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

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          <pb o="107" file="0159" n="173" rhead="HOROLOG. OSCILLATOR."/>
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        <div xml:id="echoid-div195" type="section" level="1" n="70">
          <head xml:id="echoid-head94" xml:space="preserve">PROPOSITIO X.</head>
          <note position="right" xml:space="preserve">
            <emph style="sc">De linea-</emph>
            <lb/>
            <emph style="sc">RUM CUR-</emph>
            <lb/>
            <emph style="sc">VARUM</emph>
            <lb/>
            <emph style="sc">EVOLUTIO-</emph>
            <lb/>
            <emph style="sc">NE</emph>
          .</note>
          <p style="it">
            <s xml:id="echoid-s2401" xml:space="preserve">LIneas curvas exhibere quarum evolutione elli-
              <lb/>
            pſes & </s>
            <s xml:id="echoid-s2402" xml:space="preserve">hyperbolæ deſcribantur, rectasque in-
              <lb/>
            venire iisdem curvis æquales.</s>
            <s xml:id="echoid-s2403" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2404" xml:space="preserve">Sit ellipſis vel hyperbole quælibet A B, cujus axis trans-
              <lb/>
              <note position="right" xlink:label="note-0159-02" xlink:href="note-0159-02a" xml:space="preserve">TAB. XV.
                <lb/>
              Fig. 2. & 3.</note>
            verſus A C; </s>
            <s xml:id="echoid-s2405" xml:space="preserve">centrum figuræ D; </s>
            <s xml:id="echoid-s2406" xml:space="preserve">latus rectum duplum ipſius
              <lb/>
            A E. </s>
            <s xml:id="echoid-s2407" xml:space="preserve">Et ſumpto in ſectione quovis puncto, ut B, applice-
              <lb/>
            tur ordinatim ad axem recta B K, & </s>
            <s xml:id="echoid-s2408" xml:space="preserve">ad dictum punctum B
              <lb/>
            tangens ducatur quæ conveniat cum axe in F; </s>
            <s xml:id="echoid-s2409" xml:space="preserve">ſitque B G
              <lb/>
            ipſi F B perpendicularis, axique occurrat in G; </s>
            <s xml:id="echoid-s2410" xml:space="preserve">& </s>
            <s xml:id="echoid-s2411" xml:space="preserve">produ-
              <lb/>
            catur B G usque ad H, ut B H ad H G habeat rationem
              <lb/>
            eam quæ componitur ex rationibus G F ad F K, & </s>
            <s xml:id="echoid-s2412" xml:space="preserve">A D
              <lb/>
            ad D E.</s>
            <s xml:id="echoid-s2413" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2414" xml:space="preserve">Dico curvam E H M, cujus puncta omnia inveniuntur
              <lb/>
            eodem modo quo punctum H, eſſe eam cujus evolu-
              <lb/>
            tione, unà cum recta E A, deſcribetur ſectio A B. </s>
            <s xml:id="echoid-s2415" xml:space="preserve">Ipſam
              <lb/>
            autem B H tangere curvam in H, & </s>
            <s xml:id="echoid-s2416" xml:space="preserve">eſſe toti H E A æqua-
              <lb/>
            lem. </s>
            <s xml:id="echoid-s2417" xml:space="preserve">Quamobrem, ſi ab H B auferatur E A, reliqua recta
              <lb/>
            portioni curvæ H E æquabitur. </s>
            <s xml:id="echoid-s2418" xml:space="preserve">Apparet autem, cum cur-
              <lb/>
            væ puncta quævis indifferenter, certaque ratione invenian-
              <lb/>
            tur, eſſe eam utrobique ex earum genere, quæ merè geo-
              <lb/>
            metricæ cenſentur. </s>
            <s xml:id="echoid-s2419" xml:space="preserve">Unde & </s>
            <s xml:id="echoid-s2420" xml:space="preserve">relatio horum omnium puncto-
              <lb/>
            rum ad puncta axis A C, æquatione aliqua exprimi poterit,
              <lb/>
            quam æquationem ad ſextam dimenſionem aſcendere invenio;
              <lb/>
            </s>
            <s xml:id="echoid-s2421" xml:space="preserve">minimumque habere terminorum, ſi fuerit A B hyperbola
              <lb/>
            cujus latera transverſum rectumque æqualia. </s>
            <s xml:id="echoid-s2422" xml:space="preserve">Tunc enim du-
              <lb/>
            cta ex quovis curvæ puncto, ut H, ad axem C A N per-
              <lb/>
            pendiculari H N; </s>
            <s xml:id="echoid-s2423" xml:space="preserve">vocatâque A C, a; </s>
            <s xml:id="echoid-s2424" xml:space="preserve">C N, x; </s>
            <s xml:id="echoid-s2425" xml:space="preserve">& </s>
            <s xml:id="echoid-s2426" xml:space="preserve">N H,
              <lb/>
            y; </s>
            <s xml:id="echoid-s2427" xml:space="preserve">erit ſemper cubus ab x x-y y-a a æqualis 27 x x y y a a. </s>
            <s xml:id="echoid-s2428" xml:space="preserve">
              <lb/>
            Sed hoc caſu brevius quoque multo, quam prædicta con-
              <lb/>
            ſtructione, curvæ E H M puncta reperiri poſſunt, ut in ſe-
              <lb/>
            quentibus oſtendetur.</s>
            <s xml:id="echoid-s2429" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2430" xml:space="preserve">Cæterum notandum eſt, in ellipſi ſingulos quadrantes ſin-
              <lb/>
            gularum linearum evolutione deſcribi; </s>
            <s xml:id="echoid-s2431" xml:space="preserve">ſicut quadrans A B </s>
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