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

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    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s>
                <pb xlink:href="040/01/202.jpg" pagenum="184"/>
              another point in the contact being taken as D, conjoyn the two
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              right lines A D and B D, ſo as that they make the triangle A D B;
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              of which the two ſides A D and D B ſhall be equal to the other one
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              A C B, both thoſe and this containing two ſemidiameters, which
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              by the definition of the ſphere are all equal: and thus the right
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              line A B, drawn between the two centres A and B, ſhall not be the
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              ſhorteſt of all, the two lines A D and D B being equal to it: which
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              by your own conceſſion is abſurd.</s>
            </p>
            <p type="margin">
              <s>
                <margin.target id="marg373"/>
                <emph type="italics"/>
              A demon ſtration
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              that the ſphere
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              cheth the plane but
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              in one point.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s>SIMP. </s>
              <s>This demonſtration holdeth in the abſtracted, but not in
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              the material ſpheres.</s>
            </p>
            <p type="main">
              <s>SALV. </s>
              <s>Inſtance then wherein the fallacy of my argument
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              ſiſteth, if as you ſay it is not concluding in the material ſpheres, but
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              holdeth good in the immaterial and
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                <arrow.to.target n="marg374"/>
              </s>
            </p>
            <p type="margin">
              <s>
                <margin.target id="marg374"/>
                <emph type="italics"/>
              Why the ſphere in
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              abſtract, toucheth
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              the plane onely in
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              one point, and not
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              the material in
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              conerete.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s>SIMP. </s>
              <s>The material ſpheres are ſubject to many accidents,
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              which the immaterial are free from. </s>
              <s>And becauſe it cannot be,
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              that a ſphere of metal paſſing along a plane, its own weight ſhould
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              not ſo depreſs it, as that the plain ſhould yield ſomewhat, or that
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              the ſphere it ſelf ſhould not in the contact admit of ſome
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              on. </s>
              <s>Moreover, it is very hard for that plane to be perfect, if for
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              nothing elſe, yet at leaſt for that its matter is porous: and
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              haps it will be no leſs difficult to find a ſphere ſo perfect, as that
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              it hath all the lines from the centre to the ſuperficies, exactly
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              equal.</s>
            </p>
            <p type="main">
              <s>SALV. </s>
              <s>I very readily grant you all this that you have ſaid; but
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              it is very much beſide our purpoſe: for whilſt you go about to
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              ſhew me that a material ſphere toucheth not a material plane in
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              one point alone, you make uſe of a ſphere that is not a ſphere, and
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              of a plane that is not a plane; for that, according to what you
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              ſay, either theſe things cannot be found in the world, or if they
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              may be found, they are ſpoiled in applying them to work the effect.
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              </s>
              <s>It had been therefore a leſs evil, for you to have granted the
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              cluſion, but conditionally, to wit, that if there could be made of
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              matter a ſphere and a plane that were and could continue perfect,
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              they would touch in one ſole point, and then to have denied that
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              any ſuch could be made.</s>
            </p>
            <p type="main">
              <s>SIMP. </s>
              <s>I believe that the propoſition of Philoſophers is to be
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              underſtood in this ſenſe; for it is not to be doubted, but that the
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              imperfection of the matter, maketh the matters taken in
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              crete, to diſagree with thoſe taken in abſtract.</s>
            </p>
            <p type="main">
              <s>SALV. What, do they not agree? </s>
              <s>Why, that which you your
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              ſelf ſay at this inſtant, proveth that they punctually agree.</s>
            </p>
            <p type="main">
              <s>SIMP. </s>
              <s>How can that be?</s>
            </p>
            <p type="main">
              <s>SALV. </s>
              <s>Do you not ſay, that through the imperfection of the
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              matter, that body which ought to be perfectly ſpherical, and that
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              plane which ought to be perfectly level, do not prove to be the </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>