Valerio, Luca, De centro gravitatis solidorum, 1604

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    <archimedes>
      <text>
        <body>
          <chap>
            <pb xlink:href="043/01/016.jpg" pagenum="8"/>
            <p type="head">
              <s>
                <emph type="italics"/>
              PROPOSITIO II.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s>In omni triangulo vnum dumtaxat punctum
                <lb/>
              eſt, in quo rectæ ab angulis ad latera incidentes
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              ſecant ſeſe in eaſdem rationes. </s>
              <s>& ſegmenta, quæ
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              ad angulos, ſunt reliquorum dupla. </s>
              <s>& prædictæ
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              incidentes ſecant trianguli latera bifariam. </s>
            </p>
            <p type="main">
              <s>Sit triangulum ABC, cuius duo quælibet latera AB,
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              AC, ſint bifariam ſecta in punctis D, E, & ductæ rectæ
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              lineæ BE, CFD, AFG. </s>
              <s>Dico CF duplam eſſe ipſius
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              FD, & AF, ipſius FG, & BF, ipſius FE. </s>
              <s>Et in nullo alio
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              puncto à puncto F tres rectas ab angulis ad latera inciden­
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              tes ſecare ſe ſe in eaſdem rationes. </s>
              <s>Et reliquum latus BC
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              ſectum eſſe bifariam in puncto G. </s>
              <s>Quoniam enim eſt vt BA
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              ad AD, ita CA ad AE: hoc eſt, vt triangulum ABC ad
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              triangulum ADC, ita triangulum idem ABC ad trian­
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              gulum AEB; æqualia
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              erunt triangula ADC,
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              AEB, & ablato trape­
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              zio DE communi re­
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              liquum triangulum BD
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              F reliquo triangulo C
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              EF æquale erit: ſed
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              triangulum ADF eſt
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              æquale triangulo BDF;
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              & triangulum AFE
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              triangulo EFC, pro­
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              pter æquales baſes, &
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                <figure id="id.043.01.016.1.jpg" xlink:href="043/01/016/1.jpg" number="7"/>
                <lb/>
              communes altitudines; totum igitur triangulum AFB
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              toti AFC, triangulo æquale erit: ſed vt triangulum AFB </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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