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

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        <div xml:id="echoid-div213" type="section" level="1" n="138">
          <p>
            <s xml:id="echoid-s2180" xml:space="preserve">
              <pb o="88" file="0108" n="108" rhead="GEOMETRI Æ"/>
            circulus eum ſecat, producetur ergo ab hoc ſecante plano in ipſis ſo-
              <lb/>
            lidis circulus centrum in axehabens, cuius diameter erit, BD, ha-
              <lb/>
              <note position="left" xlink:label="note-0108-01" xlink:href="note-0108-01a" xml:space="preserve">34. huius.</note>
            bemus igitur duos circulos in eodem plano, circa eandem diametrum,
              <lb/>
              <note position="left" xlink:label="note-0108-02" xlink:href="note-0108-02a" xml:space="preserve">Corol. 34
                <lb/>
              huius.</note>
            ergo illi erunt congruentes, periphæria autem circuli dicto ſecante
              <lb/>
            plano in dicto ſolido producti eſt in ſuperficie ambiente dictum ſoli-
              <lb/>
            dum, ergo, & </s>
            <s xml:id="echoid-s2181" xml:space="preserve">periphęria circuli, BNDE, deſcripti, vt dictum eſt,
              <lb/>
            erit in tali ſuperficie, ſcilicet in ſuperficie ſphæræ in figura circuli,
              <lb/>
            ſphæroidis in figura ellipſis, conoidis parabolici in figura parabolæ,
              <lb/>
            & </s>
            <s xml:id="echoid-s2182" xml:space="preserve">hyperbolici in figura hyperbolę, idem oſtendemus de alijs quibuſ-
              <lb/>
            cumque ſic deſcriptis circulis ab ordinatim applicatis ad dictos axes
              <lb/>
            tanquam à diametris, qui ſint erecti eiſdem ſectionibus, igitur quod
              <lb/>
            proponebatur demonſtratum fuit.</s>
            <s xml:id="echoid-s2183" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div215" type="section" level="1" n="139">
          <head xml:id="echoid-head150" xml:space="preserve">THEOREMA XLIV. PROPOS. XLVII.</head>
          <p>
            <s xml:id="echoid-s2184" xml:space="preserve">INFRASCRIPTIS poſitis, eadem adhuc ſequi oſten-
              <lb/>
            demus.</s>
            <s xml:id="echoid-s2185" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2186" xml:space="preserve">Ijſdem enim expoſitis figuris, præter circulum, ſupponamus ip-
              <lb/>
            fam, AC, non eſſe axem, ſed diametrum, & </s>
            <s xml:id="echoid-s2187" xml:space="preserve">ad ipſam ordinatim ap-
              <lb/>
            plicari vtcumque, BD, intelligatur autem, BD, diameter cuiuſdam
              <lb/>
            ellipſis ab eadem deſcriptæ, quæ ſit erecta plano propoſitæ figuræ,
              <lb/>
            ſit autem, in figura ellipſis, deſcriptæ ellipſis ſecunda diameter per-
              <lb/>
            pendicularis ipſi, BD, & </s>
            <s xml:id="echoid-s2188" xml:space="preserve">æqualis ductæ à puncto, B, parallelę tan-
              <lb/>
              <figure xlink:label="fig-0108-01" xlink:href="fig-0108-01a" number="61">
                <image file="0108-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0108-01"/>
              </figure>
            genti ellipſim, ABCD, in ex-
              <lb/>
            tremitate eiuſdem axis (quæ
              <lb/>
            tangat in, S,) interiectæ in-
              <lb/>
            ter, BD, & </s>
            <s xml:id="echoid-s2189" xml:space="preserve">eam, quę ducitur
              <lb/>
              <note position="left" xlink:label="note-0108-03" xlink:href="note-0108-03a" xml:space="preserve">44. huius.</note>
            à puncto, D, parallela iun-
              <lb/>
            genti puncta, S, A. </s>
            <s xml:id="echoid-s2190" xml:space="preserve">In figura
              <lb/>
            verò hyperbolæ ſit ſecunda
              <lb/>
            diameter perpendicularis, BD,
              <lb/>
            & </s>
            <s xml:id="echoid-s2191" xml:space="preserve">æqualis ei, quæ ducitur à
              <lb/>
            puncto, D, parallela tangenti
              <lb/>
            hyperbolam in extremitate a-
              <lb/>
            xis (vt in, S,) interiectæ in-
              <lb/>
            ter, BD, & </s>
            <s xml:id="echoid-s2192" xml:space="preserve">eam, quę ducitur
              <lb/>
            à puncto, B, parallela iungenti
              <lb/>
            puncta, S, A, & </s>
            <s xml:id="echoid-s2193" xml:space="preserve">tandem in párabola ſit ſecunda diameter perpendi-
              <lb/>
            cularis quoque ipſi, BD, & </s>
            <s xml:id="echoid-s2194" xml:space="preserve">æqualis diſtantiæ parallelarum eiuſdem
              <lb/>
              <note position="left" xlink:label="note-0108-04" xlink:href="note-0108-04a" xml:space="preserve">42. huius.</note>
            axi, quę ducuntur ab extremitatibus ip ſius, B, D. </s>
            <s xml:id="echoid-s2195" xml:space="preserve">Intelligantur </s>
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