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

Table of figures

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      <text>
        <body>
          <chap>
            <p type="main">
              <s>
                <pb xlink:href="040/01/789.jpg" pagenum="97"/>
              that the two augmentations of the Lengths and of the Gravities
                <lb/>
              being put together, the Moment compounded of both is in double
                <lb/>
                <figure id="id.040.01.789.1.jpg" xlink:href="040/01/789/1.jpg" number="66"/>
                <lb/>
              proportion to ei­
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              ther of them. </s>
              <s>We
                <lb/>
              conclude there­
                <lb/>
              fore, That the Mo­
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              ments of the For­
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              ces of Priſmes and
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              Cylinders of equal
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              thickneſſe, but of
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              unequal length, are
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              to one another in
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              duplicate proporti­
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              on to that of their
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              Lengths; that is,
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              are as the Squares of
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              their Lengths.</s>
            </p>
            <p type="main">
              <s>We will ſhew, in
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              the ſecond place,
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              according to what proportion the Reſiſtance of Fraction in Priſmes
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              and Cylinders encreaſeth, when they continue of the ſame length,
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              and encreaſe in thickneſs. </s>
              <s>And here I ſay, that</s>
            </p>
            <p type="head">
              <s>PROPOSITION IV.</s>
            </p>
            <p type="main">
              <s>
                <emph type="italics"/>
              In Priſmes and Cylinders of equal length, but unequal
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              thickneſs, the Reſiſtance againſt Fraction encreaſeth
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              in a proportion iriple to the Diameters of their
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              Thickneſſes, that is, of their Baſes.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s>Let the two Cylinders be theſe A and
                <emph type="italics"/>
              B, [as in
                <emph.end type="italics"/>
              Fig. </s>
              <s>5.]
                <lb/>
              whoſe equal lengths are D G, and F H, the unequal
                <emph type="italics"/>
              B
                <emph.end type="italics"/>
              aſes
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              the Circles, whoſe Diameters are C D, and E F. </s>
              <s>I ſay,
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              that the Reſiſtance of the Cylinder
                <emph type="italics"/>
              B
                <emph.end type="italics"/>
              is to the Reſiſtance of the
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              Cylinder A againſt Fraction, in a proportion triple to that which
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              the Diameter F E hath to the Diameter D C. </s>
              <s>For if we conſider
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              the abſolute and ſimple Reſiſtance that reſides in the
                <emph type="italics"/>
              B
                <emph.end type="italics"/>
              aſes, that
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              is, in the Circles E F, and D C to breaking, offering them vio­
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              lence by pulling them end-waies, without all doubt, the Reſiſtance
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              of the Cylinder
                <emph type="italics"/>
              B,
                <emph.end type="italics"/>
              is ſo much greater than that of the Cylinder A,
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              by how much the Circle E F is greater than C D; for the Fibres,
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              Filaments, or tenacious parts, which hold together the Parts of the
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              Solid, are ſo many the more.
                <emph type="italics"/>
              B
                <emph.end type="italics"/>
              ut if we conſider, that in offering </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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