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="040/01/1023.jpg" pagenum="329"/>
              drawing upon the Arm A
                <emph type="italics"/>
              F,
                <emph.end type="italics"/>
              and the other, to wit H, upon the Arm
                <lb/>
              A C: now, by the firſt Propoſition, G and H ſhall make an
                <emph type="italics"/>
              Equili­
                <lb/>
              brium
                <emph.end type="italics"/>
              upon the Balance C A F: But, by the firſt Principle, the Force
                <lb/>
              D upon the Arm A B worketh the ſame effect as the Force G on
                <lb/>
              the Arm A F: Therefore the Force D upon the Arm A B maketh
                <lb/>
              an
                <emph type="italics"/>
              Equilibrium
                <emph.end type="italics"/>
              with the Force H upon A C: And the Force H
                <lb/>
              drawing in the ſame manner upon the Arm
                <emph type="italics"/>
              A
                <emph.end type="italics"/>
              C as the Force E, by
                <lb/>
              the ſame firſt
                <emph type="italics"/>
              A
                <emph.end type="italics"/>
              xiom, the Force D upon the Arm
                <emph type="italics"/>
              A
                <emph.end type="italics"/>
              B ſhall make an
                <lb/>
                <emph type="italics"/>
              Equilibrium
                <emph.end type="italics"/>
              with the Force E upon the Arm
                <emph type="italics"/>
              A
                <emph.end type="italics"/>
              C.</s>
            </p>
            <p type="main">
              <s>Now, in the following Figure, let the Center of the Balance be
                <lb/>
                <emph type="italics"/>
              A,
                <emph.end type="italics"/>
              the Arms A B and A C, the Lines of Direction B D and C E
                <lb/>
              which are not Perpendicular to the Arms, and the Forces D and E
                <lb/>
              drawing likewiſe by the Lines of Direction, upon which Perpen­
                <lb/>
              diculars are erected unto the Center A, that is A F upon B D, and
                <lb/>
              A G upon E C, and that as A F is to A G, ſo is the Force E to the
                <lb/>
              Force D: which Forces draw one
                <lb/>
                <figure id="id.040.01.1023.1.jpg" xlink:href="040/01/1023/1.jpg" number="226"/>
                <lb/>
              againſt the other: I ſay, that they will
                <lb/>
              make an
                <emph type="italics"/>
              Equilibrium
                <emph.end type="italics"/>
              upon the Balance
                <lb/>
              C A B: For let the Lines A F and A G
                <lb/>
              be underſtood to be the two Arms of
                <lb/>
              a Balance G A F, upon which the For­
                <lb/>
              ces D and E do draw by the Lines of
                <lb/>
              Direction F D and G E: Theſe Forces
                <lb/>
              ſhall make an
                <emph type="italics"/>
              Equilibrium,
                <emph.end type="italics"/>
              by the firſt
                <lb/>
              part of this ſecond Propoſition; but, by the ſecond Axiom, the Force
                <lb/>
              D upon the Arm A F hath the ſame Effect as upon the Arm A B:
                <lb/>
              Therefore the Force D upon the Arm A B maketh an
                <emph type="italics"/>
              Equilibrium
                <emph.end type="italics"/>
                <lb/>
              with the Force E upon the Arm A C.</s>
            </p>
            <p type="main">
              <s>There are many Caſes, according to the Series of Perpendicu­
                <lb/>
              lars, but it will be eaſie for you to ſee that they have all but one
                <lb/>
              and the ſame Demonſtration.</s>
            </p>
            <p type="main">
              <s>It is alſo eaſie to demonſtrate, that if the Forces draw both on
                <lb/>
              one ſide they ſhall make the ſame Effect one as another, and that
                <lb/>
              the Effect of two together ſhall be double to that of one alone.</s>
            </p>
            <p type="head">
              <s>OF THE
                <lb/>
              GEOSTATICKS.</s>
            </p>
            <p type="main">
              <s>The Principle which you demand for the
                <emph type="italics"/>
              Geoſtaticks
                <emph.end type="italics"/>
              is,
                <lb/>
              That if two equal Weights are conjoyned by a right
                <lb/>
              Line fixed and void of Gravity, and that being ſo di­
                <lb/>
              ſpoſed they may deſcend freely, they will never reſt till
                <lb/>
              that the middle of the Line, that is the Center of Gravitation of
                <lb/>
              the Ancients, unites it ſelf to the common Center of Grave Bodies.</s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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