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

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            <s xml:id="echoid-s3929" xml:space="preserve">
              <pb o="165" file="0185" n="185" rhead="LIBER II."/>
            nibus eiuſdem planis, regula, GE, quæ & </s>
            <s xml:id="echoid-s3930" xml:space="preserve">ipſa ſunt omnia rectan-
              <lb/>
              <note position="right" xlink:label="note-0185-01" xlink:href="note-0185-01a" xml:space="preserve">ExCor. 2.
                <lb/>
              huius.</note>
            gula figuræ, CBE, regula, CE, &</s>
            <s xml:id="echoid-s3931" xml:space="preserve">ae;</s>
            <s xml:id="echoid-s3932" xml:space="preserve">què alta, acipſum, GE, ergo
              <lb/>
            omnia rectangula ipſius, AE, regula, CE, &</s>
            <s xml:id="echoid-s3933" xml:space="preserve">ae;</s>
            <s xml:id="echoid-s3934" xml:space="preserve">què alta, acipſum, G
              <lb/>
            E, ad omnia rectangula figuræ, CBE, regula, CE, &</s>
            <s xml:id="echoid-s3935" xml:space="preserve">ae;</s>
            <s xml:id="echoid-s3936" xml:space="preserve">què alta, ac
              <lb/>
              <note position="right" xlink:label="note-0185-02" xlink:href="note-0185-02a" xml:space="preserve">3. huius.</note>
            ipſum, GE, erunt vt, AE, ad figuram, BCE, .</s>
            <s xml:id="echoid-s3937" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s3938" xml:space="preserve">vt omnes lineę,
              <lb/>
            AE, ad omnes lineas, BCE, regula, CE, quod ſerua.</s>
            <s xml:id="echoid-s3939" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3940" xml:space="preserve">Conſpiciatur nunc figura Theorematis anteced. </s>
            <s xml:id="echoid-s3941" xml:space="preserve">in qua diximus,
              <lb/>
            MO, ad, OI, eſſe vt quadratum, QO, ad quadratum, OP. </s>
            <s xml:id="echoid-s3942" xml:space="preserve">Di-
              <lb/>
            co omnes lineas, AE, ad omnes lineas figurę, BCE, regula, CE,
              <lb/>
            eſſe vt omnia quadrata, BF, ad omnia quadrata figurę, B E F, quia
              <lb/>
            enim, vt, MO, ad, OI, ita (ſumpta quauis communi altitudine,
              <lb/>
            nempè ex. </s>
            <s xml:id="echoid-s3943" xml:space="preserve">gr. </s>
            <s xml:id="echoid-s3944" xml:space="preserve">altitudine conſtitutorum parallelepipedorum, quę eſt,
              <lb/>
            SE,) rectangulum ſub, MO, &</s>
            <s xml:id="echoid-s3945" xml:space="preserve">, SE, ad rectangulum ſub, IO, S
              <lb/>
            E, ideò, vt rectangulum ſub, MO, SE, ad rectangulum ſub, IO,
              <lb/>
            SE, ita erit quadratum, OQ, ad quadratum, OP, ſunt autem hæ
              <lb/>
            magnitudines eiuſdem generis, nempè omnes ſuperficies, ergo om.
              <lb/>
            </s>
            <s xml:id="echoid-s3946" xml:space="preserve">nia rectangulaipſius, AE, regula, CE, &</s>
            <s xml:id="echoid-s3947" xml:space="preserve">ae;</s>
            <s xml:id="echoid-s3948" xml:space="preserve">què alta, ac vnum eorum,
              <lb/>
              <note position="right" xlink:label="note-0185-03" xlink:href="note-0185-03a" xml:space="preserve">Exantee.</note>
            nempè, vt rectangulum ſub, CE, ES, ad omnia rectangula figurę,
              <lb/>
            BCE, regula eadem, CE, &</s>
            <s xml:id="echoid-s3949" xml:space="preserve">ae;</s>
            <s xml:id="echoid-s3950" xml:space="preserve">què alta, ac vnum eorum, vt, GE,
              <lb/>
            erunt vt omnia quadrata, BF, ad omnia quadrata figuræ, BEF,
              <lb/>
            omnia verò rectangulaipſius, AE, &</s>
            <s xml:id="echoid-s3951" xml:space="preserve">ae;</s>
            <s xml:id="echoid-s3952" xml:space="preserve">què alta, ac vnum eorum, vt,
              <lb/>
            GE, ad omnia rectangula figuræ, BCE, &</s>
            <s xml:id="echoid-s3953" xml:space="preserve">ae;</s>
            <s xml:id="echoid-s3954" xml:space="preserve">què alta, acipſum, G
              <lb/>
            E, ſunt vt omnes lineæ ipſius, AE, ad omnes lineas figuræ, BCE,
              <lb/>
              <note position="right" xlink:label="note-0185-04" xlink:href="note-0185-04a" xml:space="preserve">Ex proxi-
                <lb/>
              mè dictis.</note>
            regula, CE, ergo omnes lineæ, AE, ad omnes lineas figuræ, BC
              <lb/>
            E, regula, CE, erunt vt omnia quadrata, BF, ad omnia quadrata
              <lb/>
            figuræ, BEF, ſunt ergo proportionales, licet ſint magnitudines di-
              <lb/>
            uerſi generis, nempè lineę, & </s>
            <s xml:id="echoid-s3955" xml:space="preserve">ſuperficies, quod oſtendere opus erat.</s>
            <s xml:id="echoid-s3956" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div412" type="section" level="1" n="250">
          <head xml:id="echoid-head265" xml:space="preserve">COROLLARIVM I.</head>
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            <s xml:id="echoid-s3957" xml:space="preserve">_H_Inc igitur primò habetur, ſi fuerint parallel ogrammum, & </s>
            <s xml:id="echoid-s3958" xml:space="preserve">figurá
              <lb/>
            plana in eadem baſi, & </s>
            <s xml:id="echoid-s3959" xml:space="preserve">altitudine, regula ſumpta baſi, omnia,
              <lb/>
            rectangula parallelogrammi &</s>
            <s xml:id="echoid-s3960" xml:space="preserve">ae;</s>
            <s xml:id="echoid-s3961" xml:space="preserve">què alta ad omnia rectangula illius figu-
              <lb/>
            ræ &</s>
            <s xml:id="echoid-s3962" xml:space="preserve">ae;</s>
            <s xml:id="echoid-s3963" xml:space="preserve">què alta ac prædicta, eſſe vt dictum parallelogrammum ad dictam,
              <lb/>
            figuram, quod patuit, dum oſtenſum eſt omnia rectangulaipſius, AE,
              <lb/>
            altitudinis, SE, ad omnia rectangula figuræ, BCE, altitudinis eiuſdem,
              <lb/>
            SE, eſſe vt, AE, ad figuram, BCE.</s>
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