319 it is able to accomplish this. For a heavy mobile to be able to be moved upward violently, an impelling force greater than the resisting heaviness is necessary; otherwise the resisting heaviness would not be able to be overcome, and, consequently, the heavy thing would not be able to be carried upward. Hence, the mobile is carried upward, provided the motive impressed force is greater than the resisting heaviness. Now since this force, as has been demonstrated {1}, is continuously diminished, it will finally become so diminished that it will no longer overcome the heaviness of the mobile, and then it will not impel the mobile any further: but that impressed force will not therefore have been annihilated at the end of the violent motion, but it will only be diminished to the point that it no longer surpasses the heaviness of the mobile, but it will be equal to it; and, to put it in a word, the impelling force, which is lightness, will no longer dominate in the mobile, but will have been reduced to parity with the heaviness of the mobile: and then, at the ultimate point of the violent motion, the mobile will be neither heavy nor light. But, moreover, as the impressed force diminishes in its own way, the heaviness of the mobile begins to predominate; and hence the mobile starts to go down. But since at the beginning of such a descent a great deal of force that impels the body upward, which is lightness, still remains (even though it is no longer greater than the heaviness of the mobile), it comes about that the proper heaviness of the mobile is diminished by this lightness, and, consequently, that the motion at the beginning is slower. And, moreover, since that extrinsic force is further weakened, the heaviness of the mobile is increased by having less resistance, and the mobile is moved still faster.
I think that this is the true cause of the acceleration of motion: when I had thought it out, and, two months later, happened to be reading the things written by Alexander {1} on this subject, I learned from him that this had also been the way of thinking of that very great man of learning, who is praised by the very learned Ptolemy -- namely, Hipparchus, who is greatly esteemed and extolled with the highest praises by Ptolemy throughout the whole of his Almagest. {2} According to Alexander {1}, Hipparchus also believed that this was the cause of the acceleration of natural motion: but, since he added nothing beyond what we have said above, this opinion seemed defective, and was thought to deserve rejection by philosophers; for it seemed to apply only in the case of those natural motions that were preceded by a violent motion, and that it could not be attributed to a motion which does not follow a violent motion. {2}But they were not content to reject it as defective, but actually as false, and not even true in the case of a motion preceded by a violent [motion]. But we will add the things that have not been explained by Hipparcus, by showing how even in a motion that is not preceded by a violent [motion], the same cause applies; and we will try to free our explanation from all malicious criticisms. I would not however say that Hipparcus was wholly undeserving of reproach; for he has left undetected a difficulty of great importance: but I will only add the things that are missing, and will reveal the splendor of the truth.
I say, then, that it is for the same reason that motions, which a violent motion does not precede, are also moved more slowly at the beginning. For even in motions which a violent [motion] does not precede, the mobile begins to be moved, from a state {1} of rest, and not from a violent motion. Thus a stone projected upward, when it begins to be moved downward from that extreme {1} point at which there is equality between the impelling force and the resisting heaviness, which is a state of rest, begins to go down; this is the same thing as if it were falling from someone's hand. For even when the stone falls from someone's hand, with no force impelling it upward having been impressed on it, it leaves with a quantity of impressed force equal to its heaviness. For when the stone is at rest in someone's hand, one must not say that in that case he who holds it impresses no force on the stone: for since the stone exerts pressure downward by its heaviness, it is necessary that it be impelled upward by the hand with an equal quantity of force, neither larger nor smaller. For if the force, by which the hand impels the stone upward, was greater than the heaviness of the stone, the resisting stone would be raised by the hand; and it would not be at rest, as we are presupposing: but, on the other hand, if the stone exerted more weight than the hand lifted, the stone would proceed downwards; now we are presupposing that the stone is at rest in the hand: hence there is impressed in the stone, by the hand or by whatever else by which it is controlled, as much force impelling upward as there is heaviness of the stone tending downward; nevertheless the stone is not raised, because, as we have said, that impelling force cannot surpass the resisting heaviness, since it is not greater than that heaviness. It is thus evident how, when the stone comes out of the hand, it leaves with a quantity of impressed force equal to its heaviness: which is not different from what happens when the stone starts to proceed downward, having completed its upward motion; for in that case too, when it recedes from the state of rest, it leaves with a quantity of force equal to its heaviness: hence for the same reason it is moved more slowly at the beginning in the case of that motion, just as in the case of this one.