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

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          <p>
            <s xml:id="echoid-s6790" xml:space="preserve">
              <pb o="275" file="0295" n="295" rhead="LIBER III."/>
            genitum ex portione minori, RFV, eſſe vt ſexquialtera, FM, ad, M
              <lb/>
            w. </s>
            <s xml:id="echoid-s6791" xml:space="preserve">Reuoluatur igitur, vt ſiat noſtrum exemplum, Δ V, circa, RV,
              <lb/>
            manentem, cylindrus igitur deſcriptus à, Δ V, ad ſolidum deſcriptum
              <lb/>
            à portione, RFV, erit vt ſexquialtera, FM, ad, M w, & </s>
            <s xml:id="echoid-s6792" xml:space="preserve">ſic dere-
              <lb/>
            liquis ſolidis ſimilaribus ab ipſis genitis, &</s>
            <s xml:id="echoid-s6793" xml:space="preserve">c. </s>
            <s xml:id="echoid-s6794" xml:space="preserve">Vocetur autem ſolidum
              <lb/>
            deſcriptum per reuolutionem à portione circuli, RFV, minori; </s>
            <s xml:id="echoid-s6795" xml:space="preserve">Ma-
              <lb/>
            lum citrium.</s>
            <s xml:id="echoid-s6796" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div664" type="section" level="1" n="389">
          <head xml:id="echoid-head406" xml:space="preserve">COROLLARIVM XXI.</head>
          <p>
            <s xml:id="echoid-s6797" xml:space="preserve">IN Propof. </s>
            <s xml:id="echoid-s6798" xml:space="preserve">24. </s>
            <s xml:id="echoid-s6799" xml:space="preserve">aſſumpta adhuc figura ſuperioris, quæ reuoluitur,
              <lb/>
            colligitur ſolidum ſimilare genitum ex portione, RFV, iuxta
              <lb/>
            axim, FM, regulam, ad ſolidum ſimilare genitum ex eadem, iuxta
              <lb/>
            baſim, RV, regulam eſſe, vt rectangulum ſub, w M, & </s>
            <s xml:id="echoid-s6800" xml:space="preserve">ſub baſi, R
              <lb/>
              <figure xlink:label="fig-0295-01" xlink:href="fig-0295-01a" number="189">
                <image file="0295-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0295-01"/>
              </figure>
            V, ad tria quadrata
              <lb/>
            lineę, RM, cum qua-
              <lb/>
            drato, MF. </s>
            <s xml:id="echoid-s6801" xml:space="preserve">Fiat no-
              <lb/>
            ſtrum exemplum per
              <lb/>
            reuolutionẽ portio-
              <lb/>
            nis, RFV, ſemel cir-
              <lb/>
            ca, RV, & </s>
            <s xml:id="echoid-s6802" xml:space="preserve">iterum cir-
              <lb/>
            ca, FM, manentes
              <lb/>
            axes, primò igitur fit:
              <lb/>
            </s>
            <s xml:id="echoid-s6803" xml:space="preserve">Malum citrium per
              <lb/>
            reuolutionem circa,
              <lb/>
            RV, ſecundò fit ſeg-
              <lb/>
            mentum ſphæræ per
              <lb/>
            reuolutionem circa, FM, patet ergo, quam rationem habeat Ma-
              <lb/>
            lum citrium, ad ſegmentum ſphæræ ab eadem circuli portione per
              <lb/>
            reuolutionem genitum, quod etiam de reliquis ſimilaribus ſolidis ab
              <lb/>
            eadem portione, iuxta dictas regulas genitis concluſum eſt.</s>
            <s xml:id="echoid-s6804" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div666" type="section" level="1" n="390">
          <head xml:id="echoid-head407" xml:space="preserve">COROLLARIVM XXII.</head>
          <p>
            <s xml:id="echoid-s6805" xml:space="preserve">IN Propof. </s>
            <s xml:id="echoid-s6806" xml:space="preserve">25. </s>
            <s xml:id="echoid-s6807" xml:space="preserve">ſi ſumamus ex figura Theorem. </s>
            <s xml:id="echoid-s6808" xml:space="preserve">21. </s>
            <s xml:id="echoid-s6809" xml:space="preserve">portionem cir-
              <lb/>
            culi, vel ellipſis, RFV, vtcunque, cum integra axi, FH, à quá
              <lb/>
            ſit abſciſſa, IH, æqualis, FM, ſumatur inſuper de, MH, ipſa, M
              <lb/>
            T, ad quam, FM, ſit vt, Δ V, ad portionem, RFV, coll gemus, ex-
              <lb/>
            poſita hic figura, ſolidum ſimilare genitum ex, Δ V, ad ſibi ſimilare
              <lb/>
            genitum ex portione, BFV, eſſe vt quadratum, FM, ad rectangu-
              <lb/>
            lûm, quod remanet, dempto rectangulo ſub, IM, & </s>
            <s xml:id="echoid-s6810" xml:space="preserve">ſub, TM, à
              <lb/>
            rectangulo ſub, FM, &</s>
            <s xml:id="echoid-s6811" xml:space="preserve">, {2/3}, ipſius, MH. </s>
            <s xml:id="echoid-s6812" xml:space="preserve">Fiat noſtrum exemplum;</s>
            <s xml:id="echoid-s6813" xml:space="preserve"/>
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