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

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            <s xml:id="echoid-s9368" xml:space="preserve">
              <pb o="369" file="0389" n="389" rhead="LIBER V."/>
            NX, & </s>
            <s xml:id="echoid-s9369" xml:space="preserve">ON, & </s>
            <s xml:id="echoid-s9370" xml:space="preserve">{2/3}- NE, regula eadem, DF, retenta; </s>
            <s xml:id="echoid-s9371" xml:space="preserve">oſten-
              <lb/>
            demus?</s>
            <s xml:id="echoid-s9372" xml:space="preserve">? omnia quadrata parallelogrammi, SF, ad om-
              <lb/>
            nia quadrata fruſti hyperbolæ, HDFG, eſſe vt rectangu-
              <lb/>
            lum, OEN, ad rectangulum ſub, OE, &</s>
            <s xml:id="echoid-s9373" xml:space="preserve">, NM, vna cum re-
              <lb/>
            ctangulo ſub compoſita ex. </s>
            <s xml:id="echoid-s9374" xml:space="preserve">No, &</s>
            <s xml:id="echoid-s9375" xml:space="preserve">. ME, & </s>
            <s xml:id="echoid-s9376" xml:space="preserve">ſub, ME;
              <lb/>
            </s>
            <s xml:id="echoid-s9377" xml:space="preserve">Omnia verò quadrata trianguli, DMF, ad omnia quadra-
              <lb/>
            ta eiuſdem fruſti, HDFG, eſſe vt rectangulum, OEN, ad
              <lb/>
            rectangulum ſub, OE, & </s>
            <s xml:id="echoid-s9378" xml:space="preserve">tripla, NM, vna cum rectangulo
              <lb/>
            ſub compoſita ex, NX, & </s>
            <s xml:id="echoid-s9379" xml:space="preserve">ME, ſub, ME.</s>
            <s xml:id="echoid-s9380" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9381" xml:space="preserve">Sumatur in, ME, vtcunq; </s>
            <s xml:id="echoid-s9382" xml:space="preserve">punctum, L, & </s>
            <s xml:id="echoid-s9383" xml:space="preserve">per ipſum regulæ,
              <lb/>
            DF, parallela ducatur, LK, curuam hyp rbolicam in, I, ſecans;
              <lb/>
            </s>
            <s xml:id="echoid-s9384" xml:space="preserve">
              <figure xlink:label="fig-0389-01" xlink:href="fig-0389-01a" number="266">
                <image file="0389-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0389-01"/>
              </figure>
            Eſt ergo quadratum, EF, vel quadratum,
              <lb/>
            LK, ad quadratum, LI, vt rectangulum,
              <lb/>
            OEN, adrectangulum, OLN; </s>
            <s xml:id="echoid-s9385" xml:space="preserve">eſt autem
              <lb/>
            parallelogrammum, MF, in eadem baſi, & </s>
            <s xml:id="echoid-s9386" xml:space="preserve">
              <lb/>
            altitudine cum figura, MGFE, punctum,
              <lb/>
            L, ſumptum eſt vt cunque, perq; </s>
            <s xml:id="echoid-s9387" xml:space="preserve">ipſum re-
              <lb/>
            gulæ, DF, ducta parallela, LK, repertum
              <lb/>
            eſt, vt quadratum, KL, ad quadratum, LI,
              <lb/>
            ita eſſe rectangulum, OEN, ad rectangulũ,
              <lb/>
            OLN; </s>
            <s xml:id="echoid-s9388" xml:space="preserve">quatuor ergo ordinum magnitudi-
              <lb/>
            nes conſtructæ iuxta has quatuor inuentas
              <lb/>
            magnitudines proportionales, erunt quoq;
              <lb/>
            </s>
            <s xml:id="echoid-s9389" xml:space="preserve">proportionales .</s>
            <s xml:id="echoid-s9390" xml:space="preserve">i. </s>
            <s xml:id="echoid-s9391" xml:space="preserve">omnia quadrata: </s>
            <s xml:id="echoid-s9392" xml:space="preserve">MF, ad
              <lb/>
            omnia quadrata figuræ, MGFE, quæ ſunt
              <lb/>
            magnitudines primi, & </s>
            <s xml:id="echoid-s9393" xml:space="preserve">ſecundi ordinis conſtructæ iuxta primã, & </s>
            <s xml:id="echoid-s9394" xml:space="preserve">
              <lb/>
              <note position="right" xlink:label="note-0389-01" xlink:href="note-0389-01a" xml:space="preserve">Coroll. 3.
                <lb/>
              26. l. 2.</note>
            ſecundam .</s>
            <s xml:id="echoid-s9395" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s9396" xml:space="preserve">iuxta quadratum, KL, & </s>
            <s xml:id="echoid-s9397" xml:space="preserve">quadratum, LI, erunt, vt
              <lb/>
            rectangula ſub maximis abſciſſarum, EM, adiuncta, MO, & </s>
            <s xml:id="echoid-s9398" xml:space="preserve">ſub
              <lb/>
            maximis abſciſſarum, EM, adiuncta, MN, ad rectangula ſub om-
              <lb/>
            nibus abſciſsis, EM, adiuncta, MO, & </s>
            <s xml:id="echoid-s9399" xml:space="preserve">ſub omnibus abſciſsis, EM,
              <lb/>
            adiuncta, MN, quæ ſunt magnitudines tertij, & </s>
            <s xml:id="echoid-s9400" xml:space="preserve">quarti ordinis
              <lb/>
            collectæ iuxta tertiam, & </s>
            <s xml:id="echoid-s9401" xml:space="preserve">quartam .</s>
            <s xml:id="echoid-s9402" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s9403" xml:space="preserve">iuxta rectangulum, OEN,
              <lb/>
            OLN; </s>
            <s xml:id="echoid-s9404" xml:space="preserve">verum rectangula ſub maximis abſciſlarum, EM, adiuncta,
              <lb/>
            MO, & </s>
            <s xml:id="echoid-s9405" xml:space="preserve">ſub eiſdem adiuncta, MN, ad rectangula ſub omnibus ab-
              <lb/>
            ſciſsis, EM, adiuncta, MO, & </s>
            <s xml:id="echoid-s9406" xml:space="preserve">ſub ijſdem adiuncta, MN, omnibus
              <lb/>
              <note position="right" xlink:label="note-0389-02" xlink:href="note-0389-02a" xml:space="preserve">Corol. 21.
                <lb/>
              l. 2.</note>
            recti vel eiuſdem obliqui tranſitus ſumptis, ſunt, vt rectangulum,
              <lb/>
            OEN, ad rectangulum ſub, OE, &</s>
            <s xml:id="echoid-s9407" xml:space="preserve">, NM, vna cum rectangulo ſub
              <lb/>
            compoſita ex {1/2}. </s>
            <s xml:id="echoid-s9408" xml:space="preserve">ON, & </s>
            <s xml:id="echoid-s9409" xml:space="preserve">{1/3}. </s>
            <s xml:id="echoid-s9410" xml:space="preserve">ME, & </s>
            <s xml:id="echoid-s9411" xml:space="preserve">ſub, ME, ergo omnia quadra-
              <lb/>
            ta, MF, ad omnia quadrata figuræ, GMEF, vel horum quadru-
              <lb/>
            pla .</s>
            <s xml:id="echoid-s9412" xml:space="preserve">i. </s>
            <s xml:id="echoid-s9413" xml:space="preserve">omnia quadrata, SF, ad omnia quadrata fruſti, </s>
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