Huygens, Christiaan, Christiani Hugenii opera varia; Bd. 2: Opera geometrica. Opera astronomica. Varia de optica

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        <div xml:id="echoid-div243" type="section" level="1" n="120">
          <pb o="490" file="0210" n="220" rhead="CHRIST. HUGENII"/>
          <figure number="82">
            <image file="0210-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0210-01"/>
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        <div xml:id="echoid-div246" type="section" level="1" n="121">
          <head xml:id="echoid-head166" xml:space="preserve">II.
            <lb/>
          DEMONSTRATIO
            <lb/>
          REGULÆ
            <lb/>
          DE
            <lb/>
          MAXIMIS ET MINIMIS.</head>
          <p>
            <s xml:id="echoid-s4604" xml:space="preserve">Ad inveſtiganda Maxima & </s>
            <s xml:id="echoid-s4605" xml:space="preserve">Minima in Geometricis quæ-
              <lb/>
            ſtionibus, regulam certam primus, quod ſciam, Fer-
              <lb/>
            matius adhibuit: </s>
            <s xml:id="echoid-s4606" xml:space="preserve">cujus originem ab ipſo non traditam cum
              <lb/>
            exquirerem, inveni ſimul quo pacto ea ipſa regula ad mira-
              <lb/>
            bilem brevitatem perduci poſſet, utque inde eadem illa exiſte-
              <lb/>
            ret quam poſtea vir ampliſſimus Joh. </s>
            <s xml:id="echoid-s4607" xml:space="preserve">Huddenius dederat, tan-
              <lb/>
            quam partem regulæ ſuæ generalioris atque elegantiſſimæ,
              <lb/>
            quæ ab alio prorſus principio pendet. </s>
            <s xml:id="echoid-s4608" xml:space="preserve">Hæc à Fr. </s>
            <s xml:id="echoid-s4609" xml:space="preserve">Schote-
              <lb/>
            nio edita eſt unà cum Carteſianis de Geometria libris. </s>
            <s xml:id="echoid-s4610" xml:space="preserve">Fer-
              <lb/>
            matianæ autem regulæ examen quod inſtitui eſt hujuſ-
              <lb/>
            modi.</s>
            <s xml:id="echoid-s4611" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4612" xml:space="preserve">Quoties Maximum aut Minimum in problemate aliquo de-
              <lb/>
              <note position="left" xlink:label="note-0210-01" xlink:href="note-0210-01a" xml:space="preserve">TAB. XLV.
                <lb/>
              fig. 1.</note>
            terminandum proponitur, certum eſt utrinque æqualitatis
              <lb/>
            caſum exiſtere: </s>
            <s xml:id="echoid-s4613" xml:space="preserve">ut ſi data ſit poſitione recta E D & </s>
            <s xml:id="echoid-s4614" xml:space="preserve">puncta A,
              <lb/>
            B, oporteatque invenire in E D punctum C, unde ductis C A,
              <lb/>
            C B, quadrata earum ſimul ſumpta, ſint minima quæ eſſe poſ-
              <lb/>
            ſint; </s>
            <s xml:id="echoid-s4615" xml:space="preserve">neceſſe eſt ab utraque parte puncti C, eſſe puncta G & </s>
            <s xml:id="echoid-s4616" xml:space="preserve">
              <lb/>
            F, à quibus ducendo rectas G A, G B; </s>
            <s xml:id="echoid-s4617" xml:space="preserve">F A, F B oriatur ſum-
              <lb/>
            ma quadratorum G A, G B æqualis ſummæ quadratorum F A,
              <lb/>
            F B, & </s>
            <s xml:id="echoid-s4618" xml:space="preserve">utraque ſumma major quadratis C A, C B ſimul
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            ſumptis.</s>
            <s xml:id="echoid-s4619" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4620" xml:space="preserve">Ut igitur inveniam punctum C, unde ductis C A, C B
              <lb/>
            fiat ſumma quadratorum ab ipſis omnium minima; </s>
            <s xml:id="echoid-s4621" xml:space="preserve">ductis A E,
              <lb/>
            B D perpendicularibus in E D, quarum A E dicatur a; </s>
            <s xml:id="echoid-s4622" xml:space="preserve">B D,
              <lb/>
            b; </s>
            <s xml:id="echoid-s4623" xml:space="preserve">intervallum verò E, D, c: </s>
            <s xml:id="echoid-s4624" xml:space="preserve">fingo primùm G F, </s>
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