Lecture 3 — Preliminary notions for showing the parts perfecting the universe.

13 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. We will now speak of those parts of the whole which are specifically distinct. Let us take this as our starting-point.

14 All natural bodies and magnitudes we hold to be, as such, capable of locomotion; for nature, we say, is their principle of movement.

15 But all movement that is in place, all locomotion, as we term it, is either straight or circular or a combination of these two,

16 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.

17 Now revolution about the center is circulation,

18 while the upward and downward movements are in a straight line, 'upward***'*** meaning motion away from the middle, and 'downward' motion to the middle.

19 All simple motion, then, must be motion either away from or towards or around the middle.

20 This seems to be in exact accord with what we said above: as body found its completion in three dimensions, so its movement completes itself in three forms.

21 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 compoundᾰsimple in the case of the simple bodies, compound in that of the compositeᾰand in the latter case the motion will be that of the simple body which prevails in the composition.

19. After showing that the universe is perfect by reason both of its corporeity and its universalness, the Philosopher here shows from which parts its perfection is made up.

First, he expresses his intention;

Secondly, he proves his proposition, at this seems to be (268b14).

With respect to the first (268b11) it should be considered that, as is said in Physics III, the ancients described the infinite as that outside of which there is nothing. Now, since he has proved that the universe is perfect on the ground that nothing is outside it, but that it embraces all things, one might think it to be infinite. Accordingly, meeting this opinion, he concludes by adding that later on, in discussing the nature of the whole universe, there will be treated the question of whether it is infinite in magnitude, or finite with respect to its total mass. But meanwhile, before treating of this, something must be said about those parts of it that are according to the species, namely, those parts in which the integrity of its species consists, and which are the simple bodies. For animals and plants and other such are its secondary parts, and pertain more to the well-being of the universe than to its basic integrity. And we shall begin this consideration from a principle given below.

20. Then at all natural bodies (268b14) he starts to manifest the proposition stating of which principal parts the perfect species of the universe is made.

First, he shows that in addition to the four elements, another simple body must exist; secondly, that there is no simple body other than these five, at it is also clear from what has been said (L. 8; 270b26).

About the first he does two things:

first, he shows that there is a fifth body besides the four elements;

secondly, how it differs from the four elements, at in consequence of what has been said (L. 5; 269b18).

With respect to the first he does two things:

first, he mentions some preliminary facts needed in proving his proposition;

secondly, he argues to the proposition supposing, then, that there is such a thing as simple movement (L. 4; 269a2).

About the first he does two things:

first, he premises facts regarding motion;

secondly, facts pertaining to mobile bodies, at **bodies are either (**268b26; [32]).

About the first he does two things:

first, he mentions the connection between local motion and mobile bodies;

secondly, he distinguishes the kinds of local motion, at **but all movement.

21. He says therefore first (268b14) that all physical, i.e., natural, bodies are said to be mobile with respect to place according to themselves, i.e., according to their very natures, and the same is true for other natural magnitudes, e.g., planes and lines, insofar as they are the boundaries of natural bodies. And this is true in the sense that bodies are moved per se, but the other magnitudes per accidens, when the bodies are moved. In proof of this he adduces the definition of nature, which is the principle of motion in those things in which it exists, as is said in Physics II.

From this he argues thus: natural bodies are ones that have a nature, but nature is a principle of motion in things in which it is; therefore, natural bodies have a principle of motion in them. But whatever is moved with any sort of motion is moved locally, but not conversely, as is plain in Physics VII, because local motion is the first of motions. Therefore, all natural bodies are naturally moved with a local motion, but not all of them with all of the other motions.

22. This, however, seems to be false: for the heavens are a natural body, but their motion seems to be due, not to nature but to intellect, as is plain from what has been determined in Physics VIII and Metaphysics XII. But it must be said that there are two kinds of principles of motion: one is active, i.e., the mover, as the soul is the active principle of the motion of animals; the other is a passive principle of motion, i.e., a principle according to which a body has an aptitude to be thus moved, and such a principle of motion exists in the heavy and the light. For these are not composed of a mover and a moved, because, as the Philosopher says in Physics VIII, it is plain that none of these—i.e., the heavy and the light—moves itself, but each has, with respect to its motion, a principle not of causing motion or of acting, but of being acted upon. Consequently, it must be said that the active principle of the motion of heavenly bodies is an intellectual stance, but the passive principle is that body's nature according to which it is apt to be moved with such a motion. And the same situation would prevail in us, if the soul did not move our body in any way other than according to its natural inclination, namely, down.

23. Then at but all movement (268b17), he distinguishes local motions.

First, he distinguishes in a general way both composite and simple local motions;

secondly, he distinguishes simple motions, at now revolution about the center (268b20; [27]).

With respect to the first he does two things:

first (268b17), he proposes what he intends, namely, that every local motion—which is called latio—is either circular, or straight, or composed of these, as is the oblique motion of things that are borne this way and that.

Secondly, at which are the only simple movements (268b18), he proves what he had said, on the ground that there are just two simple motions, the straight and the circular. And the reason for this, he says, is that there exist just two simple magnitudes, namely, the straight and the circular: but local motion is specified according to places, just as every other motion is specified according to its termini.

24. But it seems that Aristotle's proof is not suitable, because, as is said in Post. Anal. I, one does not demonstrate who crosses into another genus. Consequently, it seems unfitting to use the division of magnitudes, which pertain to mathematics, in order to reach a conclusion about motion, which pertains to natural science. But it must be said that a science which is by addition to some other science uses the latter's principles in demonstrating, as geometry uses the principles of arithmetic—for magnitude adds position to number, and thus a point is said to be a positioned unit. In like manner, natural body adds sensible matter to mathematical magnitude. Consequently, it is not unfitting for the natural philosopher in his demonstrations to use the principles of mathematics—for the latter is not of a completely different genus but is in a certain way contained under the former.

25. Likewise, it seems to be false that only two magnitudes are simple, namely, the straight and the circular. For a helix [spiral] seems to be one simple line, because every one of its parts is uniform, and yet a helical line [such as a screw thread] is neither straight nor circular. But it must be said that a helix, if one considers its origin, is not a simple line, but a combination of straight and circular. For a helix is produced by two imaginary motions, one of which is the motion of a line moving round a cylinder, and the other of a point moving through the line: if two such motions take place in a regular manner at the same time, a helix will be formed by the motion of the point in the moving line.

26. Likewise, it seems that circular motion is not simple. For the parts of a sphere that is in circular motion are not in uniform motion but the parts near the poles or near the center are moved more slowly, because they traverse a smaller circle in a given time; consequently, the motion of a sphere seems to be composed of fast and slow motions. But it must be said that a continuum does not have parts in act but only in potency. Now, what is not in act is not in actual motion. Hence the parts of a sphere, since they are a continuous body, are not actually being moved. Hence, it does not follow that, in a spherical or circular motion, there is actual diversity, but this is only potentially. This does not conflict with the simplicity about which we are now speaking, for every magnitude possesses potential plurality.

27. Then, at now revolution about the center (268b20), he distinguishes simple motions.

First, he mentions one, namely, the circular;

secondly, he mentions two that are straight, at while the upward and downward movements (268b21; [29]);

thirdly, he concludes that the number of simple motions is three, at all simple motion (268b22; [30]).

He says therefore first that circulation, i.e., circular motion is around the middle (268b20.) And this is to be understood as around the middle of the world: for a wheel which is in motion around its own middle is not in circular motion in the proper sense of the word, but its motion is composed of ups and downs.

28. But it seems according to this that not all heavenly bodies are in circular motion: for according to Ptolemy, the motion of the planets is in eccentrics and epicycles, which are motions, not around the middle of the world, which is the earth's center, but around certain other centers. But it must be said that Aristotle was not of this opinion, but thought that all motions of the heavenly bodies are about the center of the earth, as did all the astronomers of his time. But later, Hipparchus and Ptolemy hit upon eccentric and epicyclic motions to save what appears to the senses in heavenly bodies. Hence this is not a demonstration, but a certain assumption. Yet, if it be true, all the heavenly bodies are still in motion about the center of the world with respect to the diurnal motion, which is the motion of the supreme sphere that revolves the entire heaven.

29. Then, at while the upward and downward movements (268b21), he distinguishes straight motion into two: namely, one which is up, and one that is down, and describes each in relation to the middle of the world, as he had described circular motion, in order to keep the description uniform. And he says that an upward motion is one from the middle of the world, but a downward motion is one to the middle of the world. The first of these is the motion of light things, the second of heavy things.

30. Then, at all simple motion (268b22), he concludes to the number of simple motions.

First, he expresses the conclusion he intended, and says that as to simple latio, i.e., simple local motion, one must be from the middle, and this is the upward motion of light bodies; another must be to the middle, and this is the downward motion of heavy bodies; still another must be about the middle, and such is the circular motion of heavenly bodies.

31. Secondly, at this seems to be (268b24), he shows that this conclusion agrees with what has been said above. And he says that what has just been said about the number of simple motions seems to be a consequence of what was said above about the perfection of body; for just as the perfection of body consists in three dimensions, so the simple motions of body are distinguished into three kinds. But he says that this is according to reason, i.e., according to a certain probability: for three motions are not properly equated to three dimensions.

32. Then at bodies are either simple or compounded (268b26), he gives some reflections about mobile bodies. In regard to this it must be known that, as was stated in Physics III, motion is an act of a mobile. Now an act is proportionate to the thing to be perfected. Hence, motions ought to be proportionate to mobile bodies. But some bodies are simple, some composite. A simple body is one that has a principle of some natural motion in it, as is plain in the case of fire, which is light simply, and in that of earth, which is heavy simply, and in their species—as a flame is said to be a species of fire, and bitumen a species of earth. He adds the phrase, and those related to them, on account of the intermediate elements, of which air has a greater affinity to fire, and water to earth. As a consequence, a mixed body must be one that, according to its proper nature, does not have in itself the principle of some simple motion. And from this he concludes that some motions must be simple and some mixed: whether the mixed motion is not one but has diverse parts, as one composed of elevation and depression, or of a push and a pull, or whether the mixed motion is one, as is plain in oblique motion and motion upon a helical line. Accordingly, the motions of simple bodies must be simple and those of mixed bodies mixed, as seen in the motion of rain, or any body of this kind in which neither heaviness nor lightness totally predominates. And if it sometimes happens that a mixed body is moved with a simple motion, that will be due to the element predominant in it, as iron is moved downwards according to the motion of earth which is predominant in its composition.