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

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        <div xml:id="echoid-div131" type="section" level="1" n="77">
          <head xml:id="echoid-head82" xml:space="preserve">COROLL. II.</head>
          <p>
            <s xml:id="echoid-s1548" xml:space="preserve">PAtet etiam quomodo datæ coni-ſectioni, vel circulo ABC per ipſius
              <lb/>
            verticem inſcribi poſſit Ellipſis, que ſit _MAXIMA_ circa idem tranſuer-
              <lb/>
            ſum, & </s>
            <s xml:id="echoid-s1549" xml:space="preserve">ipſius rectum latus ad verſum in Parabola, vel Hyperbola datam
              <lb/>
            quamcumque teneat rationem; </s>
            <s xml:id="echoid-s1550" xml:space="preserve">& </s>
            <s xml:id="echoid-s1551" xml:space="preserve">in Ellipſi, vel circulo data ratio non ſit
              <lb/>
            minor ratione recti BE, ad tranſuerſum BD.</s>
            <s xml:id="echoid-s1552" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1553" xml:space="preserve">Nam ſi exempli gratia Parabolæ, vel Hyperbolæ primæ, ac ſecundæ figu-
              <lb/>
            ræ inſcribenda ſit _MAXIMA_ Ellipſis circa idem tranſuerſum latus, & </s>
            <s xml:id="echoid-s1554" xml:space="preserve">cuius
              <lb/>
            rectum ad verſum datam habeat rationem, R nempe ad S: </s>
            <s xml:id="echoid-s1555" xml:space="preserve">fiat vt R ad S, ita
              <lb/>
            rectum EB datæ ſectionis ad BG, nam ſi cum eodem recto EB, ac tranſuerſo
              <lb/>
            BG adſcribatur per B Ellipſis GHB, ipſa erit _MAXIMA_ circa idem tranſ-
              <lb/>
            uerſum BG, per ea, quæ ſuperius demonſtrata fuerunt. </s>
            <s xml:id="echoid-s1556" xml:space="preserve">Siverò data ratio R
              <lb/>
            ad S non ſit minor ratione recti EB ad tranſuerſum BD; </s>
            <s xml:id="echoid-s1557" xml:space="preserve">in tertia, quarta, & </s>
            <s xml:id="echoid-s1558" xml:space="preserve">
              <lb/>
            quinta figura, fiat vt R ad S, ita EB ad BG, quod erit tranſuerſum quæſitæ
              <lb/>
            inſcriptæ Ellipſis, quæ erit _MAXIMA_, &</s>
            <s xml:id="echoid-s1559" xml:space="preserve">c.</s>
            <s xml:id="echoid-s1560" xml:space="preserve"/>
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        <div xml:id="echoid-div132" type="section" level="1" n="78">
          <head xml:id="echoid-head83" xml:space="preserve">PROBL. VII. PROP. XXI.</head>
          <p>
            <s xml:id="echoid-s1561" xml:space="preserve">Datæ Hyperbolæ, per eius verticem MAXIMAM Parabolen
              <lb/>
            inſcribere, & </s>
            <s xml:id="echoid-s1562" xml:space="preserve">è contra.</s>
            <s xml:id="echoid-s1563" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1564" xml:space="preserve">Per verticem datæ Parabolæ, cum dato tranſuerſo latere MINI-
              <lb/>
            MAM Hyperbolen circumſcribere.</s>
            <s xml:id="echoid-s1565" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1566" xml:space="preserve">SIt data Hyperbole ABC, cuius vertex B, diameter BD, tranſuerſum la-
              <lb/>
            tus BE, rectum BF, & </s>
            <s xml:id="echoid-s1567" xml:space="preserve">regula EFO oportet primùm per eius verticem B
              <lb/>
            _MAXIMAM_ Parabolen inſcribere.</s>
            <s xml:id="echoid-s1568" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1569" xml:space="preserve">Adſcribatur Hyperbolæ
              <note symbol="a" position="left" xlink:label="note-0068-01" xlink:href="note-0068-01a" xml:space="preserve">5. prop.
                <lb/>
              huius.</note>
              <figure xlink:label="fig-0068-01" xlink:href="fig-0068-01a" number="39">
                <image file="0068-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0068-01"/>
              </figure>
            per verticem B, & </s>
            <s xml:id="echoid-s1570" xml:space="preserve">cum recto BF Pa-
              <lb/>
            rabole GBH. </s>
            <s xml:id="echoid-s1571" xml:space="preserve">Dico hanc eſſe _MAXI_-
              <lb/>
            _MAM_ quæſitam.</s>
            <s xml:id="echoid-s1572" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1573" xml:space="preserve">Ducta enim ex F Parabolæ regula
              <lb/>
            FI, cum hæc infra contingentem BF,
              <lb/>
            regulę EFO, nunquam occurat, (cum
              <lb/>
            ſimul conueniãt in F) ſitque regula FI
              <lb/>
            propinquior diametro BD quam pro-
              <lb/>
            ducta regula FO, erit Parabole
              <note symbol="b" position="left" xlink:label="note-0068-02" xlink:href="note-0068-02a" xml:space="preserve">3. Co-
                <lb/>
              roll. prop.
                <lb/>
              19. huius.</note>
            datę Hyperbolę ABC inſcripta, eritq;
              <lb/>
            </s>
            <s xml:id="echoid-s1574" xml:space="preserve">_MAXIMA_: </s>
            <s xml:id="echoid-s1575" xml:space="preserve">quoniam quælibet alia
              <lb/>
            Parabole ipſi ABC per verticem B
              <lb/>
            adſcripta cum recto BL, quod minus
              <lb/>
            ſit recto BF datę Hyperbolæ,
              <note symbol="c" position="left" xlink:label="note-0068-03" xlink:href="note-0068-03a" xml:space="preserve">2. Co-
                <lb/>
              roll. prop.
                <lb/>
              19. huius.</note>
            eſt Parabola GBH, quælibet verò ad-
              <lb/>
            ſcripta cum recto BM, quod excedat
              <lb/>
            rectum BF datę Hyperbolæ ipſa </s>
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