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">
          <head xml:id="echoid-head94" xml:space="preserve">PROBL. XIV. PROP. XXIX.</head>
          <p>
            <s xml:id="echoid-s1929" xml:space="preserve">Datæ portioni circuli, vel Ellipſis, per eius verticem MAXI-
              <lb/>
            MAM Parabolæ portionem inſcribere; </s>
            <s xml:id="echoid-s1930" xml:space="preserve">& </s>
            <s xml:id="echoid-s1931" xml:space="preserve">è contra.</s>
            <s xml:id="echoid-s1932" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1933" xml:space="preserve">Datæ portioni Parabolæ per eius verticem, cum dato recto,
              <lb/>
            quod excedat rectum datæ Parabolæ, vel cum dato tranſuerſo,
              <lb/>
            quod maius ſit diametro datæ portionis MINIMAM Ellipſis por-
              <lb/>
            tionem circumſcribere.</s>
            <s xml:id="echoid-s1934" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1935" xml:space="preserve">SIt data circuli, aut Ellipſis portio ABC, cuius diameter ſit BE, baſis AC.
              <lb/>
            </s>
            <s xml:id="echoid-s1936" xml:space="preserve">Oporter per eius verticem B, _MAXIMAM_ Parabolæ portionem inſcri-
              <lb/>
            bere.</s>
            <s xml:id="echoid-s1937" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1938" xml:space="preserve">Sit BF tranſuerſum latus dati circuli, vel
              <lb/>
              <figure xlink:label="fig-0080-01" xlink:href="fig-0080-01a" number="50">
                <image file="0080-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0080-01"/>
              </figure>
            Ellipſis, BG rectum, & </s>
            <s xml:id="echoid-s1939" xml:space="preserve">FG regula, cui pro-
              <lb/>
            ducta AE occurrat in H, & </s>
            <s xml:id="echoid-s1940" xml:space="preserve">per H agatur LHI
              <lb/>
            ipſi BF ęquidiſtans, & </s>
            <s xml:id="echoid-s1941" xml:space="preserve">cum recto BI, per ver-
              <lb/>
            ticem B adſcribatur portioni ADBC
              <note symbol="a" position="left" xlink:label="note-0080-01" xlink:href="note-0080-01a" xml:space="preserve">5. huius.</note>
            bole AMBC, quæ per extrema A, C
              <note symbol="b" position="left" xlink:label="note-0080-02" xlink:href="note-0080-02a" xml:space="preserve">1. Co-
                <lb/>
              roll. 19. h.</note>
            ſibit, ac datæ portioni ſupra baſim AC erit
              <lb/>
            inſcripta, & </s>
            <s xml:id="echoid-s1942" xml:space="preserve">erit _MAXIMA_: </s>
            <s xml:id="echoid-s1943" xml:space="preserve">quoniam, quæ
              <lb/>
            adſcribitur cum recto, quod minus ſit BI mi-
              <lb/>
            nor eſt ipſa AMBC, quæ verò cum
              <note symbol="c" position="left" xlink:label="note-0080-03" xlink:href="note-0080-03a" xml:space="preserve">2. Co-
                <lb/>
              roll. prop.
                <lb/>
              19. huius.</note>
            quod excedat BI, veltota cadit extra Ellipſis
              <lb/>
            portionem ADB, ſinempe eius rectum
              <note symbol="d" position="left" xlink:label="note-0080-04" xlink:href="note-0080-04a" xml:space="preserve">20. h.</note>
            idem cum recto BG, & </s>
            <s xml:id="echoid-s1944" xml:space="preserve">eo magis ſi ipſum ex-
              <lb/>
            cedat; </s>
            <s xml:id="echoid-s1945" xml:space="preserve">vel ad minus ſecat datam portionem ſupra baſim AC, ſi Parabolę re-
              <lb/>
            ctum cadat inter I, & </s>
            <s xml:id="echoid-s1946" xml:space="preserve">G, vt in N. </s>
            <s xml:id="echoid-s1947" xml:space="preserve">Nam eius regula ex N ducta
              <note symbol="e" position="left" xlink:label="note-0080-05" xlink:href="note-0080-05a" xml:space="preserve">1. Co-
                <lb/>
              roll. 19. h.</note>
            ter ipſi IH omninò ſecat Ellipſis regulam HG ſupra baſim AC. </s>
            <s xml:id="echoid-s1948" xml:space="preserve">Quare Pa-
              <lb/>
            rabolæ portio AMBC eſt _MAXIMA_ inſcripta quæſita. </s>
            <s xml:id="echoid-s1949" xml:space="preserve">Quod primò, &</s>
            <s xml:id="echoid-s1950" xml:space="preserve">c.</s>
            <s xml:id="echoid-s1951" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1952" xml:space="preserve">Iam ſit data Parabolæ portio AMBC, cuius rectum BI, regula IL, diame-
              <lb/>
            ter BE, baſis AC, & </s>
            <s xml:id="echoid-s1953" xml:space="preserve">per eius verticem B oporteat _MINIMAM_ Ellipſis por-
              <lb/>
            tionem ei circumſcribere cum dato recto BG, quod excedat rectum datæ
              <lb/>
            portionis.</s>
            <s xml:id="echoid-s1954" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1955" xml:space="preserve">Conueniat applicata AE cum regula IL in H, iunctaq; </s>
            <s xml:id="echoid-s1956" xml:space="preserve">GH, & </s>
            <s xml:id="echoid-s1957" xml:space="preserve">producta,
              <lb/>
            occurrat portionis diametro in F (ſecans enim vnam parallelarum IH, ſecat
              <lb/>
            alteram BE:) </s>
            <s xml:id="echoid-s1958" xml:space="preserve">cum tranſuerſo autem BF, ac dato recto BG adſcribatur
              <note symbol="f" position="left" xlink:label="note-0080-06" xlink:href="note-0080-06a" xml:space="preserve">7. huius.</note>
            B Ellipſis ADBC, quæ datę Parabolæ AMB occurret in A, & </s>
            <s xml:id="echoid-s1959" xml:space="preserve">C, & </s>
            <s xml:id="echoid-s1960" xml:space="preserve">
              <note symbol="g" position="left" xlink:label="note-0080-07" xlink:href="note-0080-07a" xml:space="preserve">1. Co-
                <lb/>
              roll. prop.
                <lb/>
              19. huius.</note>
            circumſcripta, quàm dico eſſe _MINIMAM_. </s>
            <s xml:id="echoid-s1961" xml:space="preserve">Nam Ellipſis quæ adſcribitur
              <lb/>
            per B, cum eodem recto BG, ſed cum tranſuerſo, quod excedat BF, maior
              <lb/>
            eſt ipſa ADB; </s>
            <s xml:id="echoid-s1962" xml:space="preserve">quæ verò adſcribitur cum tranſuerſo, quod minus ſit
              <note symbol="h" position="left" xlink:label="note-0080-08" xlink:href="note-0080-08a" xml:space="preserve">4. Co-
                <lb/>
              roll. prop.
                <lb/>
              19. huius.</note>
            BF, eſt quidem minor eadem ADB, ſed omnino ſecat Parabolen
              <note symbol="i" position="left" xlink:label="note-0080-09" xlink:href="note-0080-09a" xml:space="preserve">ibidem.</note>
            ſupra baſim AC, cum & </s>
            <s xml:id="echoid-s1963" xml:space="preserve">ipſarum regulę ſe mutuò ſecent ſupra eandem AC.</s>
            <s xml:id="echoid-s1964" xml:space="preserve">
              <note symbol="l" position="left" xlink:label="note-0080-10" xlink:href="note-0080-10a" xml:space="preserve">1. Corol.
                <lb/>
              19. huius.</note>
            Quare Ellipſis portio ADBC eſt _MINIMA_ circumſcripta quæſita cum dato
              <lb/>
            recto BG. </s>
            <s xml:id="echoid-s1965" xml:space="preserve">Quod ſecundò, &</s>
            <s xml:id="echoid-s1966" xml:space="preserve">c.</s>
            <s xml:id="echoid-s1967" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1968" xml:space="preserve">Sit tandem circumſcribenda datæ portioni Parabolicæ AMB </s>
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