Galilei, Galileo, Discourse concerning the natation of bodies, 1663
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              water is to the elevation of the Priſme, as the abſolute Gravity of
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              the Priſme, is to the abſolute Gravity of the water: Therefore, the
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              Moment reſulting from the abſolute Gravity of the water A F, and
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              the Velocity of the Motion of declination, with which Moment it
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              forceth the Priſme D G, to riſe and aſcend, is equall to the Moment
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              that reſults from the abſolute Gravity of the Priſme D G, and from
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              the Velocity of the Motion, wherewith being raiſed, it would aſcend:
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              with which Moment it reſiſts its being raiſed: becauſe, therefore,
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              ſuch Moments are equall, there ſhall be an
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              Equilibrium
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              between the
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              water and the Solid. </s>
              <s>And, it is manifeſt, that putting a little more
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              water unto the other A F, it will increaſe the Gravity and Moment,
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              whereupon the Priſme D G, ſhall be overcome, and elevated till that
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              the only part B F remaines ſubmerged. </s>
              <s>Which is that that was to
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              be demonſtrated.</s>
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              <s>COROLLARY I.</s>
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              By what hath been demonſtrated, it is manifeſt, that Solids leſs grave
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              in ſpecie
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              than the water, ſubmerge only ſo far, that as much water in
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              Maſs, as is the part of the Solid ſubmerged, doth weigh abſolutely as
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              much as the whole Solid.
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            <p type="margin">
              <s>
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              H
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              ow far Solids
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              leſs grave
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              in
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              cie
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              than water,
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              do ſubmerge.</s>
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              <s>For, it being ſuppoſed, that the Specificall Gravity of the water,
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              is to the Specificall Gravity of the Priſme D G, as the Altitude
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              D F, is to the Altitude F B; that is, as the Solid D G is to the
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              Solid B G; we might eaſily demonſtrate, that as much water in Maſs
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              as is equall to the Solid B G, doth weigh abſolutely as much as the
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              whole Solid D G; For, by the
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              Lemma
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              foregoing, the Abſolute
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              Gravity of a Maſs of water, equall to the Maſs B G, hath to the
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              ſolute Gravity of the Priſme D G, a proportion compounded of the
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              proportions, of the Maſs B G to the Maſs G D, and of the Specifick
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              Gravit 7 of the water, to the Specifick Gravity of the Priſme: But
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              the Gravity
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              in ſpecie
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              of the water, to the Gravity
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              in ſpecie
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              of the
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              Priſme, is ſuppoſed to be as the Maſs G D to the Maſs G B.
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              fore, the Abſolute Gravity of a Maſs of water, equall to the Maſs
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              B G, is to the Abſolute Gravity of the Solid D G, in a proportion
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              compounded of the proportions, of the Maſs B G to the Maſs G D,
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              and of the Maſs D G to the Maſs G B; which is a proportion of
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              equalitie. </s>
              <s>The Abſolute Gravity, therefore, of a Maſs of Water
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              equall to the part of the Maſs of the Priſme B G, is equall to the
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              ſolute Gravity of the whole Solid D G.</s>
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