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

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        <div xml:id="echoid-div257" type="section" level="1" n="125">
          <p>
            <s xml:id="echoid-s5013" xml:space="preserve">
              <pb o="511" file="0235" n="247" rhead="GEOMETRICA VARIA."/>
            ram Hyperboles per Jac. </s>
            <s xml:id="echoid-s5014" xml:space="preserve">Gregorium in exercitationibus ſuis
              <lb/>
            Geometricis, ubi inde deducit ſolutionem problematis lon-
              <lb/>
            gitudinum, datis vento & </s>
            <s xml:id="echoid-s5015" xml:space="preserve">latitudinum differentiâ, quod novum
              <lb/>
            credidit Leibnitius, & </s>
            <s xml:id="echoid-s5016" xml:space="preserve">quod à Gregorio traditum tunc tem-
              <lb/>
            poris non recordabar. </s>
            <s xml:id="echoid-s5017" xml:space="preserve">Leibnitius & </s>
            <s xml:id="echoid-s5018" xml:space="preserve">Bernoullius, ut cenſeo,
              <lb/>
            pervenerunt ad Catenariæ Conſtructionem ope Curvæ,
              <lb/>
            quam poſterior illorum habet in 1
              <emph style="super">a</emph>
            . </s>
            <s xml:id="echoid-s5019" xml:space="preserve">Figurarum quas exhi-
              <lb/>
            bet ad ſolvendum hoc Problema; </s>
            <s xml:id="echoid-s5020" xml:space="preserve">nam Leibnitius mihi ſcri-
              <lb/>
            pſit, ſe etiam ad eandem perveniſſe; </s>
            <s xml:id="echoid-s5021" xml:space="preserve">Et invenio eandem
              <lb/>
            cum illâ de qua ante, cujus æquatio eſt a
              <emph style="super">4</emph>
            = xxyy -
              <lb/>
            aayy, cujus quadratura, ut dixi, dependet à quadraturâ Hy-
              <lb/>
            perboles: </s>
            <s xml:id="echoid-s5022" xml:space="preserve">licet nondum concipere potuerim, quomodo cal-
              <lb/>
            culus illos perduxerit ad hanc lineam. </s>
            <s xml:id="echoid-s5023" xml:space="preserve">Sed tranſeo ad meam
              <lb/>
            conſtructionem, quæ abſque conſideratione aliûs lineæ
              <lb/>
            curvæ, dat puncta Catenariæ per dimenſionem lineæ Pa-
              <lb/>
            rabolicæ.</s>
            <s xml:id="echoid-s5024" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5025" xml:space="preserve">Primum fundamentum totius inquiſitionis reſpectu hujus
              <lb/>
              <note position="right" xlink:label="note-0235-01" xlink:href="note-0235-01a" xml:space="preserve">TAB. XLVI.
                <lb/>
              fig. 3.</note>
            lineæ eſt hoc; </s>
            <s xml:id="echoid-s5026" xml:space="preserve">Si habeas catenam compoſitam ex variis pon-
              <lb/>
            deribus æqualibus filo appenſis, ut BCDEF ſemper trium
              <lb/>
            interſtitiorum ſe mutuo ſequentium duæ lineæ extremæ, ut CD,
              <lb/>
            F E continuatæ ſibi mutuo occurrunt in linea IH per-
              <lb/>
            pendiculari ad Horizontem, quæ dividit interſtitium me-
              <lb/>
            dium in duas partes æquales. </s>
            <s xml:id="echoid-s5027" xml:space="preserve">Conſiderando porro catenam ita
              <lb/>
            compoſitam à ponderibus connexis ad æquales diſtantias,
              <lb/>
            quas ponimus infinite exiguas, & </s>
            <s xml:id="echoid-s5028" xml:space="preserve">diſpoſitis, ita, ut inter-
              <lb/>
            ſtitium infimum BC ſit horizonti parallelum, ſi ſuper quo-
              <lb/>
            vis alio interſtitio concipiamus triangula rectangula CDK,
              <lb/>
            D E L, quorum unum latus ſit horizontale, videbimus,
              <lb/>
            quod ab infimo initium faciendo anguli DCK, EDL, FEM,
              <lb/>
            tales ſint, ut illorum Tangentes æqualiter creſcant, ut nu-
              <lb/>
            meri 1, 2, 3, 4, id quod demonſtratu facile eſt ex dicto
              <lb/>
            principio, licet forſitan eo non perveniſſemus ſine calculo Al-
              <lb/>
            gebraico.</s>
            <s xml:id="echoid-s5029" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5030" xml:space="preserve">Si porro concipiamus partes æquales catenæ CDEFG ex-
              <lb/>
            tenſas in recta horizontali in C O P Q R, & </s>
            <s xml:id="echoid-s5031" xml:space="preserve">ex prima divi-
              <lb/>
            ſione O ductam O S, quæ concurrat cum perpendiculari C </s>
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