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

Table of figures

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[Figure 11]
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    <archimedes>
      <text>
        <body>
          <chap>
            <pb pagenum="416"/>
            <p type="head">
              <s>COROLLARY
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                <arrow.to.target n="marg1418"/>
              </s>
            </p>
            <p type="margin">
              <s>
                <margin.target id="marg1418"/>
                <emph type="italics"/>
              A
                <emph.end type="italics"/>
              Rule to
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              librate
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              S
                <emph.end type="italics"/>
              olids in
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              the water.</s>
            </p>
            <p type="main">
              <s>
                <emph type="italics"/>
              It followes, moreover, that a Solid leſs grave than the water, being put
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              into a Veſſell of any imaginable greatneſs, and water being circumfuſed
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              about it to ſuch a height, that as much water in Maſs, as is the part of
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              the Solid ſubmerged, doth/> weigh abſolutely as much as the whole Solid;
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              it ſhall by that water be juſtly ſuſtained, be the circumfuſed Water in
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              quantity greater or leſſer.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s>For, if the Cylinder or Priſme M, leſs grave than the water,
                <emph type="italics"/>
              v.
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              </s>
              <s>gra.
                <emph.end type="italics"/>
              in Subſequiteriall proportion, ſhall be put into the
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              ous Veſſell A B C D, and the water raiſed about it, to three
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              quarters of its height, namely, to its Levell A D: it ſhall be ſuſtained
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              and exactly poyſed in
                <emph type="italics"/>
                <lb/>
              librium.
                <emph.end type="italics"/>
              The ſame will
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              pen, if the Veſſell E N S F
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                <figure id="fig267" number="6"/>
                <lb/>
              were very ſmall, ſo, that
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              tween the Veſſell and the
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              lid M, there were but a very
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              narrow ſpace, and only capable of ſo much water, as the hundredth
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              part of the Maſs M, by which it ſhould be likewiſe raiſed and erected,
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              as before it had been elevated to three fourths of the height of the
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              Solid: which to many at the firſt ſight, may ſeem a notable Paradox,
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              and beget a conceit, that the Demonſtration of theſe effects, were
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              ſophiſticall and fallacious: but, for thoſe who ſo repute it, the
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              periment is a means that may fully ſatisfie them. </s>
              <s>But he that ſhall
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              but comprehend of what Importance Velocity of Motion is, and how
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              it exactly compenſates the defect and want of Gravity, will ceaſe to
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              wonder, in conſidering that at the elevation of the Solid M, the great
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              Maſs of water A B C D abateth very little, but the little Maſs of
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              water E N S F decreaſeth very much, and in an inſtant, as the Solid
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              M before did liſe, howbeit for a very ſhort ſpace: Whereupon the
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              Moment, compounded of the ſmall Abſolute Gravity of the water
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              E N S F, and of its great Velocity in ebbing, equalizeth the Force and
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              and Moment, that reſults from the compoſicion of the immenſe
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              vity of the water A B C D, with its great ſlowneſſe of ebbing;
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              ſince that in the Elevation of the Sollid M, the abaſement of the leſ­</s>
            </p>
            <p type="main">
              <s>
                <arrow.to.target n="marg1419"/>
                <lb/>
              ſer water E S, is performed juſt ſo much more ſwiftly than the great
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              Maſs of water A C, as this is more in Maſs than that which we thus
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              demonſtrate.</s>
            </p>
            <p type="margin">
              <s>
                <margin.target id="marg1419"/>
                <emph type="italics"/>
              T
                <emph.end type="italics"/>
              he proportion
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              according to
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              which water
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              ſeth and falls in
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              different Veſſels
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              at the
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              on and
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              on of
                <emph type="italics"/>
              s
                <emph.end type="italics"/>
              olids.</s>
            </p>
            <p type="main">
              <s>In the riſing of the Solid M, its elevation hath the ſame proportion
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              to the circumfuſed water E N S F, that the Surface of the ſaid water,
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              hath to the Superficies or Baſe of the ſaid Solid M; which Baſe hath
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              the ſame proportion to the Surface of the water A D, that the </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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