Valerio, Luca, De centro gravitatis solidorum, 1604

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        <body>
          <chap>
            <p type="main">
              <s>
                <pb xlink:href="043/01/017.jpg" pagenum="9"/>
              ad triangulum FBG, hoc eſt vt AF ad FG, ita eſt
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              triangulum AFC ad triangulum FCG; triangulum er­
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              go FBG triangulo FCG æquale erit, & baſis BG ba­
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              ſi GC æqualis. </s>
              <s>Quoniam igitur & AE eſt æqualis
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              EC, ſimiliter vt ante, oſtenderemus, triangulum BCF,
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              triangulo ACF, eademque ratione triangulum ABF,
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              triangulo BCF æquale eſſe: igitur vnumquodque trian­
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              gulorum ABF, ACF, BCF, tertia pars eſt trianguli
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              ABC: ſed vt triangulum ABC, ad triangulum BCF,
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              ita eſt AG, ad GF; tripla igitur eſt AG ipſius GF,
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              ac proinde AF, ipſius FG dupla. </s>
              <s>Eadem ratione
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              BE, ipſius FE, & CF, ipſius FD, dupla concludetur. </s>
            </p>
            <p type="main">
              <s>Sed ſint ſi fieri poteſt, trianguli ABC duo centra qua­
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              lia diximus D, E: & ab ipſis ad ſingulos angulos du­
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              cantur binæ rectæ lineæ:
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              & eadat D in aliquo trian
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              gulo BEC. </s>
              <s>Quoniam
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              igitur D eſt centrum trian
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              guli ABC erit triangu­
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              lum BDC tertia pars
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              trianguli ABC. </s>
              <s>Eadem
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              ratione triangulum BEC
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              tertia pars erit trianguli
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              ABC; triangulum ergo
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              DBC æquale erit trian­
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              gulo BEC pars toti, quod
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              fieri non poteſt, atqui
                <expan abbr="idẽ">idem</expan>
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                <figure id="id.043.01.017.1.jpg" xlink:href="043/01/017/1.jpg" number="8"/>
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              abſurdum ſequitur, ſi punctum D cadat in aliquo latere
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              triangulorum, quorum vertex E; Manifeſtum eſt igitur
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              propoſitum. </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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