Viviani, Vincenzo, De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei

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        <div xml:id="echoid-div745" type="section" level="1" n="297">
          <head xml:id="echoid-head306" xml:space="preserve">THEOR. XXXIV. PROP. LV.</head>
          <p>
            <s xml:id="echoid-s7093" xml:space="preserve">Si rectum Conoides Parabolicum, vel Hyperbolicum, aut Sphę-
              <lb/>
            ra, aut Sphæroides rectum plano per axem ſecetur, & </s>
            <s xml:id="echoid-s7094" xml:space="preserve">communem
              <lb/>
            ſectionem plani ſecantis cum ſolidi ſuperficie quædam recta linea
              <lb/>
            in puncto contingat, per quam ductum ſit aliud planum, quod re-
              <lb/>
            ctum ſit ei per axem ducto: </s>
            <s xml:id="echoid-s7095" xml:space="preserve">huiuſmodi planum in prædicto tantùm
              <lb/>
            puncto ſolidi ſuperficiem continget, ipſaque ſuperficies cadet tota
              <lb/>
            ad alteram partem plani contingentis.</s>
            <s xml:id="echoid-s7096" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7097" xml:space="preserve">ESto rectum Conoides Parabolicum, vel Hyperbolicum, vt in prima fi-
              <lb/>
            gura; </s>
            <s xml:id="echoid-s7098" xml:space="preserve">vel Sphæra, aut Sphæroides rectum, vt in ſecunda, plano per
              <lb/>
            axem B D ſectum efficiente in ſolidi ſuperficie ſectionem A B C, (quæ erit
              <lb/>
            genitrix datiſolidi) & </s>
            <s xml:id="echoid-s7099" xml:space="preserve">per punctum E in ipſa ſumptum, ſit ei contingens
              <note symbol="a" position="left" xlink:label="note-0256-01" xlink:href="note-0256-01a" xml:space="preserve">ex com-
                <lb/>
              ment. Cõ.
                <lb/>
              mand. in
                <lb/>
              lib. Arch.
                <lb/>
              de Conoi.
                <lb/>
              & Sphær.</note>
            nea F E G, per quam concipiatur duci planum H I, quod ſit rectum plano
              <lb/>
            per axem A B C: </s>
            <s xml:id="echoid-s7100" xml:space="preserve">dico huiuſmodi planum H I in ipſo tantùm puncto E con-
              <lb/>
            uexam ſolidi ſuperficiem contingere, atque hanc totam cadere infra pla-
              <lb/>
            num H I.</s>
            <s xml:id="echoid-s7101" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7102" xml:space="preserve">Cum enim recta F E G ſe-
              <lb/>
              <figure xlink:label="fig-0256-01" xlink:href="fig-0256-01a" number="212">
                <image file="0256-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0256-01"/>
              </figure>
            ctionem A B C cõtingat, pro-
              <lb/>
            ducta conueniet cum axe
              <note symbol="b" position="left" xlink:label="note-0256-02" xlink:href="note-0256-02a" xml:space="preserve">24. 25.
                <lb/>
              pr. conic.</note>
            ctionis B D ad partes verticis
              <lb/>
            B; </s>
            <s xml:id="echoid-s7103" xml:space="preserve">qua propter ſi concipiatur
              <lb/>
            planum A B C denuò conuer-
              <lb/>
            ti circa axim B D, patet ſectio-
              <lb/>
            nem A B C, dati ſolidi, & </s>
            <s xml:id="echoid-s7104" xml:space="preserve">cõ-
              <lb/>
            tingentem F E G, coni ſuper-
              <lb/>
            ficiem deſcribere, quæ conue-
              <lb/>
            xam ſolidi ſuperficiem per cir-
              <lb/>
            culi tantùm peripheriam à pũ-
              <lb/>
            cto E deſcriptam continget
              <lb/>
            (cum punctum E ſit tum in contingente, tum in ipſa ſectione, & </s>
            <s xml:id="echoid-s7105" xml:space="preserve">in reuolu-
              <lb/>
            tione peripheriam circuli deſignet, ac reliqua puncta rectæ F G ſint extra
              <lb/>
            ſectionem A B C.) </s>
            <s xml:id="echoid-s7106" xml:space="preserve">Et quoniam planum H I per contingentem F G du-
              <lb/>
            ctum, poſitum fuit rectum ad planum per axem A B C, quod eſt idem, ac
              <lb/>
            planum per axem coni â latere F G deſcripti, ergo planum H I ſecundùm
              <lb/>
            latus tantùm F G conicam ſuperficiem continget, ſed latus F G
              <note symbol="c" position="left" xlink:label="note-0256-03" xlink:href="note-0256-03a" xml:space="preserve">53. h.</note>
            ſolidi ſuperficiem contingit tantùm in puncto E, quare planum H I in vnico
              <lb/>
            puncto E ſolidi ſuperficiem contingit, ac ideò hæc cadit tota infra planum
              <lb/>
            H I. </s>
            <s xml:id="echoid-s7107" xml:space="preserve">Quod probandum erat.</s>
            <s xml:id="echoid-s7108" xml:space="preserve"/>
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