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

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          <p>
            <s xml:id="echoid-s1785" xml:space="preserve">
              <pb o="52" file="0076" n="76" rhead=""/>
            ſed omnino, vel Ellipſim ſecat, velintra eam cadit, cum punctum I ſit quo-
              <lb/>
            que intra. </s>
            <s xml:id="echoid-s1786" xml:space="preserve">Quare circulus GBH _MINIMV S_ eſt circumſcriptibilium per ver-
              <lb/>
            ticem B maioris axis datæ Ellipſis ABC. </s>
            <s xml:id="echoid-s1787" xml:space="preserve">Quod ſecundò faciendum erat.</s>
            <s xml:id="echoid-s1788" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div160" type="section" level="1" n="85">
          <head xml:id="echoid-head90" xml:space="preserve">SCHOLIVM I.</head>
          <p>
            <s xml:id="echoid-s1789" xml:space="preserve">HInc facilè eruitur pulcherrima de _MAXIMIS_, & </s>
            <s xml:id="echoid-s1790" xml:space="preserve">_MINIMIS_ circulis,
              <lb/>
            Ellipſi inſcriptis, & </s>
            <s xml:id="echoid-s1791" xml:space="preserve">circumſcriptis proprietas. </s>
            <s xml:id="echoid-s1792" xml:space="preserve">Nempe.</s>
            <s xml:id="echoid-s1793" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1794" xml:space="preserve">_MINIMV M_ circulum per verticem minoris axis AC Ellipſi circumſcri-
              <lb/>
            ptum, cuius diameter eſt rectum latus AB.</s>
            <s xml:id="echoid-s1795" xml:space="preserve"/>
          </p>
          <note symbol="a" position="left" xml:space="preserve">1. Co-
            <lb/>
          roll. 20. h.</note>
          <p>
            <s xml:id="echoid-s1796" xml:space="preserve">_MINIMV M_ circulum per verticem maioris axis DE circumſcriptũ, cuius
              <lb/>
            diameter eſt ipſe maior axis DE.</s>
            <s xml:id="echoid-s1797" xml:space="preserve"/>
          </p>
          <note symbol="b" position="left" xml:space="preserve">26. h.</note>
          <p>
            <s xml:id="echoid-s1798" xml:space="preserve">_MAXIMV M_ circulum per verticem minoris axis AC inſcriptum, cuius
              <lb/>
            diameter eſt ipſe minor axis AC.</s>
            <s xml:id="echoid-s1799" xml:space="preserve"/>
          </p>
          <note symbol="c" position="left" xml:space="preserve">26. h.</note>
          <p>
            <s xml:id="echoid-s1800" xml:space="preserve">Et _MAXIMV M_ circulũ per ver-
              <lb/>
              <figure xlink:label="fig-0076-01" xlink:href="fig-0076-01a" number="46">
                <image file="0076-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0076-01"/>
              </figure>
            ticem maioris axis DE inſcriptum,
              <lb/>
            cuius diameter eſt rectum
              <note symbol="d" position="left" xlink:label="note-0076-04" xlink:href="note-0076-04a" xml:space="preserve">1. Co-
                <lb/>
              roll. 20. h.</note>
            DF, eſſe quatuor circulos in conti-
              <lb/>
            nua eademque ratione geometri-
              <lb/>
            ca; </s>
            <s xml:id="echoid-s1801" xml:space="preserve">nam & </s>
            <s xml:id="echoid-s1802" xml:space="preserve">ipſorum diametri AB,
              <lb/>
            DE, AC, DF ſunt quatuor lineæ
              <lb/>
            continuè proportionales.</s>
            <s xml:id="echoid-s1803" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div162" type="section" level="1" n="86">
          <head xml:id="echoid-head91" xml:space="preserve">SCHOLIVM II.</head>
          <p>
            <s xml:id="echoid-s1804" xml:space="preserve">ELicitur quoque, Ellipſim quamcunque, mediam eſſe proportionalem
              <lb/>
            inter extremos prædictos circulos, mediamque inter medios. </s>
            <s xml:id="echoid-s1805" xml:space="preserve">Cum
              <lb/>
            enim quatuor lineæ AB, DE, AC, DF ſint continuè proportionales, erit
              <lb/>
            rectangulum ſub extremis AB, DF æquale rectangulo ſub medijs DE, AC,
              <lb/>
            nempè quadrato G, quæ ſit media proportionalis inter DE, AC; </s>
            <s xml:id="echoid-s1806" xml:space="preserve">hoc eſt vt
              <lb/>
            AB ad G, ita erit G ad DF; </s>
            <s xml:id="echoid-s1807" xml:space="preserve">quare circulus ex diametro AB, ad circulum ex
              <lb/>
            diametro G, erit vt circulus G, ad circulum ex DF. </s>
            <s xml:id="echoid-s1808" xml:space="preserve">Item cum ſit DE ad G,
              <lb/>
            ita G ad AC, erit circulus ex DE ad circulum ex G, vt circulus G ad circu-
              <lb/>
              <note symbol="e" position="left" xlink:label="note-0076-05" xlink:href="note-0076-05a" xml:space="preserve">5. Arch.
                <lb/>
              de Co-
                <lb/>
              noid. &
                <lb/>
              Sphęroid.</note>
            lum ex AC, ſed circulus ex G æquatur Ellipſi; </s>
            <s xml:id="echoid-s1809" xml:space="preserve">vnde Ellipſis DAEC eſt media proportionalis inter extremos prædictos circulos AB, DF mediaque
              <lb/>
            inter medios DE, AC.</s>
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