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

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        <div xml:id="echoid-div444" type="section" level="1" n="267">
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            <s xml:id="echoid-s4443" xml:space="preserve">
              <pb o="181" file="0201" n="201" rhead="LIBER II."/>
            na ſolidi ſimilaris geniti ex, AC, iuxta regulam, BC, erit, inquam,
              <lb/>
            aſſumpta figura etiam vnum eorum, quæ dicuntur omnia plana cy-
              <lb/>
            lindrici, ACE, regula, BCE, quod etiam de cæteris ſimili modo
              <lb/>
            oſtendetur, ergo ſolidum ſimilare genitum ex, AC, iuxta regulam,
              <lb/>
            BC, & </s>
            <s xml:id="echoid-s4444" xml:space="preserve">cylindricus, ACE, habebunt omnia plana (regula, BCE,
              <lb/>
            aſiumpta) communia, ergo ſolidum ſimilare genitum ex, AC, iux-
              <lb/>
            ta regulam, BC, erit idem cylindrico, ACE, cuius baſis eſt figura,
              <lb/>
            BCE, & </s>
            <s xml:id="echoid-s4445" xml:space="preserve">latus alterum laterum, AB, LC. </s>
            <s xml:id="echoid-s4446" xml:space="preserve">Similiter oſtendemus ſo-
              <lb/>
            lidum ſimilare genitum ex triangulo, FGH, iuxta regulam, GH,
              <lb/>
            eſſe dem conico, FGHP, cuius latus alterum laterum, FG, FH,
              <lb/>
            & </s>
            <s xml:id="echoid-s4447" xml:space="preserve">baſis eſt figura, GHP, conſimili via ſupradictæ procedentes, quę
              <lb/>
            erant demonſtranda.</s>
            <s xml:id="echoid-s4448" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div446" type="section" level="1" n="268">
          <head xml:id="echoid-head283" xml:space="preserve">COROLLARIVM I.</head>
          <p style="it">
            <s xml:id="echoid-s4449" xml:space="preserve">_H_Inc manifeſtum eſt, ſi figuræ deſcriptæ à, BC, GH, ſint circuli,
              <lb/>
            quod ſolidum ſimilare genitum ex, AC, erit cylindrus, & </s>
            <s xml:id="echoid-s4450" xml:space="preserve">geni-
              <lb/>
            tum ex triangulo, FGH, conus ſiue recti, ſiue ſcaleni, ſi verò deſ criptæ
              <lb/>
            figuræ ſint rectilineæ, genitum ex, AC, erit priſma, ex, FGH, autem
              <lb/>
            pyramis, ſiue recta, ſiue ſcalena cętera autem nomine communi vo-
              <lb/>
            cantur ſolida ſimilaria genita ex eiſdem fig. </s>
            <s xml:id="echoid-s4451" xml:space="preserve">iuxta regulas, intellige,
              <lb/>
            BC, GH.</s>
            <s xml:id="echoid-s4452" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div447" type="section" level="1" n="269">
          <head xml:id="echoid-head284" xml:space="preserve">COROLLARIVM II.</head>
          <p style="it">
            <s xml:id="echoid-s4453" xml:space="preserve">_S_I intra triangulum, FGH, ducamus ipſi, GH, parallelam vtcunq;
              <lb/>
            </s>
            <s xml:id="echoid-s4454" xml:space="preserve">quæ ſit, DI, abſcindens à triangulo, FGH, trapezium, DH, oſten-
              <lb/>
            demus eodem modo, quo ſupra, ſolidum ſimilare genitum ex trape-
              <lb/>
            zio, DH, iuxta regulam, GH, eſſe fruſtum ſolidi ſimilaris geniti ex
              <lb/>
            triangulo, FGH, iuxta eandem regulam, ideſt fruſtum conici, FGHP,
              <lb/>
              <note position="right" xlink:label="note-0201-01" xlink:href="note-0201-01a" xml:space="preserve">_B. def. 4.
                <unsure/>
              _
                <lb/>
              _l. I._</note>
            .</s>
            <s xml:id="echoid-s4455" xml:space="preserve">i. </s>
            <s xml:id="echoid-s4456" xml:space="preserve">cont, cum figura deſcripta à GH, eſt circulus, vel fruſtum pyra-
              <lb/>
            midis rectæ, ſiue ſcalenæ, cum illa eſi figura rectilinea, quæ facilè
              <lb/>
            oſtendentur.</s>
            <s xml:id="echoid-s4457" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div449" type="section" level="1" n="270">
          <head xml:id="echoid-head285" xml:space="preserve">COROLLARIVM III.</head>
          <p style="it">
            <s xml:id="echoid-s4458" xml:space="preserve">_T_Andem patet vice verſa, ſi quiuis cylindricus, vel conicus, vel
              <lb/>
            eius fruſium, intelligatur ſecari per latera, de illo plano ſecante
              <lb/>
              <note position="right" xlink:label="note-0201-02" xlink:href="note-0201-02a" xml:space="preserve">_13. l. I._
                <lb/>
              _2. & Cor._
                <lb/>
              _l. I._</note>
            conceptam in ſecto ſolido figuram eſſe genitricem earumdem per deſcri-
              <lb/>
            ptionem ſimitium figurarum, & </s>
            <s xml:id="echoid-s4459" xml:space="preserve">ipſa eſſe ſolida ſimilaria genita ex ei-
              <lb/>
            ſdem figuris geni@ricibus iuxta regulas communes ſectiones </s>
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