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

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    <archimedes>
      <text>
        <body>
          <chap id="N10019">
            <p id="N176FE" type="main">
              <s id="N17764">
                <pb xlink:href="077/01/196.jpg" pagenum="192"/>
              ad parabolen DBE eam habet proportionem, quam linea
                <lb/>
              AF ad lineam L. Quoniam autem ita eſt KG ad GB, vt
                <lb/>
              HG ad L, & vt eadem KG ad GB, ita eſt DG ad GH. vt
                <lb/>
              verò DG ad GH, ita eſt AF ad DG; crunt quatuor lineæ AF
                <lb/>
              DG HG L in continua proportione. </s>
              <s id="N1778B">& quoniam cubi in tri­
                <lb/>
              pla ſunt proportione laterum, erit cubus ex AF ad cubum ex
                <lb/>
              DG, vt AF ad L. cubus ergo ex AF ad cubum ex DG eam
                <lb/>
              habet proportionem, quam parabole ABC ad parabolen
                <lb/>
              DBE. quod demonſtrare oportebat. </s>
            </p>
            <p id="N17795" type="margin">
              <s id="N17797">
                <margin.target id="marg376"/>
              17.34. A
                <emph type="italics"/>
              r
                <lb/>
              ch.de qua.
                <lb/>
              par.
                <emph.end type="italics"/>
              </s>
            </p>
            <p id="N177A4" type="margin">
              <s id="N177A6">
                <margin.target id="marg377"/>
              16.
                <emph type="italics"/>
              quinti.
                <emph.end type="italics"/>
              </s>
            </p>
            <p id="N177AF" type="margin">
              <s id="N177B1">
                <margin.target id="marg378"/>
                <emph type="italics"/>
              ex prima
                <lb/>
              ſextt.
                <emph.end type="italics"/>
              </s>
            </p>
            <p id="N177BB" type="margin">
              <s id="N177BD">
                <margin.target id="marg379"/>
                <emph type="italics"/>
              ex
                <emph.end type="italics"/>
              4.
                <emph type="italics"/>
              ſexti.
                <emph.end type="italics"/>
              </s>
            </p>
            <p id="N177CB" type="margin">
              <s id="N177CD">
                <margin.target id="marg380"/>
              20.
                <emph type="italics"/>
              primi
                <lb/>
              conicorum
                <lb/>
              Apoll. </s>
              <s id="N177D8">&
                <lb/>
              ex
                <emph.end type="italics"/>
              3. A
                <emph type="italics"/>
              rch.
                <lb/>
              de quad.
                <lb/>
              parab.
                <lb/>
              ex cor.
                <emph.end type="italics"/>
              20.
                <lb/>
                <emph type="italics"/>
              ſexti.
                <emph.end type="italics"/>
              </s>
            </p>
            <p id="N177F1" type="margin">
              <s id="N177F3">
                <margin.target id="marg381"/>
              1.
                <emph type="italics"/>
              ſexti.
                <emph.end type="italics"/>
                <lb/>
              11.
                <emph type="italics"/>
              quintl.
                <emph.end type="italics"/>
              </s>
            </p>
            <p id="N17803" type="main">
              <s id="N17805">Oportet autem banc quoquè
                <expan abbr="propoſitionẽ">propoſitionem</expan>
              nobis eſſe cogni
                <lb/>
              tam, nem pè quòd ſolida parallelepipeda in eadem baſi conſti
                <lb/>
              tuta eam inter ſe proportionem habent, quam ipſarum alti­
                <lb/>
              tudines. </s>
            </p>
            <p id="N17811" type="main">
              <s id="N17813">Hoc quidem à Federico Commandino in eius libro de cen
                <lb/>
              tro grauitatis ſolidorum propoſitione decimanona demon­
                <lb/>
              ſtratum fuit. </s>
            </p>
            <p id="N17819" type="head">
              <s id="N1781B">PROPOSITIO. X.</s>
            </p>
            <p id="N1781D" type="main">
              <s id="N1781F">Omnis fruſti à rectanguli coni portione abſciſſi
                <lb/>
              centrum grauitatis eſt in recta linea, quæ fruſti dia­
                <lb/>
              meter exiſtit, ita poſitum, vt diuiſa linea in quin­
                <lb/>
              〈que〉 partes æquales, ſit in quinta parte media; ita
                <lb/>
              vt ipſius portio propinquior minoribaſi fruſti ad
                <lb/>
              reliquam portionem eandem habeat proportio­
                <lb/>
              nem, quam habet ſolidum baſim habens quadra­
                <lb/>
              tumex dimidia maioris baſis fruſti, altitudinem au
                <lb/>
              tem lineam æqualem vtri〈que〉 ſimul duplæ mino­
                <lb/>
              ris baſis, & maiori ad ſolidum baſim habens qua­
                <lb/>
              dratum ex dimidia minoris baſis fruſti,
                <expan abbr="altitudinẽ">altitudinem</expan>
                <lb/>
              autem lineam æqualem vtri〈que〉 duplæ maioris, &
                <lb/>
              minori. </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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