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

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          <pb o="111" file="0163" n="177" rhead="HOROLOG. OSCILLATOR."/>
          <p>
            <s xml:id="echoid-s2533" xml:space="preserve">Quomodo porro ratio O B ad B P, ſive N H ad H L,
              <lb/>
              <note position="right" xlink:label="note-0163-01" xlink:href="note-0163-01a" 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>
            non tantum cum A B F parabola eſt, ſed etiam alia quæli-
              <lb/>
            bet curva geometrica, ſemper inveniri poſſit manifeſtum eſt.
              <lb/>
            </s>
            <s xml:id="echoid-s2534" xml:space="preserve">Quoniam tantum recta F H ducenda eſt, quæ curvam in
              <lb/>
              <note position="right" xlink:label="note-0163-02" xlink:href="note-0163-02a" xml:space="preserve">TAB. XV.
                <lb/>
              Fig. 4. & 5.</note>
            adſumpto puncto F tangat, & </s>
            <s xml:id="echoid-s2535" xml:space="preserve">F N ipſi F H perpendicu-
              <lb/>
            laris: </s>
            <s xml:id="echoid-s2536" xml:space="preserve">unde N H & </s>
            <s xml:id="echoid-s2537" xml:space="preserve">H L datæ erunt, ac proinde ratio quo-
              <lb/>
            que earum data.</s>
            <s xml:id="echoid-s2538" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2539" xml:space="preserve">At non æque liquet quo pacto ratio K L ad M N innoteſcat,
              <lb/>
            quam tamen ſemper quoque reperiri poſſe ſic oſten-demus.</s>
            <s xml:id="echoid-s2540" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2541" xml:space="preserve">Sint rectæ K T, L V, perpendiculares ſuper K L, ſit-
              <lb/>
            que K T æqualis K M, & </s>
            <s xml:id="echoid-s2542" xml:space="preserve">L V æqualis L N, & </s>
            <s xml:id="echoid-s2543" xml:space="preserve">ducatur
              <lb/>
            V X parallela L N, quæ occurrat ipſi K T in X. </s>
            <s xml:id="echoid-s2544" xml:space="preserve">Quo-
              <lb/>
            niam ergo ſemper eadem eſt differentia duarum L K, N M,
              <lb/>
            quæ duarum L N, K M, hoc eſt, quæ duarum L V, K T;
              <lb/>
            </s>
            <s xml:id="echoid-s2545" xml:space="preserve">eſt autem differentiæ ipſarum L V, K T æqualis X T, & </s>
            <s xml:id="echoid-s2546" xml:space="preserve">
              <lb/>
            X V ipſi L K; </s>
            <s xml:id="echoid-s2547" xml:space="preserve">erit proinde N M æqualis duabus ſimul
              <lb/>
            V X, X T, vel ei quo V X ipſam X T ſuperat. </s>
            <s xml:id="echoid-s2548" xml:space="preserve">Atque
              <lb/>
            adeo, ſi data fuerit ratio V X ad X T, data quoque erit
              <lb/>
            ratio V X ad utramque ſimul V X, X T, vel ad exceſſum V X
              <lb/>
            ſupra X T, hoc eſt, data erit ratio V X ſive L K ad N M.</s>
            <s xml:id="echoid-s2549" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2550" xml:space="preserve">Sciendum eſt autem, quoniam K T ipſi K M, & </s>
            <s xml:id="echoid-s2551" xml:space="preserve">L V
              <lb/>
            ipſi L N, æquales ſumptæ ſunt, locum punctorum T, V,
              <lb/>
            fore lineam quandam vel rectam vel curvam datam, ut mox
              <lb/>
            oſtendetur. </s>
            <s xml:id="echoid-s2552" xml:space="preserve">Et ſiquidem ſit linea recta; </s>
            <s xml:id="echoid-s2553" xml:space="preserve">ut contingit ſi A B F
              <lb/>
            coni ſectio fuerit, & </s>
            <s xml:id="echoid-s2554" xml:space="preserve">K L axis ejus; </s>
            <s xml:id="echoid-s2555" xml:space="preserve">conſtat rationem V X
              <lb/>
            ad X T datam fore, data poſitione ipſius lineæ V T, quæ
              <lb/>
            locus eſt puuctorum V, T; </s>
            <s xml:id="echoid-s2556" xml:space="preserve">ſemperque eandem tunc haberi
              <lb/>
            dictam rationem, qualecunque fuerit intervallum K L.</s>
            <s xml:id="echoid-s2557" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2558" xml:space="preserve">At ſi locus alia linea curva fuerit, diverſa erit ratio V X
              <lb/>
            ad X T, prout majus minuſve fuerit intervallum K L. </s>
            <s xml:id="echoid-s2559" xml:space="preserve">In-
              <lb/>
            quirendum eſt autem quænam futura ſit iſta ratio, cum K L
              <lb/>
            infinite parvum imaginamur, quoniam & </s>
            <s xml:id="echoid-s2560" xml:space="preserve">puncta B, F, pro-
              <lb/>
            xima invicem poſuimus. </s>
            <s xml:id="echoid-s2561" xml:space="preserve">Similiter itaque & </s>
            <s xml:id="echoid-s2562" xml:space="preserve">puncta V, T,
              <lb/>
            lineæ curvæ minimam particulam intercipere intelligendum
              <lb/>
            eſt; </s>
            <s xml:id="echoid-s2563" xml:space="preserve">unde recta V T, cum ea quæ in T curvam contingit,
              <lb/>
            coincidet. </s>
            <s xml:id="echoid-s2564" xml:space="preserve">Sit ergo tangens illa T Y; </s>
            <s xml:id="echoid-s2565" xml:space="preserve">poteſt enim duci </s>
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