Galilei, Galileo
,
Discourse concerning the natation of bodies
,
1663
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<
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>THEOREME III.</
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A Priſme or regular Cylinder, of a ſubſtance ſpecifically
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leſs grave than Water, if it ſhould be totally ſubmerged
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in Water, ſtayes not underneath, but riſeth, though the
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Water circumfuſed be very little, and in abſolute
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Gravity, never ſo much inferiour to the Gravity of the
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ſaid Priſme.
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>Let then the Priſme A E F B, be put into the Veſſell C D F B, the
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ſame being leſs grave
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in ſpecie
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than the Water: and let the
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Water infuſed riſe to the height of the Priſme: I ſay, that the
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Priſme left at liberty, it ſhall riſe, being born up
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by the Water circumfuſed C D E A. </
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>For the
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Water C E being ſpecifically more grave than
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the Solid A F, the abſolute weight of the water
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C E, ſhall have greater proportion to the
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lute weight of the Priſme A F, than the Maſs
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C E hath to the Maſs A F (in regard the Maſs
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hath the ſame proportion to the Maſs, that the
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weight abſolute hath to the weight abſolute,
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in caſe the Maſſes are of the ſame Gravity
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in ſpecie.
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) But
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the Maſs C E is to the Maſs A F, as the Surface of the water A C, is
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to the Superficies, or Baſe of the Priſme A B; which is the ſame
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portion as the aſcent of the Priſme when it riſeth, hath to the deſcent
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of the water circumfuſed C E.</
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>Therefore, the abſolute Gravity of the water C E, hath greater
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proportion to the abſolute Gravity of the Priſme A F; than the
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Aſcent of the Priſme A F, hath to the deſcent of the ſaid
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water C E. </
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>The Moment, therefore, compounded of the abſolute
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Gravity of the water C E, and of the Velocity of its deſcent, whilſt
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it forceably repulſeth and raiſeth the Solid A F, is greater than the
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Moment compounded of the abſolute Gravity of the Priſme A F, and
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of the Tardity of its aſcent, with which Moment it contraſts and
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fiſts the repulſe and violence done it by the Moment of the water:
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Therefore, the Priſme ſhall be
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The Proportion
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according to
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which the
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merſion & Na
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tation of Solids
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is made.</
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>It followes, now, that we proceed forward to demonſtrate more
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particularly, how much ſuch Solids ſhall be inferiour in Gravity to
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the water elevated; namely, what part of them ſhall reſt ſubmerged,
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and what ſhall be viſible above the Surface of the water: but firſt
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it is neceſſary to demonſtrate the ſubſequent Lemma.</
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