beare, Greek Theories of Elementary Cognition, p. 66, n.1). But his own argument, when dealing with vision, is to the contrary effect. ‘In seeing we take something in, not give something out’ (Zop. 1056); and the process is ‘from object to eye, not conversely ' (Beare, p. 86). Aristotle must be supposed here to be adopting popular or Platonic terminology. BOOK II. 8 ago" as it is called, of the moon is always seen.! Therefore, since any movement of their own which the stars possessed would presumably be one proper to themselves, and no such movement is observed in them, clearly they have no move- ment of their own.

[290a.30] There is, further, the absurdity that nature has bestowed upon them no organ appropriate to such movement. For nature leaves nothing to chance, and would not, while car- ing for animals, overlook things so precious. Indeed, nature seems deliberately to have stripped them of every- thing which makes self-originated progression possible, and to have removed them as far as possible from things which

[290a.35] have organs of movement. This is just why it seems proper that the whole heaven and every star should be 290 spherical. For while of all shapes the sphere is the most convenient for movement in one place, making possible, as it does, the swiftest and most self-contained motion, for forward movement it is the most unsuitable, least of all 5 resembling shapes which are self-moved, in that it has no dependent or projecting part, as a rectilinear figure has, and is in fact as far as possible removed in shape from ambu- latory bodies. Since, therefore, the heavens have to move in one place, and the stars are not required to move them- selves forward, it is natural that both should be spherical— a shape which best suits the movement of the one and the immobility of the other. ° ment of the stars produces a harmony, i.e. that the sounds they make are concordant, in spite of the grace and originality with which it has been stated, is nevertheless 15 untrue.2- Some thinkers suppose that the motion of bodies the same side to us it is thereby proved that it does rotate upon its axis. But such rotation (incidental, in Aristotle’s view, to the move- ment of the sphere) is quite different from the rotation involved in ‘rolling’, which Aristotle is here concerned to deny. See Heath, pes Ge Pe Phe doctrine of the ‘harmony of the spheres’ is no doubt, as Simpl. says, Pythagorean. The most famous statement of the doctrine is in Plato’s Republic (Myth of Er, 6178), and the ratios given to the planets in 7%maeus, 35B, seem to have a musical significance. For a discussion of the doctrine see Heath, A77starchus, pp. 105-15. of that size must produce a noise, since on our earth the motion of bodies far inferior in size and in speed of move- ment has that effect. Also, when the sun and the moon, they say, and all the stars, so great in number and in size, ao are moving with so rapid a motion, how should they not produce a sound immensely great? Starting from this argument and from the observation that their speeds, as measured by their distances, are in the same ratios as musical concordances, they assert that the sound given forth by the circular movement of the stars is a harmony. Since, however, it appears unaccountable that we should 25 not hear this music, they explain this by saying that the sound is in our ears from the very moment of birth and is thus indistinguishable from its contrary silence, since sound and silence are discriminated by mutual contrast. What happens to men, then, is just what happens to coppersmiths, who are so accustomed to the noise of the smithy that it 30 makes no difference to them. But, as we said before, melodious and poetical as the theory is, it cannot be a true account of the facts. There is not only the absurdity of our hearing nothing, the ground of which they try to remove, but also the fact that no effect other than sensitive is produced upon us. Excessive noises, we know, shatter the 35 solid bodies even of inanimate things: the noise of thunder,

[291a.1] for instance, splits rocks and the strongest of bodies. But if the moving bodies are so great, and the sound which penetrates to us is proportionate to their size, that sound must needs reach us in an intensity many times that of thunder, and the force of its action must be immense.

[291a.5] Indeed the reason why we do not hear, and show in our bodies none of the effects of violent force, is easily given : it is that there is no noise. But not only is the explanation evident; it is also a corroboration of the truth of the views we have advanced. For the very difficulty which made the Pythagoreans say that the motion of the stars produces roa concord corroborates our view. Bodies which are them- selves in motion, produce noise and friction: but those which are attached or fixed to a moving body, as the parts to a ship, can no more create noise, than a ship on a river BOOK II. 9 291" moving with the stream. Yet by the same argument one might say it was absurd that on a large vessel the motion of

[291a.15] mast and poop should not make a great noise, and the like might be said of the movement of thevesselitself. But sound is caused when a moving body is enclosed in an unmoved body, and cannot be caused by one enclosed in, and continuous with, a moving body which creates no friction. We may say, then, in this matter that if the heavenly bodies moved in

[291a.20] a generally diffused mass of air or fire, as every one supposes, their motion would necessarily cause a noise of tremendous strength and such a noise would necessarily reach and shatter us.1 Since, therefore, this effect is evidently not produced, it follows that none of them can move with the motion either of animate nature or of constraint.? It is as

[291a.25] though nature had foreseen the result, that if their move- ment were other than it is, nothing on this earth could maintain its character. That the stars are spherical and are not self-moved, has now been explained.

[291a.30] 10 With their order—I mean the position of each, as involving the priority of some and the posteriority of others, and their respective distances from the extremity— with this astronomy may be left to deal, since the astro- nomical discussion is adequate.* This discussion shows that the movements of the several stars depend, as regards the varieties of speed which they exhibit, on the distance 1 Prantl misprints d:axvaiey for d:axvaiey. * If the stars moved in a non-moving medium either with a self- originated motion, like that of an animal, or with a motion imposed on them by external force, like that of a stone thrown, a great and destructive noise would result. There is no such noise or destruction. Therefore they do not so move. The Pythagorean doctrine is thus used to corroborate a conclusion already reached, It might be objected that Aristotle has already postulated friction with another substance to account for the brightness of the stars, and that this friction might well be expected to be accompanied with noise as in the case of missiles on the earth. tense in the verb Aéyera, suggest that Aristotle is not here referring to other works of his own but to contemporary works on astronomy, current in the school, by other writers. These sentences also clearly imply that ‘astronomy’ is more empirical in its methods than the De Caelo. Cf. infra, 291°21.—In 1. 29 Prantl’s 6 is a misprint for év.

[291a.35] of each from the extremity. It is established that the outermost revolution of the heavens is a simple movement 291° and the swiftest of all, and that the movement of all other bodies is composite and relatively slow, for the reason that each is moving on its own circle with the reverse motion to that of the heavens. This at once leads us to expect that the body which is nearest to that first simple revolution s should take the longest time to complete its circle, and that which is farthest from it the shortest, the others taking a longer time the nearer they are and a shorter time the farther away they are. For it is the nearest body which is most strongly influenced, and the most remote, by reason of its distance, which is least affected, the influence on the intermediate bodies varying, as the mathematicians show, ro with their distance.! With regard to the shape of each star, the most reasonable 11 view is that they are spherical. It has been shown? that it is not in their nature to move themselves, and, since nature is no wanton or random creator, clearly she will have 1g given things which possess no movement a shape particularly unadapted to movement. Such a shape is the sphere, since it possesses no instrument of movement. Clearly then their mass will have the form of a sphere. Again, what 1 In regard to ‘order’ Aristotle only seeks to explain one point which might present a difficulty. It would be natural to expect the moon, which is the nearest planet to the earth, to have the slowest motion ; but in fact it is the swiftest of the planets. His answer is that the movement of the planets, being the reverse of that of the outer heaven, is hampered by proximity to it; and the planet nearest to the earth is least influenced and therefore moves swiftest. Simpl. raises the objection: is not the planetary motion then in some degree constrained or unnatural? He quotes with approval from Alex. the reply: ‘No: for the planetary sphere is not unwilling, This accords with its purpose and desire. It may be necessity, but it is also good, and recognized as such.’ Simpl. is not altogether satisfied by this solution. seChavills * Simpl. notes a circle in Aristotle’s argument, since he has already used the spherical shape of the stars to prove that they have no independent motion (c. viii). (The same charge is brought against Aristotle by Dreyer, Planetary Systems, p. 111.) He is not satisfied with Alex.’s rejoinder that neither of these arguments stands alone. The true answer is that the argument of c. viii is explicitly based, in respect of the spherical shape of the stars, on a premise borrowed from the opposition: see 290%7, Aristotle’s own proof of the matter precedes it. This argument is therefore in order. BOOK II. 1 291° holds of one holds of all, and the evidence of our eyes shows us that the moon is spherical. For how else should the moon as it waxes and wanes show for the most part 20 a crescent-shaped or gibbous figure, and only at one mo- ment a half-moon? And astronomical arguments! give further confirmation ; for no other hypothesis accounts for the crescent shape of the sun’s eclipses. One, then, of the heavenly bodies being spherical, clearly the rest will be spherical also. 12 There are two difficulties, which may very reasonably here be raised, of which we must now attempt to state the 2; probable solution: for we regard the zeal of one whose thirst after philosophy leads him to accept even slight indications where it is very difficult to see one’s way, as a proof rather of modesty than of over-confidence. Of many such problems one of the strangest is the problem why we find the greatest number of movements in 30 the intermediate bodies, and not, rather, in each successive body a variety of movement proportionate to its distance from the primary motion. For we should expect, since the primary body shows one motion only, that the body which is nearest to it should move with the fewest movements, say two, and the one next after that with three, or some similar arrangement. But the opposite is the case. The 35

[292a.1] movements of the sun and moon are fewer than those of some of the planets. Yet these planets are farther from the centre and thus nearer to the primary body than they, as observation has itself revealed. For we have seen the

[292a.5] moon, half-full, pass beneath the planet Mars, which vanished on its shadow side and came forth by the bright and shining part.* Similar accounts of other stars are ? See note on 2888 2. 8 Brandis (Berlin Aristotle, vol. 1V, 49713) quotes a scholium to the effect that Alexander in his Commentary said it was Mercury, not Mars. Both Simpl. and Them., however, give Mars without question. If it was Mars, a calculation of Kepler’s (Astronomia Nova, 1609, P- 323) fixes the date. ‘Inveni,’ he writes, ‘longissima inductione per annos L, ab anno quindecimo ad finem vitae Aristotelis, non potuisse esse alio die, quam in vespera diei 1v Aprilis, anno ante CHRISTI vulgarem epocham CCCLVII, cum Aristoteles XXI annorum audiret 7 given by the Egyptians and Babylonians, whose observa- tions have been kept for very many years past, and from whom much of our evidence about particular stars is derived.! ro A second difficulty which may with equal justice be raised is this. Why is it that the primary motion includes such a multitude of stars that their whole array seems to defy counting, while of the other stars? each one is separated off, and in no case do we find two or more attached to the same motion ?? On these questions, I say, it is well that we should seek 1s to increase our understanding, though we have but little to go upon, and are placed at so great a distance from the facts in question. Nevertheless there are certain principles on which if we base our consideration we shall not find this difficulty by any means insoluble. We may object that we have been thinking of the stars as mere bodies, and as units

[292a.20] with a serial order indeed but entirely inanimate; but should rather conceive them as enjoying life and action. On this view the facts cease to appear surprising. For it is natural that the best-conditioned of all things should have its good without action, that that which is nearest to it should achieve it by little and simple action, and that which is farther removed by a complexity of actions, just as with

[292a.25] men’s bodies one is in good condition without exercise at all, another after a short walk, while another requires running and wrestling and hard training, and there are yet Eudoxum, ut ex Diogene Laértio constat.’ Diogenes’ date for Aristotle’s birth is in fact Ol. 99, 1 (384-3 B.c.): Aristotle would therefore be 27 at the date arrived at. The calculation for Mercury does not appear to have been made. ° The term dopa (motion) is transferred from*the motion itself to the sphere which imparts the motion. * There seems to be no parallel for the use of the word kémows (tr. ‘hard training’) in connexion with the exercises of the palaestra, though xoviorpa is used in post-Aristotelian writers for the arena. Simpl. says the term stands for the training of the wrestler, d:a ré ev kovet yupvaterOat ta madaotpixd. Bywater (J. of Phil. xxviii, p. 241) objects that the third term in the phrase should be a distinct form of exercise from running or wrestling, and suggests kdxovricews. Perhaps it is best to keep the text, though there can be no certainty that it is right. BOOK II. 12 292" others who however hard they worked themselves could never secure this good, but only some substitute for it. To succeed often or in many things is difficult. For instance,

[292a.30] to throw ten thousand Coan throws with the dice would be impossible, but to throw one or two is comparatively easy. In action, again, when 4 has to be done to get B, B to get C, and C to get D, one step or two present little difficulty, but as the series extends the difficulty grows. 292” We must, then, think of the action of the lower stars as similar to that of animals and plants. For on our earth it is man that has the greatest variety of actions—for there are many goods that man can secure; hence his actions are various and directed to ends beyond them—while the perfectly conditioned has no need of action, since it is itself 5 the end, and action always requires two terms, end and means. The lower animals have less variety of action than man; and plants perhaps have little action and of one kind only. For either they have but one attainable good (as indeed man has), or, if several, each contributes directly to their ultimate good. One thing then has and enjoys the oe ° 1 Prantl’s K@ovus rests on one MS. (H) and was known as an alterna- tive reading to Simpl. Two MSS. (EL) give Xious, two others (FM) xlous } kdous. J has ytAlovs xwAovs, with xiovs f kwiovs in the margin. Simpl. thinks the point is the size of the dice (as peyddov dorpayddov év audorépas ywopévor rais vycos), Prantl takes the impossibility to be a succession of good throws or ‘sixes’, and therefore prefers ‘Coan’ to ‘Chian’, which aceording to Pollux was used for the worst throw. The impossibility is clearly the same whether the worst throw or the best is intended; but, since success is implied by the context, I have followed Prantl. The double reading Xiovs # Kwovs may how- ever be right. ® Reading mpdtre, with FHMJ and Bekker, for Prantl’s mpdrrew EL). breaks the structure of the sentence and should be removed. The succession of colons which results (for a colon must be marked after mpages,in 1, 3) is best broken by placing full-stops after uray (I. 2), évexa (1. 4), €vexa (1. 7). 4 If there is more than one good, e.g. nutriment and propagation, each is a constituent of the plant’s ‘good’ in the final sense. To be able to accept something merely as a means to something else, i.e. as indirectly good, is a distinctive mark of a higher development. Thus the variety here indicated as characteristic of human action lies not so much in the superior range of human desires (though that also is a fact) as in the variety and complexity of the means by which man effects their satisfaction. 292 ultimate good, other things attain to it, one immediately * by few steps, another by many, while yet another does not even attempt to secure it but is satisfied to reach a point not far removed from that consummation. Thus, taking health as the end, there will be one thing that always possesses health, others that attain it, one by reducing flesh, another by running and thus reducing flesh, another 15by taking steps to enable himself to run, thus further increasing the number of movements, while another cannot attain health itself, but only running or reduction of flesh, so that one or other of these is for such a being the end,’ For while it is clearly best for any being to attain the real end, yet, if that cannot be, the nearer it is to the best the 20 better will be its state. It is for this reason that the earth 2 on moves not at all and the bodies near to it with few move- ments. For they do not attain the final end, but only come as near to it as their share in the divine principle permits.° But the first heaven finds it immediately with a single movement, and the bodies intermediate between the first and last heavens attain it indeed, but at the cost of a multi- plicity of movement. As to the difficulty that into the one primary motion is crowded a vast multitude of stars, while of the other stars each has been separately given special movements of its own, there is in the first place this reason for regarding the arrangement as a natural one. In thinking of the life MSS., but is quite intolerable in view of the general contrast between attainment and approximation made here and repeated below. The influence of éyyis in the following line may be supposed to have caused its substitution for ed@vs here. Simpl. paraphrases ré dé &’ OAlyov Kinoe@v adixveirar mpds Td éavTod Tédos, and therefore appears not to have had éyyvs in his text. Them., however, has it: ‘ad illud prope per pauca accedit.’ * Place a full-stop after éd@ei (1. 13), delete bracket, comma after ioxvarvOnva (1.17). ‘Running’ or ‘reduction of flesh’ becomes in such a case the ‘end’, i.e. the content of purpose, as soon as the true end or good is recognized as unattainable. * Simpl. finds this sentence difficult. He did not see that Aristotle here, as frequently elsewhere, uses dA\d where dAX’ # would be expected. See Bonitz, Jad. Ar. 33°15. * The upshot of the argument seems to be this, that the earth and the bodies nearest to it move simply, or not at all, because they are content with little, and perfection is beyond their reach. a \ 13 BOOK II. 12 292” and moving principle of the several heavens one must regard the first as far superior to the others. Such 30 a superiority would be reasonable. For this single first motion has to move many of the divine bodies, while the

[293a.1] numerous other motions move only one each, since each single planet moves with a variety of motions, Thus, then, nature makes matters equal and establishes a certain order, giving to the single motion many bodies and to the single body many motions. And there is a second reason why

[293a.5] the other motions have each only one body, in that each of them except the last, i.e. that which contains the one star, is really moving many bodies. For this last sphere moves with many others, to which it is fixed, each sphere being actually a body; so that its movement will be a joint product. Each sphere, in fact, has its particular natural

[293a.10] motion, to which the general movement is, as it were, added. But the force of any limited body is only adequate to moving a limited body.” The characteristics of the stars which move with a circular motion, in respect of substance and shape, movement and order, have now been sufficiently explained.

[293a.15] It remains to speak of the earth, of its position, of the question whether it is at rest or in motion, and of its shape. As to its position there is some difference of opinion. Most people—all, in fact, who regard the whole heaven as finite—say it lies at the centre. But the Italian philoso- phers known as Pythagoreans take the contrary view. At the centre, they say, is fire, and the earth is one of the stars, creating night and day by its circular motion about the iS ° of a number of simple spherical motions each contributed by a single sphere. The ‘last’ sphere or motion means the outermost, viz. that to which the planet is actually attached. The inner spheres have really bodies to move even though they carry no planet: for they have to communicate their motion to the sphere or spheres in which they are included. ; ; 2° Prantl seems to find unnecessary difficulty in this sentence. These spheres, says Aristotle, have only a limited force, and they have enough to do to impart their motion to the outer spheres, and through it to the planet: the burden of several planets would be too much for them. centre. They further construct another earth in opposition as to ours to which they give the name counter-earth.’ In all this they are not seeking for theories and causes to account for observed facts, but rather forcing their observations and trying to accommodate them to certain theories and opinions of their own. But there are many others who would agree that it is wrong to give the earth the central

[293a.30] position, looking for confirmation rather to theory than to the facts of observation. Their view is that the most precious place befits the most precious thing: but fire, they say, is more precious than earth, and the limit than the intermediate, and the circumference and the centre are limits. Reasoning on this basis they take the view that it is not earth that lies at the centre of the sphere, but rather 293” fire. The Pythagoreans have a further reason. They hold that the most important part of the world, which is the centre, should be most strictly guarded, and name it, or rather the fire which occupies that place, the ‘ Guard-house of Zeus’, as if the word ‘centre’ were quite unequivocal, 5 and the centre of the mathematical figure were always the same with that of the thing or the natural centre. But it is better to conceive of the case of the whole heaven as analogous to that of animals, in which the centre of the animal and that of the body are different. For this reason they have no need to be so disturbed about the world, or to 10 call in a guard for its centre: rather let them look for the centre in the other sense and tell us what it is like and where nature has set it. That centre will be something primary and precious; but to the mere position we should give the last place rather than the first. For the middle is what is defined, and what defines it is the limit, and that which contains or limits is more precious than that which 15is limited, seeing that the latter is the matter and the former the essence of the system. As to the position of the earth, then, this is the view which some advance, and the views advanced concerning its vest or motion are similar. For here too there is no general agreement. All who deny that the earth lies at * dvopa is omitted by FHMJ, but is probably right. BOOK II. 13 293° the centre think that it revolves about the centre,! and not the earth only but, as we said before, the counter-earth as 20 well. Some of them even consider it possible that there are several bodies so moving, which are invisible to us owing to the interposition of the earth. This, they say, accounts for the fact that eclipses of the moon are more frequent than eclipses of the sun: for in addition to the earth each of these moving bodies can obstruct it. Indeed, 25 as in any case the surface of the earth is not actually a centre but distant from it a full hemisphere, there is no more difficulty, they think, in accounting for the observed facts on their view that we do not dwell at the centre, than on the common view that the earth is in the middle.?,- Even as it is, there is nothing in the observations to suggest that we are removed from the centre by half the diameter of the 3° earth. Others, again, say that the earth, which lies at the centre, is ‘rolled’, and thus in motion, about the axis of the whole heaven. So it stands written in the 7zmaeus.$ There are similar disputes about the shape of the earth. Some think it is spherical, others that it is flat and

[294a.1] For evidence they bring the fact that, as the 1 und’ in 1. 18 appears to prove that the comma should be put after xeioOa: instead of after airyy, and that g¢aow governs both infinitives. 2 Prantl’s insertion of yy in the last clause rests on a misunder- standing of the passage. The text is quite sound.—Dreyer (Planetary Systems, p. 45) thinks that the supposed movement would seriously affect observations of the sun and the moon. 8 Timaeus, 40B. For a discussion of this vexed passage see Heath, Aristarchus, pp. 174-8. J has eidetoOat cal xweioOa (in 296% 26, however, where the same pair of words recur, it has eiA\eoOat x. k.), which decreases the probability, not antecedently very great, that the words «al xweioOa are an insertion. Unless the idea of movement is contained in the phrase, the quotation would seem to be out of place here. It seems plain that Aristotle considered the word tAAecOa (‘rolled’ in the text) obscure or ambiguous, and added the words kai xiveio@a to indicate his interpretation of it. Alex. (apfud Simpl.) says that the word used in the Zimaeus means ‘pressed’ (SiafeoOac), but that it is difficult to contradict Aristotle on a point on which he was so much better informed, Simpl. says that, spelt with the diphthong « and a single A, the word does connote rotation. He points out that Aristotle promised to speak of the earth’s motion avd rest; and suggests that, taking Kal xiweioOar to be a later insertion, one might suppose that Aristotle passes in this sentence to the consideration of the view that the earth is at rest. But this will hardly do. sun rises and sets, the part concealed by the earth shows a straight and not a curved edge, whereas if the earth were spherical the line of section would have to be circular. In

[294a.5] this they leave out of account the great distance of the sun from the earth and the great size of the circumference, which, seen from a distance on these apparently small circles appears straight. Such an appearance ought not to make them doubt the circular shape of the earth. But they have another argument. They say that because it is at

[294a.10] rest, the earth must necessarily have this shape. For there are many different ways in which the movement or rest of the earth has been conceived. The difficulty must have occurred to every one. It would indeed be a complacent mind that felt no surprise that, while a little bit of earth, let loose in mid-air, moves and

[294a.15] will not stay still, and the more there is of it the faster it moves, the whole earth, free in mid-air, should show no movement at all. Yet here is this great weight of earth, and it is at rest. And again, from beneath one of these moving fragments of earth, before it falls, take away the earth, and it will continue its downward movement with nothing to stop it. The difficulty then, has naturally passed

[294a.20] into a commonplace of philosophy; and one may well wonder that the solutions offered are not seen to involve greater absurdities than the problem itself. By these considerations some have been led to assert that the earth below us is infinite, saying, with Xenophanes of Colophon, that it has ‘ pushed its roots to infinity ’,—in order to save the trouble of seeking for the cause. Hence a5 the sharp rebuke of Empedocles, in the words ‘ if the deeps of the earth are endless and endless the ample ether—such is the vain tale told by many a tongue, poured from the mouths of those who have seen but little of the whole ’.? Preller, 103b. Simpl. cannot find the quotation in the writings of Xenophanes, and doubts whether ro xatw rs yjs means ‘ the under- parts of the earth’ or ‘the ether under the earth’. A fragment, corroborating the former interpretation survives (no. 28 in Diels). Cf. Burnet, E.G.P.5 § 60. ® Diels, Vors.$ 21 B 39 (241,16). Ritter and Preller, 103b. Burnet, EGE? peeres BOOK II. 13 294° Others say the earth rests upon water. This, indeed, is the oldest theory that has been preserved, and is attributed to

[294a.30] Thales of Miletus. It was supposed to stay still because it floated like wood and other similar substances, which are so constituted as to rest upon water but not upon air. As if the same account had not to be given of the water which carries the earth as of the earth itself! It is not the nature of water, any more than of earth, to stay in mid-air: it must have something to rest upon. Again, as air is lighter 294° than water, so is water than earth: how then can they think that the naturally lighter substance lies below the heavier ? Again, if the earth as a whole is capable of floating upon water, that must obviously be the case with any part of it. But observation shows that this is not the case. Any piece 5 of earth goes to the bottom, the quicker the larger it is. These thinkers seem to push their inquiries some way into the problem, but not so far as they might. It is what we are all inclined to do, to direct our inquiry not by the matter itself, but by the views of our opponents: and even when interrogating oneself one pushes the inquiry only 10 to the point at which one can no longer offer any opposi- tion. Hence a good inquirer will be one who is ready in bringing forward the objections proper to the genus, and that he will be when he has gained an understanding of all the differences. Anaximenes and Anaxagoras and Democritus give the flatness of the earth as the cause of its staying still. Thus, they say, it does not cut, but covers like a lid, the air beneath it. This seems to be the way of flat-shaped bodies: for even the wind can scarcely move them because of their power of resistance. The same immobility, they say, is produced by the flatness of the surface which the earth presents to the air which underlies it ; while the air, subject of investigation belongs, i.e. scientific, not dialectical or sophistical, These thinkers, as Simpl. observes, have failed to investi- gate the peculiar characteristics of wood and earth in the genus ‘body’, and therefore think that, because wood floats, earth may. For the importance of a study of the ‘differences’ Simpl. refers to Top. I. xviil. 5

[294a.20] not having room enough to change its place because it is underneath the earth, stays there in a mass, like the water in the case of the water-clock.1 And they adduce an amount of evidence to prove that air, when cut off and at rest, can bear a considerable weight. Now, first, if the shape of the earth is not flat, its flat- ness cannot be the cause of its immobility. But in their a5 own account it is rather the size of the earth than its flat- ness that causes it to remain at rest. For the reason why the air is so closely confined that it cannot find a passage, and therefore stays where it is, is its great amount: and this amount is great because the body which isolates it, the earth, is very large. This result, then, will follow, even if

[294a.30] the earth is spherical, so long as it retains its size. So far as their arguments go, the earth will still be at rest. In general, our quarrel with those who speak of move- ment in this way cannot be confined to the parts?; it con- cerns the whole universe. One must decide at the outset whether bodies have a natural movement or not, whether there is no natural but only constrained movement. Seeing,

[295a.1] however, that we have already decided this matter to the best of our ability, we are entitled to treat our results as representing fact. Bodies, we say, which have no natural movement, have no constrained movement; and where there is no natural and no constrained movement there will

[295a.5] be no movement at all. This is a conclusion, the necessity of which we have already decided,® and we have seen further that rest also will be inconceivable, since rest, like before peraoriva (1. 19), a conjecture which has some support in L, which has mov in that place.—Experiments with the water-clock are frequently mentioned. See esp. Emped. fr. 100 (Diels), Arist. Prod/. 914” 26, Burnet, E.G.P.° Index I s.v. Klepsydra. ‘The water-clock’, says Simpl., ‘is a vessel with a narrow mouth and a flattish base pierced with small holes, what we now call a Aydrarpax. If this vessel is dipped in water while the mouth at the top is kept closed, no water runs in through the holes. The massed air inside resists the water and prevents its ingress, being unable to change its own place. When the mouth at the top is opened the water runs in, the air making way for it.’ The position of the water beneath the water- clock is analogous to that of the air beneath the earth. : ' e. to the single element earth or to earth and air. . ji-iv, BOOK 11, 13 movement, is either natural or constrained. But if there is any natural movement, constraint will not be the sole prin- ciple of motion or of rest. If, then, it is by constraint that the earth now keeps its place, the so-called ‘ whirling’ movement by which its parts came together at the centre was also constrained. (The form of causation supposed they all borrow from observations of liquids and of air, in which the larger and heavier bodies always move to the centre of the whirl. This is thought by all those who try to generate the heavens to explain why the earth came together at the centre. They then seek a reason for its staying there; and some say, in the manner explained, that the reason is its size and flatness, others, with Empedocles, that the motion of the heavens, moving about it at a higher speed, prevents movement of the earth, as the water in a cup, when the cup is given a circular motion, though it is often underneath the bronze, is for this same reason pre- vented from moving with the downward movement which is natural to it.) But suppose both the ‘ whirl’ and its flatness (the air beneath being withdrawn?) cease to pre- vent the earth’s motion, where will the earth move to then? Its movement to the centre was constrained, and its rest at the centre is due to constraint ; but there must be some motion which is natural to it. Will this be upward motion or downward or what? It must have some motion; and if upward and downward motion are alike to it, and the air above the earth does not prevent upward movement, then no more could air below it prevent downward movement. For the same cause must necessarily have the same effect on the same thing.® Further, against Empedocles there is another point which might be made. When the elements were separated off by 1 Simplicius seems to be right in considering the portion included within brackets in the text as a parenthetic note on divnors, interrupt- ing Aristotle’s argument. parallel to the use of tmeAdeiv in this sense. The MSS. offer no variant, and Simpl. paraphrases éxordvros. In the absence of a better suggestion I should read tme£eAOvvros. thinkers attributed a natural motion downward to the earth, since they gave it a reason for not moving in that direction only. 2 ° 35 30 35 5 Io Hate, what caused the earth to keep its place? Surely the ‘whirl’ cannot have been then also the cause. It is absurd too not to perceive that, while the whirling movement may have been responsible for the original coming together of the parts of earth at the centre, the question remains, why now do all heavy bodies move to the earth. For the whirl surely does not come near us. Why, again, does fire move upward? Not, surely, because of the whirl. But if fire is naturally such as to move in a certain direction, clearly the same may be supposed to hold of earth. Again, it cannot be the whirl which determines the heavy and the light.’ Rather that movement caused the pre-existent heavy and light things to go to the middle and stay on the surface respectively. Thus, before ever the whirl began, heavy and light existed ; and what can have been the ground of their distinction, or the manner and direction of their natural movements? In the infinite chaos there can have been neither above nor below, and it is by these that heavy and light are determined. It is to these causes that most writers pay attention: but there are some, Anaximander, for instance, among the ancients, who say that the earth keeps its place because of its indifference.? Motion upward and downward and side- ways were all, they thought, equally inappropriate to that which is set at the centre and indifferently related to every extreme point ; and to move in contrary directions * at the same time was impossible: so it must needs remain still. This view is ingenious but not true. The argument would prove that everything, whatever it be, which is put at the Literally ‘likeness’. Kranz, Index to Diels, Vors., s.v. dpotdrns, translates ‘ gleichmassige Lage’. Burnet (who formerly took a dif- ferent view) now accepts ‘indifference’ as the equivalent of dépotdrns in this passage. (E.G.P.° p. 66, n. 1.) Cf. Burnet's note on Plato, Phaedo, 109 A 2, where he proposes the translation ‘equiformity’, and the phrase mpds dpoias ywvias below (296% 20). From Aris- totle’s wording it seems probable that he had the Piaedo in mind here. The full phrase there is: rjv dpodrnra rod odpavod avrod €avT@ mavtn Kal Ths yns adrns rv icopporiay. It is to be observed that Plato makes 6pordrns an attribute of the whole heaven or universe, not of the earth. * Prantl’s evavrioy is a misprint for évavriov. “BOOK Lig 13 295° centre, must stay there. Fire, then, will rest at the centre: for the proof turns on no peculiar property of earth. But

[295a.20] this does not follow. The observed facts about earth are not only that it remains at the centre, but also that it moves to the centre. The place to which any fragment of earth moves must necessarily be the place to which the whole moves ; and in the place to which a thing naturally moves, it will naturally rest. The reason then is not in the fact that the earth is indifferently related to every extreme

[295a.25] point: for this would apply to any body, whereas move- ment to the centre is peculiar to earth. Again it is absurd to look for a reason why the earth remains at the centre and not for a reason why fire remains at the extremity. If the extremity is the natural place of fire, clearly earth must also have a natural place. But suppose that the centre is

[295a.30] not its place, and that the reason of its remaining there is this necessity of indifference—on the analogy of the hair which, it is said, however great the tension, will not break under it, if it be evenly distributed, or of the man who, though exceedingly hungry and thirsty, and both equally,’ yet being equidistant from food and drink, is therefore bound

[295a.35] to stay where he is—even so, it still remains to explain why

[296a.1] fire stays at the extremities. It is strange, too, to ask about things staying still but not about their motion,—why, I mean, one thing, if nothing stops it, moves up, and another thing to the centre. Again, their statements are not true.

[296a.5] It happens, indeed, to be the case that a thing to which movement this way and that is equally inappropriate is obliged to remain at the centre.” But so far as their argu- ment goes, instead of remaining there, it will move, only not as a mass but in fragments. For the argument applies equally to fire. Fire, if set at the centre, should stay there,

[296a.10] like earth, since it will be indifferently related to every point on the extremity. Nevertheless it will move, as in fact it always does move when nothing stops it, away from the centre to the extremity. It will not, however, move in a 1 ‘The structure of the sentence would be made clearer if commas were placed after pv and after d¢ in |. 33. to apply, as explained in what follows, only to indivisible bodies. mass to a single point on: the circumference—the only pos- sible result on the lines of the indifference theory—but

[296a.15] rather each corresponding portion of fire to the correspond- ing part of the extremity, each fourth part, for instance, to a fourth part of the circumference. For since no body is a point, it will have parts. The expansion, when the body increased the place occupied, would be on the same prin- ciple as the contraction, in which the place was diminished. Thus, for all the indifference theory shows to the contrary,

[296a.20] earth also would have moved in this manner away from the centre, unless the centre had been its natural place. We have now outlined the views held as to the shape, position, and rest or movement of the earth. Let us first decide the question whether the earth moves 14

[296a.25] or is at rest. For, as we said, there are some who make it one of the stars, and others who, setting it at the centre, suppose it to be ‘rolled’ and in motion about the pole as axis.1 That both views are untenable will be clear if we take as our starting-point the fact that the earth’s motion, whether the earth be at the centre or away from it, must

[296a.30] Needs be a constrained motion. It cannot be the movement of the earth itself. If it were, any portion of it would have this movement; but in fact every part moves in a straight line to the centre. Being, then, constrained and unnatural, the movement could not be eternal. But the order of the universe is eternal. Again, everything that moves with the

[296a.35] circular movement, except the first sphere, is observed to 296° be passed, and to move with more than one motion. The earth, then, also, whether it move about the centre or as stationary at it, must necessarily move with two motions. But if this were so, there would have to be passings and 5 turnings of the fixed stars. Yet no such thing is observed, The same stars always rise and set in the same parts of the earth.” 1 For t\AeoGa: J has eidAeoOar. See note on 29331. * This passage is examined in Heath, Avistarchus, pp. 240-1. The necessity for two motions appears to rest only on the analogy of the planets, which are ‘passed’ or left behind by the motion of the sphere of the fixed stars. The consequence, that there would be variety in BOOK II. 4 Further, the natural movement of the earth, part and whole alike, is to the centre of the whole—whence the fact that it is now actually situated at the centre—but it might be questioned, since both centres are the same, which centre it is that portions of earth and other heavy things move to. Is this their goal because it is the centre of the earth or because it is the centre of the whole? The goal, surely, must be the centre of the whole. For fire and other light things move to the extremity of the area which contains the centre. It happens, however, that the centre of the earth and of the whole is the same. Thus they do move to the centre of the earth, but accidentally, in virtue of the fact that the earth’s centre lies at the centre of the whole. That the centre of the earth is the goal of their movement is indicated by the fact that heavy bodies moving towards the earth do not move parallel but so as to make equal angles,' and thus to a single centre, that of the earth. It is clear, then, that the earth must be at the centre and im- movable, not only for the reasons already given, but also because heavy bodies forcibly thrown quite straight upward return to the point from which they started, even if they are thrown to an infinite distance.2 From these considera- tions then it is clear that the earth does not move and does not lie elsewhere than at the centre. From what we have said the explanation of the earth’s immobility is also apparent. If it is the nature of earth, as observation shows, to move from any point to the centre, as the places of rising and setting of the fixed stars, follows from the assumption of a second motion, if the second is taken to be oblique to the first (Heath, /oc. cit.). 1 j,e. at right angles to a tangent: if it fell otherwise than at right angles, the angles on each side of the line of fall would be unequal. Ct. inf. 311°34, where the argument is repeated. The phrase mpos époias ywrias, ‘at /ike angles’, appears to strike Simpl. as a rather strange equivalent for mpds toas ywvias, ‘ at eyual angles’, borrowed, as he says, from thdse who referred ‘angle’ to the category of quality— dpotas 8€ éxddouy ras toas ywvrias ol thy ywviay bro Td mov avayovres (538, 22). Cf. Burnet’s remarks on éyoidrns in Phaedo, 109 A 2, quoted in part above in note on 295" 11. It seems plain that the words xara ordOpny (‘quite straight ’) refer to the line of the throw, not, as Simpl. supposes, to the line of return. But it is difficult to see what independent test Aristotle had of the straightness of the throw. ° Lal 5 of fire contrariwise to move from the centre to the extremity, 30 it is impossible that any portion of earth should move away from the centre except by constraint. For a single thing has a single movement, and a simple thing a simple: con- trary movements cannot belong to the same thing, and movement away from the centre is the contrary of movement to it. If then no portion of earth can move away from the centre, obviously still less can the earth as a whole so move. 35 For it is the nature of the whole to move to the point to

[297a.1] which the part naturally moves. Since, then, it would require a force greater than itself to move it, it must needs stay at the centre. This view is further supported by the contributions of mathematicians to astronomy, since the

[297a.5] observations made as the shapes change by which the order of the stars is determined,! are fully accounted for on the hypothesis that the earth lies at the centre. Of the position of the earth and of the manner of its rest or movement, our discussion may here end. Its shape must necessarily be spherical. For every por- ro tion of earth has weight until it reaches the centre, and the jostling of parts greater and smaller would bring about not a waved surface, but rather compression and convergence? of part and part until the centre is reached. The process should be conceived by supposing the earth to come into being in the way that some of the natural philosophers

[297a.15] describe.2 Only they attribute the downward movement to constraint, and it is better to keep to the truth and say that the reason of this motion is that a thing which possesses } The sense of the sentence is, clearly, ‘the phenomena are accounted for on the present hypothesis: why change it?’ But the precise relevance of (apparent) changes of shape does not seem clear. Simpl. illustrates by changes which would be necessitated by the hypothesis of a moving earth; but his own paraphrase of Aristotle’s words implies that the changes in question are odserved changes. The Greek implies (1) that the order of the stars is settled by the apparent shapes or patterns which they make in combination; (2) that the changes of these shapes are accounted for on the hypothesis of a stationary earth, * avyxwpeiv is clearly used here of ‘convergence’, not, as Prantl translates, of ‘making way’. So Simpl. paraphrases, cupmAdrrerat i) Ovyx@pel Erepoy Erepo. * The cosmogony which follows is in principle that of Anaxagoras (Burnet, E.G.P.° § 133). BOOK II. 14 297° weight is naturally endowed with a centripetal movement. When the mixture, then, was merely potential, the things that were separated off moved similarly from every side towards the centre. Whether the parts which came together

[297a.20] at the centre were distributed at the extremities evenly, or in some other way, makes no difference. If, on the one hand, there were a similar movement from each quarter of the extremity to the single centre, it is obvious that the resulting mass would be similar on every side. For if an equal amount is added on every side the extremity of the

[297a.25] mass will be everywhere equidistant from its centre, i.e. the figure will be spherical. But neither will it in any way affect the argument if there is not a similar accession of concurrent fragments from every side. For the greater quantity, finding a lesser in front of it, must necessarily drive it on, both having an impulse whose goal is the centre,

[297a.30] and the greater weight driving the lesser forward till this goal is reached. In this we have also the solution of a pos- sible difficulty. The earth, it might be argued, is at the centre and spherical in shape: if, then, a weight many times that of the earth were added to one hemisphere, the centre of the earth and of the whole will no longer be coincident. So that either the earth will not stay still at the centre, or if it does, it will be at rest without having its centre at the 297° place to which it is still its nature to move.' Such is the difficulty. A short consideration will give us an easy answer, if we first give precision to our postulate that any body endowed with weight, of whatever size, moves towards the centre. Clearly it will not stop when its edge touches the centre. The greater quantity must prevail until the body’s centre occupies the centre. For that is the goal of its impulse. Now it makes no difference whether we apply on sight ; and logically they are indefensible. ‘Either the earth will not stay still at the centre, or, if it does stay still at the centre, it will not have its (new) centre at the centre which is its natural goal!’ The words émi rov pécouv, then, may be an insertion. They are, however, more probably due to the desire for a direct contradictory. The view is pévet emi rod péoov: the contradictory is therefore ov peéver ei rov peéoov: and the eimep recalls only the pever. ‘Either it does not stay still at the centre or it doesn’t stay still at the centre.’ Aa this to a clod or common fragment of earth or to the earth as a whole. The fact indicated does not depend upon 10 degrees of size but applies universally to everything that has the centripetal impulse. Therefore earth in motion whether in a mass or in fragments, necessarily continues to move until it occupies the centre equally every way, the less being forced to equalize itself by the greater owing to the forward drive of the impulse.! If the earth was generated, then, it must have been 15 formed in this way, and so clearly its generation was spherical; and if it is ungenerated and has remained so always, its character must be that which the initial genera- tion, if it had occurred, would have given it. But the spherical shape, necessitated by this argument, follows also from the fact that the motions of heavy bodies always ao make equal angles,? and are not parallel. This would be the natural form of movement towards what is naturally spherical. Either then the earth is spherical or it is at least naturally spherical. And it is right to call anything that which nature intends it to be, and which belongs to it, rather than that which it is by constraint and contrary to nature. The evidence of the senses further corroborates this. How else would eclipses of the moon show segments a5 shaped as we see them? As it is, the shapes which the moon itself each month shows are of every kind—straight, gibbous, and concave—but in eclipses the outline is always curved: and, since it is the interposition of the earth that ‘less’ here and in ® 30 and in © stand for greater and smaller portions of one body, the line of division passing through the centre which is the goal. Suppose the earth so placed in regard to the centre. The larger and heavier division would ‘drive the lesser forward’, i.e. beyond the centre (® 30) 5 it would ‘prevail until the body’s centre occupied the centre’ (°5) ; it would ‘force the less to equalize itself’, i.e, to move on until the line passing through the central goal divided the body equally. Simpl. fails to see this.—Alex. (af. Simpl. 543, 15) raises the difficulty that the final movement of the ‘less’ will be away from the centre, or upward, and hence unnatural. But this is to make a perverse abstraction of part from whole. The desire of earth to reach the centre can never be fully satisfied, since the centre is a geometrical point. * Allowing for scruples due to the evident inequalities of the earth’s surface. BOOK II. 4 aoTt makes the eclipse, the form of this line will be caused by 30 the form of the earth’s surface, which is therefore spherical. Again, our observations of the stars make it evident, not only that the earth is circular, but also that it is a circle of no great size. For quite a small change of position to south or north causes a manifest alteration of the horizon.

[298a.1] There is much change, I mean, in the stars which are over- head, and the stars seen are different, as one moves north- ward or southward. Indeed there are some stars seen in Egypt and in the neighbourhood of Cyprus which are not

[298a.5] seen in the northerly regions; and stars, which in the north are never beyond the range of observation, in those regions rise and set. All of which goes to show not only that the earth is circular in shape, but also that it is a sphere of no great size: for otherwise the effect of so slight a change of place would not be so quickly apparent. Hence one should not be too sute of the incredibility of the view of those who conceive that there is continuity between the parts about the pillars of Hercules and the parts about India, and that in this way the ocean is one. As further evidence in favour of this they quote the case of elephants, a species occurring in each of these extreme regions, suggesting that the

[298a.15] common characteristic of these extremes is explained by their continuity. Also, those mathematicians who try to calculate the size of the earth’s circumference arrive at the figure 400,000 stades.! This indicates not only that the earth’s mass is spherical in shape, but also that as compared

[298a.20] with the stars it is not of great size. ~ ° the ancients’, a summary account of the methods by which this result was attained.—This appears to be the oldest recorded estimate of the size of the earth. 400,000 stades = 9,987 geographical miles. Other estimates (in miles) are: Archimedes, 7,495; Eratosthenes and Hip- parchus, 6,292; Poseidonius, 5,992 or 4,494; present day, 5,400. (These figures are borrowed from Prantl’s note on the passage in his translation, p. 319.) BOOK Ill 298° WE have already discussed the first heaven and its parts, 1

[298a.25] the moving stars within it, the matter of which these are composed and their bodily constitution, and we have also shown that they are ungenerated and indestructible. Now things that we call natural are either substances or functions and attributes of substances. As substances I class the

[298a.30] simple bodies—fire, earth, and the other terms of the series—and all things composed of them; for example, the heaven as a whole and its parts, animals, again, and plants and their parts. By attributes and functions I mean the movements of these and of all other things in which they have power in themselves to cause movement, and 298° also their alterations and reciprocal transformations. It is obvious, then, that the greater part of the inquiry into nature concerns bodies: for a natural substance is either a body or a thing which cannot come into existence without 5 body and magnitude. This appears plainly from an analysis of the character of natural things, and equally from an inspection of the instances of inquiry into nature. Since, then, we have spoken of the primary element, of its bodily constitution, and of its freedom from destruction and generation, it remains to speak of the other two! In speaking of them we shall be obliged also to inquire into to generation and destruction. For if there is generation anywhere, it must be in these elements and things com- posed of them. This is indeed the first question we have to ask: is generation a fact or not? Earlier speculation was at variance both with itself and with the views here put for- 15 ward as to the true answer to this question. Some removed generation and destruction from the world altogether. * Aristotle speaks of the four sublunary elements as two, because generically they are two. Two are heavy, two light: two move up and two down. Books III and IV of this treatise deal solely with these elements. ba il lia al ee BOO at 298” Nothing that is, they said, is generated or destroyed, and our conviction to the contrary is an illusion. So maintained the school of Melissus and Parmenides. But however excellent their theories may otherwise be, anyhow they cannot be held to speak as students of nature. There may be things not subject to generation or any kind of move- ment, but if so they belong to another and a higher inquiry 20 than the study of nature. They, however, had no idea of any form of being other than the substance of things per- ceived ; and when they saw, what no one previously had seen, that there could be no knowledge or wisdom without some such unchanging entities, they naturally transferred what was true of them to things perceived. Others, perhaps intentionally, maintain precisely the contrary opinion to 25 this. It had been asserted that everything in the world was subject to generation and nothing was ungenerated, but that after being generated some things remained in- destructible while the rest were again destroyed. This had been asserted in the first instance by Hesiod and his followers, but afterwards outside his circle by the earliest natural philosophers.! But what these thinkers maintained was that all else has been generated and, as they said, ‘is 30 flowing away’, nothing having any solidity, except one single thing which persists as the basis of all these trans- formations. So we may interpret the statements of Heraclitus of Ephesus and many others.” And some ® sub- ject all bodies whatever to generation, by means of the

[299a.1] composition and separation of planes. Discussion of the other views may be postponed.* But this last theory which composes every body of planes is, as school of Orpheus and Musaeus’). 2 e,g. Thales, Anaximander, Anaximenes. 8 ‘The view of Timaeus the Pythagorean, recorded by Plato in the dialogue named after him’ (Simpl.). The theory criticized is certainly that advanced in the Zzmaeus, and is usually attributed to Plato, as by Zeller, PA. d. Gr. II. i, p. 804, but Aristotle probably has also in mind certain members of the Academy, particularly Xenocrates (26., pp. 1016 ff.). * The promised discussion is not to be found in the Ye Cae/o nor in its sequel, the De Generatione et Corruptione, But Aristotle has already devoted some attention to these views at the beginning of the Physics, and there is also the discussion of A7et. A. the most superficial observation shows, in many respects in plain contradiction with mathematics. It is, however, wrong

[299a.5] to remove the foundations of a science unless you can replace them with others more convincing. And, secondly, the same theory which composes solids of planes clearly composes planes of lines and lines of points, so that a part of a line need not be a line. This matter has been already considered

[299a.10] in our discussion of movement, where we have shown that an indivisible length is impossible.! But with respect to natural bodies there are impossibilities involved in the view which asserts indivisible lines, which we may briefly consider at this point. For the impossible consequences which result from this view in the mathematical sphere will reproduce themselves when it is applied to physical bodies,

[299a.15] but there will be difficulties in physics which are not present in mathematics; for mathematics deals with an abstract and physics with a more concrete object. There are many attributes necessarily present in physical bodies which are necessarily-excluded by indivisibility ; all attributes, in fact, which are divisible.2 There can be nothing divisible in an indivisible thing, but the attributes of bodies are all divisible

[299a.20] in one of two ways. They are divisible into kinds, as colour is divided into white and black, and they are divisible per accidens when that which has them is divisible. In this latter sense attributes which are simple® are nevertheless divisible. Attributes of this kind will serve, therefore, to illustrate the impossibility of the view. It is impossible, if as two parts of a thing have no weight, that the two together should have weight. But either all perceptible bodies or some, such as earth and water, have weight, as these thinkers would themselves admit. Now if the point has no weight, clearly the lines have not either, and, if they have not, neither have the planes. Therefore no body has

[299a.30] weight. It is, further, manifest that their point cannot have LAY SON lenik * The reading dSiatperdv, though preserved only in one rather inferior manuscript, must be preferred on grounds of sense to the dd:aiperor of the other manuscripts. The silence of Simplicius seems to cor- roborate the reading diaiperdv. Possibly the clause is a gloss. BOOK III. 1 299° weight. For while a heavy thing may always be heavier than something and a light thing lighter than something, 299° a thing which is heavier or lighter than something need not be itself heavy or light, just as a large thing is larger than others, but what is larger is not always large. A thing which, judged absolutely, is small may none the less be larger than other things. Whatever, then, is heavy 5 and also heavier than something else, must exceed this by something which is heavy. A heavy thing therefore is always divisible. But it is common ground. that a point is indivisible. Again, suppose that what is heavy is a dense body, and what is light rare. Dense differs from rare in containing more matter in the same cubic area. A point, then, if it may be heavy or light, may be dense or rare, 10 But the dense is divisible while a point is indivisible. And if what is heavy must be either hard or soft, an impossible consequence is easy to draw. For a thing is soft if its surface can be pressed in, hard if it cannot; and if it can be pressed in it is divisible. Moreover, no weight can consist of parts not possessing 15 weight. For how, except by the merest fiction, can they specify the number and character of the parts which will produce weight? And, further, when one weight is greater than another, the difference is athird weight; from which it will follow that every indivisible part possesses weight. For suppose that a body of four points possesses weight. A body composed of more than four points’ will be superior in weight to it, a thing which has weight. But the difference between weight and weight must be a weight, as the difference between white and whiter is white. Here the difference which makes the superior weight heavier ” is the single point which remains when the common number, four, is subtracted. A single point, therefore, has weight. Further, to assume, on the one hand, that the planes can ° 1 Prantl’s conjecture #) rovdi is unsatisfactory. The alternatives are (1) to keep the reading of the manuscripts ( rod), (2) to read rovdi, omitting 7. In the latter case the sense remains the same but the construction becomes rather easier. 2 Prantl’s conjectural duplication of the words pid oriypp, though harmless, is unnecessary. 25 only be put in linear contact? would be ridiculous. For just as there are two ways of putting lines together, namely, end to end and side by side, so there must be two ways of putting planes together. Lines can be put together so that contact is linear by laying one along the other, though not by putting them end to end.? But if, similarly, in putting the planes together, superficial contact is allowed as an 30 alternative to linear, that method will give them bodies which are not any element nor composed of elements.’ Again, if it is the number of planes in a body* that makes

[300a.1] one heavier than another, as the Z77maeus® explains, clearly the line and the point will have weight. For the three cases are, as we said before, analogous. But if the reason of differences of weight is not this, but rather the

[300a.5] heaviness of earth and the lightness of fire, then some of the planes will be light and others heavy (which involves a similar distinction in the lines and the points); the earth- plane, I mean, will be heavier than the fire-plane. In general, the result is either that there is no magnitude at all, or that all magnitude could be done away with. For 1o a point is to a line as a line is to a plane and as a plane is to a body. Now the various forms in passing into one another will each be resolved into its ultimate constituents. It might happen therefore that nothing existed except points, and that there was no body at all. A further con- sideration is that if time is similarly constituted, there would be, or might be, a time at which it was done away with. For

[300a.15] the indivisible now is like a point ina line. The same conse- quences follow from composing the heaven of numbers, as some of the Pythagoreans do who make all nature out of numbers. For natural bodies are manifestly endowed with weight and lightness, but an assemblage of units can neither be composed to form a body nor possess weight. 1 j,e. so as to form pyramids, cubes, &c. * Grammar requires the readings émiriGeuévn, mpooriOenevn instead of the émriBewévny, mpooriOeyévny of all manuscripts but one (M). * Because they will not be pyramids or instances of any other recognized figure. _* Omitting the ra before ray émuédwy, which got into E by a simple dittography and is found in no other manuscript. 5 Plato, 77272. 56 B. * i.e. point : line :: line : plane :: plane : body (as below). BOOK III. 2 300" a natural movement may be shown as follows. They mani- festly move, and if they have no proper movement they must move by constraint: and the constrained is the same as the unnatural. Now an unnatural movement presupposes a natural movement which it contravenes, and which, how- a5 ever many the unnatural movements, is always one. For naturally a thing moves in one way, while its unnatural movements are manifold! The same may be shown from the fact of rest. Rest, also, must either be constrained or natural, constrained in a place to which movement was con- strained, natural in a place movement to which was natural.

[300a.30] Now manifestly there is a body which is at rest at the centre. If then this rest is natural to it, clearly motion to this place is natural to it. If, on the other hand, its rest is constrained, what is hindering its motion? Something, perhaps, which is at rest: but if so, we shall simply repeat the same argument ; and either we shall come to an ultimate something to which rest where it is is natural, or we shall 300° have an infinite process, which isimpossible. The hindrance to its movement, then, we will suppose, is a moving thing— as Empedocles says that it is the vortex which keeps the earth still— : but in that case we ask, where would it have moved to but for the vortex?* It could not move in- finitely ; for to traverse an infinite is impossible, and im- possibilities do not happen. So the moving thing must stop somewhere, and there rest not by constraint but naturally. Buta natural rest proves a natural movement on asserts that the unnatural movement is single since it is the contrary of the natural, which is single. But it is not difficult to conceive of all movements of a body divergent from the one natural path as unnatural according to the degree of their divergence, even though, strictly construed, the unnatural path is also one. specially relevant to the hypothesis that the obstacle is in movement. There is therefore something to be said for an interpretation which, like that attributed by Simplicius to Alexander, makes the question refer to the supposed moving obstacle instead of to the earth. But Alexander’s interpretation turns out on examination to create more difficulties than it removes: and there is no great objection, after ail, to supposing that Aristotle refutes the second alternative by an argu- -ment which refutes both. to the place of rest. Hence Leucippus and Democritus, who say that the primary bodies are in perpetual movement ro in the void or infinite, may be asked to explain the manner of their motion and the kind of movement which is natural to them. For if the various elements are constrained by one another to move as they do, each must still have a natural movement which the constrained contravenes, and the prime mover must cause motion not by constraint but 15 naturally. If there is no ultimate natural cause of move- ment and each preceding term in the series is always moved by constraint, we shall have an infinite process. The same difficulty is involved even if it is supposed, as we read in the 7zmaeus, that before the ordered world was made the elements moved without order. Their movement must have been due either to constraint or to their nature. And ao if their movement was natural, a moment’s consideration shows that there was already an ordered world. For the prime mover must cause motion in virtue of its own natural movement,? and the other bodies, moving without constraint, as they came to rest in their proper places, would fall into the order in which they now stand, the heavy bodies moving 25 towards the centre and the light bodies away from it. But that is the order of their distribution in our world. There is a further question, too, which might be asked. Is it pos- sible or impossible that bodies in unordered movement should combine in some cases into combinations like those of which bodies of nature’s composing are composed, such, I mean, as bones and flesh? Yet this is what Empedocles 30 asserts to have occurred under Love. ‘Many a head’, says 1 Plato, 77. 30a. ? Taking the reading for which Alexander argued—xweiv airé xwwov- pevov kara pvow. I should put a comma after xweiy and take xara ¢. with x:vovpevov. The hypothesis is that the elements have their natural movements; and the dependent clause airéd xv. x. @. applies this hypothesis to the prime mover, as ra xwvovjeva yw) Bia applies it to the other bodies. Aristotle shows that, on this hypothesis, the present world-order would exist: the prime mover would be imparting move- ment to the bodies within it, as it does now, and the four elements would be moving towards or resting in their proper places, as now. If avré is read, we have a more disputable description of this xkécpos and less use for the words xiwotvmevov kara piow. airéd is said to be the reading of the manuscripts, but neither copyists nor collators are to be trusted with a breathing. J has auré (sic). BOOK III. 2 300” he, ‘came to birth without a neck.’! The answer to the view that there are infinite bodies moving in an infinite is that, if the cause of movement is single, they must move with a single motion, and therefore not without order; and

[301a.1] if, on the other hand, the causes are of infinite variety, their motions too must be infinitely varied. For a finite number of causes would produce a kind of order, since absence of order is not proved by diversity of direction in motions: indeed, in the world we know, not all bodies, but only bodies of the same kind, have a common goal of movement. Again, disorderly movement means in reality unnatural movement, since the order proper to perceptible things is their nature. And there is also absurdity and impossibility in the notion that the disorderly movement is infinitely con- tinued. For the nature of things is the nature which most of them possess for most of the time. Thus their view

[301a.10] brings them into the contrary position? that disorder is natural, and order or system unnatural. But no natural fact can originate in chance, This is a point which Anaxa- goras seems to have thoroughly grasped ; for he starts his cosmogony from unmoved things. The others, it is true, make things collect together somehow before they try to produce motion and separation. But there is no sense in starting generation from an original state in which bodies are separated and in movement. Hence Empedocles begins after the process ruled by Love: for he could not have constructed the heaven by building it up out of bodies in separation, making them to combine by the power of Love, since our world has its constituent elements in separation, and therefore presupposes a previous state of

[301a.20] unity and combination. These arguments make it plain that every body has its natural movement, which is not constrained or contrary to its nature. We go on to show that there are certain bodies * wn u 1 Emped. fr. 57, 1. 1 (Diels, Vors. 245, 20). 8 Putting a comma instead of a full-stop after oroiyelwv (1. 19). this kind of impetus. The introduction of necessity shows that we are dealing with a universal. Below in 301” 16, and again in 301” 30, we

[301a.1] whose necessary impetus is that of weight and lightness. Of necessity, we assert, they must move, and a moved thing

[301a.25] which has no natural impetus cannot move either towards or away from the centre. Suppose a body A without weight, and a body B endowed with weight. Suppose the weight- less body to move the distance CD, while B in the same time moves the distance CZ, which will be greater since the heavy thing must move further. Let the heavy body then

[301a.30] be divided in the proportion CZ : CD (for there is no reason why a part of B should not stand in this relation to the whole). Now if the whole moves the whole distance CZ, the part must in the same time move the distance CD. A weightless body, therefore, and one which has weight 301° will move the same distance, which is impossible. And the same argument would fit the case of lightness. Again, a body which is in motion but has neither weight nor light- ness, must be moved by constraint, and must continue its constrained movement infinitely. For there will bea force 5 which moves it, and the smaller and lighter a body is the further will a given force move it. Now let 4, the weight- less body, be moved the distance CZ, and £8, which has weight, be moved in the same time the distance CD. Dividing the heavy body in the proportion CE: CD, we 10 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. 15 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 are told that every body is either light or heavy. Aristotle’s readers would of course understand that the disjunction only applied uni- versally ‘beneath the moon’. The more cautious statement in this passage allows for the exception of the heavenly body. * Reading mporeOévros, which is given by all manuscripts except M and by Simplicius. * i.e. not infinite. Siepiopevoy is here equivalent to dpicpévor. A similar tendency is observable in other derivatives of dcopi¢ewv, e. g. adiépictos. Alexander and Simplicius made great, but not very oe BOOK III. 2 lightness. But since ‘ nature’ means a source of movement within the thing itself, while a force is a source of move- ment in something other than it or in itself gv@ other,! and since movement is always due either to nature or to con- straint, 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 gud light produces upward motion, being propelled and set in motion by the force, and gwd 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 func- tion, 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 successful, efforts to interpret the word as qualifying ‘body’: they do not consider the possibility of its qualifying Bapos f) xoudédrnra. Probably their manuscripts, like FHMJ, had ré before diwpicpévor, which would make it difficult or impossible to take S:wpiopévoy in that way. critical note to Heiberg’s edition, p. 595, 22): his interpretation requires it. * Reading Odrrw in 1. 20, with all manuscripts except F and with Simplicius. airy in 22 is somewhat vague in reference, but must stand for 9 Stvayts airy. 8 ]l. 23-5, méebuxe . . . Bapis, are grammatically a parenthesis, and should be so printed, with a colon in 23 after Bapvs, For the doctrine cf. Phys. 1V. 8 and VIII. to. 4 Simplicius and Alexander, with three of our manuscripts (FHM), have éy rovrots for ex Trovrwy. é€v rovros would go with éyovor rather than with gavepdv, qualifying the application of the second clause. The qualification, however, cannot be made very precise, and it is best to follow the other three manuscripts. ® The ydp which introduces the next sentence shows that the justification of the statement is to come. The thesis follows from what was ‘said earlier’, because in PAys. 1V. 6-9 the hypothesis of a void was investigated and refuted, and it is here shown that absolute generation, or generation of body out of not-body, requires a void. 5 30 gor? cannot be generation either of everything or in an absolute sense of anything. It is impossible that everything should

[302a.1] be generated, unless an extra-corporeal' void is possible. bh) Io 15 20 35 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 ifthe potential body was not already in actuality some other kind of body, the existence of an extra-corporeal void must be admitted.

[302a.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. The nature of the heavenly body and the views of Parmenides and Melissus, referred to by Simplicius, are not here in point. which are supposed to be distributed throughout the texture of every body. Simplicius attributes the distinction of two kinds of void to the authors of the theory themselves. * Reading in 1. 2 ro yudpevoy, ef éyévero with Bekker. The manu- scripts are confused, and offer many variants. * viz. bodies subject to generation. We read rota ray rovovrev with the manuscripts, taking ray roovtwy as a partitive genitive (after Simplicius). BOOK III. 3 302" 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.

[302a.30] 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 homoeo- merous things,! viz. flesh, bone, and the like. Earth and 302” 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 5 body has its 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. are finite or infinite in number, and, if finite, what their number is. Let us first show reason for 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 15 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 1 “Homoeomerous’ means ‘having parts like one another and like the whole of which they are parts’, Some confusion is here caused by the fact that Aristotle sometimes uses ‘homoeomerous’ as an attribute of the parts of a homoeomerous whole, i.e. as meaning ‘like one another and like the whole of which they are parts’. That is what he means when he says of a body (302” 16) that it is ‘divisible into homoeomerous parts’ or (74. 25) that it is ‘composed of homoeo- merous bodies’. The use of the term Aemropepés (= pixpopepes) is complicated by a similar transference from whole to part (cp. 304” 9, note). 2 Cp. Book I, 270° 24. 3 rovs ... movouvras must be construed (by a kind of zeugma) with Oewpnréov. 20 25 30

[303a.1] 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 homoeomerous 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 ap- propriate 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 neces- sarily 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 1 Above, 302° 18. * ‘Divisible into homoeomerous parts’ = ‘homoeomerous wholes’ (cp. note on ‘homoeomerous’ at 302°31). The argument is therefore as follows: ‘homoeomerous’ includes mixed as well as simple bodies ; but any one who understood the meaning of the term ‘element’ would have seen that a mixed body cannot be an element: instead of regarding all homoeomerous bodies as elements, he would have confined the term to such homoeomerous bodies as are simple.—As an argument against Anaxagoras this is ineffective ; for he (a) denied that flesh, bone, &c., are mixed; (4) denied that earth, air, fire, and water—cited by Simplicius as simple and homoeomerous—are simple. Aristotle is content to argue from what he regards as established fact, whether Anaxagoras admits it or not. Anaxagoras would have claimed that the suggested criterion of indivisibility xar’ «iSos was satisfied by his éyo:opeph, and could therefore plead not guilty to the charge of misapprehending the meaning of ‘ element’. * All bodies should be either elements or composed of elements. But Anaxagoras, though he makes his elements infinite, is still not able to show that every whole is composed of parts like itself. - eee Ta merepacpeva (So J, as well as three of Bekker’s manu- scripts). * The proof of the proposition is given in De Sensu, 6 (445> 20 ff.). BOOK III. 4 303°

[303a.5] 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 to 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,

[303a.15] except so far as 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

[303a.20] 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 move- ment.? 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 3° or 1 Because the atom is practically a mathematical unit, out of which bodies are formed by simple addition. Cp. et. Z. 13, 1039 3 ff. ZeGpe 03" 1a ° Esp. PAys. VI. 1-2 (231° 18 ff.). water-atom is larger than the air-atom: what is required on this theory is the extrusion from the air of the larger atoms. Conversely, if air were being formed out of water, the smaller atoms would be extruded from the water. But the supply of large (or small) atoms will soon run out, and air not reducible to water (or water not reducible to air) will be left. Bb 5 fo not seem as if the elements would be infinite in number. The atoms differ in figure, and all figures are composed of pyramids, rectilinear in the case of rectilinear figures, while the sphere has eight pyramidal parts.1_ 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. Since the number of the elements must be limited, it 5 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—embracing 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 ‘5 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, * The pyramids are tetrahedrons; and those produced by triple section of a sphere are irregular, having a spherical base. * i.e, there must be a limited number of primary figures to which all other figures are reducible. .° There are only two places to which movement can be directed, viz. the circumference and the centre. By the two simple motions Aristotle probably here means motions towards these two places, motion up and motion down. Circular motion is not possible beneath the moon. * Thales and Hippon. ° Anaximenes and Diogenes of Apollonia. ° Heracleitus and Hippasus: but see below, 304 18, note. * Anaximander. This identification has been rejected by many modern scholars. See Bonitz, /#d. 50°33, Diels, Vors.° 18, 10 and 416, I, Burnet, £.G.P.3§ 15. Diels follows Zeller in attributing the view to a certain Idaios of Himera, whom Aristotle never mentions by name and of whom hardly anything is known. Burnet refers the passage to Anaximander. BOOK III. 5 303° so that the body with the finer parts must have priority in the order of nature. But they say that fire is of all 20 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 equiva- lent to fineness and coarseness, since the fine is rare, and

[303a.25] coarse in their use means dense. But fineness and coarse- ness, 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

[303a.30] from the element by the greatness and smallness of their parts. This method of distinction makes all judgement rela- tive. There will be no absolute distinction between fire, water, and air, but one and the same body will be relatively to

[304a.1] this fire, relatively to something else air.2 The same difficulty is involved equally in the view which recognizes several 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,

[304a.5] 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 ° starting-point of the process of generation or synthesis; and a body denser than fire and rarer than earth, like air or water, or finer than water and denser than air, like Anaximander’s infinite, will not do. 2 For the attributes great and small belong to the category of relation (Caz. 5” 10 ff.). Lane of size. } * Simplicius observes that the argument is justly called crude, since ingeniously—-the position may be supported by the follow- ing argument. As all bodies are composed of that which

[304a.15] has the finest parts, so all solid figures are composed of pyramids: 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 bea pyramid.? Others, again, express no opinion on the subject of its figure, but simply regard it as the body

[304a.30] 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 incon- 25 sistent 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 30 So on, and if there is more air than water and, generally, more of the finer body than of the coarser, obviously the element cf water will be smaller than that of air. But the lesser quantity is contained in the greater. Therefore it involves an undistributed middle: ‘fire is piercing’, ‘the pyramid is piercing’: they attempt to draw an affirmative conclusion in the second figure. equivalent to Aemrouepéoraroy, which is the reading of EL and (prob- ably) of Simplicius.—The pyramid is presumably said to have the smallest parts because it contains fewer of the primary triangles than any other regular solid. But the assertion is not thereby justified. Given a certain size of triangle, the pyramid would be the smallest of the solids in cubic content; thus the body composed of pyramids would be the body with the smallest parts. The epithet Aerropepés, in short, seems to be transferred from the whole to the part, just as Opotopepes was (above, 302° 31, note). * To whom is this ‘more ingenious’ version to be attributed? ‘Heracleitus made fire the universal element but did not Say it was a pyramid, and the Pythagoreans, who said that fire was composed of pyramids, did not make it the universal element’ (Simpl.). 3 Perhaps oioy rd should be read for oioy rd. * The ascertained fact on which this argument is based is that when (e.g.) water turns into air, the volume of the resultant air is BOOK III. 5 304° the air element is divisible. And the same could be shown 304” 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 5 is either an element or composed of elements, since a part of fire will be neither fire nor any other element. And (4) 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 di- visible 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 to 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. 5 bo ° greater than that of the original water. This increase of volume can only be accounted for (since the hypothesis of a void has been refuted) by supposing an increase in the volume of the atom proportionate to the observed increase in the volume of the total mass, But the enlarged atom would be divisible, and therefore no atom. ’ i.e. a pyramid cannot be divided so that every part is a pyramid. 2 If every body is infinitely divisible, it is difficult to give a precise meaning to ‘that which has the smallest parts’. Further, the phrase, as used, is somewhat illogical; for the argument would point to the smallest part of any body, rather than the body with the smallest parts, as the element. But the use of Aemropepés (and puxpopepes) as an epithet of the part instead of the whole occurs elsewhere (cf. note on 304° 16). 5 Book I, c. ii.

[306a.1] which is indissoluble is indestructible and elementary, and earth alone cannot be dissolved into any body but itself. Again, in the case of those elements which do suffer dissolution, the ‘suspension’ of the triangles is unsatis- factory. But this takes place whenever one is dissolved into another, because of the numerical inequality of the triangles which compose them.’ Further, those who hold these views must needs suppose that generation does not

[306a.25] start from a body. For what is generated out of planes cannot be said to have been generated from a body. And they must also assert that not all bodies are divisible, coming thus into conflict with our most accurate sciences, namely the mathematical, which assume that even the intelligible is divisible, while they, in their anxiety to save

[306a.30] their hypothesis, cannot even admit this of every per- ceptible thing. For any one who gives each element a shape of its own, and makes this the ground of distinction between the substances, has to attribute to them indi- visibility ; since division of a pyramid or a sphere must leave somewhere at least a residue which is not a sphere or a pyramid. Either, then, a part of fire is not fire, so that 306° there is a body prior to the element—for every body is either an element or composed of elements—or not every body is divisible. In general, the attempt to give a shape to each of the8 simple bodies is unsound, for the reason, first, that they 5 will not succeed in filling the whole. It is agreed that there are only three plane figures which can fill a space, the triangle, the square, and the hexagon, and only two solids, the pyramid and the cube.” But the theory needs more than these because the elements which it recognizes are more in number. Secondly, it is manifest that the simple 10 bodies are often given a shape by the place in which they are included, particularly water and air. In such a case the shape of the element cannot persist ; for, if it did, the 1 e.g. the eixoodedpoy of ‘water, with its twenty triangles, has to be converted into the dxraeSpoy of air, with eight triangles. Four of the twenty component triangles of the water-particle will be ‘suspended’. ? Only regular figures are included. BOOK III. 8 306" contained mass would not be in continuous contact with the containing body; while, if its shape is changed, it will : cease to be water, since the distinctive quality is shape. Clearly, then, their shapes are not fixed! Indeed, nature 15 itself seems to offer corroboration of this theoretical con- clusion. Just as in other cases the substratum must be ; formless and unshapen—for thus the ‘all-receptive’, as we q read in the Z7zmaeus,? will be best for modelling—so the elements should be conceived as a material for composite 20 things ; and that is why they can put off their qualitative distinctions and pass into one another. Further, how can they account for the generation of flesh and bone or any other continuous body? The elements alone cannot produce them because their collocation cannot produce a continuum. 25 Nor can the composition of planes; for this produces the elements themselves, not bodies made up of them. Any one then who insists upon an exact statement of this kind of theory,’ instead of assenting after a passing glance at it, will see that it removes generation from the world. Further, the very properties, powers, and motions, to 30 which they paid particular attention in allotting shapes, show the shapes not to be in accord with the bodies. Because fire is mobile and productive of heat* and com- bustion, some made it a sphere, others a pyramid. These shapes, they thought, were the most mobile because they

[307a.1] offer the fewest points of contact and are the least stable of any; they were also the most apt to produce warmth and combustion, because the one is angular throughout ° while the other has the most acute angles, and the angles, they say, produce warmth and combustion. Now, in the first place, with regard to movement both are in error. These

[307a.5] may be the figures best adapted to movement; they are 2 Plato, Zim. 51 A. At Mr. Ross’s suggestion, I have altered the stopping of the sentence. Delete comma after dAAos (1. 17), and enclose the words pddwra yap... 7d mavdexes (Il. 18-19) within brackets. $ Reading rods rovov'rovs with FHMJ. — 4 Prantl’s text (presumably by accident) omits the xai before depuavtikov. 307° DE_CAELO not, however, well adapted to the movement of fire, which is an upward and rectilinear movement, but rather to that form of circular movement which we call rolling. Earth, again,! they call a cube because it is stable and at rest. But it rests only in its own place, not anywhere; from 1oany other it moves if nothing hinders, and fire and the other bodies do the same. The obvious inference, there- fore, is that fire and each several element is in a foreign place a sphere or a pyramid, but in its own a cube. Again, if the possession of angles makes a body produce

[307a.15] heat and combustion, every element produces heat, though one may do so more than another. For they all possess angles, the octahedron and dodecahedron as well as the pyramid; and Democritus makes even the sphere a kind of angle, which cuts things because of its mobility.2 The difference, then, will be one of degree: and this is plainly false. They must also accept the inference that the mathe- matical solids produce heat and combustion, since they too possess angles and contain atomic spheres* and pyramids, especially if there are, as they allege, atomic figures. Any- how if these functions belong to some of these things and not to others, they should explain the difference, instead of speaking in quite general terms as they do. Again,

[307a.25] combustion of a body produces fire, and fire is a sphere or a pyramid. The body, then, is turned into spheres or pyramids. Let us grant that these figures may reasonably be supposed to cut and break up bodies as fire does ; still it remains quite inexplicable that a pyramid must needs produce pyramids or a sphere spheres. One might as well postulate that a knife or a saw divides things into knives or saws. It is also ridiculous to think only of division when allotting fire its shape. Fire is generally thought of as combining and connecting rather than as separating. 2 ro) ° 3} * Though it has a low degree of angularity, it is highly mobile and therefore extremely piercing. But the double os is awkward, and perhaps the tradition is at fault. (J has réuvee os evxivnroy, supporting E against the other MSS.) * Prantl’s oaipa is a misprint for opaipar. ‘ i.e, indivisible units of line, of which the geometrical figures are composed. BOOK III. 8 307” For though it separates bodies different in kind, it combines 307° those which are the same; and the combining is essential to it, the functions of connecting and uniting being a mark of fire, while the separating is incidental. For the expulsion of the foreign body is an incident in the compacting of the homogeneous. In choosing the shape, then, they should have thought either of both functions or preferably of the 5 combining function. In addition, since hot and cold are contrary powers, it is impossible to allot any shape to the cold. For the shape given must be the contrary of that given to the hot, but there is no contrariety between figures. That is why they have all left the cold out, though properly either all or none should have their dis- 10 tinguishing figures. Some of them, however, do attempt to explain this power, and they contradict themselves. A body of large particles, they say, is cold because instead of penetrating through the passages it crushes. Clearly, then, that which is hot is that which penetrates these passages, or in other words that which has fine particles. It results that hot and cold are distinguishéd not by the 15 figure but by the size of the particles, Again, if the pyramids are unequal in size, the large ones will not be fire, and that figure will produce not combustion but its contrary. From what has been said it is clear that the difference of the elements does not depend upon their shape. Now their most important differences are those of property, function, and power; for every natural body has, we main- tain, its own functions, properties, and powers. Our first business, then, will be to speak of these, and that inquiry will enable us to explain the differences of each from each, w ° BOOK IV 307° WE have now to consider the terms ‘heavy’ and ‘light’. 1 We must ask what the bodies so called are, how they are

[307a.30] constituted, and what is the reason of their possessing these powers, The consideration of these questions is a proper part of the theory of movement, since we call things heavy and light because they have the power of being moved naturally in a certain way. The activities corresponding to these powers have not been given any name, unless

[308a.1] it is thought that ‘impetus’ is such a name. But because the inquiry into nature is concerned with movement,’ and these things have in themselves some spark (as it were) of movement, all inquirers avail themselves of these powers, though in all but a few cases without exact discrimination.

[308a.5] We must then first look at whatever others have said, and formulate the questions which require settlement in the interests of this inquiry, before we go on to state our own view of the matter. Language recognizes (a) an absolute, (4) a relative heavy and light. Of two heavy things, such as wood and bronze, we say that the one is relatively light, the other relatively 1o heavy. Our predecessors have not dealt at all with the absolute use of the terms, but only with the relative. I mean, they do not explain what the heavy is or what the light is, but only the relative heaviness and lightness of things possessing weight. This can be made clearer as follows. There are things whose constant nature it is to move away

[308a.15] from the centre, while others move constantly towards the centre ; and of these movements that which is away from the centre I call upward movement and that which is towards it I call downward movement. (The view, urged by some,’ that there is no up and no down in the heaven, - is absurd. There can be, they say, no up and no down, since * Read votxhy per etvac (E alone omits péy). * The digression is directed against Plato, Zim. 62E; but the view was held by others besides Timaeus. BOOK IV. 1 308°

[308a.20] ; the universe is similar every way, and from any point on the earth’s surface a man by advancing far enough will come to stand foot to foot with himself. But the extremity of the whole, which we call ‘above’, is in position above and in nature primary. And since the universe has an extremity and a centre, it must clearly have an up and down. Common

[308a.25] usage is thus correct,! though inadequate. And the reason of its inadequacy is that men think that the universe is not similar every way. They recognize only the hemisphere which is over us. But if they went on to think of the world as formed on this pattern all round, with a centre identically related to each point on the extremity, they would have to admit that the extremity was above and the centre below.) By absolutely light, then, we mean that which moves upward or to the extremity, and by absolutely 3° heavy that which moves downward or to the centre. By lighter or relatively light we mean that one, of two bodies endowed with weight and equal in bulk, which is exceeded by the other in the speed of its natural downward move- ment.” 2 Those of our predecessors who have entered upon this

[308a.35] inquiry have for the most part spoken of light and heavy things only in the sense in which one of two things both 308° endowed with weight is said to be the lighter. And this treatment they consider a sufficient analysis also of the ; notions of absolute heaviness and absolute lightness, to which their account does not apply. This, however, will become clearer as we advance. One use of the terms ‘lighter’ and ‘heavier’ is that which is set forth in writing 5 in the 77maeus,® that the body which is composed of the greater number of identical parts is relatively heavy, while that which is composed of a smaller number is relatively 2 Accepting Prantl’s first correction, od (for 6), which seems to be necessary to the sense. His second correction, towy (for tov), is to be rejected as unnecessary. Bywater (J. of Phil, xxviii, p. 242) suggests Oarépov, keeping 6 and fcov; but the phrase, so emended, seems to be descriptive of the heavy rather than of the light. (oe ie” light. Asa larger quantity of lead or of bronze is heavier than a smaller—and this holds good of all homogeneous masses, the superior weight always depending upon a 10 numerical superiority of equal parts—in precisely the same way, they assert, lead is heavier than wood. For all bodies, in spite of the general opinion to the contrary, are composed of identical parts and of a single material. But this analysis says nothing of the absolutely heavy and light. The facts are that fire is always light and moves upward, while earth and all earthy things move downwards or 15 towards the centre. It cannot then be the fewness of the triangles (of which, in their view, all these bodies are com- posed) * which disposes fire to move upward. If it were, the greater the quantity of fire the slower it would move, owing to the increase of weight due to the increased number of triangles. But the palpable fact, on the contrary, is that the greater the quantity, the lighter the mass is and ao the quicker its upward movement: and, similarly, in the reverse movement from above downward, the small mass will move quicker and the large slower. Further, since to be lighter is to have fewer of these homogeneous parts and to be heavier is to have more, and air, water, and fire are composed of the same triangles, the only difference being a5 in the number of such parts, which must therefore explain any distinction of relatively light and heavy between these bodies, it follows that there must be a certain quantum of air which is heavier than water. But the facts are directly opposed to this. ‘The larger the quantity of air the more readily it moves upward, and any portion of air without exception will rise up out of the water. So much for one view of the distinction between light 30 and heavy. To others * the analysis seems insufficient ; and their views on the subject, though they belong to an older generation than ours, have an air of novelty. It is apparent ? I put a colon in 1. 6 after eXarréywy and mark ll. 8-9, dpoias dé... €or, as parenthetical. This leaves an asyndeton at dSomep in 1. 7, but it seems to give the sequence of thought better than the stopping of Bekker and Prantl does. ® There should be a comma after rptydvey in 1. 15. * The atomists, Democritus and Leucippus. BOOK IV. 2 308° that there are bodies which, when smaller in bulk than others, yet exceed them in weight. It is therefore obviously insufficient to say that bodies of equal weight are composed : of an equal number of primary parts: for that would give 35 7 equality of bulk. Those who maintain that the primary or atomic parts, of which bodies endowed with weight are

[309a.1] composed, are planes, cannot so speak without absurdity ; ! but those who regard them as solids are in a better position to assert that of such bodies the larger is the heavier. But since in composite bodies the weight obviously does not correspond in this way to the bulk, the lesser bulk being

[309a.5] often superior in weight (as, for instance, if one be wool and the other bronze), there are some who think and say that the cause is to be found elsewhere. The void, they say, which is imprisoned in bodies, lightens them and sometimes makes the larger body the lighter. The reason is that there is more void. And this would also account for the fact that a body composed of a number of solid parts equal to, or even smaller than, that of another is sometimes larger in bulk than it. In short, generally and in every 1° case a body is relatively light when it contains a relatively large amount of void. This is the way they put it them- selves, but their account requires an addition. Relative lightness must depend not only on an excess of void, but also on a defect of solid: for if the ratio of solid to void

[309a.15] exceeds a certain proportion, the relative lightness will ; disappear. Thus fire, they say, is the lightest of things just for this reason that it has the most void. But it would follow that a large mass of gold, as containing more void than a small mass of fire, is lighter than it, unless it also contains many times as much solid. The addition is there- fore necessary. Of those who deny the existence of a void some, like Anaxagoras and Empedocles, have not tried to analyse the notions of light and heavy at all; and those who, while still denying the existence of a void, have attempted this,’ have ———- — = » ° 1 For, since the planes have no weight, their number cannot affect the weight of a body. 2 Plato, in the 7zmaeus. failed to explain why there are bodies which are absolutely heavy and light, or in other words why some move upward and others downward. The fact, again, that the body of

[309a.25] greater bulk is sometimes lighter than smaller bodies is one which they have passed over in silence, and what they have said gives no obvious suggestion for reconciling their views ‘with the observed facts. But those who attribute the lightness of fire to its con- taining so much void ave necessarily involved in practically the same difficulties. For though fire be supposed to

[309a.30] contain less solid than any other body, as well as more void, yet there will be a certain quantum of fire in which the amount of solid or plenum is in excess of the solids contained in some small quantity of earthh They may reply that there is an excess of void also. But the question is, how will they discriminate the absolutely heavy? Pre- sumably, either by its excess of solid or by its defect 309° of void. On the former view there could be an amount of earth so small as to contain less solid than a large mass of fire. And similarly, if the distinction rests on the amount of void, there will be a body, lighter than the absolutely light, which nevertheless moves downward as constantly as 5 the other moves upward. But that cannot be so, since the absolutely light is always lighter than bodies which have weight and move downward, while, on the other hand, that which is lighter need not be light, because in common speech we distinguish a lighter and a heavier (viz. water and earth) among bodies endowed with weight. Again, the suggestion of a certain ratio between the void and the solid in a body is no more equal to solving the problem 1o before us. This manner of speaking will issue in a similar impossibility. For any two portions of fire, small or great, will exhibit the same ratio of solid to void; but the upward movement of the greater is quicker than that of the less, just as the downward movement of a mass of gold or lead, 15 or of any other body endowed with ‘weight, is quicker in proportion to its size. This, however, should not be the case if the ratio is the ground of distinction between heavy things and light. There is also an absurdity in attributing BOOK IV. 2 309? the upward movement of bodies to a void which does not itself move. If, however, it is the nature of a void to move upward and of a plenum to move downward, and therefore each causes a like movement in other things,! there was 20 no need to raise the question why composite bodies are some light and some heavy ; they had only to explain why these two things are themselves light and heavy respectively, and to give, further, the reason why the plenum and the void are not eternally separated. It is also unreasonable to imagine a place for the void, as if the void were not 25 itself a kind of place.?_ But if the void is to move, it must have a place out of which and into which the change carries it. Also what is the cause of its movement? Not, surely, its voidness: for it is not the void only which is moved, but also the solid.* Similar difficulties are involved in all other methods of distinction, whether they account for the relative lightness 30 and heaviness of bodies by distinctions of size, or proceed on any other principle, so long as they attribute to each the same matter, or even if they recognize more than one matter, so long as that means only a pair of contraries. If there is a single matter, as with those who compose things of triangles, nothing can be absolutely heavy or light:

[310a.1] and if there is one matter and its contrary—the void, for instance, and the plenum—no reason can be given for the relative lightness and heaviness of the bodies intermediate between the absolutely light and heavy when compared either with one another or with these themselves.* The implied in Simplicius’ paraphrase. # Read atré with FHMJ and the corrector of E. The construction is certainly loose, but the other reading (air@) does not give the required sense. To give void a motion is to give it a ‘place’, i.e. a natural place to which it moves. But it is itself nothing but a place where no body is (cf. Phys. 1V. 7): and, as Simplicius punningly remarks, ‘it is out of place to give a place a place’ (rov 8€ rdémou térov Toleiy TOV Grom@TAaTaY €oTiY). 3 If movement is natural to both void and solid, the cause of move- ment must lie in something common to both and not in the peculiar nature of either, i.e. not in voidness or solidity. 4 Aristotle’s argument is that the observed diversity of movement necessarily involves a corresponding diversity of bodies: hence any view which makes the four elements one in substance fails to account 5 Io 15 20 view which bases the distinction upon differences of size is more like a mere fiction than those previously mentioned, but, in that it is able to make distinctions between the four elements, it is in a stronger position for meeting the fore- going difficulties. Since, however,’ it imagines that these bodies which differ in size are all made of one substance, it implies, equally with the view that there is but one matter, that there is nothing absolutely light and nothing which moves upward (except as being passed by other things or forced up by them) ;? and since a multitude of small atoms are heavier than a few large ones, it will follow that much air or fire is heavier than a little water or earth, which is impossible.

[310a.3] These, then, are the views which have been advanced by others and the terms in which they state them. We may begin our own statement by settling a question which to some has been the main difficulty—the question why some bodies move always and naturally upward and others down- ward, while others again move both upward and downward. After that we will inquire into light and heavy and the explanation of the various phenomena connected with them.’ The local movement of each body into its own place must be regarded as similar to what happens in con- nexion with other forms of generation and change. There for the facts of movement. He here adds that it is not enough to recognize two kinds of substance or two contrary attributes. For there are four bodies to be accounted for. A single pair of opposites may yield an account of fire and earth, but they cannot account also for the ‘intermediate bodies’, water and air. Two pairs of opposites will be required, such as those which he uses himself (warm, cold: dry, moist),—In |. 3 rv dmA@y must refer to the things also called ray ams Bapéwv xai xovpov. Simplicius tells us that Alexander read tév dmdov, but found in some MSS. rév dmAds. dmdds is tempting, but dav may be allowed to stand: for (a) the absolutely heavy and light are, on the theory criticized, pure solid and pure void respec- tively: thus ra das are ta dada: (6) all other bodies whatever will be composed of these in combination, and may therefore be opposed to them as composite to simple. * Reading rp with HMLJ. Simplicius’ paraphrase supports this. * i.e. upward movement is either (a) illusory: as all things race downward, some, moving slower, are left behind, and thus appear to move up: or (4) unnatural: due to pressure applied from without by other bodies pushing downward. * Prantl misprints yéverae for yivera. BOOK IV. 3 310° are, in fact, three kinds of movement, affecting respectively the size, the form, and the place of a thing, and in each it

[310a.25] is observable that change proceeds from a contrary to a contrary or to something intermediatc: it is never the change of any chance subject in any chance direction, nor, similarly, is the relation of the mover to its object for- tuitous: the thing altered is different from the thing increased, and precisely the same difference holds between that which produces alteration and that which produces

[310a.30] increase. In the same manner it must be thought that that which produces local motion and that which is so moved are not fortuitously related. Now,! that which pro- duces upward and downward movement is that which produces weight and lightness, and that which is moved is that which is potentially heavy or light, and the move- ment of each body to its own place is motion towards its own form. (It is best to interpret in this sense the 310° common statement of the older writers that ‘like moves to like’. For the words are not in every sense true to fact. If one were to remove the earth to where the moon now is, the various fragments of earth would each move not towards it but to the place in which it now is. In general, when a number of similar and undifferentiated bodies are moved with the same motion this result is necessarily produced, viz. that the place which is the natural goal of the move- ment of each single part is also that of the whole.” But since the place of a thing is the boundary of that which contains it, and the continent of all things that move upward or downward is the extremity and the centre, and this boundary comes to be, in a sense, the form of that which is contained, it is to its like that a body moves when —— — ae on ° and some «i peév. J has eis ov). The apodosis does not begin till 310” 16 rd dé Cyreiv, the argument being interrupted by a long note on the meaning of the saying dotov mpds 6powov, which should be marked as a parenthesis. 2 a0 brov... 7d wav is explanatory of rotro ocupBaiver. Gram- matically the predicate to be supplied to rd mav is mé puke pépec dat, though this in the context creates a slight illogicality. Aristotle’s point is that a fragment of earth moves to the mass called the earth, not because it loves its like, but fer accidens in the effort to reach the centre. It is the effort of numberless such fragments to reach the centre which has formed the mass, not the presence of the mass at the centre which causes the effort. gio” 15 it moves to its own place. For the successive members of the series! are like one another: water, I mean, is like air and air like fire, and between intermediates the relation may be converted, though not between them and the extremes; thus air is like water, but water is like earth:? for the relation of each outer body to that which is next within it is that of form to matter.) Thus‘ to ask why fire 1 éetjs should be read, with the other MSS. and Simplicius, rather than E’s ééjs. Cf. de Gen. et Corr. 331” 4, 26, 34. 2 j,e. though air is like fire, fire is not like air; and though water is like earth, earth is not like water. See next note. Prantl proposes to take péoors and dxpois in 1. 13 to mean inner and outer respectively, i.e. to make the former stand for earth and water, the latter for fire and air. His reason is grammatical: péoos is in the dative and so are dare and yj. Thus a construction is provided for peoos. He omits to observe that trois 8” dxpots of becomes meaningless: which, with the admitted difficulty of taking the terms in this sense, is sufficient reason for rejecting the proposal. It is no doubt due to époia that peoos is in the dative: /¢keness fo a péooy is convertible, likeness to an axpov not. Aristotle’s argument is formally concluded at $épeor@a: in |. 11 (‘to its own place’). The ‘place’ (centre and extremity, as explained) gives form to the body, and the body in reaching its place attains its form, i.e. completes the transition from potentiality to actuality. In a sense, then, if the potential is like the actual, it moves ‘to its like’. The yap in 1, 11 forestalls an objection. ‘There remain the intermediate bodies: what of them?’ These are given form or determined by the extreme bodies, and thus mediately determined by the ‘place’. Instead of saying ‘are given form’ or ‘are determined’ Aristotle says ‘are like’; being entitled to do so by the meaning just given to ‘like’. The like to which earth moves is that from which it receives its form, and the like to which water and air move is the extreme body—earth in the one case, fire in the other—from which each receives its form. Thus ‘like’ means ‘receptive of form from’. In this sense water is like air which is like fire, and air is like water which is like earth; but the extremes themselves, earth and fire, are like nothing but their places. The relation of likeness is reciprocal (i.e. determination is mutual) only between the intermediates ; and the chain of resemblance breaks off in each direction short of the extreme. Starting from the centre, we find in the three terms, water, air, fire, a gradual approxima- tion (dei ro av@repov .. .) to the form realized in fire ; starting from the extremity, we find in the terms air, water, earth, a gradual approxima- tion to the form realized in earth. (Of these two complementary statements Aristotle gives only the first; but the second is necessary to complete the argument.) Therefore the intermediate bodies, as well as the extremes, may be said in moving to their places to attain their form.—The above account agrees in principle with that of Simplicius, who, however, is not very clear. Alexander, he tells us, took another view, based on a different interpretation of dei ré av@repov krX. As reported the view is not easy to fit into the context.—For the relation of upper to lower bodies, cf. 31215 and De Gen. et Corr. 335° 18. * Alexander’s 5 for d€ here, like his rév d\Xwy for rovrev in |. 22, BOOK IV. 3 gio” moves upward and eartn downward is the same as to ask why the healable, when moved and changed gud healable, attains health and not whiteness; and similar questions might be asked concerning any other subject of alteration. Of course the subject of increase, when changed gud in- creasable, attains not health but a superior size. The same applies in the other cases. One thing changes in quality, another in quantity: and so in place, a light thing goes upward, a heavy thing downward. The only difference is that in the last case, viz. that of the heavy and the light, the bodies are thought to have a spring of change within themselves, while the subjects of healing and increase are thought to be moved purely from without. Sometimes, however, even they change of themselves, i.e. in response to a slight external movement reach health or increase, as the case may be. And since the same thing which is heal- able is also receptive of disease, it depends on whether it is 3° moved gud healable or gud liable to disease whether the motion is towards health or towards disease. But the reason why the heavy and the light appear more than these things to contain within themselves the source of their movements is that their matter is nearest to being. This is indicated by the fact that locomotion belongs to bodies only when isolated from other bodies,!and is generated last of the several kinds of movement; in order of being then it will be first. Now whenever air comes into being 31 out of water, light out of heavy, it goes to the upper place. It is forthwith light: becoming is at an end, and in that place it has being. Obviously, then, it is a potentiality, wb ° we 5 was advanced as a conjecture unsupported by MSS. None of our MSS. have either. The apodosis to the protasis introduced by ¢ in 310%31 begins here. 67 is therefore attractive, but 8€ 7 apodosi is easily excused in view of the long intervening parenthesis. points out, because of its later technical use (= aésolutus, absolute). Simplicius here takes it to stand for complete substances (AoxAnpwy kar’ ovciay évrwv) not involved in any process of yéveois, abfnous, or ddXolwots. Prantl says dmoAeAvuéva means ‘independent beings’ (unabhangige Wesen). Bonitz, /ad. 84°26, says ‘idem fere ac dro- kexptyévov, xopiordy’. The ‘independence’ intended is rather physical than metaphysical.

[310a.1] which, in its passage to actuality, comes into that place and quantity and quality which belong to its actuality.1 And the same fact explains why what is already actually fire or earth moves, when nothing obstructs it, towards its own place. For motion is equally immediate in the case of nutriment, when nothing hinders, and in the case of the thing healed, when nothing stays the healing. But the _10o movement is also due to the original creative force and to that which removes the hindrance or off which the moving thing rebounded, as was explained in our opening discus- sions, where we tried to show how none of these things moves itself.2 The reason of the various motions of the various bodies, and the meaning of the motion of a body to its own place, have now been explained.

[310a.15] We have now to speak of the distinctive properties of 4 these bodies and of the various phenomena connected with them. In accordance with general conviction we may dis- tinguish the absolutely heavy, as that which sinks to the bottom of all things, from the absolutely light, which is that which rises to the surface of all things. I use the term ‘absolutely ’, in view of the generic character of ‘light’ and ‘heavy’,> in order to confine the application to bodies which do not combine lightness and heaviness. It is apparent, I mean, that fire, in whatever quantity, so long as there is no external obstacle, moves upward, and earth downward ; and, if the quantity is increased, the movement is the same, though swifter. But the heaviness and light- ness of bodies which combine these qualities is different from this, since while they rise to the surface of some bodies they sink to the bottom of others. Such are air and water. Neither of them is absolutely either light or heavy. Both

[310a.25] are lighter than earth—for any portion of either risés to the surface of it—but heavier than fire, since a portion of either, whatever its quantity, sinks to the bottom of fire; compared together, however, the one has absolute weight, the other ? Omitting, with F, the words «ai émrev, which I assume to have been inserted by some one who mistook ot = wéz for the genitive of the relative. 4 PAYS. Ville, 2a Lo oan Vil wae Galion * i.e, because there are distinct species of light and heavy. 2 ° BOOK IV. 4 3u* absolute lightness, since air in any quantity rises to the sur- face of water, while water in any quantity sinks to the

[310a.30] bottom of air. Now other bodies are severally light and heavy, and evidently in them the attributes are due to the difference of their uncompounded parts: that is to say, according as the one or the other happens to preponderate the bodies will be heavy and light respectively. Therefore we need only speak of these parts, since they are primary

[310a.35] and all else consequential: and in so doing we shall be following the advice which we gave! to those who attribute

[311a.1] heaviness to the presence of plenum and lightness to that of void. It is due to the properties of the elementary bodies that a body which is regarded as light in one place is regarded as heavy in another, and vice versa. In air, for instance, a talent’s weight of wood is heavier than a mina of lead, but in water the wood is the lighter. The reason

[311a.5] is that all the elements except fire have weight and all but earth lightness. Earth, then, and bodies in which earth preponderates, must needs have weight everywhere, while water is heavy anywhere but in earth, and air is heavy when not in water or earth. In its own place each of these bodies has weight except fire, even air. Of this we have

[311a.10] evidence in the fact that a bladder when inflated weighs more than when empty. <A body, then, in which air pre- ponderates over earth and water, may well be lighter than something in water and yet heavier than it in air, since such a body does not rise in air but rises to the surface in water.

[311a.15] The following account will make it plain that there is an absolutely light and an absolutely heavy body. And by absolutely light I mean one which of its own nature always moves upward, by absolutely heavy one which of its own nature always moves downward, if no obstacle is in the way. There are, I say, these two kinds of body,’ and it is not the case, as some * maintain, that all bodies have weight. 1 Above, 309” 20: if they would only give an account of the simple bodies, their questions as to the composite would answer themselves. $ This view is maintained in its most unqualified form by those (atomists, probably) who distinguish the four elements by the size of their particles (cf. c. 11, 310% 9).

[311a.1] Different views are in fact agreed that there is a heavy body, which moves uniformly towards the centre. But a0 there is also similarly a light body.1_ For we see with our eyes, as we said before,? that earthy things sink to the bottom of all things and move towards the centre. But the centre is a fixed point. If therefore there is some body which rises to the surface of all things—and we observe fire to move upward even in air itself, while the air remains at rest >—clearly this body is moving towards the extremity. It cannot then have any weight. If it had, there would be as another body in which it sank: and if that had weight, there would be yet another which moved to the extremity and thus rose to the surface of all moving things.* In fact, however, we have no evidence of such a body. Fire, then, has no weight. Neither has earth any lightness, since it sinks to the bottom of all things, and that which sinks moves tothe centre. That there is a centre ® towards which

[311a.30] the motion of heavy things, and away from which that of light things is directed, is manifest in many ways. First, because no movement can continue to infinity. For what cannot be can no more come-to-be than be, and movement is a coming-to-be in one place from another. Secondly, like the upward movement of fire, the downward movement

[311a.35] Of earth and all heavy things makes equal angles on every side with the earth’s surface ®: it must therefore be directed gi2® towards the centre. Whether it is really the centre of the earth and not rather that of the whole to which it moves, may be left to another inquiry, since these are coincident.’ parenthesis, with Prantl. The sentences are not sufficiently self- contained nor closely enough inter-connected to justify such treatment. The argument which begins in l. 19 with 6péuev ydp is a justification of the statement last preceding: as there is, by general admission and by the evidence of observation, a heavy body, so there is a light body. 2 Above, 311%20. 8 Since the air is at rest, the explanation that the fire is ‘forced up (€kOA:Bopevory, 310% 10) is inadmissible. * Reading 6 with the MSS. _Prantl’s conjecture, of, is unnecessary. ° i.e. the line of movement is at right angles to any tangent. Cf. above, 296 20, 297” 19. " The question is discussed in II. xiv, 296” 9. BOOK IV. 4 But since that which sinks to the bottom ofall things moves to the centre, necessarily that which rises to the surface moves to the extremity of the region in which the move- ment of these bodies takes place. For the centre is opposed as contrary to the extremity, as that which sinks is opposed to that which rises to the surface. This also gives a reason- able ground for the duality of heavy and light in the spatial duality centre and extremity. Now there is also the inter- mediate region to which each name is given in opposition to the other extreme. For that which is intermediate between the two is in a sense both extremity and centre. For this reason there is another heavy and light; namely, water and air. But in our view the continent pertains to form and the contained to matter: and this distinction is present in every genus. Alike in the sphere of quality and in that of quantity there is that which corresponds rather to form and that which corresponds to matter. In the same way, among spatial distinctions, the above belongs to the determinate, the below to matter. The same holds, consequently, also of the matter itself of that which is heavy and light: as potentially possessing the one character, it is matter for the heavy, and as potentially possessing the other, for the light. It is the same matter, but its being is different, as that which is receptive of disease is the same as that which is receptive of health, though in being different from it, and therefore diseasedness is different from healthiness. 5 A thing then which has the one kind of matter is light and always moves upward, while a thing which has the peraév. (J has an erasure in the position of the second ¢ori.) 152" 50; last chapter (31015, note). A single matter is receptive of two opposed forms, weight and lightness or health and disease. But Aristotle here adds the new point that of two such alternative forms one is always more formal and the other more material. Weight and lightness, disease and health, are not true coordinates. A form, we may say, is realized in disease, in weight, in the female; but the form is realized in health, in lightness, and in the male. The principle is stated in the Mefaphysics in the form ray évavtiwy 4 érépa avaroixia atépnois (1004° 27).

[312a.1] opposite matter is heavy and always moves downward. Bodies composed of kinds of matter different from these but having relatively to each other the character which

[312a.25] these have absolutely, possess both the upward and the downward motion.! Hence air and water each have both lightness and weight, and water sinks to the bottom of all things except earth, while air rises to the surface of all things except fire. But since there is one body only which rises to the surface of all things and one only which sinks to the bottom of all things, there must needs be two other 3° bodies which sink in some bodies and rise to the surface of others. The kinds of matter, then, must be as numerous as these bodies, i.e. four, but though they are four there must be a common matter of all—particularly if they pass into one another—which in each is in being different. There 312” is no reason why? there should not be one or more inter- mediates between the contraries, as in the case of colour ; for ‘intermediate’ and ‘mean’ are capable of more than one application.® Now in its own place every body endowed with both weight and lightness has weight—whereas earth has weight 5 everywhere— but they only have lightness among bodies to whose surface they rise. Hence when a support is with- drawn such a body moves downward until it reaches the body next below it, airto the place of water and water to that of earth. But if the fire above air is removed, it will not move upward to the place of fire, except by constraint ; and in that way water also may be drawn up, when the up- 10 ward movement of air which has had a common surface with it is swift enough to overpower the downward impulse of the water. Nor does water move upward to the place of air, except in the manner just described. Earth is not so affected at all, because a common surface is not possible to 1 In 1. 24 put the comma after, not before, dmdds. (The correction is due to Mr. Ross.) The intermediates, air and water, are only relatively light and heavy. In the absolute sense these characters belong only to fire and water. : ane in Bekker and Prantl must surely be a misprint for oddé» so J). * ‘Intermediate’ stands for a region, not a point, and includes as a rule a variety of things. ‘ | 4 J 4 | BOOK IV. 5 it! Hence water is drawn up into the vessel to which fire is applied, but not earth. As earth fails to move up- ward, so fire fails to move downward when air is withdrawn from beneath it: for fire has no weight even in its own place, as earth has no lightness. The other two move downward when the body beneath is withdrawn because, while the absolutely heavy is that which sinks to the bottom of all things,? the relatively heavy sinks to its own place or to the surface of the body in which it rises, since it is similar in matter to it It is plain that one must suppose as many distinct species of matter as there are bodies. For if, first, there is a single matter of all things, as, for instance, the void or the plenum or extension or the triangles, either all things will move up- ward or all things will move downward, and the second motion will be abolished. And so, either there will be no absolutely light body, if superiority of weight is due to superior size or number of the constituent bodies or to the fullness of the body: but the contrary is a matter of obser- vation, and it has been shown that the downward and upward movements are equally constant and universal: or, if the matter in question is the void or something similar, which moves uniformly upward, there will be nothing to move uniformly downward.‘ Further, it will follow that (Simpl.), or continuity of surface, with another body. conjecture, els rjv td, is not quite convincing. determinate, having its limit at the centre. But the downward move- ment of air and water (relative weight) is not equally determinate: it is limited only by the surface of the body next beneath, air by that of water, water by that of earth, the upper body being attracted to the lower by similarity of matter. This admission inflicts some damage on the doctrine of ‘ places’—for where a body has weight it cannot be said to ‘rest naturally’ or to ‘be in its place’—and also on the symmetry of the elements—for if the fire above air were removed the air would not move upward, but if the earth below water were removed the water would move downward.—In 1. 18 «/s must be construed with dépera:, and in 1. 19 # ois, more fully expressed, would be #) eis tiv exeivwy ois, The construction is difficult, and the passage may be corrupt. is an irregular second limb to the disjunction introduced by 4 xovgov in], 23. Putacolon at mAnpy (1. 25) and at dra (1. 27), and delete the comma after mAetdvey (I. 25). 31a? 30

[313a.1] the intermediate bodies move downward in some cases quicker than earth: for air in sufficiently large quantity will contain a larger number of triangles or solids or particles. It is, however, manifest that no portion of air whatever moves downward. And the same reasoning applies to lightness, if that is supposed to depend on superiority of quantity of matter.? But if, secondly, the kinds of matter are two, it will be difficult to make the intermediate bodies behave as air and water behave. Suppose, for example, that the two asserted are void and plenum. Fire, then, as moving upward, will be void, earth, as moving downward, plenum; and in air, it will be said, fire preponderates, in water, earth. There will then be a quantity of water containing more fire than a little air, and a large amount of air will contain more earth than a little water: consequently we shall have to say that air in a certain quantity moves downward more quickly than a little water. But-such a thing has never been observed anywhere. Necessarily, then, as fire goes up because it has something, e.g. void, which other things do not have, and earth goes downward because it has plenum, so air goes to its own place above water because it has something else, and water goes downward because of some special kind of body. But if the two bodies* are one matter, or two matters both present in each,° there will be a certain quantity of each at which water will excel a little air in the upward movement and air excel water in the downward move- ment, as we have already often said. The shape of bodies will not account for their moving

[313a.5] upward or downward in general, though it will account for their moving faster or slower. The reasons for this 1 sc. in earth. . On the somewhat absurd theory that the universal ‘matter’ is void or absolute lightness. LEE eek Gc olov . . . yfs,is a parenthesis and should be so printed, with a colon, instead of a full-stop, at mAjpes and at xdro. This is proved by the infinitive éyew (after ain) in l. 3, as well as b the ydp which follows. ( pain) 3; y * viz. air and water. ® Prantl’s éxarépw is a misprint for éxarépo. 6 BOOK IV. 6 Sig4 are not difficult to see. For the problem thus raised is why a flat piece of iron or lead floats upon water, while smaller and less heavy things, so long as they are round or long—a needle, for instance—sink down; and

[313a.20] sometimes a thing floats because it is small, as with gold dust and the various earthy and dusty materials which throng the air. With regard to these questions, it is wrong to accept the explanation offered by Democritus. He says that the warm bodies moving up! out of the water hold up heavy bodies which are broad, while the 313” narrow ones fall through, because the bodies which offer this resistance are not numerous. But this would be even more likely to happen in air—an objection which he himself raises. His reply to the objection is feeble. In the air, he says, the ‘drive’ (meaning by drive the move- 5 ment of the upward moving bodies) is not uniform in direction. But since some continua are easily divided and others less easily, and things which produce division differ similarly in the ease with which they produce it, the ex- planation must be found in this fact. It is the easily bounded,” in proportion as it is easily bounded, which is easily divided ; and air is more so than water, water than 1o earth. Further, the smaller the quantity in each kind, the more easily it is divided and disrupted. Thus the reason why broad things keep their place is because they cover so wide a surface and the greater quantity is less easily disrupted. Bodies of the opposite shape sink down because they occupy so little of the surface, which is there- rs fore easily parted. And these considerations apply with far greater force to air, since it is so much more easily divided than water. But since there are two factors, the force responsible for the downward motion of the heavy body and the disruption-resisting force of the continuous surface, there must be some ratio between the two. For in proportion as the force applied by the heavy thing 1 dvahepdpeva is the better-attested reading (ELMJ Simpl.) and should be preferred to dvw gepdueva. The word is elsewhere used of upward movement by Aristotle. _ 2 j,e. the fluid or moist. Cp. de Gen. et Corr. 329» 30. ao towards disruption and division exceeds that which resides in the continuum, the quicker will it force its way down; only if the force of the heavy thing is the weaker, will it ride upon the surface. We have now finished our examination of the heavy and the light and of the phenomena connected with them. INDEX I. English [The sign + following a reference means that many other references could be given.] 68-13 = 268-313. Above-below (up-down)—(1) in ref. to motion of elements=ex- tremity and centre 68» 22, 08 18 + ; (2) applied to universe by analogy from animals : upper and lower hemispheres Ber rs above prior to below 84> 25, ‘more divine’ 888 5. Action—attributed to stars 92°14; most varied in man 92? 2, Air—one of the two elements which move upward 69% 18 + ; one of the two intermediates (g.v.) ; ignited by movement of stars 89 20; thought to sup- port the earth 94» 14; assists movement of bodies o1? 23. See also Intermediate. Aither—special name for the highest place, meaning ‘ what runs always’ 70> 21; Anaxa- goras interprets otherwise 70> 24, 02> 4. All—connexion of, with number three 68% 11. Alteration— def. movement in re- spect of quality 70 27, 10 23; not applicable to fifth element 70 13; nor to any infinite 75 I; comparison with local move- ment, 77% 14, 10 16. Anaxagoras—makes azther = fire 70> 24, 02» 4; explains immo- bility of earth by flatness 94? 14; his cosmogony o1® 11; his homoeomeries = elements 02 29; denies existence of void 09 19 ; referred to by implication 69» 11, 74° 19, 89% 17, 97° 13. Anaximander—explains immobi- lity of earth by indifference 95° 10; referred to by implication 98” 33; reference doubted 03” 13. hee een te decisinninmobility of earth by flatness 94> 14; re- Dd ferred to by implication 98» 33, 03> 12. Animals—growth of, 70% 31; spa- tial oppositions in, 84” 11; phy- sical composition 8815 ; organs for movement go 30; compari- son with stars 90? 30, 92” 1, 93° 6. Astronomy—A.’s conception of, QI 30” 21, 97% 4 ; astronomical records of Egypt and Babylon 70° 14, 92 7. Atlas—not required 84% 20. Atoms—(of Democritus and Leu- cippus) differ only in shape 75> 30, 03 10; in perpetual move- ment oo? 9; infinite in number 03° 5; in conflict with fact 04 25, with mathematics 03 25. See also Democritus, Leucippus. “Babylonians—their astronomical records 928 7, 70 14. Below—sce Above. Category—81® 32, 12% 14. Centre—of earth )( of universe 96” 10, 12 1; goal of movement of heavy bodies 68” 21, 69” 23, 76” 1,97 5, 119 29; Pythago- rean view of 93% 20, See also Earth. Chance—83 32, 87" 25, 89» 23. Circles (or spheres) — solid revolv- ing bodies, composed of the primary body, in which the stars are fixed 89” 1, 92 26; also called ‘ heavens’ and‘ motions’ (g.v.). Coan (? Chian) throw—g2® 30. Coincidence of predicates— $2 30. Commensurability — of weights 73> 10; of bodies 04% 25; of diagonal 81% 5, 7. Complete—defined 86% 20 (cf. 71” 31, 68% 4). INDEX Continuum—68 7, 80% 20, 06° 2A; 13°06. Contrary—c.s exist together and have same matter 86° 22; c.s essential to generation 70° 13 ; c.s admit of intermediates 12° 1; examples, unnatural )( natu- ral movement 69% 9 +, upward )/( downward movement 73% 7 +, hot )( cold 07” 6, spatial 71% 26, 87> 6; c. relations between any two elements 86% 30; no c. to circular movement 70? 31, to any figure 07” 7. Counter-earth—supposed by Py- thagoreans 93:25. Cyprus—98 4. Decay—see Generation. Democritus—supposes the uni- verse not continuous 75> 30; explains immobility of earth by flatness 94514; views in regard to movement oo? 8, to elements 03 4, to generation 05° 35; makes the sphere a kind of angle 078 17; his explanation of floating 13% 21; associated with Leucippus 75” 30, oo 8, 03 4; referred to by implica- tion 77 1 (extrusion), 79° 13

[313a.30] (destructible world), o8 (void). See also Atoms, Drive, Extrusion, Void. Dense-rare— 99° 8, 03° 12, » 23. Differences—importance of study- ing 94> 12; number limited 03° I. Diminution—see Increase. Divination—=inspired guess 84> 53 uses opposition right )( left 35° 2, Divisibility—conditions of 68® 25, 13 6; consequences of denial of 99° 17. Drive—term used by Democritus 13° 5. Duration—special name for the life of the universe, implying eternal existence 79 23. Earth—(1) the element: moves naturally to the centre and rests there 69° 27, 86% 20, 95 20 + ; absolutely, not merely rela- tively, heavy 118 15; acc. to the theory of planes the only true element 06% 18,—(2) the central mass: its central posi- tion 93° 17 ; its immobility 93> 16, 94° 12, 96% 24; its spheri- cal shape 93” 33, 97% 9, con- firmed by shadow on the moon 97” 25; its size 97” 31; view of Pythagoreans (in motion about the centre) 93 20; of Plato, Timaeus (similar) 93 31, 96% 24; of Xenophanes (infinite deeps) 94% 22 ; of Thales (floats on water) 94 28; of Anaxime- nes, Anaxagoras, Democritus (immobile because of its flat- ness) 94 14; of Empedocles (immobile because of the vor- tex) 95° 15; of Anaximander (immobile because of its indif- ference) 95» Io. Eclipse—of moon more frequent than of sun (Pythagoreans) 94> 23; of moon by earth gives curved outline 97525; of Mars (or Mercury ?) by moon 92® 4. Egypt—astronomical records of 92° 7, 70 14; stars seen in 98 4. Elements—normally called ‘ sim- ple bodies’ 98% 30, 02” 7, 06° 4 + specifically distinct parts 68> 5, 14; possess a principle of movement 68» 28; three in number, 77» 14, 98” 8; their distinction depends on natural movements 76> 8, 04> 20, and places 77> 14 (cf. 12% 19).— (1) the primary body, substance of the outer heavens (Bks. I, II): moves naturally in a circle 69" 5,a sign of its perfection 69 16 ; neither light nor heavy 698 19; not subject to genera- tion, increase, or alteration 70° 12, 889 34; not infinite 711 ff. ; its several movements 86% 3, 89° 1, 91> 30; why spherical 86> 10; direction of movement 87> 22; regularity of movement 88" 14; substance of the stars 89% 13 ; its movement the mea- sure of all movement 84° 2, 87% 23.—(2) below the moon (Bks. III, IV): primary constituents of bodies 02® 11 ; four in num- ber (earth and fire, with two intermediates, water and air), INDEX but treated as two, 77” 14, 98> 8 ; based on opposition light )( heavy o1 22, 07> 28; their natural movement 0o 20, 108 14; a passage to form, being, or actuality 10 1, 118 4; their serial character 10 11; dis- tinctive properties 11° 15; in- volve generation 70% 33, 98” Io, 02 10, 04> 23; pass into one another 05 14; not infinite in number 02” 10; nor reducible to one 03> 14; not distinguish- able by size 041; nor by shape 06> 3.—Views of others: early thinkers 03 13; Anaxagoras o2 29; Empedocles 95 31, 02® 30, 051; Leucippus and Democritus 03% 3; Plato, 7Z7- maeus 06% I. Elephants—found in India and in N. Africa 98 12. Empedocles—his views on the destructibility of the world 79> 15; on the immobility of the earth 84° 24, 94 25, 95% 8, 30, oo 2; on the elements 02% 29, b 23,05" 35; ignores opposition light )( heavy 09% 19 ; his prin- ciples ‘ Love’ and ‘ Hate’ 804 16, 95% 31, oo” 29, o1 16° quoted 94® 25,0030, See also Vortex, Excretion. Excretion—— process by which Em- pedocles accounts for the gene- ration of the elements 05? 1. Extrusion—forced motion of a body due to action of other bodies, a term used by ‘some writers’ (Leucippus and Demo- critus?) 77? 1. Form—opp. matter 78 1, 10” 15, 12°12; Platonic 784 16. Front-back—applied to universe 84> 21, 88 6. Generation—depends on_inter- action of contraries 70% 15; hence excluded from sphere of the primary body 70 19, 79” 4, 88 34; necessity of, below the moon 70% 33, 98> 10, 02 10; g.of elements from one another 04> 24, 05° 34; not absolute o1> 2; not admitted by Melis- sus and Parmenides 98° 15. Geometry—construction in 79> 35. God—as creative 71% 33 ; his ac- tivity eternal life 86% 9 ; popu- larly connected with the hea- vens 70> 7, 84® 123; use of number 3 in worship of 68° 15. ‘Harmony of the spheres’—a Py- thagorean view, refuted go 12. Hate—(in Empedocles) see Love. Heaven —three senses distin- guished 78” 10; sense (a) ‘first’ or ‘outermost’ h. 7o 15, 88 15, 92° 22, 98° 24 (cp. 91 35, gi>2); ‘fixed’ h.72»31;—sense (4) (including the planets) ani- mate 85% 29, Divine 86° 10, spherical »10, eternal, 87> 26; —sense (c) (=world, universe) go 6, 98° 31, 00% 15, o1% 17, 03» 13, 08 17; hemispheres 85> 10, 08 26; includes all body, place, time, 76% 18, 78% 26,79°12. See also Elements(1). Heavy-light—applied to bodies which move naturally towards and away from the centre 69? 20; imply a finite system 73° 22; not applicable to primary body 69” 19, 76% 16; not ac- counted for by Empedocles 95 30 ; nor by the theory of planes 99 24; dist. absolute-relative 08" 7; heavy the privative, light the positive term 86% 26. Heraclitus—on generation 79? 15, 98” 30; referred to by implica- tion 03” 12 (cf. o4® 18). Hercules, Pillars of—98® 11. Hesiod—on generation 98» 28 (cf. 79” 13). Hippasus— 03? 12. Hippon— 03? 11. Homoeomeries — of Anaxagoras 02" 31, 04° 26. Hydrarpax—name for water- clock in Simpl.’s day 94” 21. Hypothesis—dist. false-impossi- ble 81» 4. Idaios—of Himera 03? 13. Increase-diminution—7o 23, 84” 28, 88 15, 10% 27, 10? 20. India—98 11. Indivisible lines—99 10, 07" 22. Infinite—not predicable of body 71> 2 ff.; of weight 73° 22; of INDEX elements 03 5; of process of analysis 04° 28 ; not to be tra- versed oo? 4; as applied to line 69% 22, 72> 17; i. shapes, acc. to Democritus 03% 12. Intermediate—bodies (viz. air and water) 76° 1, 86% 29, 10° 12, 12> 28 ; places (i.e. where these bodies rest) 77> 23, 12% 9; i. body cannot be primary 03° 22; between contraries 12> 1. ixion—84° 35. Klepsydra—g4> 22. Leucippus— conjoined with Demo- critus 75> 30, oo 8, 03% 4 (cf. 77» 1, 08 30). See also Demo- critus. Light—see Heavy. ‘Like to like’—means matter to form 10? 1. Love-hate—opposed causal prin- ciples in cosmology of Empedo- cles 80% 16, 95% 31, 00” 29, o18 16. Magnitude—complete in three dimensions 6889; simple, two only, viz. straight and circular line 68> 19; minimum, impos- sible 71° Io. Mars--(or Mercury?) eclipse of, by moon, observed by A.92° 5. Mathematics—contributions of, to astronomy 91? 9, 97° 4, 98° 16; admits no minimum 71? 10; its principles finite 02” 30; in conflict with the atomic theory 03° 21; with the theory of planes 06 28; the mathemati- cal the most accurate sciences 06" 28. Melissus—and Parmenides de- nied generation 98> 17. Minimum—no m, magnitude 71> 10; nom. time 74° 9 ; m. move- ment the measure 87° 23 (cf. 88> 31). Missiles—movement of 88 23, 89 23. Moon—phases 91» 20; move- ments 91 35; so-called face go® 26. Motion—-=circle (g.v.) to which Stars are attached 79 20, g2® | 14. Movement — physics concerned with 68% 2, 087 1; not present in all things 98> 19; of three kinds, qualitative, quantitative, local 10% 23. —(1) local: belongs naturally to all bodies 68> 15; finite in character 77 17; dist. natural- constrained 76% 22, 94 32, 00# 20 +; dist. simple-compound 68> 30, oc® 20 +; kinds of simple m. 68> 17; (i) circular 70» 31, 77 3, 84% 4, 86> 2% 5 (ii) rectilinear 10? 14 + ; down- ward, goal of 96> 7; ‘makes equal angles’ 96° 20, 97” 19. —of heavens: variety 86% 3, 91° 29; direction 87> 22; regu- larity 889 14; w. ref. to stars 89> 1. —of animate things 84> 32, 85% -29; of spherical bodies go 9, g1> 15; as cause of fire 8921. —(2) qualitative—see Alteration; ‘ sense-m.’ 84? 209. —(3) quantitative—see Increase. —‘ discussion of m.’=P£Ays. V— VIII 73° 20, 75 23, 99 10; ‘of time and m.’ 03 23. Nature—as agent 68 20, 71 33, 88% 3, 9o 30, g1 25, >14, 93 2; as form 86® 18, o18 8; as source of movement 68" 16, o1? 17+; perfection of 88° 9 ; order of 03 19; inquiry into 688 1, 98> 1. Numbers—allotted to geometrical figures 86 34; compose the world, acc. to Pythagoreans 00 15; the n. three 683 15. Ocean—unity of 98 Io. Orpheus—cosmogony of 79” 13, 98> 27. Parmenides— and Melissus de- nied generation 98° 17. Philosophy—first 77° 10; popular 79 31. Physics of Aristotle—cited as ‘opening discussions’ 70 17, 11°12; Bks. I-IV cited as ‘ dis- cussion of principles’ 72° 30n., 74® 21; Bks. V-VIII as ‘dis- cussion of movement’ 72% 30, 75> 23, 99% 10; as ‘d. of time and m.’ 03 23; treated gener- ally as continuous w. De Caelo 73° 18, 85% 28, 86? 20, 05% 22+. Place—belongs to the perceptible 75> 11; contrarieties of 71° 5, 26, 73 12; proper or natural 76° 12, 10° 7; intermediate 77” 23, 128 9; w. ref. to void og? : 26; none outside the heaven 79 12. Planes, theory of —86> 27, 98” 33, 06° I. i Planets—secondary revolution of 85> 29, 91% 1; absence of twink- j ling 90% 19. See also Heaven, Mars. Plato—(not mentioned by name) his Zimaeus cited 80% 30, 93> 32, 007 1, P17, 06° 19, 08? 4. Poles—85°» 10, 93” 32, 96? 27. Possibility—notion of, examined 81" 1, 83> 8; no unrealized p. oy 26, Principle —in logical sense 71? 12, 02> 27, 03° 18, 06% 7; structur- | al, in animals 84> 11, 85% 20; in geometrical figures 032 ; of movement 68 16, 84> 32, 854 INDEX 10; suited only to movement in one place go” 2; its proper movements 90 10; spherical shape of universe 87 15, go” 1 ; of stars go® 8, >1, o1” 10; of the earth 97> 21 ; of surface of water 87> 1 ; (supposed) of par- ticles of fire 06° 33; ‘harmony of the ss’ yo 12. See also Circles. Spinning—a motion appropriate to a sphere go® Io. Stars—composition, 89% 15 ; car- ried on moving spheres 89° 29, > 31; distances 91° 30; speed of motion 91% 33; shape 91° 10; distribution 92 10; number of movements gi» 30; unchang- ing intervals 88> 10, 96 4; twinkling (dist. planets) 90°18 ; seen differently in different countries 97 31; comparison with animals go® 30, 92” 1, 93” 6. | Substrate—70 16, 06% 17. | Sun—its heat 89 32; apparent 29, » 7; ‘discussion of p.s’= | ; ; Suspension—of triangles 06° 22. Phys. {-lV 74? 21 (cf. 72% 30n.). Privation—86 26. Pyramid—o3 32, 04% 12, > 4, 06» 7, 33: Pela csemaie the number three 68% 11 ; on right and left in the heaven 84> 7; on the hemispheres 85> 26; on the motion of the earth 93% 20; their ‘counter-earth’ 93 25, b 20; ‘Guard-house of Zeus’ 93” 4; compose the world of numbers 00% 15; cf. also go” 15 (‘ harmony of the spheres’). Right-left—applied to universe 84> 6; motion of first heaven starts from right and moves to right 85> 17; right prior to left 88° 6. Rolling—a motion appropriate to a sphere 90 10 Sense-movement—84> 29. Sound—-said to be unheard if con- tinuous 90” 27; has physical effects go 34. Spheres—the primary shape 86 spinning motion 90°15; eclipses of, by moon 91” 23 ; number of movements 92% 1; distance a Text—(basis Prantl, 1881) (1) con- jectures adopted or suggested 72» 17, 80» 18, 819 1, 7, 83 29, g2” 11, 95% 22, 99” 19, ot” 19, o4 28, 12 10. —(z) alterations of punctuation 68 24, 73°25, 74° 5, 11, 76°17, 77 16, 18, 78° 15, 79” 22, 26, 80% 30, 228, 81> 29, 82% 12, 26, 83% 14, 24, 29, » 9, 21, 89% 2, 23, 92° 3, 13, 93° 18, 95% 10, 33, o1 19, » 23, 05% 28, 06 17, 08> 6, 15, 10 1, 11> 14, 12% 24 >25, 33. —(3) misprints corrected 76° 5, 18, 77 32, »27, 78> 16, 79” 6, 80% 29, 81% 16, 83” 21, 84° 20, 86> 28, 91% 22, 29, 95 15, 06 32, 07" 3, 21,10" 20, 12 33, 13° II. ‘ —(4) other alterations 68 22, > 25, 69° 7, 23, 28, » 21, 26, 708 23, 71% 29, ©5, 19, 30, 33, 72” I, 73° 16, 74% 22, 5, 32, 75% 10, 76> 21, 77° 27, 78 3, 28, 80” 34, 81> 18, 21, 33, 83" 17, °5, 7; INDEX 84° 7, 30, 86° 1, 19, 878 27, > 34, 88> 10, 26, 89° 28, 92” 4, 93> 28, 94° 20, 95° 4, 99? 22, 28, 32, O1NO, P15, 20,102" 2,582,035 250) 04 16, 27, 06° 15, 28, 08% I, 24, 32, og? 20, 25, 10° 7, 31, b 72, 16, 11% 3, 6,.°16, 26, 20, 12° 17, 13 23. —(5) other comments 684 19, 70% 26, 71% 24, 72% 14, 15,025, 70" BOM 72 2 20ug tee, BoP 20, 29, Bae 26, es" 7p 00" 10,02" 26, 29, 93° 24. > 31, 96% 26, 97% 34, G92 10, OL Mt 7 SL OS" 7.07% 71 OSuns Ul Ours B 99. Thales— said earth rests upon water 949 28; referred to by implication 03° 11. ‘Three—-mystical significance of the number 68? 15. pacer rocks by its noise go> Thule weetceivanie outside the heaven 79° 14; no minimum t. 74 93 every performance has its minimum t. 88> Transverse—in the eee def. 85> 12. Triangle—constituent of bodies, in the Zzmaeus 08 15, 09” 34 ; its Pythagorean number 87% I. DN DB ead _ Vegetables—liable to increase 70% 3 3 compared with lower stars 92? 2. Visual ray—go® 17. Void—supposed by Leucippus and Democritus to account movement oo? 10; cannot be the matterof things, either alone 12> 21, or with plenum 13? 1; extra-corporeal], impossible 02 I, 05® 17; intra-corporeal, as cause of lightness 094 6, 11° 1; as explaining expansion, 05° 17; no v. outside the heaven 79 12 (cf. 87% 15); has no natural movement og? 18 (cf. 13 1). 4 Vortex (or Whirl)—supposed by Empedocles 84% 24, 95% 8, oo” 3. Water—moves downward 697 18; proof that its surface is spheri- cal 87 1; supposed by a to support the earth 94° 28 ; be the one element 03? 11. also Intermediate. Water-clock —94? 22. one Xenocrates — possibly referred to 79° 33, 98 33. Xenophanes—cited 94° 22. Greek [The reference is to the foot-note in which the word is cited.] aytaxoXovFia 82% 30, dmoNeAvpeévos 10” 33, Staornua 71» 31. Siopi¢ery o1 17. Svvayes Si 7. eyxvKd.os 86% 12. éxataots 86% 20. eEwrepixol Adyot 79° 31. trea Oar 93 31. Képirts 92® 26, xéapos 72% 20, dpmodtns O5> Dr. ois go® 17. mAnyn 89% 28. ovyxwpety 97 12, Popa 92* 14. for - ON COMING-TO-BE AND PASSING-AWAY BOOK I

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