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

Table of figures

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      <text>
        <body>
          <chap>
            <pb xlink:href="040/01/941.jpg" pagenum="248"/>
            <p type="head">
              <s>AN
                <lb/>
              APPENDIX,
                <lb/>
              In which is contained certain
                <lb/>
              THE OREMS and their DEMONSTRATIONS:
                <lb/>
              Formerly written by the ſame Author, touching the
                <lb/>
                <emph type="italics"/>
              CENTER
                <emph.end type="italics"/>
              of
                <emph type="italics"/>
              GRAVITY,
                <emph.end type="italics"/>
              of
                <lb/>
              SOLIDS.</s>
            </p>
            <p type="head">
              <s>POSTVLATVM.</s>
            </p>
            <p type="main">
              <s>
                <emph type="italics"/>
              We preſuppoſe equall Weights to be alike diſpo­
                <lb/>
              ſed in ſever all Ballances, if the Center of Gra­
                <lb/>
              vity of ſome of thoſe Compounds ſhall divide the Ballance
                <lb/>
              according to ſome proportion, and the Ballance ſhall
                <lb/>
              alſo divide their Center of Gravity according to the
                <lb/>
              ſame proportion.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="head">
              <s>LEMMA.</s>
            </p>
            <p type="main">
              <s>
                <emph type="italics"/>
              Let the line A B be cut in two equall parts in C,
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              whoſe half A C let be divided in E, ſo that as B E is to
                <lb/>
              E A, ſo may A E be to E C. </s>
              <s>I ſay that B E is double
                <emph.end type="italics"/>
                <lb/>
                <figure id="id.040.01.941.1.jpg" xlink:href="040/01/941/1.jpg" number="165"/>
                <lb/>
                <emph type="italics"/>
              to E A. </s>
              <s>For as B E is to E
                <lb/>
              A, ſo is E A to E C: there­
                <lb/>
              fore by Compoſition and by Permutation of Proportion, as
                <lb/>
              B A is to A C, ſo is A E to E C: But as A E is to E C,
                <lb/>
              that is, B A to A C, ſo is B E to E A: Wherefore B
                <lb/>
              E is double to E A.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s>
                <emph type="italics"/>
              This ſuppoſed, we will Demonſtrate, That,
                <emph.end type="italics"/>
              </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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