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

Table of figures

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    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s>
                <pb xlink:href="040/01/953.jpg" pagenum="260"/>
                <emph type="italics"/>
              ter, as the double of the greater Baſe together with the Leſſer is to the
                <lb/>
              double of the leſſer together with the greater. </s>
              <s>Which is the Propoſition
                <lb/>
              more elegantly expreſſed.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="head">
              <s>PROPOSITION.</s>
            </p>
            <p type="main">
              <s>If any number of Magnitudes ſo diſpoſed to one
                <lb/>
              another, as that the ſecond addeth unto the firſt
                <lb/>
              the double of the firſt, the third addeth unto
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              the ſecond the triple of the firſt, the fourth
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              addeth unto the third the quadruple of the
                <lb/>
              firſt, and ſo every one of the following ones
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              addeth unto the next unto it the magnitude of
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              the firſt multiplyed according to the number
                <lb/>
              which it ſhall hold in order; if, I ſay, theſe
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              Magnitudes be ſuſpended ordinarily on the
                <lb/>
              Ballance at equal diſtances; the Center of the
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                <emph type="italics"/>
              Equilibrium
                <emph.end type="italics"/>
              of all the compounding Magni­
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              tudes ſhall ſo divide the Beam, as that the part
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              towards the leſſer Magnitudes is triple to the
                <lb/>
              remainder.</s>
            </p>
            <p type="main">
              <s>
                <emph type="italics"/>
              Let the Beam be L T, and let ſuch Magnitudes as were ſpoken of
                <lb/>
              hang upon it; and let them be A, F, G, H, K; of which A is in
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              the firſt place ſuſpended at T. </s>
              <s>I ſay, that the Center of the
                <emph.end type="italics"/>
              Equi­
                <lb/>
              librium
                <emph type="italics"/>
              ſo cuts the Beam T L as that the part towards T is triple to the
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              reſt. </s>
              <s>Let T L be triple to L I; and S L triple to L P: and Q L to L N,
                <emph.end type="italics"/>
                <lb/>
                <figure id="id.040.01.953.1.jpg" xlink:href="040/01/953/1.jpg" number="173"/>
                <lb/>
                <emph type="italics"/>
              and L P to L O: I P,
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              P N, N O, and O L
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              ſhall be equal. </s>
              <s>And
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              in F let a Magnitude
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              be placed double to A;
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              in G another trebble to
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              the ſame; in H ano­
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              ther Quadruple; and
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              ſo of the reſt: and let
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              thoſe Magnitudes be
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              taken in which there
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              is A; and let the ſame
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              be done in the Magni­
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              tudes F, G, H, K. </s>
              <s>And
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              becauſe in F the remaining Magnitude, to wit B, is equal to A; take it
                <emph.end type="italics"/>
              </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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