Viviani, Vincenzo, De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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            <s xml:id="echoid-s5441" xml:space="preserve">2. </s>
            <s xml:id="echoid-s5442" xml:space="preserve">At in ſecunda tantùm figura, quod reliquum maioris axis ſegmentum
              <lb/>
            E D, vel G D ſit _MAXIMA_ ex E, vel G ducibililium, patet: </s>
            <s xml:id="echoid-s5443" xml:space="preserve">quoniam
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            circulus ex radio H D cadit totus extra Ellipſim A B C D, ſed in
              <note symbol="a" position="left" xlink:label="note-0194-01" xlink:href="note-0194-01a" xml:space="preserve">26. pri-
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              mi huius.</note>
            lo, cuius radius H D, ipſa E D, vel G D eſt _MAXIMA_, cum in ea ſit cir-
              <lb/>
            culi centrum: </s>
            <s xml:id="echoid-s5444" xml:space="preserve">quapropter E D, vel G D eò magis erit _MAXIMA_ ad in-
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            ſcriptam Ellipſim A B C D. </s>
            <s xml:id="echoid-s5445" xml:space="preserve">Quod erat primò, &</s>
            <s xml:id="echoid-s5446" xml:space="preserve">c.</s>
            <s xml:id="echoid-s5447" xml:space="preserve"/>
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            <s xml:id="echoid-s5448" xml:space="preserve">3. </s>
            <s xml:id="echoid-s5449" xml:space="preserve">Iam in tertia figura ſit A B C
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              <figure xlink:label="fig-0194-01" xlink:href="fig-0194-01a" number="154">
                <image file="0194-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0194-01"/>
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            D Ellipſis circa minorem axim
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            B D, in quo infra verticem B
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            ſumptum ſit punctum E, quod
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            à vertice diſtet per interuallum,
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            quod primò ſit æquale dimidio
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            recti lateris axis B D. </s>
            <s xml:id="echoid-s5450" xml:space="preserve">Dico E B
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            eſſe _MAXIMAM_ ex E ducibiliũ
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            ad Ellipſis peripheriam ABCD.</s>
            <s xml:id="echoid-s5451" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5452" xml:space="preserve">Si enim facto centro E, cum
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            radio E B circulus deſcribatur
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            B F, ipſe cadet totus extra
              <note symbol="b" position="left" xlink:label="note-0194-02" xlink:href="note-0194-02a" xml:space="preserve">1. Co-
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              roll. 20. 1.
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              huius.</note>
            lipſim; </s>
            <s xml:id="echoid-s5453" xml:space="preserve">vnde, quæ ex E ad Elli-
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            pſis peripheriam ducẽtur, pręter
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            ad B, minores erunt, quàm quę
              <lb/>
            ex eodem E, ad circuli circum-
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            ſcriptam circumferentiam, hoc
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            eſt minores ipſa E B. </s>
            <s xml:id="echoid-s5454" xml:space="preserve">Quare
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            E B erit _MAXIMA_, &</s>
            <s xml:id="echoid-s5455" xml:space="preserve">c.</s>
            <s xml:id="echoid-s5456" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5457" xml:space="preserve">Si verò diſtantia à vertice B,
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            maior fuerit eodem recti dimi-
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            dio, qualis eſt G B: </s>
            <s xml:id="echoid-s5458" xml:space="preserve">cum ſit in
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            circulo B F, ipſa G B, in qua
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            eſt circuli centrum, _MAXIMA_ ad eius peripheriam ducibilium, eò ma-
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            gis _MAXIMA_ erit ad inſcriptæ Ellipſis peripheriam A B C D.</s>
            <s xml:id="echoid-s5459" xml:space="preserve"/>
          </p>
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            <s xml:id="echoid-s5460" xml:space="preserve">4. </s>
            <s xml:id="echoid-s5461" xml:space="preserve">Quod autem in eadem tertia figura reliquum minoris axis ſegmentum
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            E D, vel G D, ſit _MINIMA_ ex E, vel G ducibilium ad Ellipſis periphe-
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            riam A B C D, ſic manifeſtum fiet.</s>
            <s xml:id="echoid-s5462" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5463" xml:space="preserve">Quoniam circulus ex radio H D cadit totus intra Ellipſim A B C
              <note symbol="c" position="left" xlink:label="note-0194-03" xlink:href="note-0194-03a" xml:space="preserve">26. pri-
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              mi huius.</note>
            ſed ad peripheriam circuli ex radio H D ipſa E D, vel G D eſt _MINIMA_,
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            cum in ea non ſit circuli centrum: </s>
            <s xml:id="echoid-s5464" xml:space="preserve">quare eadem E D, vel G D eò am-
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            pliùs erit _MINIMA_ ducibilium ad eidem circulo circumſcriptam Ellipſis
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            peripheriam A B C D. </s>
            <s xml:id="echoid-s5465" xml:space="preserve">Quod erat vltimò demonſtrandum.</s>
            <s xml:id="echoid-s5466" xml:space="preserve"/>
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        <div xml:id="echoid-div564" type="section" level="1" n="228">
          <head xml:id="echoid-head236" xml:space="preserve">SCHOLIVM.</head>
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            <s xml:id="echoid-s5467" xml:space="preserve">HOC loco animaduertendum eſt, ſemper in Ellipſi circa minorem
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            axim, tertiæ figuræ, interuallum B E ſemi-rectis lateris, omnino
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            excedere minorem ſemi-axim B H, (cum integrum rectum latus excedat
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            integrum minorem axim; </s>
            <s xml:id="echoid-s5468" xml:space="preserve">vt in primo Coroll. </s>
            <s xml:id="echoid-s5469" xml:space="preserve">20. </s>
            <s xml:id="echoid-s5470" xml:space="preserve">primi huius monitum
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            fuit) ac idem punctum E cadere poſſe in quocunq; </s>
            <s xml:id="echoid-s5471" xml:space="preserve">puncto infra H, </s>
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