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

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          <p>
            <s xml:id="echoid-s10173" xml:space="preserve">
              <pb o="394" file="0414" n="414" rhead="GEOMETRIÆ"/>
            LS, ſunt autem omnia quadrata trianguli, OLS, {1/3}. </s>
            <s xml:id="echoid-s10174" xml:space="preserve">omnium qua-
              <lb/>
            dratorum parallelogrammi, SO, ergo omnia quadrata, CO, ad
              <lb/>
            omnia quadrata trianguli, LOS, erunt vt quadratum, CL, ad {1/3}.
              <lb/>
            </s>
            <s xml:id="echoid-s10175" xml:space="preserve">quadrati, LS; </s>
            <s xml:id="echoid-s10176" xml:space="preserve">& </s>
            <s xml:id="echoid-s10177" xml:space="preserve">quontam oſtenſum eſt omnia quadrata, CO, ad
              <lb/>
            rectangula bis ſub triangulo, LOS, & </s>
            <s xml:id="echoid-s10178" xml:space="preserve">figura, OVCS, vna cum
              <lb/>
              <figure xlink:label="fig-0414-01" xlink:href="fig-0414-01a" number="282">
                <image file="0414-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0414-01"/>
              </figure>
            omnibus quadratis figuræ, O
              <lb/>
            VCS, eſſe vt quadratum, ZO,
              <lb/>
            vel, CL, ad quadratum, OV,
              <lb/>
            ideò omnia quadrata, CO, ad
              <lb/>
            rectangula bis ſub triangulo,
              <lb/>
            LOS, & </s>
            <s xml:id="echoid-s10179" xml:space="preserve">figura, OVCS, vna
              <lb/>
            com omnibus quadratis tum
              <lb/>
            figuræ, OVCS, tum trianguli,
              <lb/>
              <note position="left" xlink:label="note-0414-01" xlink:href="note-0414-01a" xml:space="preserve">D. Cor.
                <lb/>
              23. l. 2.</note>
            OLS, .</s>
            <s xml:id="echoid-s10180" xml:space="preserve">i. </s>
            <s xml:id="echoid-s10181" xml:space="preserve">omnia quadrata, CO,
              <lb/>
            ad omnia quadrata figuræ, O
              <lb/>
            LCV, erunt vt quadratum, C
              <lb/>
            L, ad quadratum, OV, vna cũ
              <lb/>
              <note position="left" xlink:label="note-0414-02" xlink:href="note-0414-02a" xml:space="preserve">10. l. 2.</note>
            {1/3}. </s>
            <s xml:id="echoid-s10182" xml:space="preserve">quadrati, LS, & </s>
            <s xml:id="echoid-s10183" xml:space="preserve">anteceden-
              <lb/>
            tium dupla .</s>
            <s xml:id="echoid-s10184" xml:space="preserve">i. </s>
            <s xml:id="echoid-s10185" xml:space="preserve">omnia quadra-
              <lb/>
            ta, XC, ad omnia quadrata fi-
              <lb/>
            guræ, EVCLX, erunt vt qua-
              <lb/>
            dratum, CL, ad quadratum,
              <lb/>
            OV, cum {1/3}. </s>
            <s xml:id="echoid-s10186" xml:space="preserve">quadrati, LS, & </s>
            <s xml:id="echoid-s10187" xml:space="preserve">
              <lb/>
            adhuciſtorum quadrupla .</s>
            <s xml:id="echoid-s10188" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s10189" xml:space="preserve">omnia quadrata, FC, ad omnia qua-
              <lb/>
              <note position="left" xlink:label="note-0414-03" xlink:href="note-0414-03a" xml:space="preserve">9. l. 2.</note>
            drata figuræ, FADCVE, erunt vt quadratum, CL, ad quadratum,
              <lb/>
            OV, vna cum {1/3}. </s>
            <s xml:id="echoid-s10190" xml:space="preserve">quadrati, LS, vel vt iſſorum quadrup a, ſedicet.
              <lb/>
            </s>
            <s xml:id="echoid-s10191" xml:space="preserve">vt quadratum, CD, ad quadratum, AV, vna cum {1/3}. </s>
            <s xml:id="echoid-s10192" xml:space="preserve">quadrati, H
              <lb/>
            S, vel, NY, quod oſtendere opus erat.</s>
            <s xml:id="echoid-s10193" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div938" type="section" level="1" n="559">
          <head xml:id="echoid-head583" style="it" xml:space="preserve">A@@ter ſupradictam rationem explicare.</head>
          <p>
            <s xml:id="echoid-s10194" xml:space="preserve">Dico omnia quadrata, FC, ad omnia quadrata figuræ, FADC
              <lb/>
            VE, eſſe vt quadratum, RZ, compoſitæ ex tranſuerſo latere, AV,
              <lb/>
            & </s>
            <s xml:id="echoid-s10195" xml:space="preserve">axibus, vel diametris oppoſitarum hyperbolarum, FAD, EVC,
              <lb/>
            ad quadratum, AV, vna cum rectangulo ſub, AZ, & </s>
            <s xml:id="echoid-s10196" xml:space="preserve">ſexquitertia,
              <lb/>
            ZV, Nam oſtenſum eſt eadem eſſe, vt quadratum, CL, vel, ZO,
              <lb/>
            ad quadratum, OV, cum {1/3}. </s>
            <s xml:id="echoid-s10197" xml:space="preserve">quadrat, LS, & </s>
            <s xml:id="echoid-s10198" xml:space="preserve">quoniam rectangu-
              <lb/>
            lum, CSD, cum quadrato, SL, eſt æquale quadrato, CL, vel, ZO,
              <lb/>
              <note position="left" xlink:label="note-0414-04" xlink:href="note-0414-04a" xml:space="preserve">5 Sec. El.
                <lb/>
              Elicitur
                <lb/>
              exl@. fe@.
                <lb/>
              Con. au-
                <lb/>
              xilto 16.
                <lb/>
              pri. Con.</note>
            rectangulu n auten, CSD, eſſ æquale quadrato, OV, ideò qua-
              <lb/>
            dratum, LS, erit æquale reliquo quadrati, ZO, dempto quadra-
              <lb/>
            to, DV, .</s>
            <s xml:id="echoid-s10199" xml:space="preserve">i. </s>
            <s xml:id="echoid-s10200" xml:space="preserve">erit ælquale rectangulo ſub, OVZ, bis, vna cum qua-
              <lb/>
            drato, VZ, .</s>
            <s xml:id="echoid-s10201" xml:space="preserve">i. </s>
            <s xml:id="echoid-s10202" xml:space="preserve">rectangulo ſub, AVZ, ſemel cum quadrato, VZ, .</s>
            <s xml:id="echoid-s10203" xml:space="preserve">i.
              <lb/>
            </s>
            <s xml:id="echoid-s10204" xml:space="preserve">rectangulo ſub, AZV, & </s>
            <s xml:id="echoid-s10205" xml:space="preserve">ideò {1/3}. </s>
            <s xml:id="echoid-s10206" xml:space="preserve">quadrati, LS, erit æquale {1/3}. </s>
            <s xml:id="echoid-s10207" xml:space="preserve"/>
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