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

Table of figures

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        <body>
          <chap>
            <p type="main">
              <s>
                <pb xlink:href="040/01/948.jpg" pagenum="255"/>
                <emph type="italics"/>
              the ſame part, and not by it divided. </s>
              <s>Therefore the Center of Gravity
                <lb/>
              of the ſaid Conoid is not below the point N: Neither is it above. </s>
              <s>For,
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              if it may, let it be H: and again, as before, ſet the Line L O by it ſelf
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              equalto the ſaid H N, and divided at pleaſure in S: and the ſame pro­
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              portion that B N and S O both together have to S L, let the Conoid
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              have to R: and about the Conoid let a Figure be circumſcribed conſi­
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              ſting of Cylinders, as hath been ſaid: by which let it be exceeded a leſs
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              quantity than that of the Solid R: and let the Line betwixt the Center
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              of Gravity of the circumſcribed Figure and the point N be leſſer than
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              S O: the remainder V H ſhall be greater than S L. </s>
              <s>And becauſe that as
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              both B N and O S is to SL, ſo is the
                <emph.end type="italics"/>
                <lb/>
                <figure id="id.040.01.948.1.jpg" xlink:href="040/01/948/1.jpg" number="169"/>
                <lb/>
                <emph type="italics"/>
              Conoid to R: (and R is greater
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              than the exceſs by which the circum­
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              ſcribed Figure exceeds the Conoid:)
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              Therefore B N and S O hath leſs pro­
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              portion to S L than the Conoid to the
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              ſaid exceſs. </s>
              <s>And B V is leſſer than
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              both B N and S O; and V H is grea­
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              ter than S L: much greater proporti­
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              on, therefore, hath the Conoid to the
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              ſaid proportions, than B V hath to
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              V H. </s>
              <s>Therefore whatever proporti­
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              on the Conoid hath to the ſaid pro­
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              portions, the ſame ſhall a Line greater
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              than B V have to V H. </s>
              <s>Let the ſame be M V: And becauſe the Center
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              of Gravity of the circumſcribed Figure is V, and the Center of the
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              Conoid is H. and ſince that as the Conoid to the reſt of the proportions,
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              ſois M V to V H, M ſhall be the Center of Gravity of the remaining
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              proportions: which likewiſe is impoſſible: Therefore the Center of
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              Gravity of the Conoid is not above the point N: But it hath been de­
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              monſtrated that neither is it beneath: It remains, therefore, that it ne­
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              ceſſarily be in the point N it ſelf. </s>
              <s>And the ſame might be demonſtrated
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              of Conoidal Plane cut upon an Axis not erect. </s>
              <s>The ſame in other terms,
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              as appears by what followeth:
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="head">
              <s>PROPOSITION.</s>
            </p>
            <p type="main">
              <s>The Center of Gravity of the Parabolick Co­
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              noid falleth betwixt the Center of the cir­
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              cumſcribed Figure and the Center of the in­
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              ſcribed.</s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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