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

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        <div xml:id="echoid-div527" type="section" level="1" n="220">
          <pb o="2" file="0184" n="184" rhead=""/>
          <p>
            <s xml:id="echoid-s5175" xml:space="preserve">Nam intelligatur magnitudo E F æ-
              <lb/>
            qualis primæ A, FG verò æqualis ſecun-
              <lb/>
            dę B; </s>
            <s xml:id="echoid-s5176" xml:space="preserve">atque ipſis in directum magnitu-
              <lb/>
              <figure xlink:label="fig-0184-01" xlink:href="fig-0184-01a" number="144">
                <image file="0184-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0184-01"/>
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            do F H æqualis tertiæ C, & </s>
            <s xml:id="echoid-s5177" xml:space="preserve">F I quar-
              <lb/>
            tæ D. </s>
            <s xml:id="echoid-s5178" xml:space="preserve">Erit exceſſus magnitudinis E F
              <lb/>
            ſupra F G, hoc est E G, maios exceſſu
              <lb/>
            quantitatis H F ſupra F I, ſiue maios-
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            ipſo H I, ex ſuppoſitione, quibus addi-
              <lb/>
            ta communi quantitate G I, proueniet
              <lb/>
            E I maior G H, ſiue aggregatum ex EF,
              <lb/>
            & </s>
            <s xml:id="echoid-s5179" xml:space="preserve">F I, nempe extremarum A, & </s>
            <s xml:id="echoid-s5180" xml:space="preserve">D,
              <lb/>
            maius aggregato ex G F, & </s>
            <s xml:id="echoid-s5181" xml:space="preserve">F H, velex medijs B, & </s>
            <s xml:id="echoid-s5182" xml:space="preserve">C. </s>
            <s xml:id="echoid-s5183" xml:space="preserve">Quod erat, &</s>
            <s xml:id="echoid-s5184" xml:space="preserve">c</s>
          </p>
        </div>
        <div xml:id="echoid-div529" type="section" level="1" n="221">
          <head xml:id="echoid-head229" xml:space="preserve">THEOR. I. PROP. III.</head>
          <p>
            <s xml:id="echoid-s5185" xml:space="preserve">MINIMA linearum in Parabola ducibilium ad eius peri-
              <lb/>
            pheriam à puncto axis intra ſectionem ſumpto, quod diſtet à
              <lb/>
            vertice per interuallum non maius dimidio recti lateris, eſt ip-
              <lb/>
            ſum axis ſegmentum inter punctum, & </s>
            <s xml:id="echoid-s5186" xml:space="preserve">verticem interceptum.
              <lb/>
            </s>
            <s xml:id="echoid-s5187" xml:space="preserve">Aliarum verò ea, quæ cum MINIMA minorem conſtituit an-
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            gulum, minor eſt.</s>
            <s xml:id="echoid-s5188" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5189" xml:space="preserve">ESto Parabole AB, cuius ſegmentum axis B D non excedat dimidium
              <lb/>
            recti lateris B C datæ Parabolæ. </s>
            <s xml:id="echoid-s5190" xml:space="preserve">Dico D B eſſe _MINIMAM_ du-
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            cibilium ex eodem puncto D ad Parabolæ peripheriam A B, &</s>
            <s xml:id="echoid-s5191" xml:space="preserve">c.</s>
            <s xml:id="echoid-s5192" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5193" xml:space="preserve">Applicetur axi ex D, recta D A, Erit
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            quadratum A D æquale
              <figure xlink:label="fig-0184-02" xlink:href="fig-0184-02a" number="145">
                <image file="0184-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0184-02"/>
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            ſub D B, & </s>
            <s xml:id="echoid-s5194" xml:space="preserve">recto B C; </s>
            <s xml:id="echoid-s5195" xml:space="preserve">ſed rectangulum
              <lb/>
              <note symbol="a" position="left" xlink:label="note-0184-01" xlink:href="note-0184-01a" xml:space="preserve">Coroll.
                <lb/>
              primę pri
                <lb/>
              mi huius.</note>
            D B C maius eſt quadrato D B (cum
              <lb/>
            latus rectum B C poſitum ſit, vel du-
              <lb/>
            plum, vel magis quàm duplum ipſius
              <lb/>
            B D) igitur quadratum A D maius erit
              <lb/>
            quadrato D B, ſiue linea D A maior
              <lb/>
            D B.</s>
            <s xml:id="echoid-s5196" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5197" xml:space="preserve">Rurſus ducatur infra D A ex D quę-
              <lb/>
            cunque alia D E ad peripheriam, & </s>
            <s xml:id="echoid-s5198" xml:space="preserve">ex
              <lb/>
            A recta A F parallela ad B D, quæ to-
              <lb/>
            ta ad partes F cadet intra Parabolen;</s>
            <s xml:id="echoid-s5199" xml:space="preserve">
              <note symbol="b" position="left" xlink:label="note-0184-02" xlink:href="note-0184-02a" xml:space="preserve">26. pri-
                <lb/>
              mi conic.</note>
            nec ei ad alium punctum occurret quàm
              <lb/>
            ad A; </s>
            <s xml:id="echoid-s5200" xml:space="preserve">ideoque ſecabit eductam D E, vt in F, eritque E D maior D F,
              <lb/>
            ſed eſt D F maior D A (cum in triangulo D A F angulus ad A ſit rectus,
              <lb/>
            ſiue maior acuto ad F) & </s>
            <s xml:id="echoid-s5201" xml:space="preserve">D A maior ipſa D B, vt ſupra oſtendimus, qua-
              <lb/>
            re D E multò maior erit ipſa D B.</s>
            <s xml:id="echoid-s5202" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5203" xml:space="preserve">Ampliùs ſit quæcunque D G ducta ex D ſupra D A, & </s>
            <s xml:id="echoid-s5204" xml:space="preserve">ex G applice-
              <lb/>
            tur G H. </s>
            <s xml:id="echoid-s5205" xml:space="preserve">Cumque latus rectum B C ſit maios aggregato B D cum D H
              <lb/>
            (poſitum enim fuit B C non maius quàm duplum ſegmenti BD, </s>
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