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

Table of contents

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[71.] PROPOSITIO XI.
[72.] HOROLOGII OSCILLATORII PARS QUARTA. De centro Oſcillationis.
[73.] DEFINITIONES.
[76.] III.
[80.] VII.
[81.] VIII.
[85.] XII.
[86.] XIII.
[87.] HYPOTHESES. I.
[89.] PROPOSITIO I.
[90.] PROPOSITIO II.
[91.] PROPOSITIO III.
[92.] PROPOSITIO IV.
[93.] PROPOSITIO V.
[94.] PROPOSITIO VI.
[95.] DEFINITIO XIV.
[96.] DEFINITIO XV.
[97.] PROPOSITIO VII.
[98.] PROPOSITIO VIII.
[99.] PROPOSITIO IX.
[100.] PROPOSITIO X.
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          <head xml:id="echoid-head81" xml:space="preserve">PROPOSITIO II.</head>
          <note position="left" 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>
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            <emph style="sc">NE.</emph>
            <lb/>
          TAB. XII.
            <lb/>
          Fig. 2.</note>
          <p style="it">
            <s xml:id="echoid-s2039" xml:space="preserve">OMnis curva linea terminata, in unam partem
              <lb/>
            cava, ut A B D, ut poteſt in tot partes dividi, ut
              <lb/>
            ſi ſingulis partibus ſubtenſæ rectæ ducantur, velut
              <lb/>
            A B, B C, C D; </s>
            <s xml:id="echoid-s2040" xml:space="preserve">& </s>
            <s xml:id="echoid-s2041" xml:space="preserve">à ſingulis item diviſionis
              <lb/>
            punctis, ipſaque curvæ extremitate rectæ ducan-
              <lb/>
            tur curvam tangentes, ut A N, B O, C P, quæ
              <lb/>
            occurrant iis, quæ in proxime ſequentibus diviſionis
              <lb/>
            punctis curvæ ad angulos rectos inſiſtunt, quales
              <lb/>
            ſunt lineæ B N, C O, D P; </s>
            <s xml:id="echoid-s2042" xml:space="preserve">ut inquam ſubtenſa
              <lb/>
            quæque habeat ad ſibi adjacentem curvæ perpendi-
              <lb/>
            cularem, velut A B ad B N, B C ad C O, C D
              <lb/>
            ad D P, rationem majorem quavis ratione propo-
              <lb/>
            ſita.</s>
            <s xml:id="echoid-s2043" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2044" xml:space="preserve">Sit enim data ratio lineæ E F ad F G, quæ recto angulo
              <lb/>
            ad F jungantur, & </s>
            <s xml:id="echoid-s2045" xml:space="preserve">ducatur recta G E H.</s>
            <s xml:id="echoid-s2046" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2047" xml:space="preserve">Intelligatur primo curva A B D in partes tam exiguas ſe-
              <lb/>
            cta punctis B, C, ut tangentes quæ ad bina quæque inter
              <lb/>
            ſe proxima puncta curvam contingunt, occurrant ſibi mutuo
              <lb/>
            ſecundum angulos qui ſinguli majores ſint angulo F E H;
              <lb/>
            </s>
            <s xml:id="echoid-s2048" xml:space="preserve">quales ſunt anguli A K B, B L C, C M D. </s>
            <s xml:id="echoid-s2049" xml:space="preserve">quod quidem
              <lb/>
            fieri poſſe evidentius eſt quam ut demonſtratione indigeat. </s>
            <s xml:id="echoid-s2050" xml:space="preserve">
              <lb/>
            Ductis jam ſubtenſis A B, B C, C D, & </s>
            <s xml:id="echoid-s2051" xml:space="preserve">erectis curvæ
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            perpendicularibus B N, C O, D P, quæ occurrant pro-
              <lb/>
            ductis A K, B L, C M, in N, O, P: </s>
            <s xml:id="echoid-s2052" xml:space="preserve">dico rationes ſin-
              <lb/>
            gulas rectarum, A B ad B N, B C ad C O, C D ad D P,
              <lb/>
            majores eſſe ratione E F ad F G.</s>
            <s xml:id="echoid-s2053" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2054" xml:space="preserve">Quia enim angulus A K B major eſt angulo H E F, erit
              <lb/>
            reſiduus illius ad duos rectos, nimirum angulus N K B,
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            minor angulo G E F. </s>
            <s xml:id="echoid-s2055" xml:space="preserve">Angulus autem B trianguli K B N
              <lb/>
            eſt rectus, ſicut & </s>
            <s xml:id="echoid-s2056" xml:space="preserve">angulus F in triangulo E F G. </s>
            <s xml:id="echoid-s2057" xml:space="preserve"/>
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