Galilei, Galileo, De Motu Antiquiora

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Having examined these things in the case of the scale pan, returning to natural mobiles, we can put forward the following as a general proposition: namely, that the heavier cannot be raised by the less heavy. {1} With this presupposed, it is easy to understand why solids that are lighter than water are not completely submerged. For if, for example, we let down a beam into water, then, if the beam is to be submerged, it is necessary that water move out of the place into which the beam enters, and be raised upward, that is be moved away from the center of the world. Consequently if the water, which is to be raised, is heavier than the beam itself, then surely it will not be able to be raised by the beam: but if the beam is completely submerged, then it is necessary that from the place, into which the beam enters, an amount of water as great in size as the size of the beam itself should be removed: but an amount of water as great in size, as is the size of the beam, is heavier then the beam (for it is assumed that the beam is lighter than water): therefore it will not be possible for the beam to be completely submerged. And this corresponds to what has been said in the case of the scale pan, namely that a lesser weight cannot raise a greater one. But if the beam were equally as heavy as water, that is if the water, which is raised by the beam that is to be submerged, is not heavier than but equally as heavy as the beam, then the beam surely will be completely submerged, since it does not have resistance from the water that is to be raised; but in addition, when it is completely under water, it will be carried no more upward than downward: and this corresponds by analogy to what has been said in the case of the scale pan concerning equal weights, of which neither is carried either upward or downward.But if, on the other hand, the beam is heavier than that water which is to be raised by the beam, that is if the beam is heavier than an amount of water as great in size, as its own proper size (for there is raised by the submerged beam, as has often been said, an amount of water as great in size as its own size), then certainly the beam will be carried downward: which indeed corresponds by analogy to what has been said in the case of the scale pan,

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