Galilei, Galileo, De Motu Antiquiora

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307 forced; because, of course, there is resistance exerted at the pivots of the axis. For since it happens that the sphere is outside its proper place, it happens also that it exerts weight and is in need of support; that is why the extremities of the axis of the sphere, by exerting weight on the pivots, hinder the motion. But the more the ends of the axis are polished and thin, the less they will suffer resistance: so that, if we imagine them to be indivisibles {1}, then no resistance will develop from them. It also happens that such a motion is retarded by the surface of the sphere, if the surface is rough and unevenly cut: for the air flowing round and retained in the cavities of the surface will hinder the motion, and will not help it, as someone has believed; this will be explained in its place {1}. But if the sphere is heterogeneous, in such a way as to have a center of heaviness outside the center of size [i.e. magnitude], but it rotates around the center of magnitude, in this case, independently of the other accidental causes adduced above, there will be in addition a cause per se why such a motion is not, as the other was, neither natural neither forced, but sometimes natural, sometimes forced. For since the center of heaviness in such a circular motion describes a circle about the center of magnitude, when it goes up from the lowest point towards the highest, it will be moved by force, since it recedes from the center of the world; but when it tends from the highest to the lowest, it will surely be carried by nature.
Older Works on Motion, Book II, chapter 4 [17] [307.24-314.25]By what projectiles are moved.

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Searching "tower" (fulltextMorph)
1. Page 16, Sentence 4:How ridiculous this opinion is, is clearer than daylight: for who will ever believe that if, for example, two lead balls were released from the sphere of the Moon, one being a hundred times larger than the other, if the larger took an hour to come to Earth, the smaller would use in its motion a space of time of a hundred hours? or, if from a high tower {1}, two stones, one being double the size of the other, were thrown at the same moment, that, when the smaller was at mid-tower, the larger would already have reached the ground?
2. Page 24, Sentence 18:For if one takes two different mobiles, which have such properties that one is carried twice as swiftly as the other, and then releases them from the top of a tower, it will certainly not hit the ground faster, twice as swiftly: what is more, if one makes the observation, the one which is lighter at the beginning of the motion will precede the heavier and will be faster.
3. Page 68, Sentence 9:But this way of thinking is not only false, but ridiculous: for, if it were true, it would follow that a stone going down from a very high tower would be moved more slowly at mid-tower, than if the same stone were falling to the ground from a very low place, and for this reason the mobile [falling from a greater height] would also make a lesser impact.
4. Page 76, Sentence 3:There is a fourth well-known argument concerning a large stone going down from a tower, which will not be sufficiently blocked by a pebble impelled upward by force, so as to permit the pebble to be at rest for any time: hence surely the pebble will not be at rest at the ultimate point of its upward motion, and Aristotle notwithstanding, it will make use of the ultimate point for the two limits, namely of upward motion and of downward motion; and the ultimate instant is taken twice, namely, for the end of one time and for the beginning of the other.
5. Page 79, Sentence 4:Now in the case of heavier things, since a great amount of contrary force must be consumed in their descent, a greater time will be required for it to be consumed; in which time, since they are carried swiftly, they will descend a great distance: since we cannot avail ourselves of such great distances from which to release heavy things, it is not astonishing if the stone, released from merely the height of a tower, will seem to accelerate all the way to the ground; for this short distance and short time of motion are not sufficient to destroy the whole contrary force.
6. Page 84, Sentence 6:Yet experience shows the contrary: for it is true that wood at the beginning of its motion is carried more speedily than lead; but a little later the motion of lead is so accelerated that it leaves the wood behind, and, if they are released from a high tower, the lead gets ahead of it by a large distance: and I have often put this to the test. {1}
7. Page 134, Sentence 6:But if we go up a very high tower, on the top of which there is a bathtub, the same thing will happen to us when in it as if we were to go into the sea: for we will not be weighed down by the water, even though the latter, having air underneath it, is outside its proper place.
8. Page 150, Sentence 12:For if a stone goes down from a high tower, its swiftness seems always to be increased: yet this happens because the stone, in comparison /// with the medium through which it is carried, namely air, is very heavy; and since it goes away with an amount of impressed force as great as its heaviness, it assuredly goes away with a great impressed force, which the motion from the height of a tower is not sufficient to consume, so that the swiftness is always intensified all through the height of a single tower.

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