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

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    <archimedes>
      <text>
        <body>
          <chap id="N10019">
            <p id="N1269A" type="main">
              <s id="N126C3">
                <pb xlink:href="077/01/073.jpg" pagenum="69"/>
              habebit proportionem kN ad C, quàm kM ad eandem
                <lb/>
              C. tota verò KM ad C eſt, vt DE ad EF; ergo KN ad
                <lb/>
              C minorem habet proportionem; quàm DE ad EF.
                <emph type="italics"/>
              Quo
                <lb/>
              niam igitur magnitudines AC,
                <emph.end type="italics"/>
              hoc eſt KN C,
                <emph type="italics"/>
              ſunt commenſurabi­
                <lb/>
              les, & minorem habet proportionem A,
                <emph.end type="italics"/>
              hoc eſt kN
                <emph type="italics"/>
              ad C, quàm DE
                <lb/>
              ad EF; non æ〈que〉ponderabunt A C,
                <emph.end type="italics"/>
              hoc eſt KN C,
                <emph type="italics"/>
              ex distantiis
                <emph.end type="italics"/>
                <arrow.to.target n="marg61"/>
                <lb/>
                <emph type="italics"/>
              DE EF, poſito quidem A,
                <emph.end type="italics"/>
              hoc eſt KN
                <emph type="italics"/>
              ad F, C verò ad D.
                <emph.end type="italics"/>
              &
                <lb/>
              vt æ〈que〉ponderent, oporter, vt in F maior ſit magnitudo,
                <lb/>
              quàm KN; ita vt ipſi C in D æ〈que〉ponderate poſſit. </s>
              <s id="N12736">Ac
                <lb/>
              propterea cùm ſit kH adhuc minor, quàm KN, ſi igitur
                <lb/>
              KH ponatur ad F, & C ad D, nullo modo æ〈que〉ponde­
                <lb/>
              rabunt. </s>
              <s id="N1273E">quod tamen fieri non poteſt. </s>
              <s id="N12740">ſupponebatur enim eas
                <lb/>
              æ〈que〉ponderare. </s>
              <s id="N12744">Non igitur magnitudo minor, quàm tota
                <lb/>
              KM in F magnitudini C in D æ〈que〉ponderat.
                <emph type="italics"/>
              Eadem au­
                <lb/>
              tem ratione, ne〈que〉 ſi C maior fuerit, quàm vt æ〈que〉ponderet ipſi A
                <emph.end type="italics"/>
              B,
                <lb/>
              hoc eſt ipſi KM. etenim grauiore
                <expan abbr="exiſtẽte">exiſtente</expan>
              C ad D, quàm KM
                <lb/>
              ad F. primùm auferatur ex C exceſſus, quo C grauior eſt,
                <lb/>
              quàm KM, ita vt æ〈que〉ponderet ipſi KM. Deinde rurſus
                <lb/>
              auferatur quædam magnitudo minor exceſſu, quo grauior
                <lb/>
              eſt C, quàm kM, ita vt æ〈que〉ponderent; reſiduum verò ſit
                <lb/>
              ipſi KM commenſurabile, & c. </s>
              <s id="N12760">ſimiliter oſtendetur
                <expan abbr="nullã">nullam</expan>
                <lb/>
              magnitudinem ipſa C minorem poſitam ad D vllo modo
                <lb/>
              æ〈que〉ponderare ipſi KM ad F poſitæ. </s>
              <s id="N1276A">Quare magnitudo
                <lb/>
              C ad D, kM verò ad F ę〈que〉ponderant. </s>
              <s id="N1276E">Vnde ſequitur ma
                <lb/>
              gnitudinis ex vtriſ〈que〉 magnitudinibus compoſitæ centrum
                <lb/>
              grauitatis eſſe punctum E. ac propterea incommenſurabiles
                <lb/>
              magnitudines AB C ex diſtantiijs ED EF, quæ permutatim
                <lb/>
              eandem habent proportionem, vt magnitudines, æ〈que〉pon­
                <lb/>
              derare. </s>
              <s id="N1277A">quod demonſtrare oportebat. </s>
            </p>
            <p id="N1277C" type="margin">
              <s id="N1277E">
                <margin.target id="marg60"/>
                <emph type="italics"/>
              ex proxi­
                <lb/>
              mo proble­
                <lb/>
              mate.
                <emph.end type="italics"/>
                <lb/>
              8.
                <emph type="italics"/>
              quinti.
                <emph.end type="italics"/>
              </s>
            </p>
            <p id="N12791" type="margin">
              <s id="N12793">
                <margin.target id="marg61"/>
                <emph type="italics"/>
              ex præce­
                <lb/>
              denti.
                <lb/>
              ex prima
                <lb/>
              propoſitio­
                <lb/>
              ne.
                <emph.end type="italics"/>
              </s>
            </p>
            <p id="N127A3" type="head">
              <s id="N127A5">SCHOLIVM.</s>
            </p>
            <p id="N127A7" type="main">
              <s id="N127A9">In demonſtratione occurrit obſeruandum, quòd ſi exceſ­
                <lb/>
              ſus HL ita diuideret magnitudinem KM, vt reſiduum KH
                <lb/>
              fuerit commenſurabile ipſi C; tunc abſ〈que〉 alia conſtructio­
                <lb/>
              ne, magnitudines commenſurabiles KH C ex diſtantijs DE
                <lb/>
              EF æ〈que〉ponderarent; quod fieri non poteſt. </s>
              <s id="N127B3">cùm minorem </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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