Lecture 7 — Every body moving naturally in a straight line has either gravity or lightness, Natural and violent motions

439 We go on to show that there are certain bodies whose necessary impetus is that of weight and lightness.

440 Of necessity, we assert, they must move, and a moved thing which has no natural impetus cannot move either towards or away from the center.

441 Suppose a body A without weight, and a body B endowed with weight. Suppose the weightless body to move the distance CD, while B in the same time moves the distance CE, which will be greater since the heavy thing must move further. Let the heavy body then be divided in the proportion CE: 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 CE, the part must in the same time move the distance CD. A weightless body, therefore, and one which has weight will move the same distance, which is impossible. And the same argument would fit the case of lightness.

442 Again, a body which is in motion but has neither weight nor lightness, must be moved by constraint, and must continue its constrained movement infinitely. For there will be a force which moves it, and the smaller and lighter a body is the further will a given force move it. Now let A, the weightless body, be moved the distance CE, and B, which has weight, be moved in the same time the distance CD. Dividing the heavy body in the proportion CE:CD, we 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. 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.

443 It is therefore obvious that every body must have a definite weight or lightness.

444 But since 'nature' means a source of movement within the thing itself, while a force is a source of movement in something other than it or in itself qua other, and since movement is always due either to nature or to constraint,

445 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.

446 In either case the air is as it were instrumental to the force. For air is both light and heavy, and thus qua light produces upward motion, being propelled and set in motion by the force, and qua 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 function, constrained movement would be impossible.

447 And the natural movement of a body may be helped on in the same way.

448 This discussion suffices to show that all bodies are either light or heavy, and how unnatural movement takes place.

586. After showing that natural bodies have natural motions, and disproving the positions of philosophers who erred on this matter, the Philosopher here shows that bodies naturally moved with a straight motion have heaviness and lightness; for the principles of natural motion in such bodies are reckoned with respect to heaviness and lightness.

First, therefore, he proposes what he intends (301a22) and says that it will be plain from what follows that certain bodies, namely, those naturally moved with a straight motion must have heaviness and lightness by which they are inclined to their appropriate places. He says certain bodies, in order to distinguish them from those that are circularly moved.

587. Secondly, at of necessity, we assert, they must move (301a23) he presents a proof of his proposition, saying: Here we say in a general way that it is necessary for natural bodies to be moved, for they are called "natural" from having within themselves the principle of motion, as is plain from Physics II. But if what is moved does not have a natural inclination by which it tends to some determinate place, it cannot be moved either to the center, which comes about through the inclination of heaviness, or from the center, which is due to the inclination of lightness. Therefore it is necessary that bodies which are moved in a straight motion have heaviness and lightness.

588. Thirdly, at suppose a body A (301a26), he proves what he had presupposed, namely, that if the bodies in question did not have heaviness and lightness, they would not be moved.

First, he shows that they would not be moved naturally;

secondly, that they would not be moved by violence, at again, a body which is (301b1; [589]).

He says therefore first (301a26) that if any of the lower bodies does not possess heaviness or lightness, let there be two bodies, and let A be the body lacking heaviness and B the body having heaviness. Now let A, which is the non-heavy body, be moved for a certain period of time, say for the space of one hour, over a magnitude GD, with a motion directed to the center. Then B, which has heaviness, will, during the same time be moved with the same type of motion over a larger magnitude GE; for a body having heaviness must in an equal time traverse a greater distance than a body not having heaviness, just as a heavier body is carried downward more swiftly than a less heavy. Now let B which has heaviness be divided in the ratio of GE to GD so that the whole of B is related to a part, say C, as the whole GE is to GD; for there is nothing to prevent such a division of body B, since every finite body can be divided according to any given ratio. Therefore, let us go on thus. As GE is to GD, so B is to its part C; therefore, by commutative proportion, B is to GE as C (which is part of B) is to GD. If, therefore, the whole B traverses in a given time the entire magnitude GE, then the part of B must traverse the magnitude GD in the same time. But body A (the one having no heaviness) traversed the same magnitude in the same amount of time. Therefore, it will follow that a body having heaviness, and one not having heaviness, will traverse the same magnitude in equal time. And the same argument is valid if the other body is assumed to have lightness. Consequently, it is plain that something irreconcilable follows, if any of the lower bodies is assumed to have neither heaviness nor lightness.

589. Then, at again, a body which is (301b1) he shows that if any of the lower bodies lacks heaviness or lightness, it cannot be moved by violence. And he says: From the fact that it was shown by the foregoing argument that a body lacking heaviness or lightness cannot be moved naturally with a straight motion, then, if it is moved at all, it must be through violence, for every motion of such bodies is either natural or compulsory. But it cannot be moved by violence either, because, if it were moved by violence, its motion would have to be infinite, i.e., of infinite speed, which is impossible. And that this would follow he proves by using the principle that if any power, i.e., violence, moves a body, a lesser and lighter will be moved by the same power, i.e., by the same violence, more, i.e., more swiftly, in motion, namely, upward—for a larger and heavier body offers more resistance to violence. Therefore let A be a body not having heaviness and let it be moved upward violently through the magnitude GE; but let B be a body having heaviness which by the same force in an equal time is moved through the magnitude GD, which is of course less than GE. Just as the heavier is moved less by the same force, so the heavy is moved less than the non-heavy. Let then the body B, having heaviness, be divided in the ratio which is that of the ratio of magnitude GE to GD. It will follow, therefore, just as it did before, that what is taken away through division from body B which has heaviness, will be moved through magnitude GE in a time equal to that in which body A, which lacks heaviness, was moved through it, because the whole body B in the same time was moved through magnitude GE which is less. For the ratio of the speed of the lesser magnitude to the greater must be as the ratio of the greater body to the lesser, so that, in the same time, the greater body is moved a smaller distance, and the lesser body a greater distance, because a lesser body is moved more swiftly by an equal power. It will follow, therefore, that in the same period of time a non-heavy body and one having heaviness are moved an equal distance—which is impossible. But no matter what heavy body is taken and no matter how swiftly it is moved, a non-heavy body will be moved a greater distance in the same time. Accordingly, it will follow that a body lacking heaviness would be moved with an infinite speed through violence—which is impossible. And the same argument holds for a non-light body.

Therefore, in summary, he concludes (301b14) that plainly every body which is determinate, i.e., which is moved with a straight motion has heaviness or lightness. He calls the body which is moved with a straight motion determinate, either because he is here speaking determinately of it, or because such bodies are moved with a straight motion insofar as they are segregated and divided and not insofar as they are taken all together.

590. Then, at but since 'nature' (301b17), because he had mentioned both natural and violent motion, he now shows how both types are produced. Regarding this he does two things:

first, he shows the difference between natural and violent motion;

secondly, how both are found in air, at in either case (301b22; [591]).

About the first he does two things:

first, he shows the difference between natural and violent motion;

secondly, how violence enters in even to natural motion, at movement which is natural (301b20; [590]).

Now, natural and violent motions differ with respect to their principles, and therefore he first defines the principles of each of these motions (301b17). And he says that nature is a principle of a motion existing in that which is moved, as is plain in Physics II: force, however, i.e., a power that causes motion violently, is a principle existing in another, as it is other. He says this because it could accidentally happen that a principle of violent motion exist in one and the same thing, but not insofar as it is one and the same, but insofar as it is other, as when a doctor heals himself not as doctor but as sick. And from this it is plain that there is a motion that is natural and a motion that is violent. For a motion is according to nature whose principle is in what is moved, not only as active principle, but also as passive, which, indeed, is the potency by which something is naturally capable of undergoing motion from another. Consequently, when lower bodies are moved by the higher bodies, the motion is not violent but natural, because in the lower bodies there is a natural aptitude to follow the motions of the higher bodies. But a motion is violent when no principle of the motion is from within but only from without, as when a man throws a heavy body upward, in which body there is no natural aptitude for such motion.

Then at (301b20) he shows as a consequence how violence enters into natural motion. For in the case of a motion which is natural to some body, as for a stone to be moved downward naturally, a force that acts violently sometimes quickens that motion. Consequently, such a motion is in a certain sense mixed, since the kind of motion it is is due to nature, but the addition in speed is due to the violent mover. But in the case of a violent motion, it is violence that entirely produces it and makes it the type of motion it is, and accounts for the amount of its speed—for to the extent that something from nature should happen to be present in it, to that extent it would not be beside nature.

591. Then, at in either case (301b22), he explains the role that air plays in both these motions.

First, the part it plays in violent motion;

secondly, how it serves natural motion, at and the natural movement (301b29; [592]).

He says therefore first (301b22) that the force of a violent mover uses the air as an instrument for both, i.e., for upward and downward motion. For air is apt by nature to be light and heavy: for, as was said above, and as will be explained at greater length in Book IV, fire is absolutely light and earth absolutely heavy, but air and water are intermediate between these two, since air is heavy compared to fire, but light compared to water and earth; but water is light compared to earth, while compared to fire and air it is heavy. Accordingly, air, insofar as it is light, will perfect a violent motion that is upward (but only insofar as it is moved and insofar as the principle of such a motion is the power of the violent mover); and insofar as it is heavy, it will perfect a motion that is downward.. For the force of the violent mover, by a kind of impression, imparts a motion to both, i.e., either to the air moved upwards and moved downwards, or to the air and to the heavy body, such as a stone. This does not mean that the force of the violent mover impresses upon the stone which is moved by violence some force by which it might be moved, in the way that the power of the generator impresses on the thing generated a form upon which natural motion follows—for then the violent motion would proceed from an intrinsic principle, and that is contrary to the notion of a violent motion. It would also follow that a stone, by the very fact that it is in local motion through violence, would be altered — and this is contrary to what we sense. Therefore, the violent mover impresses motion alone upon the stone, and this it does while it touches it. But because air is more susceptible to such an impression (both because it is more subtle and because it is in a sense light), it is moved more swiftly through the impression of the violent mover than the stone. Consequently, when the violent mover desists, the air moved by it continues to propel the stone and also the adjoining air, which likewise moves the stone farther, and this continues so long as the impression of the first violent mover endures, as is said in Physics VIII. Hence it is that the violent mover, even though it does not follow the mobile that is being carried along through violence, e.g., a stone, so as to move it by being present to it, yet it moves it through the impression of the air —if there were no body such as is the air, there would not be violent motion. From this it is plain that air is a necessary instrument of violent motion and not simply an improving one.

592. Then, at and the natural movement (301b29), he shows what role air plays in natural motion. And he says that air promotes the natural motion of each body in the same way as its violent motion, namely, insofar as by its lightness it helps an upward motion, and by its heaviness a downward motion.

593. But the question can be raised whether the air serves the natural motion of heavy bodies and light bodies so as to be necessary or merely helpful. Averroes says that it also serves natural motion of necessity, and for two reasons.

First, because, as he says in his commentary on this passage, the mover of heavy and of light things is their generator which, in giving the form, gives as a consequence the natural motion, just as it gives all the natural accidents which follow the form. Consequently, the generator causes natural motion through the form. Now a natural motion should follow from its mover immediately. Hence, since the natural motion does not follow immediately from the generator but from the form, it seems that the form is the proper mover in natural motion. Accordingly, it seems that heavy and light bodies in a sense move themselves. But not by themselves, because a thing that moves itself is distinguished into mover and moved, as was proved in Physics VIII—a distinction not found in heavy and light bodies, which are divided only into form and matter, the latter of which is not apt to be moved, as is proved in Physics, V. Hence it remains that a heavy or light body moves itself ear accidens, in the way that a sailor moves a ship through whose movement he himself is moved. Similarly, the light and the heavy body through their form move the air, upon whose motion the heavy and the light body are moved. And thus he concludes that air is necessary for natural motion.

Secondly, because, as he says in his commentary on Physics IV, there must be some resistance between mover and mobile. But the matter of a heavy or a light body does not resist its form, which is the principle of motion. Therefore, it is necessary that there be some resistance from the medium, which is air or water. Thus, air is necessary for natural motion.

594. But both of these arguments proceed from the source of error. For he believed the form of a heavy and of a light body to be an active principle of motion after the manner of a mover, in such a way that resistance would be required to the form's inclination, and also that motion does not proceed immediately from the generator which gives the form. But this is completely false. For the form of a heavy and of a light body is not a principle of motion as though it were an agent itself moved, but as that by which the mover causes motion, just as color is a principle of seeing, by which something is seen. That is why Aristotle in Physics III, after discussing the motion of the heavy and light, says: it is plain that neither of these moves itself but that they have a principle of motion, not indeed of moving something or making something, but of being acted upon. Consequently, the motion of the heavy and the light does not come from the generator through the medium of some moving principle; nor is it necessary to look for any other resistance in this motion than that which prevails between the generator and the thing generated. Consequently it remains that air is not required for natural motion of necessity as it is in violent motion. For what is moved naturally has been endowed with a power which is a principle of motion. Hence, it does not need to be moved by something else impelling it, as in the case of a thing violently moved, since the latter has no inherent power, upon which such a motion follows. The very words of Aristotle point up this difference: for when speaking of violent motion he says, unless there were such a body, there would not be motion by constraint; but in speaking of natural motion he says, air helps that motion of each thing which is according to nature.

Finally, in summary, he concludes (301b30) that it is plain from the aforesaid that all bodies are either light or heavy, and how unnatural movement takes place.