Our present position, then, is this: We have argued that there always was motion and always will be motion throughout all time, and we have explained what is the first principle of this eternal motion: we have explained further which is the primary motion and which is the only motion that can be eternal: and we have pronounced the first movent to be unmoved.
10 We have now to assert that the first movent must be without parts and without magnitude, (10) beginning with the establishment of the premisses on which this conclusion depends.
One of these premisses is that nothing finite can cause motion during an infinite time. We have three things, the movent, the moved, and thirdly that in which the motion takes place, namely the time: and these are either all infinite or all finite or partly—that is to say two of them or one of them—finite and partly infinite. (15) Let A be the movent, B the moved, and C the infinite time. Now let us suppose that D46 moves E, a part of B. Then the time occupied by this motion cannot be equal to C: for the greater the amount moved, the longer the time occupied.47 It follows that the time F48 is not infinite. Now we see that by continuing to add to D, I shall use up A, (20) and by continuing to add to E, I shall use up B: but I shall not use up the time by continually subtracting a corresponding amount from it, because it is infinite. Consequently the duration of the part of C which is occupied by all A in moving the whole of B, will be finite. Therefore a finite thing cannot impart to anything an infinite motion. It is clear, then, that it is impossible for the finite to cause motion during an infinite time.
It has now to be shown that in no case is it possible for an infinite force to reside in a finite magnitude. (25) This can be shown as follows: we take it for granted that the greater force is always that which in less time than another does an equal amount of work when engaged in any activity—in heating, for example, or sweetening or throwing; in fact, in causing any kind of motion. Then that on which the forces act must be affected to some extent by our supposed finite magnitude possessing an infinite force as well as by anything else, in fact to a greater extent than by anything else, since the infinite force is greater than any other. But then there cannot be any time in which its action could take place. (30) Suppose that A is the time occupied by the infinite power in the performance of an act of heating or pushing, and that AB is the time occupied by a finite power in the performance of the same act: then by adding to the latter another finite power and continually increasing the magnitude of the power so added I shall at some time or other reach a point at which the finite power has completed the motive act in the time A: for by continual addition to a finite magnitude I must arrive at a magnitude that exceeds any assigned limit, and in the same way by continual subtraction I must arrive at one that falls short of any assigned limit. [266b] So we get the result that the finite force will occupy the same amount of time in performing the motive act as the infinite force. But this is impossible. (5) Therefore nothing finite can possess an infinite force. So it is also impossible for a finite force to reside in an infinite magnitude. It is true that a greater force can reside in a lesser magnitude: but the superiority of any such greater force can be still greater if the magnitude in which it resides is greater. Now let AB be an infinite magnitude. Then BC49 possesses a certain force that occupies a certain time, let us say the time EF50 in moving D. Now if I take a magnitude twice as great as BC, (10) the time occupied by this magnitude in moving D will be half of EF (assuming this to be the proportion51): so we may call this time FG. That being so, by continually taking a greater magnitude in this way I shall never arrive at the full AB, whereas I shall always be getting a lesser fraction of the time originally given. Therefore the force must be infinite, since it exceeds any finite force. (15) Moreover the time occupied by the action of any finite force must also be finite: for if a given force moves something in a certain time, a greater force will do so in a lesser time, but still a definite time, in inverse proportion. But a force must always be infinite—just as a number or a magnitude is—if it exceeds all definite limits. (20) This point may also be proved in another way—by taking a finite magnitude in which there resides a force the same in kind as that which resides in the infinite magnitude, so that this force will be a measure of the finite force residing in the infinite magnitude.
It is plain, (25) then, from the foregoing arguments that it is impossible for an infinite force to reside in a finite magnitude or for a finite force to reside in an infinite magnitude. But before proceeding to our conclusion it will be well to discuss a difficulty that arises in connexion with locomotion. If everything that is in motion with the exception of things that move themselves is moved by something else, how is it that some things, e. g. things thrown, continue to be in motion when their movent is no longer in contact with them? If we say that the movent in such cases moves something else at the same time, (30) that the thrower e. g. also moves the air, and that this in being moved is also a movent, then it would be no more possible for this second thing than for the original thing to be in motion when the original movent is not in contact with it or moving it: all the things moved would have to be in motion simultaneously and also to have ceased simultaneously to be in motion when the original movent ceases to move them, even if, like the magnet, it makes that which it has moved capable of being a movent. [267a] Therefore, while we must accept this explanation to the extent of saying that the original movent gives the power of being a movent either to air or to water or to something else of the kind, (5) naturally adapted for imparting and undergoing motion, we must say further that this thing does not cease simultaneously to impart motion and to undergo motion: it ceases to be in motion at the moment when its movent ceases to move it, but it still remains a movent, and so it causes something else consecutive with it to be in motion, and of this again the same may be said. The motion begins to cease when the motive force produced in one member of the consecutive series is at each stage less than that possessed by the preceding member, and it finally ceases when one member no longer causes the next member to be a movent but only causes it to be in motion. (10) The motion of these last two—of the one as movent and of the other as moved—must cease simultaneously, and with this the whole motion ceases. Now the things in which this motion is produced are things that admit of being sometimes in motion and sometimes at rest, and the motion is not continuous but only appears so: for it is motion of things that are either successive or in contact, (15) there being not one movent but a number of movents consecutive with one another: and so motion of this kind takes place in air and water. Some say52 that it is ‘mutual replacement’: but we must recognize that the difficulty raised cannot be solved otherwise than in the way we have described. So far as they are affected by ‘mutual replacement’, all the members of the series are moved and impart motion simultaneously, so that their motions also cease simultaneously: but our present problem concerns the appearance of continuous motion in a single thing, (20) and therefore, since it cannot be moved throughout its motion by the same movent, the question is, what moves it?
Resuming our main argument, we proceed from the positions that there must be continuous motion in the world of things, that this is a single motion, that a single motion must be a motion of a magnitude (for that which is without magnitude cannot be in motion), and that the magnitude must be a single magnitude moved by a single movent (for otherwise there will not be continuous motion but a consecutive series of separate motions), and that if the movent is a single thing, it is either itself in motion or itself unmoved: if, then, it is in motion, it will have to be subject to the same conditions as that which it moves, (25) that is to say it will itself be in process of change and in being so will also have to be moved by something: so we have a series that must come to an end, and a point will be reached at which motion is imparted by something that is unmoved. [267b] Thus we have a movent that has no need to change along with that which it moves but will be able to cause motion always (for the causing of motion under these conditions involves no effort
): and this motion alone is regular, or at least it is so in a higher degree than any other, since the movent is never subject to any change. So, too, in order that the motion may continue to be of the same character, (5) the moved must not be subject to change in respect of its relation to the movent. Moreover the movent must occupy either the centre or the circumference, since these are the first principles from which a sphere is derived. But the things nearest the movent are those whose motion is quickest, and in this case it is the motion of the circumference that is the quickest: therefore the movent occupies the circumference.
There is a further difficulty in supposing it to be possible for anything that is in motion to cause motion continuously and not merely in the way in which it is caused by something repeatedly pushing (in which case the continuity amounts to no more than successiveness). (10) Such a movent must either itself continue to push or pull or perform both these actions, or else the action must be taken up by something else and be passed on from one movent to another (the process that we described before as occurring in the case of things thrown, since the air or the water, being divisible, is a movent only in virtue of the fact that different parts of the air are moved one after another): and in either case the motion cannot be a single motion, (15) but only a consecutive series of motions. The only continuous motion, then, is that which is caused by the unmoved movent: and this motion is continuous because the movent remains always invariable, so that its relation to that which it moves remains also invariable and continuous.
Now that these points are settled, it is clear that the first unmoved movent cannot have any magnitude. For if it has magnitude, this must be either a finite or an infinite magnitude. (20) Now we have already53 proved in our course on Physics that there cannot be an infinite magnitude: and we have now proved that it is impossible for a finite magnitude to have an infinite force, and also that it is impossible for a thing to be moved by a finite magnitude during an infinite time. But the first movent causes a motion that is eternal and does cause it during an infinite time. (25) It is clear, therefore, that the first movent is indivisible and is without parts and without magnitude.
* * *
1 iii. 1.
2 i. e. by means of his knowledge he can be sure of giving a wrong opinion and thus deceiving some one.
3 Aristotle is thinking of a passage in the Timaeus (38 B).
4 Chapter 8.
5 Chapter 6.
6 ii. 1. 192b 21.
7 Melissus is meant; cf. 185a 32.
8 Cf. De An. iii. 3. 428b 11.
9 i. e. the material of which a body is composed may be so light as naturally to have an upward tendency.
10 i. e. causing to become hot.
11 sc. upward motion and downward motion respectively.
12 The real cause here is the upward or downward tendency.
13 i. e. the thing that is moved.
14 Chapter 1.
15 i. e. not necessarily continuously: e. g. a thing thrown continues its course after contact with the thrower has ceased.
16 The reference is apparently to vi. 4. 234b 10 sqq.
17 Ch. 1. 251a 9 sqq.
18 i. e. any particular characteristic such as heat.
19 i. e. the whole of itself: there is no question of one part of a thing heating another part.
20 e. g. individual souls.
21 Chapter 1.
22 Chapter 3.
23 Chapter 4.
24 Chapter 5.
25 253a 7 sqq.
26 sc. locomotion.
27 sc. locomotion.
28 Chapter 1.
29 sc. the planets.
30 e. g. any one of the heavenly bodies.
31 Chapter 3.
32 Cf. De An. ii. 4. 416a 21 sqq.
33 Chapter 8.
34 253a 29.
35 v. 4.
36 vi. 2. 233a 21 sqq., and vi. 9.
37 v. 2.
38 v. 6. 229b 28 sqq.
39 Because finite lines may be extended, whereas a circle is once for all complete.
40 Ch. 8. 261b 28.
41 And therefore the motion must have limits.
42 The motive forces in the system of Empedocles.
43 Leucippus and Democritus.
44 The early Ionian school: Thales, Anaximenes, and Heraclitus, the last two of whom are known to have employed these terms.
45 Plato and the Platonists.
46 sc. a part of A.
47 Clearly D must be a larger fraction of A than E is of B.
48 The time occupied by D in moving E to the same extent as B is moved by A.
49 sc. a part of AB.
50 E being presumably the time occupied by AB in moving D.
51 He assumes that the force increases proportionately to the magnitude, so that the time decreases proportionately. This simplifies the argument, though of course it is not essential to it.
52 Cf. Pl. Tim. 59 A, 79 B, C, E, 80 c.
53 iii. 5.
De Caelo
Translated by J. L. Stocks
CONTENTS
BOOK I. OF THE HEAVENLY BODIES
CHAPTER
1. The subject of inquiry
2. That in addition to the four elements, earth, water, air, and fire, there is a fifth element, the movement of which is circular
3. That this body is exempt from alteration and decay
4. That the circular movement has no contrary
5. That no body is infinite.—(i) Not the primary body, or fifth element
6. (ii) None of the other elements
7. (iii) In general, an infinite body is impossible
8. That there cannot be more than one Heaven.—(i) Proved from a consideration of the natural movements and places of the elements
9. (ii) Proved by the principles of form and matter, the three different senses of the term ‘heaven’ being explained. Corollary.—There is no place or void or time outside the Heaven
10. That the Heaven is ungenerated and indestructible.—(i) Review of previous theories
11. (ii) Definition of the terms ‘ungenerated’ and ‘indestructible’, and of their opposites
12. (iii) Proof of the thesis
BOOK II. OF THE HEAVENLY BODIES (Continued)
[Chapters 1–12 omitted.]
13. Of the Earth.—(i) Review of previous theories
14. (ii) That it is at rest at the centre, and spherical in shape
BOOK III. OF THE SUBLUNARY BODIES
1. Previous theories concerning generations stated; the analysis of bodies into planes refuted
2. That every simple body possesses a natural movement; that this movement is either upward or downward; how unnatural movement occurs. General results concerning generation
3. Of bodies subject to generation.—(i) What the elements are
4. (ii) That trie elements are limited in number; the view of Leucippus and Democritus refuted
5. (iii) That the elements cannot be reduced to one
6. (iv) That the elements are not eternal, but are generated out of one another
7. (v) Of the manner of their generation: the view of Empedocles and the explanation by planes refuted
8. (vi) Refutation of the attempt to differentiate the elements by their shapes
BOOK IV. OF THE SUBLUNARY BODIES (Continued)
1. Of the meaning of the terms ‘heavy’ and ‘light’
2. Review of previous theories concerning these
3. Explanation of the variety of motions exhibited by the elements
4. Of the distinctive constitution and properties of the four elements
5. In what sense the matter of which the elements are composed may be regarded as one
6. That the shape of a body cannot account for the direction, but only for the pace, of its movement
DE CAELO
(On the Heavens)
BOOK I
1 [268a] The science which has to do with nature clearly concerns itself for the most part with bodies and magnitud
es and their properties and movements, but also with the principles of this sort of substance, (5) as many as they may be. For of things constituted by nature some are bodies and magnitudes, some possess body and magnitude,1 and some are principles of things which possess these.2 Now a continuum is that which is divisible into parts always capable of subdivision, 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. (10) Beyond these there is no other magnitude, because the three dimensions are all that 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 three3 from nature as (so to speak) laws of it, (15) 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, (20) 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 matter and in that to which they are applied, body alone among magnitudes can be complete. For it alone is determined by the three dimensions, that is, is an ‘all’. But if it is divisible in three dimensions it is every way divisible, (25) while the other magnitudes are divisible in one dimension or in two alone: for the divisibility and continuity of magnitudes depend upon the number of the dimensions, one sort being continuous in one direction, another in two, another in all. All magnitudes, then, which are divisible are also continuous. Whether we can also say that whatever is continuous is divisible does not yet, on our present grounds, (30) appear. One thing, however, is clear. We cannot pass beyond body to a further kind, as we passed from length to surface, and from surface to body. [268b] For if we could, it would cease to be true that body is complete magnitude. We could pass beyond it only in virtue of a defect in it; and that which is complete cannot be defective, since it has being in every respect. (5) Now bodies which are classed as parts of the whole4 are each complete according to our formula, since each possesses every dimension. But each is determined relatively to that part which is next to it by contact, for which reason each of them is in a sense many bodies. But the whole of which they are parts must necessarily be complete, and thus, in accordance with the meaning of the word, have being, not in some respects only, (10) but in every respect.
The Basic Works of Aristotle (Modern Library Classics) Page 56