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

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          <pb o="33" file="0053" n="53" rhead="LIBERI."/>
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        <div xml:id="echoid-div112" type="section" level="1" n="79">
          <head xml:id="echoid-head90" xml:space="preserve">THEOREMA XIV. PROPOS. XVII.</head>
          <p>
            <s xml:id="echoid-s911" xml:space="preserve">SI conicus ſecetur vtcumque planis per verticem, diuidi-
              <lb/>
            tur ab eiſdem in conicos: </s>
            <s xml:id="echoid-s912" xml:space="preserve">Etſiſecetur vtcumque planis
              <lb/>
            coincidentibus omnibus eiuſdem lateribus, ſolida ab ijſdem
              <lb/>
            abſciſſa verſus verticem erunt pariter conici, & </s>
            <s xml:id="echoid-s913" xml:space="preserve">eorum baſes
              <lb/>
            ipſæ ſiguræ abſcindentes.</s>
            <s xml:id="echoid-s914" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s915" xml:space="preserve">Sit quilibet conicus, AMV, ſectus plano vtcum que per verticem
              <lb/>
            ducto, quod in eo producat triangulum, ACD. </s>
            <s xml:id="echoid-s916" xml:space="preserve">Dico ab hoc pla-
              <lb/>
            no ſecante in conicos, ACVD, ACMD, fuiſſe diuiſum. </s>
            <s xml:id="echoid-s917" xml:space="preserve">Sin. </s>
            <s xml:id="echoid-s918" xml:space="preserve">in-
              <lb/>
            telligamus latus trianguli, ACD, quod ſit, AC, vel, AD, inni-
              <lb/>
            xum puncto, A, indefinitè productum ferri per rectam, CD, ipſa
              <lb/>
            deſcribet ſuperriciem trianguli, ACD, ad modum ſuperficiei coni-
              <lb/>
            cularis, eſt autem reliqua, quę inſiſtit ambitui, CVD, ſic deſcripta,
              <lb/>
              <figure xlink:label="fig-0053-01" xlink:href="fig-0053-01a" number="26">
                <image file="0053-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0053-01"/>
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            ergo tota ſuperficies, ACDV, eſt co-
              <lb/>
              <note position="right" xlink:label="note-0053-01" xlink:href="note-0053-01a" xml:space="preserve">AD, ef.4.</note>
            nicularis deſcripta latere, AC, vel, AD,
              <lb/>
            properante per circuitum figuræ planæ,
              <lb/>
            CVD, ergo erit, ACVD, conicus,
              <lb/>
            cuius baſis ipſa figura, CVD, & </s>
            <s xml:id="echoid-s919" xml:space="preserve">ver-
              <lb/>
            tex, A. </s>
            <s xml:id="echoid-s920" xml:space="preserve">Eodem modo oſtendemus, A
              <lb/>
            CMD, eſſe conicum, cuius baſis, CM
              <lb/>
            D, vertex, A. </s>
            <s xml:id="echoid-s921" xml:space="preserve">Secetur nunc plano vt-
              <lb/>
            cumque omnibus conici, AMV, late-
              <lb/>
            ribus concidente, quod in eo producat
              <lb/>
            figuram, BNEO. </s>
            <s xml:id="echoid-s922" xml:space="preserve">Dico, ANO, eſſe
              <lb/>
            conicum, cuius baſis figura, BNEO,
              <lb/>
            vertex, A, nam dum latus conici, AM
              <lb/>
            V, properat per circuitum baſis, CMD
              <lb/>
            V, vt deſcribat eius conicularem ſuperficiem, properat etiam per
              <lb/>
            circuitum figurę, BNEO, & </s>
            <s xml:id="echoid-s923" xml:space="preserve">deſcribit ſupra ipiam ſuperficiem co-
              <lb/>
            nicularem, igitur ſuperficies ab eadem figura, BE, ablciſia verſus,
              <lb/>
            A, eſt conicularis, & </s>
            <s xml:id="echoid-s924" xml:space="preserve">ſolidum comprehenſum ab ipſa, & </s>
            <s xml:id="echoid-s925" xml:space="preserve">figura pla-
              <lb/>
            na, BNEO, erit conicus, & </s>
            <s xml:id="echoid-s926" xml:space="preserve">eiuſdem baſis ipſa figura, BNEO,
              <lb/>
            vertex autem, A, quod oſtendere opus erat.</s>
            <s xml:id="echoid-s927" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div114" type="section" level="1" n="80">
          <head xml:id="echoid-head91" xml:space="preserve">COROLLARIVM.</head>
          <p style="it">
            <s xml:id="echoid-s928" xml:space="preserve">_H_Inc habetur, ſi planum tranſeat per verticem conici, & </s>
            <s xml:id="echoid-s929" xml:space="preserve">quamli-
              <lb/>
            bet rectam lineam intra baſim conici exiſtentem, qui quidem ſe-
              <lb/>
            cetur alio plano coincidente cum omnibus eiuſdem conici </s>
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