Galilei, Galileo, Discourse concerning the natation of bodies, 1663

Table of figures

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                <pb pagenum="451"/>
              Therefore, the abſolute weight of B, to the abſolute weight of C, is
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              as the Maſs A C to the Maſs
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              C
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              : But as the Maſs AC, is to the Maſs C,
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              ſo is the abſolute weight of A C, to the abſolute weight of C:
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              fore the abſolute weight of B, hath the ſame proportion to the
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              lute weight of C, that the abſolute weight of A C, hath to the
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              ſolute weight of C: Therefore, the two Solids A C and B are equall
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              in abſolute Gravity: which was to be demonſtrated. </s>
              <s>Having
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              monſtrated this, I ſay,</s>
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            <p type="head">
              <s>THEOREME X.</s>
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            <p type="main">
              <s>
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              That it is poſſible of any aſſigned Matter, to form a Pi-
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                <arrow.to.target n="marg1516"/>
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              ramide or Cone upon any Baſe, which being put upon
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              the Water ſhall not ſubmerge, nor wet any more than
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              its Baſe.
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            <p type="margin">
              <s>
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              There may be
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              Cones and
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              mides of any
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                <emph type="italics"/>
              M
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              atter, which
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              demittedinto the
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              water, reſt only
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              their Baſes.</s>
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            <p type="main">
              <s>Let the greateſt poſſible Altitude of the Rampart be the Line D B,
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              and the Diameter of the Baſe of the Cone to be made of any
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              ter aſſigned B C, at right angles to D B: And as the Specificall Gravity
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              of the Matter of the Piramide or Cone to be made, is to the Specificall
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              Gravity of the water, ſo let the Altitude of the
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                <figure id="fig274" number="13"/>
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              Rampart D B, be to the third part of the Piramide
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              or Cone A B C, deſcribed upon the Baſe, whoſe
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              Diameter is B C: I ſay, that the ſaid Cone A B C,
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              and any other Cone, lower then the ſame, ſhall reſt
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              upon the Surface of the water B C without ſinking.
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              </s>
              <s>Draw D F parallel to B C, and ſuppoſe the Priſme
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              or Cylinder E C, which ſhall be tripple to the Cone
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              A B C. And, becauſe the Cylinder D C hath the ſame proportion
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              to the Cylinder C E, that the Altitude D B, hath to the Altitude B E:
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              But the Cylinder C E, is to the Cone A B C, as the Altitude E B is to
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              the third part of the Altitude of the Cone: Therefore, by Equality of
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              proportion, the Cylinder D C is to the Cone A B C, as D B is to the
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              third part of the Altitude B E: But as D B is to the third part of B E,
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              ſo is the Specificall Gravity of the Cone A B C, to the Specificall
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              vity of the water: Therefore, as the Maſs of the Solid D C, is to the
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              Maſs of the Cone A
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              B
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              C, ſo is the Specificall Gravity of the ſaid Cone,
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              to the Specificall Gravity of the water: Therefore, by the precedent
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              Lemma, the Cone A B C weighs in abſolute Gravity as much as a
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              Maſs of Water equall to the Maſs D C: But the water which by the
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              impoſition of the Cone A B C, is driven out of its place, is as much
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              as would preciſely lie in the place D C, and is equall in weight to the
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              Cone that diſplaceth it: Therefore, there ſhall be an
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              Equilibrium,
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                <lb/>
              and the Cone ſhall reſt without farther ſubmerging. </s>
              <s>And its
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              nifeſt,</s>
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          </chap>
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