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

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            <s xml:id="echoid-s2005" xml:space="preserve">
              <pb o="91" file="0135" n="145" rhead="HOROLOG. OSCILLATOR."/>
            C D & </s>
            <s xml:id="echoid-s2006" xml:space="preserve">ipſa D G. </s>
            <s xml:id="echoid-s2007" xml:space="preserve">Sed propter evolutionem, apparet utris-
              <lb/>
              <note position="right" xlink:label="note-0135-01" xlink:href="note-0135-01a" 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>
            que ſimul, rectæ C D, & </s>
            <s xml:id="echoid-s2008" xml:space="preserve">lineæ D G, æquari rectam H G.
              <lb/>
            </s>
            <s xml:id="echoid-s2009" xml:space="preserve">Ergo duæ ſimul C F, F G majores quoque erunt recta H G.</s>
            <s xml:id="echoid-s2010" xml:space="preserve">
              <unsure/>
              <lb/>
            & </s>
            <s xml:id="echoid-s2011" xml:space="preserve">ablata communi F G, erit C F major quam H F. </s>
            <s xml:id="echoid-s2012" xml:space="preserve">Sed
              <lb/>
            F E major eſt quam F C, quia angulus C trianguli F C E
              <lb/>
            eſt rectus. </s>
            <s xml:id="echoid-s2013" xml:space="preserve">Ergo F E omnino major quam F H. </s>
            <s xml:id="echoid-s2014" xml:space="preserve">Unde ap-
              <lb/>
            paret, ab hac quidem parte puncti C, fili extremitatem non
              <lb/>
            pertingere ad rectam C E.</s>
            <s xml:id="echoid-s2015" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2016" xml:space="preserve">Sit jam punctum H propinquius principio evolutionis A
              <lb/>
              <note position="right" xlink:label="note-0135-02" xlink:href="note-0135-02a" xml:space="preserve">TAB. XII.
                <lb/>
              Fig. 1.</note>
            quam punctum C, ſitque fili poſitio H G, tunc cum ejus
              <lb/>
            extremitas eſſet in H, & </s>
            <s xml:id="echoid-s2017" xml:space="preserve">ducantur rectæ D G, D H, qua-
              <lb/>
            rum hæc occurrat rectæ C E in E: </s>
            <s xml:id="echoid-s2018" xml:space="preserve">apparet autem D G re-
              <lb/>
            ctam non poſſe eſſe in directum ipſi H G, adeoque H G D
              <lb/>
            fore triangulum. </s>
            <s xml:id="echoid-s2019" xml:space="preserve">Jam quia recta D G vel minor eſt quam
              <lb/>
            D K G, vel eadem, ſi nempe evolutæ pars D G recta ſit;
              <lb/>
            </s>
            <s xml:id="echoid-s2020" xml:space="preserve">additâ utrique G H, erunt rectæ D G, G H ſimul mino-
              <lb/>
            res vel æquales duabus iſtis, ſcilicet D K G & </s>
            <s xml:id="echoid-s2021" xml:space="preserve">G H, ſive
              <lb/>
            his æquali rectæ D C. </s>
            <s xml:id="echoid-s2022" xml:space="preserve">Duabus autem rectis D G, G H mi-
              <lb/>
            nor eſt recta D H. </s>
            <s xml:id="echoid-s2023" xml:space="preserve">Ergo hæc minor utique erit rectâ D C. </s>
            <s xml:id="echoid-s2024" xml:space="preserve">
              <lb/>
            Sed D E major eſt quam D C, quia in triangulo D C E
              <lb/>
            angulus C eſt rectus. </s>
            <s xml:id="echoid-s2025" xml:space="preserve">Ergo D H multo minor quam D E. </s>
            <s xml:id="echoid-s2026" xml:space="preserve">
              <lb/>
            Situm eſt ergo punctum H, hoc eſt extremitas fili G H, in-
              <lb/>
            tra angulum D C E. </s>
            <s xml:id="echoid-s2027" xml:space="preserve">Unde apparet neque inter A & </s>
            <s xml:id="echoid-s2028" xml:space="preserve">C us-
              <lb/>
            quam illam pertingere ad rectam C E. </s>
            <s xml:id="echoid-s2029" xml:space="preserve">Ergo C E tangit
              <lb/>
            curvam A C in C; </s>
            <s xml:id="echoid-s2030" xml:space="preserve">ac proinde D C, cui C E ducta eſt
              <lb/>
            perpendicularis, occurrit curvæ ad angulos rectos. </s>
            <s xml:id="echoid-s2031" xml:space="preserve">quod
              <lb/>
            erat demonſtrandum.</s>
            <s xml:id="echoid-s2032" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s2033" xml:space="preserve">Hinc etiam manifeſtum eſt curvam A H C in partem u-
              <lb/>
            nam inflexam eſſe, & </s>
            <s xml:id="echoid-s2034" xml:space="preserve">in eandem partem cavam ac ipſa A G B,
              <lb/>
            cujus evolutione deſcripta eſt. </s>
            <s xml:id="echoid-s2035" xml:space="preserve">Omnes enim tangentes lineæ
              <lb/>
            A H C, cadunt extra ſpatium D G A H C: </s>
            <s xml:id="echoid-s2036" xml:space="preserve">omnes vero
              <lb/>
            tangentes lineæ A G D, intra dictum ſpatium. </s>
            <s xml:id="echoid-s2037" xml:space="preserve">unde liquet
              <lb/>
            cavitatem A H C reſpicere convexitatem A G D.</s>
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