Galilei, Galileo
,
Discourse concerning the natation of bodies
,
1663
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[Figure 1]
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[Figure 2]
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[Figure 3]
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[Figure 4]
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[Figure 5]
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[Figure 6]
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[Figure 7]
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[Figure 8]
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[Figure 9]
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[Figure 10]
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[Figure 11]
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[Figure 12]
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[Figure 13]
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[Figure 14]
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[Figure 15]
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[Figure 16]
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[Figure 17]
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[Figure 18]
Page: 58
[Figure 19]
Page: 76
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Maſs I S. </
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>I ſay, that the Solid I S ſhall not
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ſinke, but being never ſo little thicker it ſhall
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go to the bottom: For being that as A I is
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to I O, ſo is the Exceſs of the Gravity of the
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Solid I S, above the Gravity of a Maſs of water
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equall to the Maſs I S, to the Gravity of the
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ſaid Maſs of water: Therefore, compounding, as A O is to O I, ſo
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ſhall the Gravity of the Solid I S, be to the Gravity of a Maſs of water
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equall to the Maſs I S: And, converting, as I O is to O A, ſo ſhall the
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Gravity of a Maſs of water equall to the Maſs I S, be to the Gravity
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of the Solid I S: But as I O is to O A, ſo is a Maſs of water I S, to a
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Maſs of water equall to the Maſs A B S O: and ſo is the Gravity of
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a Maſs of water I S, to the Gravity of a Maſs of water A S: Therefore
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as the Gravity of a Maſs of water, equall to the Maſs I S, is to the
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Gravity of the Solid I S, ſo is the ſame Gravity of a Maſs of water
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I S, to the Gravity of a Maſs of Water A S: Therefore the
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vity of the Solid I S, is equall to the Gravity of a Maſs of water
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quall to the Maſs A S: But the Gravity of the Solid I S, is the ſame
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with the Gravity of the Solid A S, compounded of the Solid I S,
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and of the Air A B C I. </
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<
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>Therefore the whole compounded Solid
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A O S B, weighs as much as the water that would be compriſed in the
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place of the ſaid Compound A O S B: And, therefore, it ſhall make
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an
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Equilibrium
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and reſt, and that ſame Solid I O S C ſhall ſinke no
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farther. </
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>But if its thickneſs I O ſhould be increaſed, it would be
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ceſſary alſo to encreaſe the Altitude of the Rampart A I, to
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tain the due proportion: But by what hath been ſuppoſed, the
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tude of the Rampart A I, is the greateſt that the Nature of the
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Water and Air do admit, without the waters repulſing the Air
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herent to the Superficies of the Solid I C, and poſſeſſing the ſpace
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A I C B: Therefore, a Solid of greater thickneſs than I O, and of the
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ſame Matter with the Solid I S, ſhall not reſt without ſubmerging,
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but ſhall deſcend to the bottome: which was to be demonſtrated.
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>In conſequence of this that hath been demonſtrated, ſundry and
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rious Concluſions may be gathered, by which the truth of my
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cipall Propoſition comes to be more and more confirmed, and the
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imperfection of all former Argumentations touching the preſent
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Queſtion cometh to be diſcovered.</
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And firſt we gather from the things demonstrated, that,
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