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

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            <s xml:id="echoid-s4861" xml:space="preserve">
              <pb o="198" file="0218" n="218" rhead="GEOMETRIÆ"/>
            ergo intra, EB, vtcumque punctum, C, & </s>
            <s xml:id="echoid-s4862" xml:space="preserve">per, C, ducaturipſi, D
              <lb/>
            P, parallela, CM, ſecans curuam circuli, vel ellipſis, EDRP, in,
              <lb/>
            N; </s>
            <s xml:id="echoid-s4863" xml:space="preserve">Eſt igitur quadratum, BP, vel, MC, ad quadratum, CN, vt
              <lb/>
            rectangulum, RBE, ad rectangulum, RCE; </s>
            <s xml:id="echoid-s4864" xml:space="preserve">eſt autem, EP, pa-
              <lb/>
              <figure xlink:label="fig-0218-01" xlink:href="fig-0218-01a" number="132">
                <image file="0218-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0218-01"/>
              </figure>
            rallelogrammum in eadem baſi, & </s>
            <s xml:id="echoid-s4865" xml:space="preserve">alti-
              <lb/>
            tudine, cum ſemiportione, EBP, regu-
              <lb/>
            la eſt ipſa baſis, &</s>
            <s xml:id="echoid-s4866" xml:space="preserve">, CM, ducta vtcum-
              <lb/>
            que parallela ipſi baſi, repertumque eſt
              <lb/>
            quadratum, CM, ad quadratum, CN,
              <lb/>
            eſſe vt rectangulum, RBE, ad rectan
              <lb/>
            gulum, RCE, ergo magnitudines ho-
              <lb/>
            rum quatuor ordinum erunt proportio-
              <lb/>
            nales.</s>
            <s xml:id="echoid-s4867" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s4868" xml:space="preserve">omnia quadrata parallelogram-
              <lb/>
              <note position="left" xlink:label="note-0218-01" xlink:href="note-0218-01a" xml:space="preserve">Coroll.3.
                <lb/>
              26.lib. 2.</note>
            mi, EP, magnitudines primi ordinis col-
              <lb/>
            lectæ, iuxta primam, nempè iuxta qua-
              <lb/>
            dratum, CM, ad omnia quadrata ſemi-
              <lb/>
            portionis, EBP, magnitudines ſecundi
              <lb/>
            ordinis collectas, iuxta ſecundam. </s>
            <s xml:id="echoid-s4869" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s4870" xml:space="preserve">iux-
              <lb/>
            ta quadratum, CN, erunt vt rectangu-
              <lb/>
            la ſub maximis abſciſſarum, EB, & </s>
            <s xml:id="echoid-s4871" xml:space="preserve">ſub
              <lb/>
            adiunctis, BR, magnitudines tertij or-
              <lb/>
            dinis collectæ, iuxta tertiam .</s>
            <s xml:id="echoid-s4872" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s4873" xml:space="preserve">iuxta re-
              <lb/>
            ctangulum, RBE, ad rectangula ſub
              <lb/>
            omnibus abſciſſis, EB, & </s>
            <s xml:id="echoid-s4874" xml:space="preserve">reſiduis earun-
              <lb/>
            dem, adiuncta, BR, (recti, vel obliqui
              <lb/>
            tranſitus ſupradictis exiſtentibus) quæ
              <lb/>
            ſunt magnitudines quarti ordinis colle-
              <lb/>
            ctæ, iuxta quartam.</s>
            <s xml:id="echoid-s4875" xml:space="preserve">ſ.</s>
            <s xml:id="echoid-s4876" xml:space="preserve">iuxta rectangulum,
              <lb/>
            R CE; </s>
            <s xml:id="echoid-s4877" xml:space="preserve">quoniam verò rectangula ſub
              <lb/>
            maximis abſciſſarum, EB, & </s>
            <s xml:id="echoid-s4878" xml:space="preserve">ſub adiun-
              <lb/>
            ctis, BR, ad rectangula ſub omnibus ab-
              <lb/>
            ſciſſis, EB, adiuncta, BR, & </s>
            <s xml:id="echoid-s4879" xml:space="preserve">ſub earum
              <lb/>
            reſiduis, ſunt vt, BR, ad compoſitam ex
              <lb/>
              <note position="left" xlink:label="note-0218-02" xlink:href="note-0218-02a" xml:space="preserve">Cor. 30.
                <lb/>
              lib.2.</note>
            dimidia, BR, & </s>
            <s xml:id="echoid-s4880" xml:space="preserve">ſexta parte, EB, ergo conuertendo omnia quadrata
              <lb/>
            ſemiportionis, BEP, ad omnia quadrata parallelogrammi, EP, vel
              <lb/>
              <note position="left" xlink:label="note-0218-03" xlink:href="note-0218-03a" xml:space="preserve">8. lib. 2.</note>
            iſtorum quadrupla .</s>
            <s xml:id="echoid-s4881" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s4882" xml:space="preserve">omnia quadrata portionis, DEP, ad omnia
              <lb/>
            quadrata parallelogrammi, FP, erunt vt compoſita ex, {1/6}, BE, &</s>
            <s xml:id="echoid-s4883" xml:space="preserve">,
              <lb/>
            {1/2}, BR, ad eandem, BR; </s>
            <s xml:id="echoid-s4884" xml:space="preserve">Iungantur nunc, DE, EP.</s>
            <s xml:id="echoid-s4885" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4886" xml:space="preserve">Dico vlterius omnia quadrata portionis, EDP, ad omnia qua-
              <lb/>
            drata trianguli, DEP, eſſe vt compoſita ex dimidia totius, ER, & </s>
            <s xml:id="echoid-s4887" xml:space="preserve">
              <lb/>
            ipſa, BR, ad eandem, BR. </s>
            <s xml:id="echoid-s4888" xml:space="preserve">Cum enim oſtenderimus omnia qua-
              <lb/>
            drata parallelogrammi, FP, ad omnia quadrata portionis, </s>
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