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

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        <div xml:id="echoid-div124" type="section" level="1" n="75">
          <head xml:id="echoid-head80" xml:space="preserve">PROBL. VI. PROP. XX.</head>
          <p>
            <s xml:id="echoid-s1487" xml:space="preserve">Datæ coni ſectioni, vel circulo, per eius verticem, cum dato
              <lb/>
            tranſuerſo latere, quod in Ellipſi, vel circulo non excedat eius
              <lb/>
            tranſuerſum, MAXIMAM Ellipſim inſcribere, & </s>
            <s xml:id="echoid-s1488" xml:space="preserve">è contra.</s>
            <s xml:id="echoid-s1489" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1490" xml:space="preserve">DAtæ Ellipſi, vel circulo, per eius verticem _MINIMAM_ coni-ſectionem
              <lb/>
            circumſcribere cum dato, pro circumſcribenda Hyperbola, quocunq;
              <lb/>
            </s>
            <s xml:id="echoid-s1491" xml:space="preserve">tranſuerſo latere, pro Ellipſi verò, cum tranſuerſo dato, quod maius ſit tranſ-
              <lb/>
            uerſo datæ Ellipſis, vel circuli.</s>
            <s xml:id="echoid-s1492" xml:space="preserve"/>
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          <figure number="38">
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            <s xml:id="echoid-s1493" xml:space="preserve">Sit quælibet coni-ſectio, vel circulus ABC, cuius diameter BD, latus
              <lb/>
            rectum BE, regula EF; </s>
            <s xml:id="echoid-s1494" xml:space="preserve">oportet circa diametri ſegmentum BG per verticem
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            B _MAXIMAM_ Ellipſin inſcribere.</s>
            <s xml:id="echoid-s1495" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s1496" xml:space="preserve">Adſcribatur ſectioni ABC per eius verticem, & </s>
            <s xml:id="echoid-s1497" xml:space="preserve">circa diametrum
              <note symbol="a" position="left" xlink:label="note-0066-01" xlink:href="note-0066-01a" xml:space="preserve">7. huius.</note>
            cum recto BE Ellipſis GHB. </s>
            <s xml:id="echoid-s1498" xml:space="preserve">Dico hanc eſſe _MAXIMAM_ quæſitam.</s>
            <s xml:id="echoid-s1499" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s1500" xml:space="preserve">Nam iuncta ipſius regula GE, cum hæc diſiunctim procedat à regula EF,
              <lb/>
            ſitque propior diametro, Ellipſis quoq; </s>
            <s xml:id="echoid-s1501" xml:space="preserve">GHB inſcripta erit ſectioni
              <note symbol="b" position="left" xlink:label="note-0066-02" xlink:href="note-0066-02a" xml:space="preserve">1. Co-
                <lb/>
              roll. prop.
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              19. huius.</note>
            & </s>
            <s xml:id="echoid-s1502" xml:space="preserve">erit _MAXIMA_ inſcriptibilium: </s>
            <s xml:id="echoid-s1503" xml:space="preserve">quoniam quæcunque Ellipſis cum eadem
              <lb/>
            tranſuerſa diametro BG adſcripta, & </s>
            <s xml:id="echoid-s1504" xml:space="preserve">cum recto BI, quod minus ſit recto BE
              <lb/>
            minor eſt Ellipſi GBH, quælibet verò Ellipſis eidem diametro BG
              <note symbol="c" position="left" xlink:label="note-0066-03" xlink:href="note-0066-03a" xml:space="preserve">2. Co-
                <lb/>
              roll. prop.
                <lb/>
              19. huius.</note>
            pta cum recto BL, quod maius ſit dato recto BE maior eſt quidem
              <note symbol="d" position="left" xlink:label="note-0066-04" xlink:href="note-0066-04a" xml:space="preserve">2. Co-
                <lb/>
              roll. prop.
                <lb/>
              19. huius.</note>
            GHB, ſed omnino _e_ ſecat ſectionem ABC, cum eius regula GL ſecet ſectio-
              <lb/>
            nis regulam EL, infra contingentem BE. </s>
            <s xml:id="echoid-s1505" xml:space="preserve">Vnde Ellipſis GHB eſt _MAXIMA_.
              <lb/>
            </s>
            <s xml:id="echoid-s1506" xml:space="preserve">Quod primò, &</s>
            <s xml:id="echoid-s1507" xml:space="preserve">c.</s>
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