Galilei, Galileo
,
Discourse concerning the natation of bodies
,
1663
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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]
Page: 57
[Figure 18]
Page: 58
[Figure 19]
Page: 76
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ment or ebbing of the water A C, hath to the riſe or elevation of
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the ſaid Solid M. Therefore, by Perturbation of proportion, in the
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aſcent of the ſaid Solid M, the abaſement of the water A B C D, to
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the abaſement of the water E N S F, hath the ſame proportion, that the
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Surface of the water E F, hath to the Surface of the water A D;
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that is, that the whole Maſs of the water E N S F, hath to the whole
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Maſs A B C D, being equally high: It is manifeſt, therefore, that
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in the expulſion and elevation of the Solid M, the water E N S F
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ſhall exceed in Velocity of
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M
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otion the water A B C D, aſmuch as it
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on the other ſide is exceeded by that in quantity: whereupon their
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Moments in ſuch operations, are mutually equall.</
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And, for ampler confirmation, and clearer explication of this, let us
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conſider the preſent Figure, (which if I be not deceived, may ſerve to
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detect the errors of ſome Practick Mechanitians, who upon a falſe
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tion ſome times attempt impoſſible enterprizes,) in which, unto the large
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Veſſell E I D F, the narrow Funnell or Pipe I C A B is continued, and
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poſe water infuſed into them, unto the Levell L G H, which water ſhall
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reſt in this poſition, not without admiration in ſome, who cannot conceive
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how it can be, that the heavie charge of the great
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Maſs of water G D, preſſing downwards, ſhould
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not elevate and repulſe the little quantity of the
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other, contained in the Funnell or Pipe C L, by
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which the deſcent of it is reſisted and hindered:
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But ſuch wonder ſhall ceaſe, if we begin to ſuppoſe
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the water G D to be abaſed only to Q D, and
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ſhall afterwards conſider, what the water C L
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hath done, which to give place to the other, which
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is deſcended from the Levell G H, to the Levell
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Q O, ſhall of neceſſity have aſcended in the ſame
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time, from the Levell Lunto A B. </
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>And the
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aſcent L B, ſhall be ſo much greater than the
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ſcent G Q, by how much the breadth of the Veſſell
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G D, is greater than that of the Funnell I C;
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which, in ſumme, is as much as the water G D,
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is more than the water L C: but in regard that the Moment of the Velocity
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of the Motion, in one Moveable, compenſates that of the Gravity of
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ther, what wonder is it, if the ſwift aſcent of the leſſer Water C L, ſhall
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reſiſt the ſlow deſcent of the greater G D
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?</
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>The ſame, therefore, happens in this operation, as in the Stilliard,
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in which a weight of two pounds counterpoyſeth an other of 200,
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asoften as that ſhall move in the ſame time, a ſpace 100 times
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er than this: which falleth out when one Arme of the Beam is an </
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