Cavalieri, Buonaventura, Geometria indivisibilibvs continvorvm : noua quadam ratione promota

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            <s xml:id="echoid-s10125" xml:space="preserve">
              <pb o="392" file="0412" n="412" rhead="GEOMETRIÆ"/>
            ipſam, QP, parallelam ipſi, BD, quæerit tangens fectionem, BN
              <lb/>
            D, in puncto, N, oſtendemus omnia quadrata, BS, ad reliquum,
              <lb/>
            demptis omnibus quadratis. </s>
            <s xml:id="echoid-s10126" xml:space="preserve">hyperbolæ, BND, (ſumptis medijs
              <lb/>
            omnibus quadratis, BP,) eſſe vt rectangulum, MFO, ad rectangu,
              <lb/>
            lum bis ſub, MOF, cum {2/3}. </s>
            <s xml:id="echoid-s10127" xml:space="preserve">quadrati, FN, .</s>
            <s xml:id="echoid-s10128" xml:space="preserve">i. </s>
            <s xml:id="echoid-s10129" xml:space="preserve">vt rectangulum, NE
              <lb/>
            O, ad rectangulum bis ſub, NOE, cum {2/3}. </s>
            <s xml:id="echoid-s10130" xml:space="preserve">quadrati, EM, nam, E
              <lb/>
            M, eſt æqualis, NF, & </s>
            <s xml:id="echoid-s10131" xml:space="preserve">ideò etiam, EN, ęqualis, MF, &</s>
            <s xml:id="echoid-s10132" xml:space="preserve">, EO, pa-
              <lb/>
            riter eſt æqualis ipſi, OF. </s>
            <s xml:id="echoid-s10133" xml:space="preserve">Tandem vt vnum ad vnum, ita omnia
              <lb/>
            ad omnia .</s>
            <s xml:id="echoid-s10134" xml:space="preserve">i. </s>
            <s xml:id="echoid-s10135" xml:space="preserve">vt omnia quadrata, BS, ad reliquum, demptis omni.
              <lb/>
            </s>
            <s xml:id="echoid-s10136" xml:space="preserve">bus quadratis hyperbolæ, BND, .</s>
            <s xml:id="echoid-s10137" xml:space="preserve">i. </s>
            <s xml:id="echoid-s10138" xml:space="preserve">vt rectangulum, MFO, ad re-
              <lb/>
            ctangulum bis ſub, MOF, cum {2/3}. </s>
            <s xml:id="echoid-s10139" xml:space="preserve">quadrati, FN, ita omnia qua-
              <lb/>
            drata, BC, adreliquum. </s>
            <s xml:id="echoid-s10140" xml:space="preserve">demptis ab eiſdem omnibus quadratis hy-
              <lb/>
            perbolarum oppolitarum, AMC, BND, eſt autem, vt rectangu-
              <lb/>
            lum, MFO, ad rectangulum bis ſub, MOF, cum {2/3} quadrati, FN,
              <lb/>
            ita rectangulum, NOE, ad rectangulum bis ſub, NOE, cum {2/3}. </s>
            <s xml:id="echoid-s10141" xml:space="preserve">
              <lb/>
            quadra @, EM, ergo omnia quadrata, BC, ad reliquum demptis
              <lb/>
            ab j@d@m omnibus quadratis oppoſitarum hyperbolarum, AMC,
              <lb/>
            BND, erunt vt rectangulum ſub, NEO, ad rectangulum bis ſub,
              <lb/>
            NOE, cum {2/3}. </s>
            <s xml:id="echoid-s10142" xml:space="preserve">quadrati, ME, quod oſtendereopus erat.</s>
            <s xml:id="echoid-s10143" xml:space="preserve"/>
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        <div xml:id="echoid-div935" type="section" level="1" n="558">
          <head xml:id="echoid-head582" xml:space="preserve">THEOREMA XX. PROPOS. XXI.</head>
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            <s xml:id="echoid-s10144" xml:space="preserve">SI, veluti in anteced. </s>
            <s xml:id="echoid-s10145" xml:space="preserve">ſit parallelogrammum habens op-
              <lb/>
            poſita latera, quæ ſint ad diametrum tranſuerſam op-
              <lb/>
            poſitaruin ſectionem ordinatim applicata, quæq; </s>
            <s xml:id="echoid-s10146" xml:space="preserve">oppoſi-
              <lb/>
            tarum hyperbolarum ſint baſes, inſuper deſcribantur earũ
              <lb/>
            aſymptoti, & </s>
            <s xml:id="echoid-s10147" xml:space="preserve">regula ſit latus tranſuerſum, conſtituti paral-
              <lb/>
            lelogra nmi omnia quadrata ad omnia quadrata figuræ,
              <lb/>
            quæ continetur lateribus parallelogrammi iam dicti, late-
              <lb/>
            ritranſuerſo parallelis, & </s>
            <s xml:id="echoid-s10148" xml:space="preserve">portionibus oppoſitarum ſectio-
              <lb/>
            num inter eadem latera comprehenſis, erunt vt quadratũ
              <lb/>
            vniuſcuiuſuis laterum dicti para llelogrammi lateri tran-
              <lb/>
            ſuerſo æquidiſtantium ad quadratum lateris tranſuerſi,
              <lb/>
            vna cum. </s>
            <s xml:id="echoid-s10149" xml:space="preserve">quadrati portionis dicti lateris eiuſdem paral-
              <lb/>
            lelogrammi, quæ inter aſymptotos incluſa manet.</s>
            <s xml:id="echoid-s10150" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10151" xml:space="preserve">Sint oppoſitæ ſectiones, FAD, EVC, quarum latus tranſuer-
              <lb/>
            ſum, AV, centrum, O, per quod tranſeant earum aſymptoti, </s>
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