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

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    <archimedes>
      <text>
        <body>
          <chap>
            <pb pagenum="449"/>
            <p type="main">
              <s>Now let us ſee on which of theſe three dimenſions of the Solid
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              depends the terminating, what and how much the Maſs of that ought
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              to be, that ſo the aſſiſtance of the Air contiguous unto it, may ſuffice
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              to render it ſpecifically leſs grave than the water, whereupon it may
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              reſt without Submerſion. </s>
              <s>It ſhall undoubtedly be found, that the
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              length and breadth have not any thing to do in the ſaid
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              tion, but only the height, or if you will the thickneſs: for, if we take
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              a Plate or Board, as for Example, of Ebony, whoſe Altitude hath
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              unto the greateſt poſſible Altitude of the Rampart, the proportion
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              above declared, for which cauſe it ſwims indeed, but yet not if we
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              never ſo little increaſe its thickneſs; I ſay, that retaining its
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              neſs, and encreaſing its Superficies to twice, four times, or ten times
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              its bigneſs, or dminiſning it by dividing it into four, or ſix, or
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              twenty, or a hundred parts, it ſhall ſtill in the ſame manner continue
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              to float: but encreaſing its thickneſs only a Hairs breadth, it will
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              alwaies ſubmerge, although we ſhould multiply the Superficies a
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              hundred and a hundred times. </s>
              <s>Now foraſmuch as that this is a
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              Cauſe, which being added, we adde alſo the Effect, and being
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              ved, it is removed; and by augmenting or leſſening the length or
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              breadth in any manner, the effect of going, or not going to the
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              tom, is not added or removed: I conclude, that the greatneſs and
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              ſmalneſs of the Superficies hath no influence upon the Natation or
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              Submerſion. </s>
              <s>And that the proportion of the Altitude of the
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              parts of Water, to the Altitude of the Solid, being conſtituted in
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              the manner aforeſaid, the greatneſs or ſmalneſs of the Superficies,
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              makes not any variation, is manifeſt from that which hath been above
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              demonſtrated, and from this, that,
                <emph type="italics"/>
              The Priſms and Cylinders which
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              </s>
            </p>
            <p type="main">
              <s>
                <arrow.to.target n="marg1513"/>
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                <emph type="italics"/>
              have the ſame Baſe, are in proportion to one another as their heights:
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              Whence Cylinders or Prifmes, namely, the Board, be they great or
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              little, ſo that they be all of equall thickneſs, have the ſame proportion
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              to their Conterminall Air, which hath for Baſe the ſaid Superficies of
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              the Board, and for height the Ramparts of water; ſo that alwayes
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              of that Air, and of the Board, Solids are compounded, that in Gravity
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              equall a Maſs of water equall to the Maſs of the Solids, compounded
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              of Air, and of the Board: whereupon all the ſaid Solids do in the
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              ſame manner continue afloat. </s>
              <s>We will conclude in the third place,
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              that,</s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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