406 which has preceded a natural motion: for even in the case of a natural motion which is preceded by a violent one, the mobile recedes as from a ratio of equality {2}, which is the ratio of rest. Now pay attention in order to understand this more clearly. {1}Let o be a mobile whose heaviness is 4: and let the line along which the violent motion takes place be oe. Thus it is manifest that in mobile o there can be impressed a force great enough to move {1} it as far as r; this force will necessarily be greater than 4, which is the heaviness of the mobile: again a force can be impressed which moves it only as far as t; again it will be greater than 4, and smaller than that which impelled it as far as r: again, a force can be impressed that is great enough to move the piece only as far as s; however it will be greater than 4, but smaller than that which impelled it as far as t: and so on, indefinitely, a force can always be impressed which will impel the mobile over any distance, however small; and yet this force will always be greater than 4. It remains, therefore, that that force is 4 which impels the mobile with a violent motion over no distance at all: from this it is evident that when mobile o recedes from the hand, it recedes with a force that is as great as 4; which then, since it is successively consumed by the heaviness, is the cause of the intensification of the motion. And what I have said will appear even more lucid if we consider that, when a heavy thing is at rest in the hand {1}, since by its heaviness it exerts pressure downward, it is necessary that it be impelled upward by something, namely the hand, with a force equal to it own heaviness, which exerts pressure downward: otherwise, unless it were hindered by another force, as great, impelling it upward, it would head downward, if the resistance were smaller; but upward, it it were greater. Therefore it is evident that, when it is abandoned by what sustains it, a heavy thing goes down with an impressed force equal to its proper heaviness; from which it follows, etc.
DO. What you say is quite satisfying; and yet there still remains something I do not understand, which troubles my mind. {1}For if the slowness of the natural motion at the beginning occurs by the resistance of the impressed force, this force will eventually be consumed, since you assert that it is continuously weakened; therefore the natural motion, when the said force will be annihilated, will no longer be subject to any more violent motion: which, however, is opposed to the opinion of many.