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

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            <s xml:id="echoid-s10151" xml:space="preserve">
              <pb o="393" file="0413" n="413" rhead="LIBER V."/>
            H, NOS, ſit autem, veluti in anteced. </s>
            <s xml:id="echoid-s10152" xml:space="preserve">Prop. </s>
            <s xml:id="echoid-s10153" xml:space="preserve">conſſitutum paralle-
              <lb/>
            logrammum, FC, cuius oppoſita latera, FD, EC, ſint ad axim,
              <lb/>
            vel diametrum, AV, in eadem productam, órdinatim applica@a,
              <lb/>
              <figure xlink:label="fig-0413-01" xlink:href="fig-0413-01a" number="281">
                <image file="0413-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0413-01"/>
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            erunt, DC, FE, ipſi, AV, ęqui
              <lb/>
            diftantes, ſint earum portiones
              <lb/>
            inter aſymptotos concluſæ, H
              <lb/>
            S, NY, regula ſit, AV. </s>
            <s xml:id="echoid-s10154" xml:space="preserve">Dico
              <lb/>
            ergo omnia quadrata, FC, ad
              <lb/>
            omnia quadrata figuræ, FAD
              <lb/>
            CVE, ideſt figuræ concluſæ in-
              <lb/>
            ter latera, FE, DC, & </s>
            <s xml:id="echoid-s10155" xml:space="preserve">oppoſi-
              <lb/>
            tarum ſectionum portiones in-
              <lb/>
            ter eadem manentes, quę ſunt,
              <lb/>
            FAD, EVC, eſſe, vt quadratũ,
              <lb/>
            DC, vel, FE, ad quadratum,
              <lb/>
            AV, cum {1/3}. </s>
            <s xml:id="echoid-s10156" xml:space="preserve">quadrati, HS, vel,
              <lb/>
            NY. </s>
            <s xml:id="echoid-s10157" xml:space="preserve">Per puncta ergo, O, V,
              <lb/>
            ducantur, XL, VP, ad ipſam,
              <lb/>
            AV, ordinatim applicatæ, erit
              <lb/>
            igitur, XL, ſecunda diameter,
              <lb/>
            &</s>
            <s xml:id="echoid-s10158" xml:space="preserve">, VP, tanget ſectionem, EV
              <lb/>
            C. </s>
            <s xml:id="echoid-s10159" xml:space="preserve">Quoniam ergo rectangulum, HCS, æquatur quadrato. </s>
            <s xml:id="echoid-s10160" xml:space="preserve">OV,
              <lb/>
            ideſt quadrato, LP, rectangulum verò, HCS, æquatur rectangu-
              <lb/>
              <note position="right" xlink:label="note-0413-01" xlink:href="note-0413-01a" xml:space="preserve">II. Secun.
                <lb/>
              Con.</note>
            lo, LSC, bis vna cum quadrato, SC, ideò, rectangulum, LSC, bis
              <lb/>
            vna cum quadrato, SC, erit æquale quadrato, LP; </s>
            <s xml:id="echoid-s10161" xml:space="preserve">eodem pacto
              <lb/>
            ſi intelligamus ipſi, LC, æquidiſſantem vtcunq; </s>
            <s xml:id="echoid-s10162" xml:space="preserve">ductam intra pa-
              <lb/>
            rallelogrammum, OP, viq; </s>
            <s xml:id="echoid-s10163" xml:space="preserve">ad ſectionem, VC, productam, oſten-
              <lb/>
            demus rectangulum bis ſub eius portionibus inter, OL, OS, & </s>
            <s xml:id="echoid-s10164" xml:space="preserve">in-
              <lb/>
            ter, OS, & </s>
            <s xml:id="echoid-s10165" xml:space="preserve">ſectionem, VC, concluſis, vna cum quadrato eius, quę
              <lb/>
            inter, OS, & </s>
            <s xml:id="echoid-s10166" xml:space="preserve">ſectionem, VC, clauditur, æquari quadrato eius, quę
              <lb/>
            manet inter, OL, VP, & </s>
            <s xml:id="echoid-s10167" xml:space="preserve">ſic de reliquis conſimihter ſumptis; </s>
            <s xml:id="echoid-s10168" xml:space="preserve">vnde
              <lb/>
            patebit tandem rectangula ſub trianguio, LOS, & </s>
            <s xml:id="echoid-s10169" xml:space="preserve">figura, OVCS,
              <lb/>
            bis ſumpta, vna cum omnibus quadratis figuræ, CVCS, æquari
              <lb/>
            omnibus quadratis, OP, regula, AV, iam ſuppoſita, quia ergo
              <lb/>
              <note position="right" xlink:label="note-0413-02" xlink:href="note-0413-02a" xml:space="preserve">9. lib. 2.</note>
            omnia quadrata, CO, ad omnia quadrata, OP, ſunt vt quadratũ,
              <lb/>
            ZO, ad quadratum, OV, ideò pam
              <unsure/>
            teron @ a quadrata, OC, ad
              <lb/>
            rectangula ſub triangulo, LOS, & </s>
            <s xml:id="echoid-s10170" xml:space="preserve">figura, OVCS, bis, vna cum om-
              <lb/>
            nibus quadratis figuræ, OVCS, erunt vt quadratum, ZO, ad qua-
              <lb/>
            dratum, OV; </s>
            <s xml:id="echoid-s10171" xml:space="preserve">quod ſerua.</s>
            <s xml:id="echoid-s10172" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10173" xml:space="preserve">Inſuper omnia quadrata, CO, ad omnia quadrata parallelogrã-
              <lb/>
            mi, SO, ſi compleretur, eſſent vt quadiatum, CL, ad </s>
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