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

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              <pb o="71" file="0107" n="113" rhead="HOROLOG. OSCILLATOR."/>
            fublatum in V: </s>
            <s xml:id="echoid-s1538" xml:space="preserve">& </s>
            <s xml:id="echoid-s1539" xml:space="preserve">jungantur C N, N V, V C, V L. </s>
            <s xml:id="echoid-s1540" xml:space="preserve">E-
              <lb/>
              <note position="right" xlink:label="note-0107-01" xlink:href="note-0107-01a" xml:space="preserve">
                <emph style="sc">De de-</emph>
                <lb/>
                <emph style="sc">SCENSU</emph>
                <lb/>
                <emph style="sc">GRAVIUM</emph>
              .</note>
            rit ergo V N æqualis C A; </s>
            <s xml:id="echoid-s1541" xml:space="preserve">imo erit ipſa C A translata in
              <lb/>
            V N. </s>
            <s xml:id="echoid-s1542" xml:space="preserve">Jam quia recta L C æquatur curvæ L V, ac proin-
              <lb/>
            de major eſt recta L V, erit in triangulo C L V angulus
              <lb/>
            L V C major quam L C V. </s>
            <s xml:id="echoid-s1543" xml:space="preserve">Quare addito inſuper angulo
              <lb/>
            L V N ad L V C, fiet totus N V C major utique quam
              <lb/>
            L C V, ac proinde omnino major angulo N C V, qui pars
              <lb/>
            eſt L C V. </s>
            <s xml:id="echoid-s1544" xml:space="preserve">Ergo in triangulo C V N latus C N majus erit
              <lb/>
            latere V N, cui æquatur C A, ideoque C N major quo-
              <lb/>
            que quam C A, hoc eſt quam C M. </s>
            <s xml:id="echoid-s1545" xml:space="preserve">Unde apparet pun-
              <lb/>
            ctum N cadere extra circulum M A F, qui proinde tanget
              <lb/>
            curvam in puncto A. </s>
            <s xml:id="echoid-s1546" xml:space="preserve">quod erat demonſtrandum.</s>
            <s xml:id="echoid-s1547" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1548" xml:space="preserve">Eſt autem eadem quoque tum conſtructio tum demonſtra-
              <lb/>
            tio, ſi curva genita ſit à puncto deſcribente, vel intra vel
              <lb/>
            extra ambitum figuræ circumvolutæ ſumpto. </s>
            <s xml:id="echoid-s1549" xml:space="preserve">Niſi quod,
              <lb/>
            hoc poſteriori caſu, pars quædam curvæ infra regulam de-
              <lb/>
            ſcendit, unde nonnulla in demonſtratione oritur diverſitas.</s>
            <s xml:id="echoid-s1550" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1551" xml:space="preserve">Sit enim punctum A, per quod tangens ducenda eſt, da-
              <lb/>
              <note position="right" xlink:label="note-0107-02" xlink:href="note-0107-02a" xml:space="preserve">TAB. VIII.
                <lb/>
              Fig. 1.</note>
            tum in parte curvæ N A B, quæ infra regulam C L de-
              <lb/>
            ſcendit, deſcripta nimirum à puncto N extra figuram revo-
              <lb/>
            lutam ſumpto, ſed certam poſitionem in eodem ipſius pla-
              <lb/>
            no habente. </s>
            <s xml:id="echoid-s1552" xml:space="preserve">Invento igitur puncto C, ubi figura revoluta
              <lb/>
            tangit regulam C D quum punctum deſcribens eſſet in A,
              <lb/>
            ducatur recta C A. </s>
            <s xml:id="echoid-s1553" xml:space="preserve">Dico hanc curvæ N A B occurrere ad
              <lb/>
            rectos angulos, ſive circumferentiam radio C A centro C
              <lb/>
            deſcriptam tangere curvam N A B in puncto A. </s>
            <s xml:id="echoid-s1554" xml:space="preserve">Oſtendetur
              <lb/>
            autem exterius ipſam contingere, cum in curvæ parte ſupra
              <lb/>
            regulam C D poſita interius contingat.</s>
            <s xml:id="echoid-s1555" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1556" xml:space="preserve">Poſitis enim & </s>
            <s xml:id="echoid-s1557" xml:space="preserve">deſcriptis iisdem omnibus quæ prius, os-
              <lb/>
            tenditur rurſus angulus E C H major quam C E H. </s>
            <s xml:id="echoid-s1558" xml:space="preserve">atqui
              <lb/>
            ad E C H addito H C B fit angulus E C B; </s>
            <s xml:id="echoid-s1559" xml:space="preserve">& </s>
            <s xml:id="echoid-s1560" xml:space="preserve">à C E H
              <lb/>
            auferendo H E B, qui æqualis eſt D C A, fit angulus
              <lb/>
            C E B. </s>
            <s xml:id="echoid-s1561" xml:space="preserve">Ergo E C B major omnino quam C E B. </s>
            <s xml:id="echoid-s1562" xml:space="preserve">unde in
              <lb/>
            triangulo E C B latus E B majus quam C B. </s>
            <s xml:id="echoid-s1563" xml:space="preserve">ſed ipſi E B
              <lb/>
            æqualis eſt C A, ſive C F. </s>
            <s xml:id="echoid-s1564" xml:space="preserve">Ergo & </s>
            <s xml:id="echoid-s1565" xml:space="preserve">C F major quam C B:
              <lb/>
            </s>
            <s xml:id="echoid-s1566" xml:space="preserve">ideoque punctum circumferentiæ F eſt ultra curvam N A B
              <lb/>
            à centro remotum.</s>
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