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

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        <div xml:id="echoid-div178" type="section" level="1" n="89">
          <p>
            <s xml:id="echoid-s1968" xml:space="preserve">
              <pb o="57" file="0081" n="81" rhead=""/>
            Ellipſis portio per verticem B, cum dato tranſuerſo BF, excedent, diame-
              <lb/>
            trum BE.</s>
            <s xml:id="echoid-s1969" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1970" xml:space="preserve">Iungatur FH, & </s>
            <s xml:id="echoid-s1971" xml:space="preserve">producatur, contingentem BI ſecans in G, & </s>
            <s xml:id="echoid-s1972" xml:space="preserve">cum dato
              <lb/>
            tranſuerſo BF, ac recto BG adſcribatur per B Ellipſis portio ADBC,
              <note symbol="a" position="right" xlink:label="note-0081-01" xlink:href="note-0081-01a" xml:space="preserve">7. huius.</note>
            item datæ portioni AMB occurret in punctis A, C eritque circumſcripta:</s>
            <s xml:id="echoid-s1973" xml:space="preserve">
              <note symbol="b" position="right" xlink:label="note-0081-02" xlink:href="note-0081-02a" xml:space="preserve">1. Co-
                <lb/>
              roll. prop.
                <lb/>
              19. huius.</note>
            Nam quæ cum eodem tranſuerſo BF adſcribitur, ſed cum recto maiore ipſo
              <lb/>
            BG eſt quoque maior Ellipſi ADB; </s>
            <s xml:id="echoid-s1974" xml:space="preserve">quæ verò cum recto, quod deficiat à BG eſt quidem minor ipſa ADB, ſed vel tota cadit intra AMB, quãdo re-
              <note symbol="c" position="right" xlink:label="note-0081-03" xlink:href="note-0081-03a" xml:space="preserve">4. Co-
                <lb/>
              roll. prop.
                <lb/>
              19. huius.</note>
            ctum Ellipſis idem fuerit cum recto Parabolæ BI, & </s>
            <s xml:id="echoid-s1975" xml:space="preserve">eò magis cum fuerit minus; </s>
            <s xml:id="echoid-s1976" xml:space="preserve">vel ſaltem ſecat Parabolen AMBC ſupra applicatam AC, cum
              <note symbol="d" position="right" xlink:label="note-0081-04" xlink:href="note-0081-04a" xml:space="preserve">ibidem.</note>
            ctum cadat inter BI, & </s>
            <s xml:id="echoid-s1977" xml:space="preserve">BG, quale eſt BN; </s>
            <s xml:id="echoid-s1978" xml:space="preserve">nam iuncta regula FN ſecat om-
              <lb/>
              <note symbol="e" position="right" xlink:label="note-0081-05" xlink:href="note-0081-05a" xml:space="preserve">20. h.</note>
            nino regulam IH ſupra eandem AC. </s>
            <s xml:id="echoid-s1979" xml:space="preserve">Quare huiuſmodi portio Elliptica
              <lb/>
              <note symbol="f" position="right" xlink:label="note-0081-06" xlink:href="note-0081-06a" xml:space="preserve">1. Co-
                <lb/>
              roll. prop.
                <lb/>
              19. huius.</note>
            ADBC, eſt _MINIMA_ circumſcripta quæſita cum dato tranſuerſo BF. </s>
            <s xml:id="echoid-s1980" xml:space="preserve">Quod
              <lb/>
            tandem erat faciendum.</s>
            <s xml:id="echoid-s1981" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div182" type="section" level="1" n="90">
          <head xml:id="echoid-head95" xml:space="preserve">PROBL. XV. PROP. XXX.</head>
          <p>
            <s xml:id="echoid-s1982" xml:space="preserve">Datæ portioni circuli, vel Ellipſis, cum dato quocunque tranſ-
              <lb/>
            uerſo latere, vel cum dato recto, quod minus ſit latitudine ſemi-ap-
              <lb/>
            plicatæ baſis portionis, per eius verticem MAXIMAM Hyperbo-
              <lb/>
            lę portionem inſcribere; </s>
            <s xml:id="echoid-s1983" xml:space="preserve">& </s>
            <s xml:id="echoid-s1984" xml:space="preserve">è contra.</s>
            <s xml:id="echoid-s1985" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1986" xml:space="preserve">Datæ portioni Hyperbolæ, cum dato quocunque tranſuerſo la-
              <lb/>
            tere, quod maius ſit diametro datæ portionis, vel cum dato recto,
              <lb/>
            quod excedat prædictam latitudinem, per eius verticem MINI-
              <lb/>
            MAM Ellipſis portionem circumſcribere.</s>
            <s xml:id="echoid-s1987" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1988" xml:space="preserve">SIt data circuli, aut Ellipſis portio AB-
              <lb/>
              <figure xlink:label="fig-0081-01" xlink:href="fig-0081-01a" number="51">
                <image file="0081-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0081-01"/>
              </figure>
            CD, cui is diameter CE, baſis AD,
              <lb/>
            tranſuerſum latus CE, rectum CG, & </s>
            <s xml:id="echoid-s1989" xml:space="preserve">re-
              <lb/>
            gula F G. </s>
            <s xml:id="echoid-s1990" xml:space="preserve">Oportet per eius verticem C,
              <lb/>
            cum dato quocunque tranſuerſo CI _MA-_
              <lb/>
            _XIMAM_ Hyperbolę portionem inſcribere.</s>
            <s xml:id="echoid-s1991" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1992" xml:space="preserve">Producatur AE, vſq; </s>
            <s xml:id="echoid-s1993" xml:space="preserve">ad occurſum cum
              <lb/>
            regula FG in L, & </s>
            <s xml:id="echoid-s1994" xml:space="preserve">iungatur IL contingen-
              <lb/>
            tem CG ſecans in M, & </s>
            <s xml:id="echoid-s1995" xml:space="preserve">cum dato tranſ-
              <lb/>
            uerſo CI, ac recto CM adſcribatur per
              <note symbol="a" position="right" xlink:label="note-0081-07" xlink:href="note-0081-07a" xml:space="preserve">6. huius.</note>
            Hyperbolæ portio ANCD, quæ datæ por-
              <lb/>
            tion; </s>
            <s xml:id="echoid-s1996" xml:space="preserve">ABCD occurret in A, & </s>
            <s xml:id="echoid-s1997" xml:space="preserve">D, eritq; </s>
            <s xml:id="echoid-s1998" xml:space="preserve">
              <note symbol="b" position="right" xlink:label="note-0081-08" xlink:href="note-0081-08a" xml:space="preserve">1. Co-
                <lb/>
              roll prop.
                <lb/>
              19. huius.</note>
            inſcripta; </s>
            <s xml:id="echoid-s1999" xml:space="preserve">quàm dico eſſe _MAXIMAM_: </s>
            <s xml:id="echoid-s2000" xml:space="preserve">nã
              <lb/>
            quę adſcribitur cum eodem tranſuerſo CI,
              <lb/>
            ſed cum recto minore ipſo CM, eſt quoq;
              <lb/>
            </s>
            <s xml:id="echoid-s2001" xml:space="preserve">minor Hyperbola ANCD, quę verò
              <note symbol="c" position="right" xlink:label="note-0081-09" xlink:href="note-0081-09a" xml:space="preserve">2. corol.
                <lb/>
              prop. 19.
                <lb/>
              huius.</note>
            recto maiore CM, veltota cadit extra da-
              <lb/>
            tam Ellipſim ABCD, quando
              <note symbol="d" position="right" xlink:label="note-0081-10" xlink:href="note-0081-10a" xml:space="preserve">20. h.</note>
            eius rectum latus æquet ipſum CG, & </s>
            <s xml:id="echoid-s2002" xml:space="preserve">eò magis ſi rectum excedat CG; </s>
            <s xml:id="echoid-s2003" xml:space="preserve"/>
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