The Basic Works of Aristotle (Modern Library Classics) (68 page)

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. 192
^b
21.

⁷
Melissus is meant; cf. 185
^a
32.

⁸
Cf.
De An.
iii. 3. 428
^b
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. 234
^b
10 sqq.

¹⁷
Ch. 1. 251
^a
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
253
^a
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. 416
^a
21 sqq.

³³
Chapter 8.

³⁴
253
^a
29.

³⁵
v. 4.

³⁶
vi. 2. 233
^a
21 sqq., and vi. 9.

³⁷
v. 2.

³⁸
v. 6. 229
^b
28 sqq.

³⁹
Because finite lines may be extended, whereas a circle is once for all complete.

⁴⁰
Ch. 8. 261
^b
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.

   
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

  
13.
   Of the Earth.—(i) Review of previous theories

  
14.
   (ii) That it is at rest at the centre, and spherical in shape

  
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

  
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

1
     
[268a]
The 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,
(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 three
³
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 whole
⁴
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.

2
     The question as to the nature of the whole, whether it is infinite in size or limited in its total mass, is a matter for subsequent inquiry.
⁵
We will now speak of those parts of the whole which are specifically distinct. Let us take this as our starting-point.
(15)
All natural bodies and magnitudes we hold to be, as such, capable of locomotion; for nature, we say, is their principle of movement. But all movement that is in place, all locomotion, as we term it, is either straight or circular or a combination of these two, which are the only simple movements. And the reason of this is that these two, the straight and the circular line, are the only simple magnitudes.
(20)
Now revolution about the centre is circular motion, while the upward and downward movements are in a straight line, ‘upward’ meaning motion away from the centre, and ‘downward’ motion towards it. All simple motion, then, must be motion either away from or towards or about the centre. This seems to be in exact accord with what we said above: as body found its completion in three dimensions,
(25)
so its movement completes itself in three forms.

Bodies are either simple or compounded of such; and by simple bodies I mean those which possess a principle of movement in their own nature, such as fire and earth with their kinds, and whatever is akin to them. Necessarily, then, movements also will be either simple or in some sort compound—simple in the case of the simple bodies,
(30)
compound in that of the composite—and in the latter case the motion will be that of the simple body which prevails in the composition.
[269a]
Supposing, then, that there is such a thing as simple movement, and that circular movement is an instance of it, and that both movement
of a simple body is simple and simple movement is of a simple body (for if it is movement of a compound it will be in virtue of a prevailing simple element),
(5)
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 of the natural and a thing can have no more than one contrary,
(10)
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 the contraries of one another.
(15)
If, on the other hand, (2) the body moving with this circular motion which is unnatural to it is something different 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.
(20)
For the 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 belongs to the body which is naturally prior,
(25)
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 be the movement of some simple body. For the movement of composite bodies is, as we said, determined by that simple body which preponderates in the composition.
(30)
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,
(35)
is the case with the upward and downward movements, which are natural and unnatural to fire and earth respectively.
[269b]
It necessarily follows that circular movement, being unnatural to these bodies, is the natural movement of some other. Further, if, on the one hand, circular movement is
natural
to something, it must surely be some simple and primary
body which is ordained to move with a natural circular motion,
(5)
as fire is ordained 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 inconceivable 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,
(10)
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 confidence that there is something beyond the bodies that are about us on this earth,
(15)
different and separate from them; and that the superior glory of its nature is proportionate to its distance from this world of ours.