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

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    <archimedes>
      <text>
        <body>
          <chap id="N10019">
            <pb xlink:href="077/01/076.jpg" pagenum="72"/>
            <p id="N12891" type="main">
              <s id="N12893">Sint incom­
                <lb/>
                <arrow.to.target n="fig30"/>
                <lb/>
                <expan abbr="mẽſurabiles">menſurabiles</expan>
              ma
                <lb/>
              gnitudines AC,
                <lb/>
              diſtantiæ verò
                <lb/>
              DE EF. ſitquè vt
                <lb/>
              A ad C, ita DE
                <lb/>
              ad EF. Dico A
                <lb/>
              in F, C verò in
                <lb/>
              D æ〈que〉ponde­
                <lb/>
              rare. </s>
              <s id="N128AF">Si autem (ſi fieri poteſt) non æ〈que〉pondera bunt;
                <expan abbr="diſtã">diſtam</expan>
                <lb/>
              tiæ DE EF aliter ſeſe habere debebunt, vt magnitudines AC
                <lb/>
              ę〈que〉ponderent. </s>
              <s id="N128B9">Quocirca vel longior eſt EF, quàm opus
                <lb/>
              ſit, vel longior eſt ED. ſit EF longior. </s>
              <s id="N128BD">ſitquè exceſſus GF, ita
                <lb/>
              vt poſita magnitudine A in G ipſi C in D æ〈que〉ponde­
                <lb/>
                <arrow.to.target n="marg66"/>
              ret. </s>
              <s id="N128C7">Fiat EH maior EG, minor verò EF. ſit autem EH
                <lb/>
              ipſi ED commenſurabilis. </s>
              <s id="N128CB">Quoniam igitur DE ad EH
                <lb/>
              maiorem habet proportionem, quàm ad EF; & vt DE ad
                <lb/>
              EF, ita eſt A ad C; maiorem habebit proportionem DE
                <lb/>
              ad EH, quàm A ad C. ſuntquè longitudines ED EH in­
                <lb/>
              terſe commenſurabiles; ergo magnitudo A in H ipſi C in
                <lb/>
                <arrow.to.target n="marg67"/>
              D non æ〈que〉ponderabit, ſed vt ę〈que〉ponderet, maiori opus
                <lb/>
              eſt longitudine, quàm ſit EH; ita vt A ipſi C in D æ〈que〉
                <lb/>
              ponderare poſſit. </s>
              <s id="N128DF">at〈que〉 adeò cùm adhuc minor ſit EG, quàm
                <lb/>
              EH; magnitudo A in G magnitudini C in D nullo modo
                <lb/>
              æ〈que〉ponderabit. </s>
              <s id="N128E5">quod fieri non poteſt. </s>
              <s id="N128E7">ſupponebatur enim
                <lb/>
              A in G, & C in D ę〈que〉ponderare. </s>
              <s id="N128EB">eademquè prorſus ra­
                <lb/>
              tione, ſi ED longior fuerit, quàm opus ſit, ita vt magnitu­
                <lb/>
              dines æ〈que〉ponderent, oſtendetur
                <expan abbr="magnitudinẽ">magnitudinem</expan>
              C nullo pa­
                <lb/>
              cto æ〈que〉ponderare poſſe ipſi A in F in minori diſtantia,
                <lb/>
              quàm DE. Quare magnitudines in commenſurabiles AC ex
                <lb/>
              diſtantijs ED EF, quæ eandem permutatim habent propor­
                <lb/>
              tionem, vt magnitudines, æ〈que〉ponderant. </s>
              <s id="N128FD">quod demonſtra­
                <lb/>
              re oportebat. </s>
            </p>
            <p id="N12901" type="margin">
              <s id="N12903">
                <margin.target id="marg66"/>
                <emph type="italics"/>
              problema
                <lb/>
              ante
                <emph.end type="italics"/>
              7.
                <emph type="italics"/>
              bu­
                <lb/>
              ius
                <emph.end type="italics"/>
              8.
                <emph type="italics"/>
              quinti
                <emph.end type="italics"/>
              </s>
            </p>
            <p id="N1291B" type="margin">
              <s id="N1291D">
                <margin.target id="marg67"/>
                <emph type="italics"/>
              ex pxima
                <lb/>
              ppoſitione
                <emph.end type="italics"/>
              </s>
            </p>
            <figure id="id.077.01.076.1.jpg" xlink:href="077/01/076/1.jpg" number="45"/>
            <p id="N1292B" type="main">
              <s id="N1292D">In prioribus ſermonibus ante quintam propoſitionem ha­
                <lb/>
              bitis, diximus propoſitionum præcedentium demonſtratio­
                <lb/>
              nes planiores euadere, ſi intelligamus magnitudines eiuſdem
                <lb/>
              eſſe ſpeciei, & homogeneas. </s>
              <s id="N12935">Quòd quidem ſi Archimedem </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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