Salusbury, Thomas, Mathematical collections and translations (Tome I), 1667

Table of figures

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    <archimedes>
      <text>
        <body>
          <chap>
            <pb xlink:href="040/01/1031.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
                <lb/>
              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
                <lb/>
              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
                <lb/>
              the chief Liquid, that is Water: The other, becauſe that all the Propoſitions of
                <lb/>
              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,
                <lb/>
              as in Wine, Oyl, and the like: and therefore the Author might have uſed the word
                <lb/>
                <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
                <lb/>
              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
                <lb/>
              Point, and the Section be alwaies the Circumference
                <lb/>
              of a Circle, whoſe Center is the ſaid Point: that Su­
                <lb/>
              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
                <lb/>
              Point K; and let the Section alwaies deſcribe the Circumfe­
                <lb/>
              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
                <lb/>
                <figure id="id.040.01.1031.1.jpg" xlink:href="040/01/1031/1.jpg" number="228"/>
                <lb/>
              drawing the two Lines K A and
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              K B, let them, if poſſible, be une­
                <lb/>
              qual: Then by theſe two Lines let
                <lb/>
              a Plane be drawn cutting the ſaid
                <lb/>
              Superficies, and let the Section in
                <lb/>
              the Superficies make the Line
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              D A B G: Now this Line D A B G
                <lb/>
              is, by our pre-ſuppoſal, a Circle, and
                <lb/>
              the Center thereof is the Point K, for ſuch the ſaid Superficies was
                <lb/>
              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:
                <lb/>
              It followeth therefore, of neceſſity, that the ſaid Superficies be
                <lb/>
              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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