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

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        <div xml:id="echoid-div164" type="section" level="1" n="87">
          <head xml:id="echoid-head92" xml:space="preserve">PROBL. XII. PROP. XXVII.</head>
          <p>
            <s xml:id="echoid-s1811" xml:space="preserve">Datæ portioni Parabolæ, cum dato quocunque tranſuerſo late-
              <lb/>
            re, vel cum dato recto, quod ſit minus recto datæ Parabolæ, per
              <lb/>
            eius verticem MAXIMAM Hyperbolæ portionem inſcribere; </s>
            <s xml:id="echoid-s1812" xml:space="preserve">& </s>
            <s xml:id="echoid-s1813" xml:space="preserve">
              <lb/>
            è contra.</s>
            <s xml:id="echoid-s1814" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1815" xml:space="preserve">Datæ portioni Hyperbolæ, per eius verticem MINIMAM Pa-
              <lb/>
            rabolæ portionem circumſcribere.</s>
            <s xml:id="echoid-s1816" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1817" xml:space="preserve">SIt data Parabolę portio ABCDE, cuius rectum CF, regula FG, baſis AE,
              <lb/>
            diameter CI, & </s>
            <s xml:id="echoid-s1818" xml:space="preserve">oporteat primùm cum dato quocunque tranſuerſo CH
              <lb/>
            _MAXIMAM_ Hyperbolæ portionem inſcribere.</s>
            <s xml:id="echoid-s1819" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1820" xml:space="preserve">Producatur applicata AI vſque ad occurſum
              <lb/>
              <figure xlink:label="fig-0077-01" xlink:href="fig-0077-01a" number="47">
                <image file="0077-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0077-01"/>
              </figure>
            cum regula in G, & </s>
            <s xml:id="echoid-s1821" xml:space="preserve">iungatur HG, ſecans CF in
              <lb/>
            L, & </s>
            <s xml:id="echoid-s1822" xml:space="preserve">cum tranſuerſo CH, rectoque CL adſcriba-
              <lb/>
            tur portioni ABCDE per verticem C
              <note symbol="a" position="right" xlink:label="note-0077-01" xlink:href="note-0077-01a" xml:space="preserve">6. huius.</note>
            bole AMCNE, quæ Parabolen ABCDE ſecabit
              <lb/>
            in A, & </s>
            <s xml:id="echoid-s1823" xml:space="preserve">E (cum & </s>
            <s xml:id="echoid-s1824" xml:space="preserve">ipſarum regulæ ſe mutuò
              <note symbol="b" position="right" xlink:label="note-0077-02" xlink:href="note-0077-02a" xml:space="preserve">1. Co-
                <lb/>
              roll. prop.
                <lb/>
              19. huius.</note>
            in occurſu eiuſdem communis applicatæ AE) & </s>
            <s xml:id="echoid-s1825" xml:space="preserve">
              <lb/>
            ſupra baſim AE erit datæ Parabolę inſcripta. </s>
            <s xml:id="echoid-s1826" xml:space="preserve">Iam
              <lb/>
            dico hanc portionem AMCNE eſſe _MAXIMAM_
              <lb/>
            quæſitam.</s>
            <s xml:id="echoid-s1827" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1828" xml:space="preserve">Quoniam quælibet alia Hyperbole adſcripta
              <lb/>
            cum eodem tranſuerſo CH, ſed cum recto, quod
              <lb/>
            minus ſit recto CL, minor eſt ipſa
              <note symbol="c" position="right" xlink:label="note-0077-03" xlink:href="note-0077-03a" xml:space="preserve">2. Co-
                <lb/>
              roll. prop.
                <lb/>
              19. huius.</note>
            quælibet verò adſcripta cum recto, quod excedat CL, eſt quidem
              <note symbol="d" position="right" xlink:label="note-0077-04" xlink:href="note-0077-04a" xml:space="preserve">ibidem.</note>
            ipſa AMCNE, ſed veltota cadit extra ABCDE, cum Hyperbole, cuius re-
              <lb/>
            gula ſit quæ ducitur per H & </s>
            <s xml:id="echoid-s1829" xml:space="preserve">F ſit circumſcripta Parabolæ ABC, & </s>
            <s xml:id="echoid-s1830" xml:space="preserve">eò
              <note symbol="e" position="right" xlink:label="note-0077-05" xlink:href="note-0077-05a" xml:space="preserve">21. h.</note>
            gis, quæ cum recto CO maiore ipſo CF; </s>
            <s xml:id="echoid-s1831" xml:space="preserve">vel ſaltem ſecat Parabolen
              <note symbol="f" position="right" xlink:label="note-0077-06" xlink:href="note-0077-06a" xml:space="preserve">2. Co-
                <lb/>
              roll. prop.
                <lb/>
              19. huius.</note>
            ſupra portionis baſim AE, cum quælibet regula ducta ex H inter L, & </s>
            <s xml:id="echoid-s1832" xml:space="preserve">F, vt
              <lb/>
            per P, & </s>
            <s xml:id="echoid-s1833" xml:space="preserve">infra contingentem CF producta, ſecet regulam FG inter ipſam
              <lb/>
            contingentem, & </s>
            <s xml:id="echoid-s1834" xml:space="preserve">applicatam AEG. </s>
            <s xml:id="echoid-s1835" xml:space="preserve">Quare talis Hyperbolæ portio AMC-
              <lb/>
            NE eſt _MAXIMA_ inſcripta quæſita cũ dato tranſuerſo CH. </s>
            <s xml:id="echoid-s1836" xml:space="preserve">Quod primò, &</s>
            <s xml:id="echoid-s1837" xml:space="preserve">c.</s>
            <s xml:id="echoid-s1838" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1839" xml:space="preserve">Si verò inſcribenda ſit _MAXIMA_ Hyperbolæ portio cum dato recto CL,
              <lb/>
            quod minus ſit recto Parabolæ CF, (nam cum æquali, vel maiori ſemper eſ-
              <lb/>
            ſet circumſcripta) iungatur GL, & </s>
            <s xml:id="echoid-s1840" xml:space="preserve">producatur, ipſa productam diametrum
              <lb/>
            IC ſecabit in H, cum eadem ſecet FG alteram Parallelarum ipſi diametro;
              <lb/>
            </s>
            <s xml:id="echoid-s1841" xml:space="preserve">& </s>
            <s xml:id="echoid-s1842" xml:space="preserve">cum tranſuerſo HC, rectoque CL adſcribatur per C Hyperbole
              <note symbol="g" position="right" xlink:label="note-0077-07" xlink:href="note-0077-07a" xml:space="preserve">6. huius.</note>
            NE, quæ ſecabit, vt ſupra, Parabolen ABCDE in A, & </s>
            <s xml:id="echoid-s1843" xml:space="preserve">E, eique erit
              <note symbol="h" position="right" xlink:label="note-0077-08" xlink:href="note-0077-08a" xml:space="preserve">1. Co-
                <lb/>
              roll. prop.
                <lb/>
              19. huius.</note>
            ſcripta, eritque _MAXIMA_. </s>
            <s xml:id="echoid-s1844" xml:space="preserve">Nam quæ cum eodem recto CL, ſed cum tranſ-
              <lb/>
            uerſo, quod excedat CH, minor eſt ipſa AMCNE; </s>
            <s xml:id="echoid-s1845" xml:space="preserve">quæ verò cum
              <note symbol="i" position="right" xlink:label="note-0077-09" xlink:href="note-0077-09a" xml:space="preserve">3. Corol.
                <lb/>
              19. huius.</note>
            uerſo CQ minore ipſo CH, eſt quidem maior Hyperbola AMCNE,
              <note symbol="l" position="right" xlink:label="note-0077-10" xlink:href="note-0077-10a" xml:space="preserve">ibidem.</note>
            omnino ſecat Parabolen ABCDE ſupra baſim AE, cum & </s>
            <s xml:id="echoid-s1846" xml:space="preserve">eius regula
              <note symbol="m" position="right" xlink:label="note-0077-11" xlink:href="note-0077-11a" xml:space="preserve">3. Co-
                <lb/>
              rol. 19. h.</note>
            infra contingentem producta, ſecet regulam FG ſupra eandem applicatam.
              <lb/>
            </s>
            <s xml:id="echoid-s1847" xml:space="preserve">Quare huiuſmodi portio Hyperbolæ AMCNE eſt _MAXIMA_ inſcripta </s>
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