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

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              <pb o="259" file="0279" n="279" rhead="LIBER III."/>
            bunt, eſſe eorundem axes. </s>
            <s xml:id="echoid-s6490" xml:space="preserve">His autem prædemonſtratis ſequentia Corol-
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            laria colliguntur, quæ quidem cum Typographo deeſſent conſueti buiu-
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            ſcemodi caracteres, diuerſis imprimineceſſe fuit.</s>
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        <div xml:id="echoid-div619" type="section" level="1" n="359">
          <head xml:id="echoid-head376" xml:space="preserve">COROLLARIVMI.</head>
          <p>
            <s xml:id="echoid-s6492" xml:space="preserve">IN Propoſ. </s>
            <s xml:id="echoid-s6493" xml:space="preserve">prima igitur, ſi ſuppoſuerimus, PRDE, eſſe circu-
              <lb/>
            lum, vel ellipſim, & </s>
            <s xml:id="echoid-s6494" xml:space="preserve">axem, ER, & </s>
            <s xml:id="echoid-s6495" xml:space="preserve">circa eandem in baſi, DP,
              <lb/>
            parallelogrammum, FP, quę quidem ſit baſis portionis, DEP, re-
              <lb/>
            ctè ſecans axim, ER, deinde intellexerimus omnes figuras ſimiles
              <lb/>
            po@@onis, DEP, eſſe circulos diametros in figura genitrice, DEP,
              <lb/>
            (cui ſut erecti) ſitos habentes, tunc, FP, erit figura genitrix ſolidi
              <lb/>
            ſimilaris, quod erit cylindrus rectus, & </s>
            <s xml:id="echoid-s6496" xml:space="preserve">DEP, erit figura genitrix
              <lb/>
            ſolidi præ@@ ſimilatis, quod erit portio ſphæræ, vel ſphæroidis,
              <lb/>
            cuius axis, ER, & </s>
            <s xml:id="echoid-s6497" xml:space="preserve">quia patet ex ſupradictis, quam rationem habeat
              <lb/>
            ſolidum ſimilare genitum ex, FP, ad ſibi ſimilare genitum ex, DE
              <lb/>
            P@uxta regulam, DP, ide@ patet ex ſupradictis, quam rationem ha-
              <lb/>
            beat cylindrus, FP, ad portionem ſphæræ, vel ſphæroidis, DEP,
              <lb/>
            ſiue, DP, tranſeat per centrum, A, ſiue non. </s>
            <s xml:id="echoid-s6498" xml:space="preserve">Similiter ſi ſuppoſue-
              <lb/>
            rimus, EDRP, eſſe ſphæroidem, &</s>
            <s xml:id="echoid-s6499" xml:space="preserve">, ER, non axim, ſed diame-
              <lb/>
            trum, & </s>
            <s xml:id="echoid-s6500" xml:space="preserve">ſecari per ellipſim, DSPR, obliquè ad diametrum, ER,
              <lb/>
            & </s>
            <s xml:id="echoid-s6501" xml:space="preserve">circa eandem diametrum, EB, in eadem baſi ellipſi, DSPR,
              <lb/>
            eſſe cylindricum, FP, ſecari autem cylindricum, & </s>
            <s xml:id="echoid-s6502" xml:space="preserve">portionem ſphæ-
              <lb/>
            roidis planis parallelis ipſi ellipſi, DP, quę intelligatur erecta plano,
              <lb/>
            DEPR, conceptæ in ipſo cylindrico figuræ erunt omnes figuræ ſi-
              <lb/>
              <note position="right" xlink:label="note-0279-01" xlink:href="note-0279-01a" xml:space="preserve">Corollar.
                <lb/>
              47. lib. @.</note>
            miles parallelogrammi, FP, & </s>
            <s xml:id="echoid-s6503" xml:space="preserve">quæ ſiunt in portione ſphæroidis, D
              <lb/>
            EP, erunt omnes figuræ ſimiles portionis, DEP, omnes inquam
              <lb/>
            ellipſes ſimiles ellipſi, DP, (eſt enim idem, ſiue intelligas has figu-
              <lb/>
            ras ſimiles deſcribi omnibus lineis figurarum genitricium, FP, DE
              <lb/>
            P, ſiue percipias ealdem produci per ſectionem corporum per plana
              <lb/>
            factam ipſi, DP, parallela) & </s>
            <s xml:id="echoid-s6504" xml:space="preserve">quia patet ratio harum omnium ſimi-
              <lb/>
            lium ſigurarum, ſiue ellipſium inter ſe ex ſupradictis, & </s>
            <s xml:id="echoid-s6505" xml:space="preserve">ſubinde ſoli-
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            dorum ſimilarium genitorum ex, FP, & </s>
            <s xml:id="echoid-s6506" xml:space="preserve">portione, DEP, qucrum
              <lb/>
            vnum eſt cylmdricus, alterum eſt portio ſphæroidis ſecta plano, D
              <lb/>
            P, ideo patet, quam rationem habeat cylindricus, FP, ad portio-
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            nem, DEP, .</s>
            <s xml:id="echoid-s6507" xml:space="preserve">@. </s>
            <s xml:id="echoid-s6508" xml:space="preserve">eſſeeandem, quam habet compoſita ex ſexta parte,
              <lb/>
            EB, & </s>
            <s xml:id="echoid-s6509" xml:space="preserve">dimidia, BR, ad ipſam, BR, & </s>
            <s xml:id="echoid-s6510" xml:space="preserve">hoc, ſiue, ER, ſit axis,
              <lb/>
            ſiuenon; </s>
            <s xml:id="echoid-s6511" xml:space="preserve">Quod ſi, DP, tranſeat per centrum, A, cylindricum, FP,
              <lb/>
            eſſe ſexquialterum portionis ſphærę, vel ſphęroidis, DEP. </s>
            <s xml:id="echoid-s6512" xml:space="preserve">Ijſdem
              <lb/>
            vijs patebit conum, ſiue conicum, EDP, ad portionem ſphærę, vel
              <lb/>
            ſphæroidis, DEP, eſſe vt, BR, ad compoſitam ex, BR, & </s>
            <s xml:id="echoid-s6513" xml:space="preserve">dimi-
              <lb/>
            dia totius, ER, quod ſi, DP, per centrum tran@eat, conum, vel </s>
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