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

Table of contents

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[41.] PROPOSITIO XVIII.
[42.] PROPOSITIO XIX.
[43.] PROPOSITIO XX.
[44.] PROPOSITIO XXI.
[45.] PROPOSITIO XXII.
[46.] LEMMA.
[47.] PROPOSITIO XXIII.
[48.] PROPOSITIO XXIV.
[49.] PROPOSITIO XXV.
[50.] PROPOSITIO XXVI.
[51.] HOROLOGII OSCILLATORII PARS TERTIA.
[52.] DEFINITIONES. I.
[53.] II.
[54.] III.
[56.] PROPOSITIOI.
[57.] PROPOSITIO II.
[58.] PROPOSITIO III.
[59.] PROPOSITIO IV.
[60.] PROPOSITIO V.
[61.] PROPOSITIO VI.
[62.] PROPOSITIO VII.
[63.] PROPOSITIO VIII.
[64.] PROPOSITIO IX.
[65.] Conoidis parabolici ſuperficiei curvæ circulum æqualem invenire.
[66.] Sphæroidis oblongi ſuperſiciei circulum æqualem invenire.
[67.] Sphæroidis lati ſive compreſſi ſuperficiei circulum æqualem invenire.
[68.] Conoidis hyperbolici ſuperficiei curvæ circulum æqualem invenire.
[69.] Curvæ parabolicæ æqualem rectam lineam invenire.
[70.] PROPOSITIO X.
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            <s xml:id="echoid-s2057" xml:space="preserve">
              <pb o="93" file="0139" n="150" rhead="HOROLOG. OSCILLATOR."/>
            major erit ratio K B ad B N quam E F ad F G. </s>
            <s xml:id="echoid-s2058" xml:space="preserve">Sed A B
              <lb/>
              <note position="right" xlink:label="note-0139-01" xlink:href="note-0139-01a" xml:space="preserve">
                <emph style="sc">De linea-</emph>
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                <emph style="sc">RUM CUR-</emph>
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                <emph style="sc">VARUM</emph>
                <lb/>
                <emph style="sc">EVOLUTIO-</emph>
                <lb/>
                <emph style="sc">NE.</emph>
              </note>
            major eſt quam K B, quoniam angulus K in triangulo A K B
              <lb/>
            eſt obtuſus, eſt enim major angulo H E F qui eſt obtuſus
              <lb/>
            ex conſtructione. </s>
            <s xml:id="echoid-s2059" xml:space="preserve">Ergo ratio A B ad B N major erit ratio-
              <lb/>
            ne K B ad B N, ac proinde omnino major ratione E F ad
              <lb/>
            F G. </s>
            <s xml:id="echoid-s2060" xml:space="preserve">Eodem modo & </s>
            <s xml:id="echoid-s2061" xml:space="preserve">ratio B C ad C O, & </s>
            <s xml:id="echoid-s2062" xml:space="preserve">C D ad D P,
              <lb/>
            major oſtendetur ratione E F ad F G. </s>
            <s xml:id="echoid-s2063" xml:space="preserve">Itaque conſtat pro-
              <lb/>
            poſitum.</s>
            <s xml:id="echoid-s2064" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div157" type="section" level="1" n="58">
          <head xml:id="echoid-head82" xml:space="preserve">PROPOSITIO III.</head>
          <p style="it">
            <s xml:id="echoid-s2065" xml:space="preserve">DUæ curvæ in unam partem inflexæ & </s>
            <s xml:id="echoid-s2066" xml:space="preserve">in eas-
              <lb/>
            dem partes cavæ ex eodem puncto egredi ne-
              <lb/>
            queunt, ita ad ſe invicem comparatæ, ut recta
              <lb/>
            omnis quæ alteri earum ad angulos rectos occurrit,
              <lb/>
            ſimiliter occurrat & </s>
            <s xml:id="echoid-s2067" xml:space="preserve">reliquæ.</s>
            <s xml:id="echoid-s2068" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2069" xml:space="preserve">Sint enim, ſi fieri poteſt, hujuſmodi lineæ curvæ A C E,
              <lb/>
              <note position="right" xlink:label="note-0139-02" xlink:href="note-0139-02a" xml:space="preserve">TAB. XII.
                <lb/>
              Fig. 3.</note>
            A G K, communem terminum habentes A, & </s>
            <s xml:id="echoid-s2070" xml:space="preserve">ſumpto in ex-
              <lb/>
            teriore illarum puncto quolibet K, ſit inde educta K E recta,
              <lb/>
            curvæ A G K occurrens ad angulos rectos, ac proinde
              <lb/>
            etiam curvæ A C E.</s>
            <s xml:id="echoid-s2071" xml:space="preserve"/>
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            <s xml:id="echoid-s2072" xml:space="preserve">Poteſt jam recta quædam ſumi major curva K G A, quæ
              <lb/>
            ſit Q. </s>
            <s xml:id="echoid-s2073" xml:space="preserve">Diviſa autem intelligatur ipſa K G A, ut in propo-
              <lb/>
            ſitione antecedenti dictum fuit, in tot partes punctis H G F,
              <lb/>
            ut ſubtenſæ ſingulæ K H, H G, G F, F A, ad perpen-
              <lb/>
            diculares curvæ ſibi contiguas H M, G N, F O, A P
              <lb/>
            majorem rationem habeant quam linea Q ad rectam K E.
              <lb/>
            </s>
            <s xml:id="echoid-s2074" xml:space="preserve">Itaque & </s>
            <s xml:id="echoid-s2075" xml:space="preserve">omnes ſimul dictæ ſubtenſæ ad omnes dictas per-
              <lb/>
            pendiculares majorem habebunt rationem quam Q ad K E. </s>
            <s xml:id="echoid-s2076" xml:space="preserve">
              <lb/>
            Producantur autem perpendiculares eædem & </s>
            <s xml:id="echoid-s2077" xml:space="preserve">occurrant cur-
              <lb/>
            væ A C E in D, C, B, nimirum ad angulos rectos ex
              <lb/>
            hypotheſi. </s>
            <s xml:id="echoid-s2078" xml:space="preserve">Erit jam K E minor quam M D. </s>
            <s xml:id="echoid-s2079" xml:space="preserve">Etenim, ducta
              <lb/>
            E L ipſi K E perpendiculari, quoniam K E occurrit lineæ
              <lb/>
            curvæ E C A ad angulos rectos, tanget E L curvam A C E,
              <lb/>
            occurretque neceſſario rectæ M D inter D & </s>
            <s xml:id="echoid-s2080" xml:space="preserve">M. </s>
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