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

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        <div xml:id="echoid-div464" type="section" level="1" n="191">
          <pb o="140" file="0164" n="164" rhead=""/>
          <p>
            <s xml:id="echoid-s4699" xml:space="preserve">Quoniam ducta AQN parallela ad GF,
              <lb/>
              <figure xlink:label="fig-0164-01" xlink:href="fig-0164-01a" number="129">
                <image file="0164-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0164-01"/>
              </figure>
            & </s>
            <s xml:id="echoid-s4700" xml:space="preserve">DQR ad HM; </s>
            <s xml:id="echoid-s4701" xml:space="preserve">cum ſit RD minor MG, & </s>
            <s xml:id="echoid-s4702" xml:space="preserve">
              <lb/>
            DQ æqualis GN, erit rectangulum RDQ,
              <lb/>
            ſiue quadratum DA, (in triangulo rectan-
              <lb/>
            gulo RAD) minus rectangulo MGN
              <note symbol="a" position="left" xlink:label="note-0164-01" xlink:href="note-0164-01a" xml:space="preserve">37. pri-
                <lb/>
              mi conic.</note>
            quadrato GI; </s>
            <s xml:id="echoid-s4703" xml:space="preserve">hoc eſt intercepta linea D A
              <lb/>
            minor ſemi-axe minori GI. </s>
            <s xml:id="echoid-s4704" xml:space="preserve">Quod ter-
              <lb/>
            tiò, &</s>
            <s xml:id="echoid-s4705" xml:space="preserve">c.</s>
            <s xml:id="echoid-s4706" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4707" xml:space="preserve">Tandem, dico interceptam perpendi-
              <lb/>
            cularem AH minorẽ eſſe quàm dimidium
              <lb/>
            recti lateris minoris axis.</s>
            <s xml:id="echoid-s4708" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4709" xml:space="preserve">Etenim cum ſit IG maior AD, vt ſupra
              <lb/>
            oſtendimus; </s>
            <s xml:id="echoid-s4710" xml:space="preserve">habebit IG ad AH maiorem
              <lb/>
            rationem quàm AD ad AH, vel quàm NG
              <lb/>
            ad NH, vel quàm eadem I G ſemi-
              <note symbol="b" position="left" xlink:label="note-0164-02" xlink:href="note-0164-02a" xml:space="preserve">3. Co-
                <lb/>
              roli. 90. h.</note>
            uerſum ad ſemi- rectum; </s>
            <s xml:id="echoid-s4711" xml:space="preserve">quare intercepta
              <lb/>
            AH erit minor ſemi-recto minoris axis IL.
              <lb/>
            </s>
            <s xml:id="echoid-s4712" xml:space="preserve">Quod vltimò oſtendere proponebatur.</s>
            <s xml:id="echoid-s4713" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div470" type="section" level="1" n="192">
          <head xml:id="echoid-head197" xml:space="preserve">COROLL. I.</head>
          <p>
            <s xml:id="echoid-s4714" xml:space="preserve">HInc eſt, quod ſemper in Ellipſi intercepta maioris axis portio inter cõ-
              <lb/>
            tingenti perpendicularem, & </s>
            <s xml:id="echoid-s4715" xml:space="preserve">verticem, maior eſt dimidio recti late-
              <lb/>
            ris maioris axis. </s>
            <s xml:id="echoid-s4716" xml:space="preserve">Nam in figura huius, oſtenſa eſt AD ad numerum 2. </s>
            <s xml:id="echoid-s4717" xml:space="preserve">maior
              <lb/>
              <note symbol="c" position="left" xlink:label="note-0164-03" xlink:href="note-0164-03a" xml:space="preserve">88. h.</note>
            ſemi-recto maioris axis BC, ſed eſt DB maior DA, quare DB eò maior erit prædicto ſemi-recto.</s>
            <s xml:id="echoid-s4718" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div472" type="section" level="1" n="193">
          <head xml:id="echoid-head198" xml:space="preserve">COROLL. II.</head>
          <p>
            <s xml:id="echoid-s4719" xml:space="preserve">PAtet etiam in Ellipſi, quod intercepta minoris axis portio inter contin-
              <lb/>
            genti perpendicularem, & </s>
            <s xml:id="echoid-s4720" xml:space="preserve">verticem, eſt minor dimidio recti lateris
              <lb/>
              <note symbol="d" position="left" xlink:label="note-0164-04" xlink:href="note-0164-04a" xml:space="preserve">ibidem.</note>
            eiuſdem minoris axis. </s>
            <s xml:id="echoid-s4721" xml:space="preserve">Quoniam ſupra ad numerum 4. </s>
            <s xml:id="echoid-s4722" xml:space="preserve">demonſtrauimus AH
              <lb/>
            minorem eſſe ſemi-recto minoris axis IL, ſed eſt IH minor AH, quare IH eò minor erit prædicto ſemi-recto.</s>
            <s xml:id="echoid-s4723" xml:space="preserve"/>
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