DelMonte, Guidubaldo, In duos Archimedis aequeponderantium libros Paraphrasis : scholijs illustrata

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    <archimedes>
      <text>
        <body>
          <chap id="N10019">
            <p id="N13E54" type="main">
              <s id="N13EA2">
                <pb xlink:href="077/01/108.jpg" pagenum="104"/>
              uitatis cuiuſlibet trianguli eſſe in recta linea ab angulo ad di­
                <lb/>
              midiam baſim ducta (vt Archimedes demonſtrauit) & inſu­
                <lb/>
              per in eo puncto, quod dictam lineam diuidatita, vt pars ad
                <lb/>
              angulum reliquę ad baſim ſit dupla. </s>
              <s id="N13EB0">Quare hoc prius ita
                <expan abbr="oſtẽ">oſtem</expan>
                <lb/>
              demus. </s>
            </p>
            <p id="N13EB8" type="margin">
              <s id="N13EBA">
                <margin.target id="marg158"/>
              13.
                <emph type="italics"/>
              huius.
                <emph.end type="italics"/>
              </s>
            </p>
            <p id="N13EC3" type="head">
              <s id="N13EC5">PROPOSITIO.</s>
            </p>
            <p id="N13EC7" type="main">
              <s id="N13EC9">Omnis trianguli centrum grauitatis eſt punctum in recta
                <lb/>
              linea ab angulo ad dimidiam baſim ducta exiſtens, quod li­
                <lb/>
              neam diuidat, ita vt poitio ad angulum reliquæ ad baſim, ſit
                <lb/>
              dupla. </s>
            </p>
            <p id="N13ED1" type="main">
              <s id="N13ED3">Sit triangulum ABC, in quo ab an
                <lb/>
                <arrow.to.target n="fig48"/>
                <lb/>
              gulo A ad dimidiam baſim BC re­
                <lb/>
              cta ducatur linea AD. Ducaturquè
                <lb/>
              ab angulo B ad dimidiom baſim
                <lb/>
              AC linea BE, quæſecet AD in F. Et
                <lb/>
              quoniam centrum grauitatis
                <expan abbr="triãgu-">triangu­
                  <lb/>
                </expan>
                <arrow.to.target n="marg159"/>
              li ABC eſt punctum F;
                <expan abbr="oſtendendũ">oſtendendum</expan>
                <lb/>
              eſt lineam FA ipſius FD duplam eſ­
                <lb/>
              ſe. </s>
              <s id="N13EF5">iungatur FC. quoniam enim AE
                <lb/>
              eſt equalis ipſi EC, erit triangulum
                <lb/>
                <arrow.to.target n="marg160"/>
              ABE triangulo EBC æquale, cùm
                <lb/>
              ſint ſub eadem altitudine. </s>
              <s id="N13F01">Ob eandemquè cauſam
                <expan abbr="triangulũ">triangulum</expan>
                <lb/>
              AFE triangulo EFC exiſtit æquale. </s>
              <s id="N13F09">ſi igitur à triangulo ABE
                <lb/>
              auferatur triangulum AFE, & à triangulo EBC triangulum
                <lb/>
              auferatur EFC; relin〈que〉tur triangulum ABF triangulo BFC
                <lb/>
              æquale. </s>
              <s id="N13F11">Rurſus quoniam BD eſt æqualis ipſi DC; erit trian­
                <lb/>
                <arrow.to.target n="marg161"/>
              gulum BFD triangulo DFC æquale, ſiquidem candem ha­
                <lb/>
              bentaltitudinem. </s>
              <s id="N13F1B">duplum igitur eſt triangulum BFC
                <expan abbr="triãgu-li">triangu­
                  <lb/>
                li</expan>
              BFD. Quare & triangulum ABF trianguli BFD duplum
                <lb/>
                <arrow.to.target n="marg162"/>
              exiſtit. </s>
              <s id="N13F29">quia verò triangula ABF FBD in eadem ſunt altitudi
                <lb/>
              ne, idcirco ſeſe habebunt, vt baſes AF FD. at〈que〉 triangulum
                <lb/>
              ABF. duplum eſt ipſius FBD; ergo portio AF ipſius FD dupla
                <lb/>
              exiſtit. </s>
              <s id="N13F31">quod demonſtrare oportebat. </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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