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

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          <p>
            <s xml:id="echoid-s5179" xml:space="preserve">
              <pb o="212" file="0232" n="232" rhead="GEOMETRIÆ"/>
            H, vt etiam parallelogrammum, DH, eſtin eadem baſi, & </s>
            <s xml:id="echoid-s5180" xml:space="preserve">altitu-
              <lb/>
            dinecum ſemiportione, AFH; </s>
            <s xml:id="echoid-s5181" xml:space="preserve">ſumatur vtcunque in, AH, pun-
              <lb/>
            ctum, O, & </s>
            <s xml:id="echoid-s5182" xml:space="preserve">per ipſum ducatur ipſi, FT, parallela, OE, ſecans cur-
              <lb/>
            uam, AG, in, N, CG, in, I, curuam, AF, in, M, &</s>
            <s xml:id="echoid-s5183" xml:space="preserve">, DF, in,
              <lb/>
              <figure xlink:label="fig-0232-01" xlink:href="fig-0232-01a" number="144">
                <image file="0232-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0232-01"/>
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            E. </s>
            <s xml:id="echoid-s5184" xml:space="preserve">Igitur quadratum, FH, ad quadratum,
              <lb/>
              <note position="left" xlink:label="note-0232-01" xlink:href="note-0232-01a" xml:space="preserve">Ex 40.1.1.
                <lb/>
              & eius
                <lb/>
              Scholio.</note>
            MO, erit vt rectangulum, VHA, adre-
              <lb/>
            ctangulum, VOA, .</s>
            <s xml:id="echoid-s5185" xml:space="preserve">i. </s>
            <s xml:id="echoid-s5186" xml:space="preserve">vt quadratum, GH,
              <lb/>
            ad quadratum, NO, ergo quadratum, F
              <lb/>
              <note position="left" xlink:label="note-0232-02" xlink:href="note-0232-02a" xml:space="preserve">16. Lib.2.</note>
            H, vel quadratum, EO, ad quadratum,
              <lb/>
            MO, erit vt quadratum, IO, ad quadra-
              <lb/>
            tum, ON, ergo, EO, ad, OM, erit vt,
              <lb/>
            IO, ad, ON, eſt autem, EO, ducta vt-
              <lb/>
            cunque parallela, FT, & </s>
            <s xml:id="echoid-s5187" xml:space="preserve">ſunt parallelo-
              <lb/>
            gramma, DH, CH, in ijſdem baſibus, & </s>
            <s xml:id="echoid-s5188" xml:space="preserve">
              <lb/>
            altitudinibus cum ſemiportionibus, AFH,
              <lb/>
            AGH, ergo omnes lineæ parallelogram-
              <lb/>
              <note position="left" xlink:label="note-0232-03" xlink:href="note-0232-03a" xml:space="preserve">Coroll.3.
                <lb/>
              26.lib.2.</note>
            mi, DH, ad omnes lineas ſemiportionis, FAH, erunt vt omnes li-
              <lb/>
            neæ parallelogrammi, CH, ad omnes lineas ſemiportionis, AG
              <lb/>
              <note position="left" xlink:label="note-0232-04" xlink:href="note-0232-04a" xml:space="preserve">3.Lib.2.</note>
            H, ergo parallelogrammum, DH, ad ſemiportionem, AFH, erit
              <lb/>
            vt parallelogrammum, CH, ad ſemiportionem, AGH, ergo, per-
              <lb/>
            mutando, DH, ad, CH, parallelogrammum erit, vt ſemiportio,
              <lb/>
            AFH, ad ſemiportionem, AGH, ergo vt, DH, ad, CH, .</s>
            <s xml:id="echoid-s5189" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s5190" xml:space="preserve">vt
              <lb/>
              <note position="left" xlink:label="note-0232-05" xlink:href="note-0232-05a" xml:space="preserve">5.Lib.2.</note>
            baſis, FH, ad baſim, HG, vel vt, FT, ad, GS, ita erit ſemipor-
              <lb/>
            tio, AFH, adſemiportionem, AGH, vel ſic eorum quadrupla .</s>
            <s xml:id="echoid-s5191" xml:space="preserve">ſ.
              <lb/>
            </s>
            <s xml:id="echoid-s5192" xml:space="preserve">ita erit circulus, vel ellipſis, AFVT, ad circulum, vel ellipſim, A
              <lb/>
            GVS, quod, &</s>
            <s xml:id="echoid-s5193" xml:space="preserve">c.</s>
            <s xml:id="echoid-s5194" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div526" type="section" level="1" n="314">
          <head xml:id="echoid-head331" xml:space="preserve">COROLLARIVM.</head>
          <p style="it">
            <s xml:id="echoid-s5195" xml:space="preserve">_H_INC etiam habetur, quoniam quadratum, EO, ad quadratum,
              <lb/>
            OM, eſt vt quadratum, IO, ad quadratum, ON, idcircò, quòd
              <lb/>
            eodem pacto, iuxta Th. </s>
            <s xml:id="echoid-s5196" xml:space="preserve">antecedens, concludere poſſumus omnia qua-
              <lb/>
            drata, DH, ad omnia quadrata, CH, eſſe, vt omnia quadrata ſemi-
              <lb/>
            portionis, AFH, ad omnia quadrata ſemiportionis, AGH, vel vt
              <lb/>
            omnia quadrata circuli, vel ellipſis, AFVT, ad omnia quadrata cir-
              <lb/>
            culi, vel ellipſis, AGVS, ſunt autem omnia quadrata parallelogram-
              <lb/>
            mi, DH, ad omnia quadrata parallelogrammi, CH, vt quadratum,
              <lb/>
              <note position="left" xlink:label="note-0232-06" xlink:href="note-0232-06a" xml:space="preserve">_9.Lib.2._</note>
            FH, ad quadratum, GH, habetur ergo inquam, quod omnia quadrata
              <lb/>
            circuli, vel ellipſis, AFVT, ad omnia quadrata circuli, vel elli-
              <lb/>
            pſis, AGVS, ſunt vt quadratum, FH, ad quadratum, HG, vel vt qua-
              <lb/>
            dratum, FT, ad quadratum, GS, ſcilicet ſunt vt quadrata ſecundorum
              <lb/>
            axium, vel diametrorum.</s>
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