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

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    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s>
                <pb xlink:href="040/01/200.jpg" pagenum="182"/>
              amongſt thoſe who know nothing thereof. </s>
              <s>Now to ſhew you how
                <lb/>
              great their errour is who ſay, that a Sphere
                <emph type="italics"/>
              v.g.
                <emph.end type="italics"/>
              of braſſe, doth not
                <lb/>
              touch a plain
                <emph type="italics"/>
              v.g.
                <emph.end type="italics"/>
              of ſteel in one ſole point, Tell me what
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              ceipt you would entertain of one that ſhould conſtantly aver, that
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              the Sphere is not truly a Sphere.</s>
            </p>
            <p type="margin">
              <s>
                <margin.target id="marg368"/>
                <emph type="italics"/>
              The truth
                <lb/>
              ſometimes gaines
                <lb/>
              ſtrength by
                <lb/>
              tradiction.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s>SIMP. </s>
              <s>I would eſteem him wholly devoid of reaſon.</s>
            </p>
            <p type="main">
              <s>SALV. </s>
              <s>He is in the ſame caſe who ſaith that the material Sphere
                <lb/>
                <arrow.to.target n="marg369"/>
                <lb/>
              doth not touch a plain, alſo material, in one onely point; for to
                <lb/>
              ſay this is the ſame, as to affirm that the Sphere is not a Sphere.
                <lb/>
              </s>
              <s>And that this is true, tell me in what it is that you conſtitute the
                <lb/>
              Sphere to conſiſt, that is, what it is that maketh the Sphere differ
                <lb/>
              from all other ſolid bodies.</s>
            </p>
            <p type="margin">
              <s>
                <margin.target id="marg369"/>
                <emph type="italics"/>
              The sphere
                <lb/>
              though material,
                <lb/>
              toucheth the
                <lb/>
              rial plane but in
                <lb/>
              one point onely.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s>SIMP. </s>
              <s>I believe that the eſſence of a Sphere conſiſteth in
                <lb/>
                <arrow.to.target n="marg370"/>
                <lb/>
              ving all the right lines produced from its centre to the
                <lb/>
              rence, equal.</s>
            </p>
            <p type="margin">
              <s>
                <margin.target id="marg370"/>
                <emph type="italics"/>
              The definition of
                <lb/>
              the ſphere.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s>SALV. </s>
              <s>So that, if thoſe lines ſhould not be equal, there ſame
                <lb/>
              ſolidity would be no longer a ſphere?</s>
            </p>
            <p type="main">
              <s>SIMP. True.</s>
            </p>
            <p type="main">
              <s>SALV. </s>
              <s>Go to; tell me whether you believe that amongſt the
                <lb/>
              many lines that may be drawn between two points, that may be
                <lb/>
              more than one right line onely.</s>
            </p>
            <p type="main">
              <s>SIMP. </s>
              <s>There can be but one.</s>
            </p>
            <p type="main">
              <s>SALV. </s>
              <s>But yet you underſtand that this onely right line ſhall
                <lb/>
              again of neceſſity be the ſhorteſt of them all?</s>
            </p>
            <p type="main">
              <s>SIMP. </s>
              <s>I know it, and alſo have a demonſtration thereof,
                <lb/>
              duced by a great
                <emph type="italics"/>
              Peripatetick
                <emph.end type="italics"/>
              Philoſopher, and as I take it, if my
                <lb/>
              memory do not deceive me, he alledgeth it by way of reprehending
                <lb/>
                <emph type="italics"/>
              Archimedes,
                <emph.end type="italics"/>
              that ſuppoſeth it as known, when it may be
                <lb/>
              ſtrated.</s>
            </p>
            <p type="main">
              <s>SALV. </s>
              <s>This muſt needs be a great Mathematician, that knew
                <lb/>
              how to demonſtrate that which
                <emph type="italics"/>
              Archimedes
                <emph.end type="italics"/>
              neither did, nor could
                <lb/>
              demonſtrate. </s>
              <s>And if you remember his demonſtration, I would
                <lb/>
              gladly hear it: for I remember very well, that
                <emph type="italics"/>
              Archimedes
                <emph.end type="italics"/>
              in his
                <lb/>
              Books,
                <emph type="italics"/>
              de Sphærà & Cylindro,
                <emph.end type="italics"/>
              placeth this Propoſition amongſt the
                <lb/>
                <emph type="italics"/>
              Poſtulata
                <emph.end type="italics"/>
              ; and I verily believe that he thought it demonſtrated.</s>
            </p>
            <p type="main">
              <s>SIMP. </s>
              <s>I think I ſhall remember it, for it is very eaſie and
                <lb/>
              ſhort.</s>
            </p>
            <p type="main">
              <s>SALV. </s>
              <s>The diſgrace of
                <emph type="italics"/>
              Archimedes,
                <emph.end type="italics"/>
              and the honour of this
                <lb/>
              loſopher ſhall be ſo much the greater.</s>
            </p>
            <p type="main">
              <s>SIMP. </s>
              <s>I will deſcribe the Figure of it. </s>
              <s>Between the points
                <lb/>
                <arrow.to.target n="marg371"/>
                <lb/>
              A and B, [
                <emph type="italics"/>
              in Fig.
                <emph.end type="italics"/>
              5.] draw the right line A B, and the curve line
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              A C B, of which we will prove the right to be the ſhorter: and
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              the proof is this; take a point in the curve-line, which let be C,
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              and draw two other lines, A C and C B, which two lines together;
                <lb/>
              are longer than the ſole line A B, for ſo demonſtrateth
                <emph type="italics"/>
              Euelid.
                <emph.end type="italics"/>
              </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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