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

Page concordance

< >
Scan Original
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
< >
page |< < of 207 > >|
    <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>
Impressum