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

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          <pb o="80" file="0100" n="100" rhead="GEOMETRIÆ"/>
          <p>
            <s xml:id="echoid-s2006" xml:space="preserve">Sit ſolidum rotundum, APCQ, & </s>
            <s xml:id="echoid-s2007" xml:space="preserve">conusicalenus, APEQM,
              <lb/>
            vtraque autem ſecentur plano per axem, quod producat figuram, A
              <lb/>
            PCQ, in ſolido, & </s>
            <s xml:id="echoid-s2008" xml:space="preserve">triangulum, APQ, in cono, deinde ſecentur
              <lb/>
            altero plano, cuius, & </s>
            <s xml:id="echoid-s2009" xml:space="preserve">plani recti ad axem (quo productus ſit circu-
              <lb/>
            lus, PMQE,) communis ſectio ſit, EM, perpendicularis ipſi, PQ,
              <lb/>
            communi ſectioni eiuſdem, & </s>
            <s xml:id="echoid-s2010" xml:space="preserve">plani per axem ducti. </s>
            <s xml:id="echoid-s2011" xml:space="preserve">Dico figuram,
              <lb/>
            BEDM, in ſolido rotundo eſſe circa axem, & </s>
            <s xml:id="echoid-s2012" xml:space="preserve">in cono circa axem,
              <lb/>
              <note position="left" xlink:label="note-0100-01" xlink:href="note-0100-01a" xml:space="preserve">6. Defin.</note>
            vel diametrum, & </s>
            <s xml:id="echoid-s2013" xml:space="preserve">axem, vel diametrum eſſe, BD, communem ſe-
              <lb/>
            ctionem productarum figurarum. </s>
            <s xml:id="echoid-s2014" xml:space="preserve">Si ergo ſecundò producta figura
              <lb/>
            per axem pariter ducta eſſet, manifeſtum eſt in ſolido rotundo fore
              <lb/>
              <note position="left" xlink:label="note-0100-02" xlink:href="note-0100-02a" xml:space="preserve">33. huius.</note>
            figuram talem circa axem, & </s>
            <s xml:id="echoid-s2015" xml:space="preserve">in cono fore triangulum, in quo axis,
              <lb/>
              <note position="left" xlink:label="note-0100-03" xlink:href="note-0100-03a" xml:space="preserve">16. huius.</note>
            AC, ſi ſecaret æquidiſtantes baſi talis trianguli ad angulos rectos,
              <lb/>
            cum illas bifariam diuidat, eſſet talis triangulus figura circa axem, ſi
              <lb/>
            verò ad angulos non rectos, eſſet figura circa diametrum, nempè
              <lb/>
            circa, AC. </s>
            <s xml:id="echoid-s2016" xml:space="preserve">Sed non tranſeat hęc ſecunda figura per axem, ſint au-
              <lb/>
            tem puncta, B, D, extrema communis ſectionis primæ, & </s>
            <s xml:id="echoid-s2017" xml:space="preserve">ſecundę
              <lb/>
            figuræ, ideſt ip-
              <lb/>
              <figure xlink:label="fig-0100-01" xlink:href="fig-0100-01a" number="55">
                <image file="0100-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0100-01"/>
              </figure>
            ſius, BD, ergo
              <lb/>
            in ſolido rotun-
              <lb/>
            do (& </s>
            <s xml:id="echoid-s2018" xml:space="preserve">in-cono,
              <lb/>
            dum triangulus,
              <lb/>
            APQ, per axem
              <lb/>
            ductus tranſit e-
              <lb/>
            tiam per ductam
              <lb/>
            à vertice, A, per-
              <lb/>
            pẽdicularem ipſi
              <lb/>
            baſi, PEQM,
              <lb/>
            ideſt cum trian-
              <lb/>
            gulus, APQ, eſt
              <lb/>
            erectus baſi, PE
              <lb/>
            QM,) ipſa, EM, communis ſectio ſecundi plani ſecantis, &</s>
            <s xml:id="echoid-s2019" xml:space="preserve">, PQ,
              <lb/>
              <note position="left" xlink:label="note-0100-04" xlink:href="note-0100-04a" xml:space="preserve">4. Defin.
                <lb/>
              vndec. El.</note>
            plani rectè axim ſecantis, cum ſit perpendicularis, PQ, communi ſe-
              <lb/>
            ctioni planorum, PEQM, APQ, ad inuicem erectorum, erit etiam
              <lb/>
            perpendicularis plano per axem, & </s>
            <s xml:id="echoid-s2020" xml:space="preserve">ideò erit perpendicularis ad om-
              <lb/>
            nes per eam in tali plano tranſeuntes, ideò, BD, rectè ſecabit ipſam,
              <lb/>
            EM, & </s>
            <s xml:id="echoid-s2021" xml:space="preserve">quæ ducuntur per extrema, BD, æquidiſtantes ipſi, EM,
              <lb/>
            tangent ipſa ſolida, vnde, B, D, erunt oppoſiti vertices figurarum,
              <lb/>
            BEDM, reſpectu ipſius, EM, ſumptarum, quare, BD, ſecabit
              <lb/>
              <note position="left" xlink:label="note-0100-05" xlink:href="note-0100-05a" xml:space="preserve">1. Defin.</note>
            omnes illi æquidiſtantes in figura, BEDM, ductas, & </s>
            <s xml:id="echoid-s2022" xml:space="preserve">quia ſumpto
              <lb/>
              <note position="left" xlink:label="note-0100-06" xlink:href="note-0100-06a" xml:space="preserve">Corol. 2.
                <lb/>
              4. Huius.</note>
            in figura, BEDM, puncto, qui non ſit vertex reſpectu ipſius, EM,
              <lb/>
            & </s>
            <s xml:id="echoid-s2023" xml:space="preserve">ab eo ducta eidem, EM, parallela intra figuram cadit, ſit is pun-
              <lb/>
              <note position="left" xlink:label="note-0100-07" xlink:href="note-0100-07a" xml:space="preserve">Coroll. 1.
                <lb/>
              4. Huius.</note>
            ctus, O, à quo ipſi, EM, ſit ducta parallela ipſa, OR, igitur, </s>
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