Huygens, Christiaan, Christiani Hugenii opera varia; Bd. 1: Opera mechanica

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            <s xml:id="echoid-s1713" xml:space="preserve">
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            tiones B D & </s>
            <s xml:id="echoid-s1714" xml:space="preserve">E F, æqualis altitudinis, hoc eſt, ejusmodi
              <lb/>
              <note position="left" xlink:label="note-0118-01" xlink:href="note-0118-01a" xml:space="preserve">
                <emph style="sc">De motu</emph>
                <lb/>
                <emph style="sc">IN</emph>
                <emph style="sc">Cy-</emph>
                <lb/>
                <emph style="sc">CLOIDE</emph>
              .</note>
            ut parallelæ horizontales B C, D H, quæ ſuperiorem por-
              <lb/>
            tionem B D includunt, æque inter ſe diſtent ac E G,
              <lb/>
            F K, inferiorem partionem E F includentes. </s>
            <s xml:id="echoid-s1715" xml:space="preserve">Dico tempus
              <lb/>
            deſcenſus per curvam B D brevius fore tempore per E F.</s>
            <s xml:id="echoid-s1716" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1717" xml:space="preserve">Sumatur enim in B D punctum quodlibet L, & </s>
            <s xml:id="echoid-s1718" xml:space="preserve">in E F
              <lb/>
            punctum M, ita ut eadem ſit altitudo E ſupra M quæ B
              <lb/>
            ſupra L. </s>
            <s xml:id="echoid-s1719" xml:space="preserve">Et deſcripto ſuper axe A C ſemicirculo, occurrant
              <lb/>
            ei rectæ horizontales L N, M O, in N & </s>
            <s xml:id="echoid-s1720" xml:space="preserve">O, & </s>
            <s xml:id="echoid-s1721" xml:space="preserve">jungan-
              <lb/>
            tur N A, O A. </s>
            <s xml:id="echoid-s1722" xml:space="preserve">Itaque quum punctum N ſit altius puncto
              <lb/>
            O, manifeſtum eſt rectam N A minus ad horizontem incli-
              <lb/>
            nari quam O A. </s>
            <s xml:id="echoid-s1723" xml:space="preserve">Eſt autem ipſi N A parallela tangens curvæ
              <lb/>
            in L puncto , & </s>
            <s xml:id="echoid-s1724" xml:space="preserve">ipſi O A parallela tangens curvæ in M.</s>
            <s xml:id="echoid-s1725" xml:space="preserve">
              <note symbol="*" position="left" xlink:label="note-0118-02" xlink:href="note-0118-02a" xml:space="preserve">Prop. 15.
                <lb/>
              huj.</note>
            Ergo curva B D in puncto L minus inclinata eſt quam curva
              <lb/>
            E F in puncto M. </s>
            <s xml:id="echoid-s1726" xml:space="preserve">Quod ſi igitur portio E F, invariata in-
              <lb/>
            clinatione, altius extolli intelligatur velut in e f, ita ut in-
              <lb/>
            ter eaſdem parallelas cum portione B D comprehendatur,
              <lb/>
            invenietur punctum M in m, æquali altitudine cum puncto
              <lb/>
            L. </s>
            <s xml:id="echoid-s1727" xml:space="preserve">eritque etiam inclinatio curvæ e f in puncto m, quæ ea-
              <lb/>
            dem eſt inclinationi curvæ E F in M, major inclinatione
              <lb/>
            curvæ B D in L. </s>
            <s xml:id="echoid-s1728" xml:space="preserve">Similiter vero, & </s>
            <s xml:id="echoid-s1729" xml:space="preserve">in quolibet alio puncto
              <lb/>
            curvæ e f, major oſtendetur inclinatio quam curv æ B D
              <lb/>
            in puncto æque alto. </s>
            <s xml:id="echoid-s1730" xml:space="preserve">Itaque tempus deſcenſus per B D bre-
              <lb/>
            vius erit tempore per e f, ſive, quod idem eſt, per E F.</s>
            <s xml:id="echoid-s1731" xml:space="preserve">
              <note symbol="*" position="left" xlink:label="note-0118-03" xlink:href="note-0118-03a" xml:space="preserve">Prop.
                <lb/>
              præced.</note>
            quod erat demonſtrandum.</s>
            <s xml:id="echoid-s1732" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div119" type="section" level="1" n="46">
          <head xml:id="echoid-head68" xml:space="preserve">LEMMA.</head>
          <p style="it">
            <s xml:id="echoid-s1733" xml:space="preserve">ESto circulus diametro A C, quem ſecet ad an-
              <lb/>
              <note position="left" xlink:label="note-0118-04" xlink:href="note-0118-04a" xml:space="preserve">TAB. IX.
                <lb/>
              Fig. 4.</note>
            gulos rectos D E, & </s>
            <s xml:id="echoid-s1734" xml:space="preserve">à termino diametri A e-
              <lb/>
            ducta recta A B occurrat circumferentiæ in B, ipſi
              <lb/>
            vero D E in F. </s>
            <s xml:id="echoid-s1735" xml:space="preserve">Dico tres haſce, A B, A D, A F,
              <lb/>
            proportionales eſſe.</s>
            <s xml:id="echoid-s1736" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s1737" xml:space="preserve">Sit enim primo interſectio F intra circulum; </s>
            <s xml:id="echoid-s1738" xml:space="preserve">& </s>
            <s xml:id="echoid-s1739" xml:space="preserve">arcui B D
              <lb/>
            recta ſubtenſa ducatur. </s>
            <s xml:id="echoid-s1740" xml:space="preserve">Quia igitur arcus æquales ſunt A </s>
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