LECTURE 22 (266 b 27-267 a 21)

THE PROBLEM OF PROJECTILE MOTION

1160. After the Philosopher has proven two things which are necessary for the proof of his main point, namely, that a finite power cannot move in an infinite time, and that an infinite power cannot reside in a finite magnitude, he now proceeds to prove a third point, namely, the unity of the first mover.

             Concerning this he does two things. First he shows that because of a diversity of movers the continuity or unity of motion fails in certain mobile objects which seem to be moved continuously. Secondly, where he says, 'Resuming our main argument . . .' (267 a 22), he shows that the first mover must be one.

             Concerning the first part he makes three points. First he raises an objection concerning things which are thrown. Secondly, where he says, 'Therefore, while we must . . .' (267 a 3), he answers the objection. Thirdly, where he says, 'Now the things in which . . .' (267 a 12), he shows that the motion of a thrown body is not continuous.

             Concerning the first part he makes two points. First he raises the objection. Secondly, where he says, 'If we say that . . .' (266 b 30), he rejects a certain solution.

             Therefore he first states a difficulty concerning things which are thrown. The difficulty is as follows.

             It was shown above, at the beginning of Book VIII, that whatever is moved is moved by another, excluding self-movers, such as animals. A thrown stone is not included in this latter group. Moreover, a body moves as a result of contact. There is a difficulty, therefore, concerning the way in which a thrown thing continues to be moved even after it is no longer in contact with the mover. For it seems that it is then being moved without having a mover.

             1161. Next where he says, 'If we say that . . .' (266 b 30), he rejects a certain solution, said to have been Plato's, which holds that the thrower which first moves the stone moves something else together with the stone, namely the air, and the moved air moves the stone subsequent to the contact of the thrower.

             But he rejects this solution because it seems to be just as impossible for the air to be moved without contact with the first mover, that is, the thrower, as it was for the stone. Rather it seems to be necessary that while the first mover moves, everything is moved, and while the first mover rests, that is, ceases from moving, everything rests, even though that which was moved by the first mover, for example, the stone, causes something to be moved, just as that which moved first, moved.

             1162. Next where he says, 'Therefore, while we must . . .' (267 a 3), he give his own solution.

             He says that if the second mover moves what has been moved by the first mover, it must be said that the first mover, that is, the thrower, gives to the second mover, that is, air or water or any such body which can naturally move a thrown body, the power to move and to be moved. For the air or water receives from the thrower both the power to move and to be moved. But to move and to be moved are not necessarily in the same being, for we have found that there is a mover which is not moved. Therefore, the mover and that which is moved do not stop simultaneously, that is, the air moved by the thrower does not simultaneously cease to move and to be moved. Rather as soon as the first mover, that is, the thrower, ceases to move, the air ceases to be moved, but it is still a mover.

             And this is clear to the senses. For when a mobile object has reached the terminus of its motion, at that ultimate point it can move. It is not then being moved but rather has already been moved. Moreover, while the second mover moves, it moves that which is related consecutively to it. And the same principle [ratio] holds for this third being, for it remains a mover even when it is no longer moved. And because the second mover has less power of moving than the first, and the third less than the second, the motion of throwing must cease because there is less power of moving in the consecutive mover than there was in the first mover.

             And finally, because of the decrease in the power of the motive force, we reach a point where that which will be prior to the next object will not cause that next object to have the power of moving but will only cause it to be moved. When this last mover stops moving, that which is moved by it must simultaneously stop from being moved. And consequently, the whole motion will cease, since the last thing moved cannot move something else.

             1163. Next where he says, 'Now the things in which . . .' (267 a 12), he concludes from the above that the motion of throwing is not continuous.

             He says, therefore, that this motion of throwing occurs in bodies which are sometimes moved and sometimes at rest. This is clear from what has been said, for the motion of throwing ceases due to the decrease of the motive power, as was said.

             It is also clear from the above that that motion is not continuous, though it may seem to be. It appears to be continuous because of the unity of the mobile object. It is not continuous, however, because there are many movers, as was said. For that motion results either from many movers which are consecutive or from many movers which are in contact. (It was explained above in Book V and in Book VI how consecutiveness differs from contact.)

             And it is apparent to the senses that, in whichever way the diverse movers are related, they are able to move one mobile object insofar as they themselves are moved by some first mover. For in things which are moved by the motion of throwing, there is not just one mover, but many, which are related to each other both consecutively and by contact. And since diversity involves division, the motion of throwing mentioned above occurs through a medium which is readily divisible, namely, through air or water, in which there are a diversity of movers because they are easily divided.

             Some say, however, that this motion of throwing is 'mutual replacement', that is, contrary-resistance, such that the surrounding air which is moved in some way moves the thrown body, as was said above in Book IV. But the above problem can be solved only in the way set down. For if the 'mutual replacement' of the air is said to be the cause of the throwing, it follows that everything moves and is moved simultaneously, that is, the whole of the air moves and is moved simultaneously, and consequently, everything rests simultaneously. But this is clearly false. For we see that there is one thing which is moved continuously no matter what moves it. I say this because it does not have one and the same determinate mover, but many movers.