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

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    <archimedes>
      <text>
        <body>
          <chap>
            <pb pagenum="411"/>
            <p type="head">
              <s>THEOREME II.</s>
            </p>
            <p type="main">
              <s>
                <emph type="italics"/>
              When in one of the above ſaid Veſſels, of what ever
                <emph.end type="italics"/>
                <lb/>
                <arrow.to.target n="marg1412"/>
                <lb/>
                <emph type="italics"/>
              breadth, whether wide or narrow, there is placed ſuch
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              a Priſme or Cylinder, inviron'd with Water, if we
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              vate that Solid perpendicularly, the Water
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              ſed ſhall abate, and the Abatement of the Water,
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              ſhall have the ſame proportion to the Elevation of the
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              Priſme, as one of the Baſes of the Priſme, hath to
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              the Surface of the Water Circumfuſed.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s>
                <margin.target id="marg1412"/>
              The proportion
                <lb/>
              of the water
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              ted, to the Solid
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              raiſed.</s>
            </p>
            <p type="main">
              <s>Imagine in the Veſſell, as is aforeſaid, the
                <lb/>
                <figure id="fig263" number="2"/>
                <lb/>
              Priſme A C D B to be placed, and in the
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              reſt of the Space the Water to be
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              fuſed as far as the Levell E A: and
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              ſing the Solid, let it be transferred to
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              G M, and let the Water be abaſed from
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              E A to N O: I ſay, that the deſcent of
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              the Water, meaſured by the Line A O,
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              hath the ſame proportion to the riſe of the
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              Priſme, meaſured by the Line G A, as the Baſe of the Solid G H
                <lb/>
              hath to the Surface of the Water N O. </s>
              <s>The which is manifeſt:
                <lb/>
              becauſe the Maſs of the Solid G A B H, raiſed above the firſt Levell
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              E A B, is equall to the Maſs of Water that is abaſed E N O A.
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              Therefore, E N O A and G A B H are two equall Priſmes; for of
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              equall Priſmes, the Baſes anſwer contrarily to their heights:
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              fore, as the Altitude A O is to the Altitude A G, ſo is the
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              cies or Baſe G H to the Surface of the Water N O. </s>
              <s>If therefore,
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              for example, a Pillar were erected in a waſte Pond full of Water,
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              or elſe in a Well, capable of little more then the Maſs of the ſaid
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              Pillar, in elevating the ſaid Pillar, and taking it out of the Water,
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              according as it riſeth, the Water that invirons it will gradually abate,
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              and the abaſement of the Water at the inſtant of lifting out the
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              Pillar, ſhall have the ſame proportion, that the thickneſs of the Pillar
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              hath to the exceſs of the breadth of the ſaid Pond or Well, above
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              the thickneſs of the ſaid Pillar: ſo that if the breadth of the Well
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              were an eighth part larger than the thickneſs of the Pillar, and the
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                <arrow.to.target n="marg1413"/>
                <lb/>
              breadth of the Pond twenty five times as great as the ſaid thickneſs,
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              in the Pillars aſcending one foot, the water in the Well ſhall deſcend
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              ſeven foot, and that in the Pond only 1/25 of a foot.</s>
            </p>
            <p type="margin">
              <s>
                <margin.target id="marg1413"/>
              Why a Solid
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              leſs grave
                <emph type="italics"/>
              in
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              cie
                <emph.end type="italics"/>
              than water,
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              ſtayeth not
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              der water, in
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              ry ſmall depthst.</s>
            </p>
            <p type="main">
              <s>This Demonſtrated, it will not be difficult to ſhew the true
                <lb/>
              cauſe, how it comes to paſs, that,</s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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