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

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            <s xml:id="echoid-s6532" xml:space="preserve">
              <pb o="261" file="0281" n="281" rhead="LIBER III."/>
            ea nempè, qua omnes figuræ ſimiles circuli eſſe ſupponuntur, cæte-
              <lb/>
            ras ergo variationes ex his facillimè auidus veritatis indagator pro-
              <lb/>
            prio marte comprehendere poterit, quæ pro huius Theor. </s>
            <s xml:id="echoid-s6533" xml:space="preserve">declarat.
              <lb/>
            </s>
            <s xml:id="echoid-s6534" xml:space="preserve">adieq. </s>
            <s xml:id="echoid-s6535" xml:space="preserve">quoq; </s>
            <s xml:id="echoid-s6536" xml:space="preserve">dilucidat. </s>
            <s xml:id="echoid-s6537" xml:space="preserve">fatis effe reor.</s>
            <s xml:id="echoid-s6538" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div621" type="section" level="1" n="360">
          <head xml:id="echoid-head377" xml:space="preserve">COROLLARIVM II.</head>
          <p>
            <s xml:id="echoid-s6539" xml:space="preserve">IN Propofitione fecunda, expoſita figura Coroll. </s>
            <s xml:id="echoid-s6540" xml:space="preserve">antec. </s>
            <s xml:id="echoid-s6541" xml:space="preserve">confor-
              <lb/>
            miter, patet, quam rationem habeat folidum fimilare genitum
              <lb/>
            ex, DN, ideft cylindricus in bafi figura deſcripta à baſi, PN, cuius
              <lb/>
            latus eſt, HN, ad ſolidum ſibi ſimilare genitum ex portione, VCB
              <lb/>
            FR,. </s>
            <s xml:id="echoid-s6542" xml:space="preserve">i. </s>
            <s xml:id="echoid-s6543" xml:space="preserve">(ſi omnes figuræ ſimiles ipſius, DN, ſint circuli diametros
              <lb/>
            in, DN, habentes, & </s>
            <s xml:id="echoid-s6544" xml:space="preserve">omnes figuræ fimiles portionis, VCBFR,
              <lb/>
            ſint pariter circuli rectè axem, BO, ſecantes, & </s>
            <s xml:id="echoid-s6545" xml:space="preserve">diametros in eadem
              <lb/>
            portione ſitos habentes, quicirculi ſint genitricibus erecti) cylindrus,
              <lb/>
            DN, ad portionem ſphæræ, velſphæroidis, VCBFR, velſi figu-
              <lb/>
              <figure xlink:label="fig-0281-01" xlink:href="fig-0281-01a" number="173">
                <image file="0281-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0281-01"/>
              </figure>
            ræ ſint recti lineę, patetratio, quam
              <lb/>
            habet prifma, DN, ad ſolidum ſibi
              <lb/>
            ſimilare genitum ex portione, VCB
              <lb/>
            FR, circuli, vel ellipſis, BCOF.
              <lb/>
            </s>
            <s xml:id="echoid-s6546" xml:space="preserve">Ductis autem rectis, BP, PN, pa-
              <lb/>
            tet ſimiliter ratio, quam habet co-
              <lb/>
            nus, BPN, ad portionem ſphæræ,
              <lb/>
            vel ſphæroidis, VCBFR, fiue py
              <lb/>
            ramis, BPN, ad ſolldum ſimilare
              <lb/>
            genitum ex triangulo, BPN, (in-
              <lb/>
            telligeiemper hęc ſolida inuicem ge-
              <lb/>
            nita iuxta regulas in Theorematibus
              <lb/>
            aſſumptas, ne toties id repetatur)
              <lb/>
            ſiue tandem, quam habet vniuerſa-
              <lb/>
            liter ſolidum ſimilare genitum ex, DN, vel triangulo, BPN, ad ſo-
              <lb/>
            lidum ſibi ſimilare genitum ex portione, VCBFR, & </s>
            <s xml:id="echoid-s6547" xml:space="preserve">hocſi, BO,
              <lb/>
            ſit axis quod ſi tantum fit diameter eædem rationes colligentur ad
              <lb/>
            modum ſuperioris Theorematis. </s>
            <s xml:id="echoid-s6548" xml:space="preserve">Eſtergo in figura cylindricus, D
              <lb/>
            N, adportionem ſphæræ, vel ſphæroidis, VCBFR, vel priſma,
              <lb/>
            DN, ad ſolidum ſimilare genitum ex portione, VCBFR, veltan-
              <lb/>
            dem quodlibet ſolidum ſimilare genitum ex, DN, ſiue quilibet cy-
              <lb/>
            lindricus genitus ex, DN, ad ſolidum ſibi ſimilare genitum ex por-
              <lb/>
            tione, VCBFR, vt rectangulum ſub, BA, & </s>
            <s xml:id="echoid-s6549" xml:space="preserve">tripla, AO, adre-
              <lb/>
            ctangulum ſub, BM, & </s>
            <s xml:id="echoid-s6550" xml:space="preserve">ſub compofita ex, MO, OA. </s>
            <s xml:id="echoid-s6551" xml:space="preserve">Solidum ve-
              <lb/>
            rò ſimilare genitum ex triangulo, BPN, ſiue ſit conus, ſiue pyramis,
              <lb/>
            ſiue tantum conicus, ad ſibi ſimilare genitum ex portione, </s>
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