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

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    <archimedes>
      <text>
        <body>
          <chap id="N10019">
            <p id="N127F2" type="main">
              <s id="N127F4">
                <pb xlink:href="077/01/075.jpg" pagenum="71"/>
              eſſe longitudine, quàm ſit EH. exponatur altera magnitu­
                <lb/>
              do G, quæ ad C eandem habeat proportionem, quàm habet
                <lb/>
              DE ad EH. erunt vti〈que〉 magnitudines GC inter ſe
                <expan abbr="commẽ">commen</expan>
                <lb/>
              ſurabiles. </s>
              <s id="N12808">Deinde fiat EK æqualis EH, exponaturquè ma­
                <lb/>
              gnitudo L ipſi G æqualis. </s>
              <s id="N1280C">Quoniam igitur G ad C eſt,
                <lb/>
              vt DE ad EH, ob commenſurabilitatem æ〈que〉pondera
                <arrow.to.target n="marg62"/>
                <lb/>
              G in H, & C in D. ſimiliter æ〈que〉pondera bunt magnitudi­
                <lb/>
              nes æquales GL ex æqualibus diſtantijs EK EH. Cùm igitur
                <lb/>
              C in D ipſi G in H æ〈que〉ponderet; L verò in K ipſi quo­
                <lb/>
              〈que〉 G in H æ〈que〉ponderet; eandem habebit grauitatem
                <arrow.to.target n="marg63"/>
                <lb/>
              in D, ut L in K. Quoniam autem maiorem habet propor­
                <lb/>
              tionem DE ad EH, quàm A ad C, & vt DE ad EH, ita eſt
                <lb/>
              G ad C; maiorem habebit proportionem G ad C, quàm A
                <lb/>
              ad C. ergo maior eſt G, quàm A. ac propterea magnitudo
                <arrow.to.target n="marg64"/>
                <lb/>
              minor eſt magnitudine L. poſita igitur magnitudine L in K,
                <lb/>
              & A in H, non æ〈que〉pondera bunt; & vt ę〈que〉ponderent, o­
                <lb/>
              portet, vt A in longiori ſit diſtantia, quàm ſit EH: Inęqualia
                <lb/>
              enim grauia LA ex inęqualibus diſtantijs
                <arrow.to.target n="marg65"/>
                <lb/>
              maius quidem L in minori diſtantia EK, minus verò graue
                <lb/>
              A in maiori, quàm ſit EK, hoc eſt in maiori, quàm ſit EH.
                <lb/>
              Ita〈que〉 cùm ſit C in D æ〈que〉grauis, vt L in k; longitudo,
                <lb/>
              quæ efficit, vt A æ〈que〉ponderetipſi L in K; eadem prorſus
                <lb/>
              efficiet, vt A ipſi C in D ę〈que〉ponderare poſſit. </s>
              <s id="N1283E">A verò in
                <lb/>
              maiori diſtantia, quàm EH, ipſi L in K ę〈que〉ponderat; ergo
                <lb/>
              in maiori diſtantia, quàm EH, magnitudo A ipſi C in D
                <lb/>
              ę〈que〉ponderabit. </s>
              <s id="N12846">quod demonſtrare oportebat. </s>
            </p>
            <p id="N12848" type="margin">
              <s id="N1284A">
                <margin.target id="marg62"/>
              6.
                <emph type="italics"/>
              buius.
                <emph.end type="italics"/>
              </s>
            </p>
            <p id="N12853" type="margin">
              <s id="N12855">
                <margin.target id="marg63"/>
                <emph type="italics"/>
                <expan abbr="cõmunis">communis</expan>
              no
                <lb/>
              tio ſupradi
                <lb/>
              cta.
                <emph.end type="italics"/>
              </s>
            </p>
            <p id="N12864" type="margin">
              <s id="N12866">
                <margin.target id="marg64"/>
              10.
                <emph type="italics"/>
              quinti.
                <emph.end type="italics"/>
              </s>
            </p>
            <p id="N1286F" type="margin">
              <s id="N12871">
                <margin.target id="marg65"/>
              3.
                <emph type="italics"/>
              huius.
                <emph.end type="italics"/>
              </s>
            </p>
            <p id="N1287A" type="main">
              <s id="N1287C">Hoc demonſtrato Archimedis propoſitionem de incom­
                <lb/>
              menſurabilibus magnitudinibus aliter oſtendemus hoc
                <lb/>
              pacto. </s>
            </p>
            <p id="N12882" type="head">
              <s id="N12884">ALITER.</s>
            </p>
            <p id="N12886" type="main">
              <s id="N12888">Incommenſurabiles magnitudines ex diſtantijs permuta­
                <lb/>
              tim eandem, at〈que〉 magnitudines, proportionem habenti­
                <lb/>
              bus; ę〈que〉ponderant. </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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