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

Page concordance

< >
Scan Original
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
< >
page |< < of 701 > >|
    <archimedes>
      <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
                <lb/>
              ther of them. </s>
              <s>We
                <lb/>
              conclude there­
                <lb/>
              fore, That the Mo­
                <lb/>
              ments of the For­
                <lb/>
              ces of Priſmes and
                <lb/>
              Cylinders of equal
                <lb/>
              thickneſſe, but of
                <lb/>
              unequal length, are
                <lb/>
              to one another in
                <lb/>
              duplicate proporti­
                <lb/>
              on to that of their
                <lb/>
              Lengths; that is,
                <lb/>
              are as the Squares of
                <lb/>
              their Lengths.</s>
            </p>
            <p type="main">
              <s>We will ſhew, in
                <lb/>
              the ſecond place,
                <lb/>
              according to what proportion the Reſiſtance of Fraction in Priſmes
                <lb/>
              and Cylinders encreaſeth, when they continue of the ſame length,
                <lb/>
              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
                <lb/>
              thickneſs, the Reſiſtance againſt Fraction encreaſeth
                <lb/>
              in a proportion iriple to the Diameters of their
                <lb/>
              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
                <lb/>
              the Circles, whoſe Diameters are C D, and E F. </s>
              <s>I ſay,
                <lb/>
              that the Reſiſtance of the Cylinder
                <emph type="italics"/>
              B
                <emph.end type="italics"/>
              is to the Reſiſtance of the
                <lb/>
              Cylinder A againſt Fraction, in a proportion triple to that which
                <lb/>
              the Diameter F E hath to the Diameter D C. </s>
              <s>For if we conſider
                <lb/>
              the abſolute and ſimple Reſiſtance that reſides in the
                <emph type="italics"/>
              B
                <emph.end type="italics"/>
              aſes, that
                <lb/>
              is, in the Circles E F, and D C to breaking, offering them vio­
                <lb/>
              lence by pulling them end-waies, without all doubt, the Reſiſtance
                <lb/>
              of the Cylinder
                <emph type="italics"/>
              B,
                <emph.end type="italics"/>
              is ſo much greater than that of the Cylinder A,
                <lb/>
              by how much the Circle E F is greater than C D; for the Fibres,
                <lb/>
              Filaments, or tenacious parts, which hold together the Parts of the
                <lb/>
              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>
Impressum