Galilei, Galileo, De Motu Antiquiora

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AL. From the things that have been assumed above it is evident that a heavy thing which goes down, receding from a state of rest, is accelerated in its motion until the resisting impressed force is annihilated ; but if that force is extinguished by an external motor, then it will no longer be accelerated in its motion. As, for example, if a heavy thing whose heaviness is 4 goes down from a state of rest, assuredly it will recede with a resistance of 4; since this must be destroyed by the heaviness of the mobile, the natural motion at the beginning will be weaker {1}: but if the said force as 4 is consumed by an external motor, by impressing on the mobile a force which exerts pressure downward as 4, then without a doubt the heavy thing will no longer be accelerated in its motion, since at the beginning it would not be retarded by any force resisting [the downward motion]. But if the force which is impressed by the external motor impelling downward is smaller than 4, that is, less than the force which had been impressed in the mobile while it was in a state of rest, assuredly the mobile will be accelerated [in its motion downward]; because there is a certain amount of contrary force to be consumed that had not been completely removed by the external motor. Now if there is impressed on the mobile a force propelling downward that is greater than 4, then the natural motion will be faster at the beginning: for it will be moved with a motion that is greater than natural, and which exceeds the motion required by its own proper heaviness {1}. So that its heaviness would then have the effect of lightness {1}, since the heaviness by itself, free and simple, would go down more slowly than when joined with the impetus; and thus the proper and natural slowness of the descending [mobile] would resist the violence impelling {2} [it] downward. And this will be rendered manifest with an example of what happens often to any swimmer.For, when a man is in the water, if he wishes, his heaviness is great enough for him to go down to the very bottom of the water, if he wants to; and then, pulled by his proper heaviness, he will be submerged with a uniform motion: now if he is impelled downward by an external motor with a force as great as can be, as if he were to be cast down from a very lofty place, at the beginning his motion in the water will be very vivacious and greater than natural: and yet his motion will be retarded by his proper absolute {1} heaviness, which then, in comparison to the heaviness which has been joined with the impetus received, is as lightness, and [it will be retarded] until in going down he reaches his natural slowness; and in such a way that, if the water is deep enough, he will not suffer any greater injury at the bottom than if he had gone down from the surface of the water with his proper natural motion.

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