Archimedes, Natation of bodies, 1662

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    <archimedes>
      <text>
        <body>
          <chap>
            <pb xlink:href="073/01/005.jpg" pagenum="334"/>
            <p type="main">
              <s>NIC. </s>
              <s>The Cauſe of all theſe Effects is aſſigned by
                <emph type="italics"/>
              Archimedes,
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              the
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              Siracuſan,
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              in
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                <arrow.to.target n="marg1126"/>
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              that Book
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              De Incidentibus (^{*}) Aquæ,
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              by me publiſhed in Latine, and dedicated to
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              your ſelf, as I alſo ſaid in the beginning of that my
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              Induſtrions Invention.
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              </s>
            </p>
            <p type="margin">
              <s>
                <margin.target id="marg1126"/>
              *
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              Aquæ,
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              tanſlated
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              by me
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              Humido,
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              as
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              the more Compre­
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              henſive word, for
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              his Doctrine holds
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              true in all Liquids
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              as well as in Wa­
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              ter,
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              ſoil.
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              in Wine,
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              Oyl, Milk,
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              &c.
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              </s>
            </p>
            <p type="main">
              <s>RIC. </s>
              <s>I have ſeen that ſame
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              Archimedes,
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              and have very well underſtood thoſe
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              two Books in which he treateth
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              De Centro Gravitatis æquerepentibus,
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              or of the
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              Center of Gravity in Figures plain, or parallel to the Horizon; and likewiſe thoſe
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                <emph type="italics"/>
              De Quadratura Parabolæ,
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              or, of Squaring the Parabola; but ^{*}
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              that
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              in which he treat­
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              eth of Solids that Swim upon, or ſink in Liquids, is ſo obſcure, that, to ſpeak the
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              truth, there are many things in
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              it
                <emph.end type="italics"/>
              which I do not underſtand, and therefore before
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                <arrow.to.target n="marg1127"/>
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              we proceed any farther, I ſhould take it for a favour if you would declare it to me
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              in your Vulgar Tongue, beginning with his firſt
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              Suppoſition,
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              which ſpeaketh in this
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              manner.</s>
            </p>
            <p type="margin">
              <s>
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              * He ſpeaks of but
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              one Book,
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              Tartag­
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              lia
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              having tranſla­
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              ted no more.</s>
            </p>
            <p type="head">
              <s>SVPPOSITION I.</s>
            </p>
            <p type="main">
              <s>
                <emph type="italics"/>
              It is ſuppoſed that the Liquid is of ſuch a nature, that
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              its parts being equi-jacent and contiguous, the leſs
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              preſſed are repulſed by the more preſſed. </s>
              <s>And
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              that each of its parts is preſſed or repulſed by the
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              Liquor that lyeth over it, perpendicularly, if the
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              Liquid be deſcending into any place, or preſſed any
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              whither by another.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s>NIC. </s>
              <s>Every Science, Art, or Doctrine (as you know,
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              Honoured Companion,
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              )
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              hath its firſt undemonſtrable Principles, by which (they being
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              granted or ſuppoſed) the ſaid Science is proved, maintained, or de­
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              monſtrated. </s>
              <s>And of theſe Principles, ſome are called
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              Petitions,
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                <lb/>
              and others
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              Demands,
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              or
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              Suppoſitions.
                <emph.end type="italics"/>
              I ſay, therefore, that the Science or Doctrine
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              of thoſe Material Solids that Swim or Sink in Liquids, hath only two undemon­
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              ſtrable
                <emph type="italics"/>
              Suppoſitions,
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              one of which is that above alledged, the which in compliance
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              with your deſire I have ſet down in our Vulgar Tongue.</s>
            </p>
            <p type="main">
              <s>RIC. </s>
              <s>Before you proceed any farther tell me, how we are to underſtand the
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              parts of a Liquid to be
                <emph type="italics"/>
              Equijacent.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s>NIC. </s>
              <s>When they are equidiſtant from the Center of the World, or of the
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              Earth (which is the ſame, although ^{*} ſome hold that the Centers of the Earth
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              and Worldare different.)</s>
            </p>
            <p type="main">
              <s>RIC. </s>
              <s>I underſtand you not unleſs you give me ſome Example thereof in
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              Figure.
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                <arrow.to.target n="marg1128"/>
              </s>
            </p>
            <p type="margin">
              <s>
                <margin.target id="marg1128"/>
              * The Coperni­
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              cans.</s>
            </p>
            <p type="main">
              <s>NIC. </s>
              <s>To exemplifie this particular, Let us ſuppoſe a quantity of Liquor (as
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              for inſtance of Water) to be upon the Earth; then let us with the Imagination
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              cut the whole Earth together with that Water into two equal parts, in ſuch a
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              manner as that the ſaid Section may paſs ^{*} by the Center of the Earth: And let
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              us ſuppoſe that one part of the Superficies of that Section, as well of the Water
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              as of the Earth, be the Superficies A B, and that the Center of the Earth be the
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              point K. </s>
              <s>This being done, let us in our Imagination deſcribe a Circle upon the </s>
            </p>
            <p type="main">
              <s>
                <arrow.to.target n="marg1129"/>
                <lb/>
              ſaid Center K, of ſuch a bigneſs as that the Circumference may paſs by the Super­
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              ficies of the Section of the Water: Now let this Circumference be E F G: and
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              let many Lines be drawn from the point K to the ſaid Circumference, cutting the
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              ſame, as KE, KHO, KFQ KLP, KM. </s>
              <s>Now I ſay, that all theſe parts of
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              the ſaid Water, terminated in that Circumference, are Equijacent, as being all </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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