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

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          <p>
            <s xml:id="echoid-s4802" xml:space="preserve">6. </s>
            <s xml:id="echoid-s4803" xml:space="preserve">IN quarta autem figura Ellipſis
              <lb/>
            circa minorem axim BR, in
              <lb/>
              <figure xlink:label="fig-0168-01" xlink:href="fig-0168-01a" number="133">
                <image file="0168-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0168-01"/>
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            qua prædictæ contingentibus
              <lb/>
            perpendiculares ipſi BR occur-
              <lb/>
            runt: </s>
            <s xml:id="echoid-s4804" xml:space="preserve">dico AC, quæ à remotiori
              <lb/>
            contactu educitur minorem eſſe
              <lb/>
            DG, quæ à propinquiori. </s>
            <s xml:id="echoid-s4805" xml:space="preserve">Nam
              <lb/>
            cum ſit DO ad DG, vt I L ad IG,
              <lb/>
            vel vt tranſuerſum latus ad
              <note symbol="a" position="left" xlink:label="note-0168-01" xlink:href="note-0168-01a" xml:space="preserve">3. Co-
                <lb/>
              roll. 90. h.</note>
            ctum, vel vt HL ad HC, vel vt
              <lb/>
            AN ad AC, erit DO ad DG, vt
              <lb/>
            AN ad AC, & </s>
            <s xml:id="echoid-s4806" xml:space="preserve">permutando, vt
              <lb/>
            DO ad AN, ita DG ad AC, ſed
              <lb/>
            eſt DO maior AN, vt ſupra ad numerum 5. </s>
            <s xml:id="echoid-s4807" xml:space="preserve">oſtenſum eſt, ergo, & </s>
            <s xml:id="echoid-s4808" xml:space="preserve">DG maior
              <lb/>
            erit ipſa AC. </s>
            <s xml:id="echoid-s4809" xml:space="preserve">Quod ſecundò oſtendere propoſitum fuit.</s>
            <s xml:id="echoid-s4810" xml:space="preserve"/>
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        <div xml:id="echoid-div485" type="section" level="1" n="196">
          <head xml:id="echoid-head201" xml:space="preserve">PROBL. XXXIV. PROP. XCIV.</head>
          <p>
            <s xml:id="echoid-s4811" xml:space="preserve">Dato angulo rectilineo, ad punctum in eius latere datum MA-
              <lb/>
            XIMVM circulum inſcribere.</s>
            <s xml:id="echoid-s4812" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4813" xml:space="preserve">SIt datus angulus rectilineus ABC, & </s>
            <s xml:id="echoid-s4814" xml:space="preserve">punctum in eius latere datum ſit A,
              <lb/>
            ad quod oporteat _MAXIMVM_ circulum inſcribere.</s>
            <s xml:id="echoid-s4815" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4816" xml:space="preserve">Bifariam ſecetur angulus à recta BD, & </s>
            <s xml:id="echoid-s4817" xml:space="preserve">ex A ipſi AB perpendicularis eri-
              <lb/>
            gatur AE, occurrens BD in E; </s>
            <s xml:id="echoid-s4818" xml:space="preserve">& </s>
            <s xml:id="echoid-s4819" xml:space="preserve">centro E, interuallo EA deſcribatur circu-
              <lb/>
            lus. </s>
            <s xml:id="echoid-s4820" xml:space="preserve">Dico hunc eſſe _MAXIMVM_ quæſitum.</s>
            <s xml:id="echoid-s4821" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4822" xml:space="preserve">Nam ſumpta BC ipſi BA æquali, iunctiſque AC, EC; </s>
            <s xml:id="echoid-s4823" xml:space="preserve">cum latera AB,
              <lb/>
            BE, æqualia ſint lateribus CB, BE, & </s>
            <s xml:id="echoid-s4824" xml:space="preserve">anguli ad B æquales, erit EA æqualis
              <lb/>
            EC. </s>
            <s xml:id="echoid-s4825" xml:space="preserve">Inſuper ſunt BA, AE, ipſis BC, CE æqualia, vtrunque vtrique, & </s>
            <s xml:id="echoid-s4826" xml:space="preserve">ba-
              <lb/>
            ſis BE communis, ergo angulus BAE angulo BCE æqualis, nempe rectus
              <lb/>
            quare circulus ex EA per C tranſibit, contigetque latera BA, BC, ſiue erit
              <lb/>
            angulo ABC inſcriptus. </s>
            <s xml:id="echoid-s4827" xml:space="preserve">Dico hunc eſſe _MAXIMVM_ quæſitum.</s>
            <s xml:id="echoid-s4828" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s4829" xml:space="preserve">Nam ſi centra circulorum ad A pertinen-
              <lb/>
              <figure xlink:label="fig-0168-02" xlink:href="fig-0168-02a" number="134">
                <image file="0168-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0168-02"/>
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            tium, fuerint in portione perpendicularis
              <lb/>
            AE, inter A, & </s>
            <s xml:id="echoid-s4830" xml:space="preserve">E; </s>
            <s xml:id="echoid-s4831" xml:space="preserve">ipſi, vt ſatis conſtat, erũt
              <lb/>
            quidem angulo inſcripti, cum circulo quo-
              <lb/>
            que inſcripti ſint; </s>
            <s xml:id="echoid-s4832" xml:space="preserve">ſed minores erunt circulo
              <lb/>
            ADC cum ſint minoris radij; </s>
            <s xml:id="echoid-s4833" xml:space="preserve">illi verò quo-
              <lb/>
            rum centra ſunt in producta AE, vt in F, ſunt
              <lb/>
            quidem maiores, ſed latus BC omnino ſecát:
              <lb/>
            </s>
            <s xml:id="echoid-s4834" xml:space="preserve">quoniam ducta F G parallela ad E C, quæ
              <lb/>
            productæ A C occurrat in G, cum ſit AF ad
              <lb/>
            FG, vt AE ad EC, ſitque AE ipſi EC æqua-
              <lb/>
            lis, erit quoque AF æqualis FG: </s>
            <s xml:id="echoid-s4835" xml:space="preserve">quare cir-
              <lb/>
            culus ex FA tranſibit per punctum G, quod
              <lb/>
            eſt extra angulum; </s>
            <s xml:id="echoid-s4836" xml:space="preserve">ideoque in ſe remeans ſecabit omnino latus BC, quod
              <lb/>
            eſt infinitæ extenſionis. </s>
            <s xml:id="echoid-s4837" xml:space="preserve">Si verò centrum ſumatur extra prædicta </s>
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