Commentary Aristotle Physics
Lecture 22
The problem of projectile motion
But, before proceeding to our conclusion, it will be well to discuss a difficulty that arises in connection 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—for instance, things thrown—continue to be in motion when their mover is no longer in contact with them?
If we say that the mover in such cases moves something else at the same time that the thrower (for instance) also moves the air, and that this, in being moved, is also a mover, then it would be no more possible for this second thing to be in motion than for the original thing to be when the first mover is not in contact with it or moving it.
All the things moved would have to be in motion simultaneously and also at rest simultaneously when the first mover rests, even if, like the magnet, it makes that which it has moved capable of being a mover.
Therefore, while we must accept this explanation to the extent of saying that the first mover gives the power of being a mover either to air or to water or to something else of the kind naturally adapted for imparting and undergoing motion, we must say further that the mover and moved do not pause simultaneously.
It ceases to be in motion at the moment when its mover ceases to move it, but it still remains a mover, and so it causes something else contiguous 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 contiguous 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 mover, but only causes it to be in motion.
The motion of these last two—of the one as mover 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, there being not one mover, but a number of movers next to one another, and so motion of this kind takes place in air and water.
Some say that it is “antiperistasis,” 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, such that their motions also cease simultaneously.
But our present problem concerns the appearance of continuous motion in a single thing, and therefore, since it cannot be moved throughout its motion by the same mover, the question is, “What moves it?”
1160. After proving two of the things needed for demonstrating his proposition—namely, that a finite power cannot move for an infinite time, and that an infinite power cannot exist in a finite magnitude—the Philosopher now starts to prove the third, namely, the unity of the first mover.
About this, he does two things:
first, he shows that, on account of the diversity of movers, the continuity or unity of motion fails in certain mobiles that seem to be in continuous motion;
second, he shows from this that the first mover is necessarily one, at “we proceed from the positions” (267a21; [1164]).
About the first, he does three things:
first, he raises a doubt about projectiles;
second, he resolves the doubt, at “therefore, while we must” (267a2; [1162]);
third, from this, he shows that the motion of a projectile is not continuous, at “now, the things in which” (267a12; [1163]). About the first, he does two things: first, he states the doubt;
second, he rejects one solution, at if we say that (266b30).
He first proposes, therefore (266b27), a doubt about projectiles. It is this. It was proved above in the beginning of this book 8 that whatever is being moved is being moved by another, provided we are not referring to things that move themselves, such as animals, of which a projected stone is not one. Now, a bodily thing causes motion through contact. Therefore, there is doubt as to how projectiles remain in continuous motion even after contact with the mover ceases. For they seem to be moved without anything moving them.
1161. Then, at “if we say that” (266b30), he rejects a solution attributed to Plato, who said that the projector who first moves a stone moves not only the stone but something else, namely, the air, and the moved air moves the stone, even after contact by the projector. But he rejects this solution on the ground that it appears just as impossible for the air as it was for the stone to be moved when the first mover (namely, the projector) is no longer in contact with it nor moving it. But, rather, it seems to be necessary that, while the first mover is acting, all are being moved, and when the first mover rests (that is, ceases to act), all rest, although also something moved by the first mover, such as the stone, may cause something to be moved, just as the first mover did.
1162. Then, at “therefore, while we must” (267a2), he gives his own solution. And he says that, if the second mover causes motion insofar as it is moved by the first mover, then it is necessary to say that the first mover (namely, the projector) gives to the second mover (namely, the air or water or any such body apt to move a thrown body) the ability both to cause motion and to be moved.
For both of these are received into the air or water from the thrower, namely, to cause motion and to be moved. But, since to cause motion and to be moved are not of necessity in the same thing—since there is found a mover that is not itself moved—the mover and moved do not pause simultaneously; that is, the air moved by the thrower does not simultaneously cease causing motion and cease being moved, but as soon as the first mover (the thrower) ceases acting, the air ceases to be moved, but still moves.
And this is evident to the senses. For when a mobile has now arrived at the terminus of its motion, it is able to cause motion in the ultimate moment of its arrival, at which time it is no longer being moved but is in the state of having been moved.
Now, while the second mover moves, that which is contiguous—that is, which is next to it—is being moved. And the same applies to this third, for it remains a mover even when it is not being moved. And, because a second mover has less power for acting than did the first, and the third less than the second, the motion called “projection” must cease on account of the fact that the power for moving is less in one member of the contiguous series, that is, the subsequent mover, than it was in the first.
Thus, at length, on account of the diminution of the power to move, a state is reached where that which was prior with respect to the one following will not confer upon the one following the power to cause motion, but will solely cause it to be moved. And, at that time, it is necessary that, when this last mover ceases to act upon the one following it, simultaneously that moved by it will cease being moved. Consequently, the entire motion will cease because the last moved object is unable to cause motion in any other.
1163. Then, at “now, the things in which” (267a12), he concludes from the foregoing that a motion of projection is not continuous.
He says, therefore, that this motion (projection) comes to be in bodies that are capable of being moved at one time and of resting at another time—if indeed there are bodies to which such a motion belongs. And this is evident from what was said, for the motion called “projection” ceases through a failing of the power to cause motion, as has been said.
It is also evident from the foregoing that this motion is not continuous, although it appears to be continuous. For it seems to be continuous, because there is one mobile involved; yet it is not continuous, because there are diverse movers, as has been said. For that motion results either from a series of consecutive movers or from a series of movers that are in contact. (How “consecutive” and “in contact” differ has been explained above in books 5 and 6.)
And it is plain to sense that, in both cases, the different movers can move one mobile inasmuch as they are moved by some first mover. For in things that are moved in the way that projectiles are moved, there is not just one mover but many next to each other (that is, following each other), which are consecutive and in contact. And because diversity is not without division, the projection in question comes to be through a medium that is easy to divide—namely, air and water—in which a diversity of movers can function on account of the easy divisibility of the medium.