Archimedes, Natation of bodies, 1662

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    <archimedes>
      <text>
        <body>
          <chap>
            <pb xlink:href="073/01/007.jpg" pagenum="336"/>
            <p type="main">
              <s>NIC. </s>
              <s>You ſay truth.</s>
            </p>
            <p type="main">
              <s>RIC. </s>
              <s>I have another queſtion to aske you, which is this, Why the Author
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              uſeth the word
                <emph type="italics"/>
              L
                <emph.end type="italics"/>
              iquid, or Humid, inſtead of Water.</s>
            </p>
            <p type="main">
              <s>NIC. </s>
              <s>It may be for two of theſe two Cauſes; the one is, that Water being the
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              principal of all
                <emph type="italics"/>
              L
                <emph.end type="italics"/>
              iquids, therefore ſaying
                <emph type="italics"/>
              Humidum
                <emph.end type="italics"/>
              he is to be underſtood to mean
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              the chief Liquid, that is Water: The other, becauſe that all the Propoſitions of
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              this Book of his, do not only hold true in Water, but alſo in every other
                <emph type="italics"/>
              L
                <emph.end type="italics"/>
              iquid,
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              as in Wine, Oyl, and the like: and therefore the Author might have uſed the word
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                <emph type="italics"/>
              Humidum,
                <emph.end type="italics"/>
              as being a word more general than
                <emph type="italics"/>
              Aqua.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s>RIC. </s>
              <s>This I underſtand, therefore let us come to the firſt
                <emph type="italics"/>
              Propoſition,
                <emph.end type="italics"/>
              which, as
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              you know, in the Original ſpeaks in this manner.</s>
            </p>
            <p type="head">
              <s>PROP. I. THEOR. I.</s>
            </p>
            <p type="main">
              <s>
                <emph type="italics"/>
              If any Superficies ſhall be cut by a Plane thorough any
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              Point, and the Section be alwaies the Circumference
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              of a Circle, whoſe Center is the ſaid Point: that Su­
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              perficies ſhall be Spherical.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s>Let any Superficies be cut at pleaſure by a Plane thorow the
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              Point K; and let the Section alwaies deſcribe the Circumfe­
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              rence of a Circle that hath for its Center the Point K: I ſay,
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              that that ſame Superficies is Sphærical. </s>
              <s>For were it poſſible that the
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              ſaid Superficies were not Sphærical, then all the Lines drawn
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              through the ſaid Point K unto that Superficies would not be equal,
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              Let therefore A and B be two
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              Points in the ſaid Superficies, ſo that
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                <figure id="id.073.01.007.1.jpg" xlink:href="073/01/007/1.jpg" number="2"/>
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              drawing the two Lines K A and
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              K B, let them, if poſſible, be une­
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              qual: Then by theſe two Lines let
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              a Plane be drawn cutting the ſaid
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              Superficies, and let the Section in
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              the Superficies make the Line
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              D A B G: Now this Line D A B G
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              is, by our pre-ſuppoſal, a Circle, and
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              the Center thereof is the Point K, for ſuch the ſaid Superficies was
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              ſuppoſed to be. </s>
              <s>Therefore the two Lines K A and K B are equal:
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              But they were alſo ſuppoſed to be unequal; which is impoſſible:
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              It followeth therefore, of neceſſity, that the ſaid Superficies be
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              Sphærical, that is, the Superficies of a Sphære.</s>
            </p>
            <p type="main">
              <s>RIC. </s>
              <s>I underſtand you very well; now let us proceed to the ſecond
                <emph type="italics"/>
              Propoſition,
                <emph.end type="italics"/>
                <lb/>
              which, you know, runs thus.</s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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