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

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          <p>
            <s xml:id="echoid-s6551" xml:space="preserve">
              <pb o="262" file="0282" n="282" rhead="GEOMETRI E"/>
            ſiue hoc ſit portio ſphæræ, vel ſphæroidis, ſiue tantum ſolidum ſi-
              <lb/>
            milare genitum ex portione, VCBFR, vtrectangulum, BAO, ſiue
              <lb/>
            quadratum, BA, ad rectangulum ſub, BM, & </s>
            <s xml:id="echoid-s6552" xml:space="preserve">ſub compoſita ex, M
              <lb/>
            O, OA, nam ſicut rectangulum, BAO, eſt tertia pars rectanguli
              <lb/>
              <note position="left" xlink:label="note-0282-01" xlink:href="note-0282-01a" xml:space="preserve">I. Propol.
                <lb/>
              24, lib. 2.</note>
            ſub, BA, & </s>
            <s xml:id="echoid-s6553" xml:space="preserve">tripla, AO, ita ſolidum ſimilare genitum ex triangulo,
              <lb/>
            BPN, eſt tertia pars ſolidi ſimilaris geniti ex, DN, vnde patet, &</s>
            <s xml:id="echoid-s6554" xml:space="preserve">c.</s>
            <s xml:id="echoid-s6555" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div623" type="section" level="1" n="361">
          <head xml:id="echoid-head378" xml:space="preserve">COROLLARIVM III.</head>
          <p>
            <s xml:id="echoid-s6556" xml:space="preserve">IN Propoſit. </s>
            <s xml:id="echoid-s6557" xml:space="preserve">tertia colligitur, quam rationem habeat ſolidum ſi-
              <lb/>
            milare genitum ex, BF, ſiue ſit cylindrus, ſiue priſma, ſiue tan-
              <lb/>
            tum conicus, ad ſibi ſimilare genitum ex portione circuli, vel ellipſis,
              <lb/>
            ICFS, ſiue hoc ſit fruſtum ſphærę, vel ſphæroidis, ſiue tantum ſo-
              <lb/>
            lidum ſimilare genitum ex portione, ICFS, ſiue, AD, ſit a@is ſiue
              <lb/>
              <figure xlink:label="fig-0282-01" xlink:href="fig-0282-01a" number="174">
                <image file="0282-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0282-01"/>
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            non, quę eadem eſt ei, quam habet re-
              <lb/>
            ctangulum, DRA, ad rectangulum
              <lb/>
            ſub, DR, & </s>
            <s xml:id="echoid-s6558" xml:space="preserve">ſub compoſita ex, {1/2}, R
              <lb/>
            M, & </s>
            <s xml:id="echoid-s6559" xml:space="preserve">ex, MA, vna cam rectangulo
              <lb/>
            ſub, RM, & </s>
            <s xml:id="echoid-s6560" xml:space="preserve">ſub compoſita ex, {1/6}, R
              <lb/>
            M, &</s>
            <s xml:id="echoid-s6561" xml:space="preserve">, {1/2}, MA. </s>
            <s xml:id="echoid-s6562" xml:space="preserve">Solidum autem ſimi-
              <lb/>
            lare genitum ex triangulo, MCF, ſiue
              <lb/>
            ſit conus, ſiue priſma, ſiue tantum co-
              <lb/>
            nicus, ad ſibi ſimilare genitum ex por-
              <lb/>
            tione, ICFS, ſiue hoc ſit fruſtum
              <lb/>
            ſphæræ, vel ſphæroidis, ſiue tantum
              <lb/>
            ſolidum ſimilare genitum ex tali por-
              <lb/>
            tione, ICFS, erit vt rectangulum,
              <lb/>
            DRA, ad rectangulum ſub compoſita ex, MD, DR, & </s>
            <s xml:id="echoid-s6563" xml:space="preserve">ſub ſex-
              <lb/>
            quialtera, MA, vna cum rectangulo ſub compoſita ex, MD, &</s>
            <s xml:id="echoid-s6564" xml:space="preserve">dupla, DR, & </s>
            <s xml:id="echoid-s6565" xml:space="preserve">ſub, {1/2}, MR, ſiue, AD, ſit axis, ſiue tantum dia-
              <lb/>
            meter, quę iuxta antecedẽtium declarationem facilè percipi poſſunt.</s>
            <s xml:id="echoid-s6566" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div625" type="section" level="1" n="362">
          <head xml:id="echoid-head379" xml:space="preserve">COROLLARIVM IV.</head>
          <p>
            <s xml:id="echoid-s6567" xml:space="preserve">IN Propof. </s>
            <s xml:id="echoid-s6568" xml:space="preserve">quarta patet ratio, quam habet ſolidum ſimilare ge-
              <lb/>
            nitum ex, GX, quod apparet in ſuperioris figura, ad ſibi ſimilare
              <lb/>
            genitum ex portione, ICFS, quæratio ibi conſpiciatur.</s>
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