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="040/01/1020.jpg" pagenum="326"/>
              without impediment by this Line, the Force and the Line ſhall
                <lb/>
              take ſome certain poſition in which they ſhall reſt, and the Line
                <lb/>
              ſhall of neceſſity be ſtreight, let that Line be termed
                <emph type="italics"/>
              the Pendant,
                <emph.end type="italics"/>
                <lb/>
              or
                <emph type="italics"/>
              Line of Direction of the Force.
                <emph.end type="italics"/>
              And let the Point by which it is
                <lb/>
              faſtned to the Fulciment be called
                <emph type="italics"/>
              the Point of Suſpenſion
                <emph.end type="italics"/>
              : which
                <lb/>
              may ſometimes be the Arm of a Leaver or Ballance; and then let
                <lb/>
              the Line drawn from the Center of the Fulciment of the Leaver
                <lb/>
              or Ballance to the Point of Suſpenſion be named
                <emph type="italics"/>
              the Diſtance
                <emph.end type="italics"/>
              or
                <lb/>
                <emph type="italics"/>
              the Arm of the Force
                <emph.end type="italics"/>
              : which we ſuppoſe to be a Line fixed, and
                <lb/>
              conſidered without Gravity. </s>
              <s>Moreover, let the Angle comprehen­
                <lb/>
              ded betwixt the Arm of the Force and the Line of Direction be
                <lb/>
              termed
                <emph type="italics"/>
              the Angle of the Direction of the Force.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="head">
              <s>AXIOM I.</s>
            </p>
            <p type="main">
              <s>After theſe Definitions we lay down for a Principle, that in the
                <lb/>
              Leaver, and in the Ballance, Equal Forces drawing by Arms
                <lb/>
              that are equal, and at equall Angles of Direction, do draw equal­
                <lb/>
              ly. </s>
              <s>And if in this Poſition they draw one againſt the other they
                <lb/>
              ſhall make an
                <emph type="italics"/>
              Equilibrium
                <emph.end type="italics"/>
              : but if they draw together, or towards
                <lb/>
              the ſame part, the Effect ſhall be double.</s>
            </p>
            <p type="main">
              <s>If the Forces being equal, and the Augles of Direction alſo
                <lb/>
              equal, the Arms be unequal, the Force that ſhall be ſuſpended at
                <lb/>
              the greater Arm ſhall work the greater Effect.</s>
            </p>
            <p type="main">
              <s>As in this Figure, the Center of the Ballance or Leaver being A,
                <lb/>
                <figure id="id.040.01.1020.1.jpg" xlink:href="040/01/1020/1.jpg" number="222"/>
                <lb/>
              if the Arms A B and A C are equal,
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              as alſo the Angles A B D, and A C E,
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              the equal Forces D and E ſhall
                <lb/>
              draw equally, and make an
                <emph type="italics"/>
              Equili­
                <lb/>
              brium.
                <emph.end type="italics"/>
              So likewiſe the Arm A F be­
                <lb/>
              ing equal to A B, the Angle A F G
                <lb/>
              to the Angle A B D, and the Force
                <lb/>
              G to D, theſe two Forces ^{*} G and D
                <lb/>
                <arrow.to.target n="marg1124"/>
                <lb/>
              draw equally; and in regard that
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              they draw both one way, the Effect
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              ſhall be double.</s>
            </p>
            <p type="margin">
              <s>
                <margin.target id="marg1124"/>
              * In the M. S.
                <lb/>
              </s>
              <s>Copy it is
                <emph type="italics"/>
              C and
                <lb/>
              D.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s>In the ſame manner the Forces G and E ſhall make an
                <emph type="italics"/>
              Equilibri­
                <lb/>
              um
                <emph.end type="italics"/>
              ; as alſo I and L ſhall counterpoiſe, if (being equal) the Arms
                <lb/>
              A K and A H, and the Angles A H T, and A K L be equal.</s>
            </p>
            <p type="main">
              <s>The ſame ſhall befall in the Forces P and R, if all things be
                <lb/>
              diſpoſed as before. </s>
              <s>And in this caſe we make no other diſtinction
                <lb/>
              betwixt Weights and other Forces ſave only this, that Weights all
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              tend towards the Center of Grave Bodies, and Forces may be un­
                <lb/>
              derſtood to tend all towards all parts of the Univerſe, with ſo
                <lb/>
              much greater or leſſer
                <emph type="italics"/>
              Impetus
                <emph.end type="italics"/>
              than Weights. </s>
              <s>So that Weights and </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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