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

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          <pb o="82" file="0102" n="102" rhead="GEOMETRI Æ"/>
          <p>
            <s xml:id="echoid-s2043" xml:space="preserve">Sit conus, cuius vertex, A, baſis circulus, CEFD, ſecetur autem
              <lb/>
            prius plano per axem, quod in eo producat triangulum, ACF, ſe-
              <lb/>
              <note position="left" xlink:label="note-0102-01" xlink:href="note-0102-01a" xml:space="preserve">16, huius.</note>
            cetur deinde altero plano baſim ſecante ſecundum rectam, ED, per-
              <lb/>
            pendicularem ipfi, CF, cuius in cono concepta ſit figura, BED,
              <lb/>
              <note position="left" xlink:label="note-0102-02" xlink:href="note-0102-02a" xml:space="preserve">Ex antec.</note>
            erit ergo hæc figura circa axem, vel diametrum, BV, quę ſit paral-
              <lb/>
            lela ipſi, AF, cuius vertex reſpectu ipſius, ED, erit, B; </s>
            <s xml:id="echoid-s2044" xml:space="preserve">ducaturà
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            puncto, M, qui non ſit punctus, B, ſed vtcumque ſumptus in linea,
              <lb/>
            EBD, extra baſim, ED, ipſi, ED, recta ęquidiſtans, MO, pro-
              <lb/>
            ducta vſq; </s>
            <s xml:id="echoid-s2045" xml:space="preserve">ad ambientem ſuperficiem, cui occurrat in, O, igitur hęc
              <lb/>
            erit vna ex ordinatim applicatis ad axim, vel diametrum, BV, ęqui-
              <lb/>
            diſtans ipſi, ED, quę bifariam diuidetur ab ipſa, BV, in puncto, N,
              <lb/>
            ducatur per, N, ipſi, CF, parallela, HR, eſt verò etiam, MO, ipſi,
              <lb/>
            ED, parallela, ergo planum tranſiens per, HR, MO, æquidiſta-
              <lb/>
              <note position="left" xlink:label="note-0102-03" xlink:href="note-0102-03a" xml:space="preserve">15. Vnde-
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              cim. El.</note>
            bit baſi, CEFD, & </s>
            <s xml:id="echoid-s2046" xml:space="preserve">quatuor puncta, H, M, R, O, erunt in circuli
              <lb/>
              <figure xlink:label="fig-0102-01" xlink:href="fig-0102-01a" number="56">
                <image file="0102-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0102-01"/>
              </figure>
            periphæria, cuius diameter, HR, quem
              <lb/>
              <note position="left" xlink:label="note-0102-04" xlink:href="note-0102-04a" xml:space="preserve">15. huius.</note>
            ſecat, MO, perpendiculariter, nam an-
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            gulus, HNM, æquatur angulo, CVE,
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              <note position="left" xlink:label="note-0102-05" xlink:href="note-0102-05a" xml:space="preserve">14. Secun.
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              Elem.</note>
            quirectus eſt, ergo quadratum, MN, æ-
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            quatur rectangulo, HNR, & </s>
            <s xml:id="echoid-s2047" xml:space="preserve">quadra-
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            tum, EV, rectangulo, CVF, eſt autem
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            rectangulum, CVF, ad rectangulum, H
              <lb/>
            NR, (quia eorum altitudines, VF, NR,
              <lb/>
            ſunt æ quales, cum ſint parallelogrammi,
              <lb/>
            NF, oppoſita latera) vt baſis, CV, ad,
              <lb/>
            HN, ex prima Sexti Elem. </s>
            <s xml:id="echoid-s2048" xml:space="preserve">vel ex quinta
              <lb/>
            libro ſequentis independénter ab hac de-
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            monſtrata, & </s>
            <s xml:id="echoid-s2049" xml:space="preserve">quia, HN, eſt parallela
              <lb/>
            ipſi, CV, trianguli, BHN, BCV, ſunt æquianguli, ideò, vt, C
              <lb/>
              <note position="left" xlink:label="note-0102-06" xlink:href="note-0102-06a" xml:space="preserve">4. Sexti
                <lb/>
              Elem.</note>
            V, ad, HN, ita, VB, ad, BN, ergo rectangulum, CVF, ad re-
              <lb/>
            ctangulum, HNR, ideſt quadratum, EV, ad quadratum, MN,
              <lb/>
            erit vt, VB, ad, BN, eſt autem quadratum, ED, quadruplum
              <lb/>
            quadrati, EV, nam eſt æquale quadratis, EV, VD, & </s>
            <s xml:id="echoid-s2050" xml:space="preserve">rectangulis
              <lb/>
              <note position="left" xlink:label="note-0102-07" xlink:href="note-0102-07a" xml:space="preserve">4. Secun.
                <lb/>
              Elem.</note>
            fub, EVD, bis, ideſt duobus quadratis, EV, quæ cum prædictis
              <lb/>
            conficiunt quatuor quadrata, EV, & </s>
            <s xml:id="echoid-s2051" xml:space="preserve">eadem ratione quadratum, M
              <lb/>
            O, eſt quadruplum quadrati, MN, ergo quadratum, ED, ad qua-
              <lb/>
            dratum, MO, erit vt, BV, ad, BN, quæſunt abſciſſæ ab ipſa axi,
              <lb/>
            vel diametro, BV, verſus verticem, B, per ipſas, ED, MO, ordi-
              <lb/>
            natim adipſam, BV, applicatas, quod oſtendere opus erat; </s>
            <s xml:id="echoid-s2052" xml:space="preserve">hęc au-
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            tem vocatur ab Apolonio Parabola.</s>
            <s xml:id="echoid-s2053" xml:space="preserve"/>
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