Galilei, Galileo, De Motu Antiquiora
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It is evident, then, why and how upward motion comes from lightness: and, from the things that have been conveyed in this chapter as well as in the preceding one, it can easily be concluded that things that are heavier than water are completely submerged and are necessarily carried downward.That they are completely submerged is necessary: for if they were not completely submerged, they would then , contrary to what has been presupposed, be lighter than water; for that things that are not completely submerged are lighter than water is evident from the converse of the demonstration just adduced. In addition, these things must be carried downward.For if they were not, either they would be at rest, or they would be moved upward: but they would not be at rest; for it has been demonstrated in the preceding chapter that things that are equally as heavy as water are at rest and are no more carried upward than downward: and it has just become apparent that things lighter than water are carried upward.Consequently, from all these considerations, since it is necessary that things that are moved downward be heavier than the medium through which they are carried, it can adequately be grasped how heavier things are moved downward by heaviness; and how in the case of a stone thrown into the sea, the reckoning must be made not with all the water of the sea, but only with that very small part which must be removed from the place into which the stone enters.But, because all these things that have been conveyed in the two preceding chapters can be made clear in a manner still less mathematical and more physical, by reducing them to a consideration of the scale pan, I have decided in the following chapter to explain the correspondence that these natural mobiles observe with the weights of an equal-armed balance{1}: and the purpose of this is to attain a richer knowledge of the things that will be conveyed and more exact knowledge on the part of my readers.

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