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

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        <div xml:id="echoid-div98" type="section" level="1" n="39">
          <pb o="73" file="0111" n="118" rhead="HOROLOG. OSCILLATOR."/>
        </div>
        <div xml:id="echoid-div100" type="section" level="1" n="40">
          <head xml:id="echoid-head62" xml:space="preserve">PROPOSITIO XVII.</head>
          <note position="right" 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>
          <p style="it">
            <s xml:id="echoid-s1597" xml:space="preserve">IIsdem poſitis, ſi tertia recta prioribus parallela
              <lb/>
              <note position="right" xlink:label="note-0111-02" xlink:href="note-0111-02a" xml:space="preserve">TAB. VIII.
                <lb/>
              Fig. 3.</note>
            D K, circulum ſecuerit, quæ ab ea quæ centro
              <lb/>
            propior eſt A F, tantundem diſtet quantum hæc à
              <lb/>
            reliqua B G: </s>
            <s xml:id="echoid-s1598" xml:space="preserve">dico partem tangentis in A, à pa-
              <lb/>
            rallela ultimo adjecta, & </s>
            <s xml:id="echoid-s1599" xml:space="preserve">media interceptam, nem-
              <lb/>
            pe A D, arcu A C à primis duabus parallelis in-
              <lb/>
            tercepto minorem eſſe.</s>
            <s xml:id="echoid-s1600" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1601" xml:space="preserve">Hoc enim patet quum A D ipſi A B æqualis ſit, quam
              <lb/>
            antea oſtendimus arcu A C minorem eſſe.</s>
            <s xml:id="echoid-s1602" xml:space="preserve"/>
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        <div xml:id="echoid-div102" type="section" level="1" n="41">
          <head xml:id="echoid-head63" xml:space="preserve">PROPOSITIO XVIII.</head>
          <p style="it">
            <s xml:id="echoid-s1603" xml:space="preserve">SI circulum, cujus centrum E, duæ rectæ paral-
              <lb/>
              <note position="right" xlink:label="note-0111-03" xlink:href="note-0111-03a" xml:space="preserve">TAB. VIII.
                <lb/>
              Fig. 4.</note>
            lelæ ſecuerint A F, B G; </s>
            <s xml:id="echoid-s1604" xml:space="preserve">& </s>
            <s xml:id="echoid-s1605" xml:space="preserve">à puncto B, ubi
              <lb/>
            quæ à centro remotior eſt, vel tantundem atque
              <lb/>
            altera diſtat, circumferentiæ occurrit, ducatur
              <lb/>
            recta circumferentiam tangens: </s>
            <s xml:id="echoid-s1606" xml:space="preserve">erit pars hujus
              <lb/>
            B A, à parallelis intercepta, major arcu ab iis-
              <lb/>
            dem parallelis intercepto B C.</s>
            <s xml:id="echoid-s1607" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1608" xml:space="preserve">Ducatur enim in puncto C, recta M C L circumferentiam
              <lb/>
            tangens, quæ occurrat tangenti B A in L. </s>
            <s xml:id="echoid-s1609" xml:space="preserve">In triangulo igi-
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            tur A C L, angulus C æqualis eſt angulo M C F, hoc eſt,
              <lb/>
            ei quem capit portio circuli C B F. </s>
            <s xml:id="echoid-s1610" xml:space="preserve">angulus autem A æqua-
              <lb/>
            tur angulo quem capit portio circuli B C G, quæ portio
              <lb/>
            quum ſit major vel æqualis portioni C B F, quippe quum
              <lb/>
            B G vel ulterius diſtet à centro quam C F, vel tantun-
              <lb/>
            dem: </s>
            <s xml:id="echoid-s1611" xml:space="preserve">erit proinde trianguli A C L angulus A minor vel
              <lb/>
            æqualis angulo C: </s>
            <s xml:id="echoid-s1612" xml:space="preserve">& </s>
            <s xml:id="echoid-s1613" xml:space="preserve">conſequenter latus C L vel minus
              <lb/>
            vel æquale lateri A L. </s>
            <s xml:id="echoid-s1614" xml:space="preserve">Atqui C L una cum L B majores
              <lb/>
            ſunt arcu C B. </s>
            <s xml:id="echoid-s1615" xml:space="preserve">Ergo & </s>
            <s xml:id="echoid-s1616" xml:space="preserve">A L una cum L B, hoc eſt, </s>
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