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

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        <div xml:id="echoid-div651" type="section" level="1" n="260">
          <head xml:id="echoid-head268" xml:space="preserve">THEOR. XX. PROP. XXXII</head>
          <p>
            <s xml:id="echoid-s6237" xml:space="preserve">Rectorum laterum in Ellipſi MAXIMVM eſt rectum minoris
              <lb/>
            axis, MINIMVM verò rectum maioris.</s>
            <s xml:id="echoid-s6238" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6239" xml:space="preserve">ESto Ellipſis A B C D, cuius centrum E, axis minor A C, rectum A
              <lb/>
            G, & </s>
            <s xml:id="echoid-s6240" xml:space="preserve">axis maior B D, rectum B F. </s>
            <s xml:id="echoid-s6241" xml:space="preserve">Dico A G rectorum omnium
              <lb/>
            eſſe _MAXIMVM_; </s>
            <s xml:id="echoid-s6242" xml:space="preserve">B F verò _MINIMVM_.</s>
            <s xml:id="echoid-s6243" xml:space="preserve"/>
          </p>
          <figure number="185">
            <image file="0223-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0223-01"/>
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          <p>
            <s xml:id="echoid-s6244" xml:space="preserve">Sit enim quælibet alia tranſuerſa diame-
              <lb/>
            ter H I, cuius rectum H L, ſitque diame-
              <lb/>
            ter M N ipſi H I coniugata, quæ media
              <lb/>
            proportionalis erit inter I H, & </s>
            <s xml:id="echoid-s6245" xml:space="preserve">H L; </s>
            <s xml:id="echoid-s6246" xml:space="preserve">vn-
              <lb/>
            de quadratum ipſius M N æquabitur re-
              <lb/>
            ctangulo I H L, vti etiam quadratum A C
              <lb/>
            æquatur rectangulo D B F, & </s>
            <s xml:id="echoid-s6247" xml:space="preserve">quadratum
              <lb/>
            B D rectangulo C A G; </s>
            <s xml:id="echoid-s6248" xml:space="preserve">ſed eſt quadratum
              <lb/>
            A C, minus quadrato M N, cum ſit tranſ-
              <lb/>
            uerſa A C minor tranſuerſa M N,
              <note symbol="a" position="right" xlink:label="note-0223-01" xlink:href="note-0223-01a" xml:space="preserve">24. h.</note>
            rectangulum D B F minus erit rectangulo
              <lb/>
            I H L, quare B D ad H I minorem habe-
              <lb/>
            bit rationem quàm H L ad B F, eſtque B
              <lb/>
            D maior H I, ergo & </s>
            <s xml:id="echoid-s6249" xml:space="preserve">rectum H L
              <note symbol="b" position="right" xlink:label="note-0223-02" xlink:href="note-0223-02a" xml:space="preserve">ibidem.</note>
            maior recto B F.</s>
            <s xml:id="echoid-s6250" xml:space="preserve"/>
          </p>
          <note symbol="c" position="right" xml:space="preserve">31. h.</note>
          <p>
            <s xml:id="echoid-s6251" xml:space="preserve">Præterea, cum ſit M N minor D
              <note symbol="d" position="right" xlink:label="note-0223-04" xlink:href="note-0223-04a" xml:space="preserve">24. h.</note>
            erit quadratum M N minus quadrato D B, ſiue rectangulum I H L minus
              <lb/>
            rectangulo C A G, vnde I H ad C A minorem habebit rationem quàm
              <lb/>
            A G ad H L, ſed eſt I H maior C A, ergo rectum A G erit maior
              <note symbol="e" position="right" xlink:label="note-0223-05" xlink:href="note-0223-05a" xml:space="preserve">ibidem.</note>
            H L. </s>
            <s xml:id="echoid-s6252" xml:space="preserve">Cum ſit ergo A G maior H L, & </s>
            <s xml:id="echoid-s6253" xml:space="preserve">H L maior B F erit A G adhuc
              <lb/>
              <note symbol="f" position="right" xlink:label="note-0223-06" xlink:href="note-0223-06a" xml:space="preserve">31. h.</note>
            maior B F. </s>
            <s xml:id="echoid-s6254" xml:space="preserve">Quare A G rectum minoris axis eſt _MAXIMVM_, B F verò
              <lb/>
            maioris axis rectum, eſt _MINIMVM_. </s>
            <s xml:id="echoid-s6255" xml:space="preserve">Quod erat demonſtrandum.</s>
            <s xml:id="echoid-s6256" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div654" type="section" level="1" n="261">
          <head xml:id="echoid-head269" xml:space="preserve">PROBL. IV. PROP. XXXIII.</head>
          <p>
            <s xml:id="echoid-s6257" xml:space="preserve">A puncto dato intra angulum rectilineum rectam applicare,
              <lb/>
            cuius rectangulum ſegmentorum ſit MINIMVM.</s>
            <s xml:id="echoid-s6258" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6259" xml:space="preserve">ESto ABC angulus rectilineus, in quo datum punctum ſit D. </s>
            <s xml:id="echoid-s6260" xml:space="preserve">Opor-
              <lb/>
            tet ex D rectam in angulo applicare, ita vt rectangulum ſub ipſius
              <lb/>
            ſegmentis ſit _MINIMVM_.</s>
            <s xml:id="echoid-s6261" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6262" xml:space="preserve">Ducatur B E angulum A B C bifariam ſecans, cui per D recta perpen-
              <lb/>
            dicularis applicetur A D C. </s>
            <s xml:id="echoid-s6263" xml:space="preserve">Dico hanc ipſam quæſitum ſoluere.</s>
            <s xml:id="echoid-s6264" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6265" xml:space="preserve">Cum enim in triangulis B E A, B E C anguli ad E ſint recti, & </s>
            <s xml:id="echoid-s6266" xml:space="preserve">ad B
              <lb/>
            facti æquales, erunt reliqui anguli B A E, B C E æquales, & </s>
            <s xml:id="echoid-s6267" xml:space="preserve">qui infra A
              <lb/>
            C, baſim trianguli æquicruris A B C, pariter æquales.</s>
            <s xml:id="echoid-s6268" xml:space="preserve"/>
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