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

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        <div xml:id="echoid-div944" type="section" level="1" n="378">
          <head xml:id="echoid-head387" xml:space="preserve">PROBL. XX. PROP. C.</head>
          <p>
            <s xml:id="echoid-s9067" xml:space="preserve">In dato quocunque Cono ſcaleno, MAXIMAM MAXIMA-
              <lb/>
            RVM, & </s>
            <s xml:id="echoid-s9068" xml:space="preserve">MAXIMARVM MINIMAM Parabolæ portionem
              <lb/>
            aſſignare.</s>
            <s xml:id="echoid-s9069" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9070" xml:space="preserve">ESto Conus ſcalenus A B C, cuius vertex B, baſis B C, centrum D.
              <lb/>
            </s>
            <s xml:id="echoid-s9071" xml:space="preserve">Oportet inter _MAXIMAS._ </s>
            <s xml:id="echoid-s9072" xml:space="preserve">Parabolas, & </s>
            <s xml:id="echoid-s9073" xml:space="preserve">_MAXIMAM_, & </s>
            <s xml:id="echoid-s9074" xml:space="preserve">_MINIMAM_
              <lb/>
            aſſignare.</s>
            <s xml:id="echoid-s9075" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9076" xml:space="preserve">Secetur Conus plano per axem, & </s>
            <s xml:id="echoid-s9077" xml:space="preserve">ad baſim erecto, efficiente triangulum
              <lb/>
            A B C. </s>
            <s xml:id="echoid-s9078" xml:space="preserve">Patet alterum ipſius laterum, vt puta B A eſſe _MAXIMVM_,
              <note symbol="a" position="left" xlink:label="note-0326-01" xlink:href="note-0326-01a" xml:space="preserve">15. ſec.
                <lb/>
              Sereni.</note>
            rum verò B C _MINIMVM._</s>
            <s xml:id="echoid-s9079" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9080" xml:space="preserve">Radius D A ad partes _MAXIMI_ lateris ſecetur bifariam in E, ita vt C
              <lb/>
            E ſit tripla ad E A; </s>
            <s xml:id="echoid-s9081" xml:space="preserve">& </s>
            <s xml:id="echoid-s9082" xml:space="preserve">per E iuxta regulam _MAXIMI_ lateris B A concipia-
              <lb/>
              <note symbol="b" position="left" xlink:label="note-0326-02" xlink:href="note-0326-02a" xml:space="preserve">96. h.</note>
            tur ductum planum efficiens Parabolen: </s>
            <s xml:id="echoid-s9083" xml:space="preserve">patet hanc eſſe _MAXIMAM_ iuxta idem latus B A, quam dico eſſe quoque _MAXIMARVM MAXIMAM,_ vbi-
              <lb/>
            cunque cadat punctum H veſtigium verticis.</s>
            <s xml:id="echoid-s9084" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9085" xml:space="preserve">Nam _MAXIMA_ Parabole, ducta per E iuxta latus B A, ad quamlibet
              <lb/>
            aliam _MAXIMAM_ Parabolen iuxta aliud quodcunque latus, nempe iuxta
              <lb/>
            B F (cum ipſæ ſint æqualium baſium) eſt homologè, vt altitudo vnius
              <note symbol="c" position="left" xlink:label="note-0326-03" xlink:href="note-0326-03a" xml:space="preserve">Coroll.
                <lb/>
              96. h.</note>
            altitudinem alterius, ſed altitudo ad altitudinem eſt vt perpendicularis
              <note symbol="d" position="left" xlink:label="note-0326-04" xlink:href="note-0326-04a" xml:space="preserve">15. pri-
                <lb/>
              mi h.</note>
              <note symbol="e" position="left" xlink:label="note-0326-05" xlink:href="note-0326-05a" xml:space="preserve">99. h.</note>
            B ſuper contingentem circuli B C peripheriam ad punctum A, quæ
              <note symbol="f" position="left" xlink:label="note-0326-06" xlink:href="note-0326-06a" xml:space="preserve">1. Co-
                <lb/>
              roll. 98. h.</note>
            ipſum latus B A, ad perpendicularem ex B ſuper contingentem ad pun-
              <lb/>
            ctum F, atque perpendicularis B A maior eſt perpendiculari ex B ſuper
              <lb/>
            contingentem ad F, cum ipſa B A ſit earundem perpendicularium
              <note symbol="g" position="left" xlink:label="note-0326-07" xlink:href="note-0326-07a" xml:space="preserve">98. h. ad
                <lb/>
              num. 1.</note>
            _MA,_ ergo, & </s>
            <s xml:id="echoid-s9086" xml:space="preserve">_MAXIMA_ Parabole ducta per E iuxta latus B A erit maior
              <lb/>
            _MAXIMA_ Parabola ducta iuxta latus B F, & </s>
            <s xml:id="echoid-s9087" xml:space="preserve">hoc ſemper, vnde ipſa ducta
              <lb/>
            per E iuxta _MAXIMVM_ Coni latus B A, erit _MAXIMARVM MAXIMA:_
              <lb/>
            </s>
            <s xml:id="echoid-s9088" xml:space="preserve">quod primò erat, &</s>
            <s xml:id="echoid-s9089" xml:space="preserve">c.</s>
            <s xml:id="echoid-s9090" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9091" xml:space="preserve">Præterea ſi H veſtigium verticis B ce-
              <lb/>
              <figure xlink:label="fig-0326-01" xlink:href="fig-0326-01a" number="259">
                <image file="0326-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0326-01"/>
              </figure>
            ciderit, vel intra circulum B C, vel in ip-
              <lb/>
            ſius peripheria: </s>
            <s xml:id="echoid-s9092" xml:space="preserve">ſecto radio D C, (qui eſt
              <lb/>
            ad partem _MINIMI_ lateris B C Coni A
              <lb/>
            B C) bifariam in G, & </s>
            <s xml:id="echoid-s9093" xml:space="preserve">per ipſum ducto
              <lb/>
            plano iuxta regulam lateris B C efficiente
              <lb/>
              <note symbol="h" position="left" xlink:label="note-0326-08" xlink:href="note-0326-08a" xml:space="preserve">96. h.</note>
            _MAXIMA_ Parabola. </s>
            <s xml:id="echoid-s9094" xml:space="preserve">Dico hanc eſſe _MAXIMARVM, MINIMAM_ quæſitam.</s>
            <s xml:id="echoid-s9095" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9096" xml:space="preserve">Etenim _MAXIMA_ Parabole per G iux-
              <lb/>
            ta latus B C, ad quamcumque aliam _MA_-
              <lb/>
            _XIMAM_ iuxta quodcunque aliud latus B
              <lb/>
            F, eſt homologè vt altitudo vnius ad
              <note symbol="i" position="left" xlink:label="note-0326-09" xlink:href="note-0326-09a" xml:space="preserve">15. primi
                <lb/>
              huius.</note>
            titudinem alterius, cum ipſæ ſint
              <note symbol="l" position="left" xlink:label="note-0326-10" xlink:href="note-0326-10a" xml:space="preserve">Coroll.
                <lb/>
              96. h.</note>
            lium baſium; </s>
            <s xml:id="echoid-s9097" xml:space="preserve">ſed altitudo ad altitudinem
              <lb/>
            eſt vt perpendicularis, ex B ſuper contingentem ad C, quæ eſt
              <note symbol="m" position="left" xlink:label="note-0326-11" xlink:href="note-0326-11a" xml:space="preserve">99. h.</note>
              <note symbol="n" position="left" xlink:label="note-0326-12" xlink:href="note-0326-12a" xml:space="preserve">1. Co-
                <lb/>
              roll. 98. h.</note>
            _MINIMVM_ latus B C, ad perpendicularem ex B ſuper contingentem ad </s>
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