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

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          <p>
            <s xml:id="echoid-s873" xml:space="preserve">
              <pb o="31" file="0051" n="51" rhead="LIBERI."/>
            ergo, SM, æquidiſtans ipſi, TP, regulæ homologarum figurę, A
              <lb/>
            T, veluti, RK, æquidiſtat ipſi, NL, regulæ homologarum figu-
              <lb/>
            ræ, F N, & </s>
            <s xml:id="echoid-s874" xml:space="preserve">ſecant incidentes, BP, HL, ſimiliter ad eandem par-
              <lb/>
            tem in punctis, M, K, ergo ipſæ, SV, RI, erunt homologę di-
              <lb/>
            ctarum figurarum ſimilium, & </s>
            <s xml:id="echoid-s875" xml:space="preserve">ęqualium, quę ideò erunt æquales,
              <lb/>
            ſicut etiam ipſæ, VM, IK. </s>
            <s xml:id="echoid-s876" xml:space="preserve">& </s>
            <s xml:id="echoid-s877" xml:space="preserve">ſunt ęquidiſtantes, ergo eas iungen-
              <lb/>
            tes erunt ęquales, & </s>
            <s xml:id="echoid-s878" xml:space="preserve">ęquidiſtantes, ſcilicet, SR, VI, MK, eſtau-
              <lb/>
            tem, MK, parallela, & </s>
            <s xml:id="echoid-s879" xml:space="preserve">ęqualis ipſi, PL, ergo, SR, VI, erunt
              <lb/>
            ęquales, & </s>
            <s xml:id="echoid-s880" xml:space="preserve">parallelęipſi, PL: </s>
            <s xml:id="echoid-s881" xml:space="preserve">Eodem pacto per, EG, extendentes
              <lb/>
            planum ęquidiſtans plano, TL, quod ſecet figurarum, AT, FN,
              <lb/>
            productarum plana in rectis, QE, DG, oſtendemus ipſas, QO, D
              <lb/>
            C, eſſe homologas figurarum ſimilium, & </s>
            <s xml:id="echoid-s882" xml:space="preserve">ęqualium, AT, FN, & </s>
            <s xml:id="echoid-s883" xml:space="preserve">
              <lb/>
            ideò eas eſſe ęquales, vt & </s>
            <s xml:id="echoid-s884" xml:space="preserve">ipſas, OE, CG, ergo ſi iungantur, QD,
              <lb/>
            OC, iſtę erunt ęquales, & </s>
            <s xml:id="echoid-s885" xml:space="preserve">parallelę ipfi, EG, ideſt ipſi, PL; </s>
            <s xml:id="echoid-s886" xml:space="preserve">ſimi-
              <lb/>
            liter in cæteris planis procedemus, quæ inter plana, TL, AH, ip-
              <lb/>
            ſis æquidiſtantia ducuntur, oſtendentes, quæ iungunt extrema ho-
              <lb/>
            mologarum earundem figurarum, AT, FN, eſſe æquales, & </s>
            <s xml:id="echoid-s887" xml:space="preserve">ęqui-
              <lb/>
            diſtantesipſi, PL, ſi igitur, PL, regula ſtatuatur, erunt omnes di-
              <lb/>
            ctæ iungentes in ſuperficie quadam, per quam ipſi, PL, properan-
              <lb/>
            te quadam recta linea æquali ſemper ęquidiſtanter, eiuſdem extrema
              <lb/>
              <note position="right" xlink:label="note-0051-01" xlink:href="note-0051-01a" xml:space="preserve">Def.3.</note>
            iugiter manent in ambitu ſigurarum, AT, FN, ergo hæc erit ſu-
              <lb/>
            perficies cylindrici, cuius oppoſitę baſes erunt ipſę, AT, FN, ſunt
              <lb/>
            igitur, AT, FN, cylindrici cuiuſdam (nempè cuius latus eſt quod-
              <lb/>
            uis ipſorum, QD, SR, VI, OC,) oppoſirę baſes, quod erat no-
              <lb/>
            bis oſtendendum.</s>
            <s xml:id="echoid-s888" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div106" type="section" level="1" n="75">
          <head xml:id="echoid-head86" xml:space="preserve">THEOREMA XII. PROPOS. XV.</head>
          <p>
            <s xml:id="echoid-s889" xml:space="preserve">PVnctus manens, cui in reuolutione innititur latus coni-
              <lb/>
            ci, eſt vnicus vertex conicireſpectu eiuſdem baſis.</s>
            <s xml:id="echoid-s890" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s891" xml:space="preserve">Sit conicus, ABD, baſis, BD, punctus, eui innititur latus co-
              <lb/>
              <note position="right" xlink:label="note-0051-02" xlink:href="note-0051-02a" xml:space="preserve">A. Def.4.</note>
            nici, ABD, in reuolutione, quę ab eo fit per circuitum baſis, BD,
              <lb/>
              <figure xlink:label="fig-0051-01" xlink:href="fig-0051-01a" number="24">
                <image file="0051-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0051-01"/>
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            ſit, A. </s>
            <s xml:id="echoid-s892" xml:space="preserve">Dico, A, eſſe vnicum verticem conici, A
              <lb/>
            BD, reſpectu baſis, BD. </s>
            <s xml:id="echoid-s893" xml:space="preserve">Intelligatur per pun-
              <lb/>
            ctum, A, ductum planum ęquidiſtans baſi, dico
              <lb/>
            hoc planum tantummodo in hoc puncto tangere
              <lb/>
            conicum, ſi enim poſſibile eſt eundem tangat, ſeu
              <lb/>
            ſecet in duobus punctis, vt in, C, A, iuncta ergo,
              <lb/>
            AC, illa erit in ſuperficie coniculari, & </s>
            <s xml:id="echoid-s894" xml:space="preserve">cum de-
              <lb/>
            ſcendat à puncto, A, per ipſum tranſiet aliquando
              <lb/>
            latus conici, vt, AB, igitur, AB, erit in plano ducto per, A, </s>
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