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

Table of contents

< >
< >
page |< < (169) of 434 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div353" type="section" level="1" n="126">
          <pb o="169" file="0243" n="268" rhead="HOROLOG. OSCILLATOR."/>
          <note position="right" xml:space="preserve">
            <emph style="sc">Decentro</emph>
            <lb/>
            <emph style="sc">OSCILLA-</emph>
            <lb/>
            <emph style="sc">TIONIS</emph>
          .</note>
        </div>
        <div xml:id="echoid-div354" type="section" level="1" n="127">
          <head xml:id="echoid-head153" style="it" xml:space="preserve">Centrum oſcillationis Conoidis Hyperbolici.</head>
          <p>
            <s xml:id="echoid-s3832" xml:space="preserve">In conoide quoque hyperbolico centrum oſcillationis inve-
              <lb/>
              <note position="right" xlink:label="note-0243-02" xlink:href="note-0243-02a" xml:space="preserve">TAB. XXVI.
                <lb/>
              Fig. 3.</note>
            niri poteſt. </s>
            <s xml:id="echoid-s3833" xml:space="preserve">Si enim, exempli gratia, ſit conoides cujus ſe-
              <lb/>
            ctio per axem, hyperbola B A B; </s>
            <s xml:id="echoid-s3834" xml:space="preserve">axem habens A D, la-
              <lb/>
            tus tranſverſum A F: </s>
            <s xml:id="echoid-s3835" xml:space="preserve">erit figura plana ipſi proportionalis
              <lb/>
            B K A K B, contenta baſi B B, & </s>
            <s xml:id="echoid-s3836" xml:space="preserve">parabolicæ lineæ por-
              <lb/>
            tionibus ſimilibus A K B, quæ parabolæ per verticem A
              <lb/>
            tranſeunt, axemque habent G E, dividentem bifariam latus
              <lb/>
            tranſverſum A F, ac parallelum baſi B B. </s>
            <s xml:id="echoid-s3837" xml:space="preserve">Et hujus quidem
              <lb/>
            figuræ B K A K B, centrum gravitatis L, tantum diſtat à
              <lb/>
            vertice A, quantum centrum gravitatis conoidis A B B; </s>
            <s xml:id="echoid-s3838" xml:space="preserve">eſt-
              <lb/>
            que axis A D ad A L, ſicut tripla F A cum dupla A D,
              <lb/>
            ad duplam F A cum ſesquialtera A D. </s>
            <s xml:id="echoid-s3839" xml:space="preserve">Deinde & </s>
            <s xml:id="echoid-s3840" xml:space="preserve">diſtantia
              <lb/>
            centri gr. </s>
            <s xml:id="echoid-s3841" xml:space="preserve">figuræ dimidiæ A D B K, ab A D, inveniri po-
              <lb/>
            teſt, atque etiam ſubcentrica cunei ſuper figura B K A K B,
              <lb/>
            abſciſſi plano per A P, parallelam B B; </s>
            <s xml:id="echoid-s3842" xml:space="preserve">hujus inquam cu-
              <lb/>
            nei ſubcentrica, ſuper ipſa A P, inveniri quoque poteſt;
              <lb/>
            </s>
            <s xml:id="echoid-s3843" xml:space="preserve">atque ex his conſequenter centrum agitationis conoidis, in
              <lb/>
            quavis ſuſpenſione; </s>
            <s xml:id="echoid-s3844" xml:space="preserve">dummodo axis, circa quem movetur,
              <lb/>
            ſit baſi conoidis parallelus. </s>
            <s xml:id="echoid-s3845" xml:space="preserve">Atque invenio quidem, ſi axis
              <lb/>
            A D lateri tranſverſo A F æqualis ponatur, ſpatium appli-
              <lb/>
            candum æquari {1/20} quadrati A D, cum {31/200
              <unsure/>
            } quadrati D B. </s>
            <s xml:id="echoid-s3846" xml:space="preserve">
              <lb/>
            Tunc autem A L eſt {7/10} A D.</s>
            <s xml:id="echoid-s3847" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3848" xml:space="preserve">Unde, ſi conoides hujuſmodi ex vertice A ſuſpendatur,
              <lb/>
            invenitur longitudo penduli iſochroni, A S, æqualis {2/3}{7/5} A D,
              <lb/>
            cum {31/140} tertiæ proportionalis duabus A D, D B.</s>
            <s xml:id="echoid-s3849" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div356" type="section" level="1" n="128">
          <head xml:id="echoid-head154" style="it" xml:space="preserve">Centrum oſcillationis dimidii Coni.</head>
          <p>
            <s xml:id="echoid-s3850" xml:space="preserve">Denique & </s>
            <s xml:id="echoid-s3851" xml:space="preserve">in ſolidis dimidiatis quibuſdam, quæ fiunt
              <lb/>
              <note position="right" xlink:label="note-0243-03" xlink:href="note-0243-03a" xml:space="preserve">TAB. XXVII.
                <lb/>
              Fig. 2.</note>
            ſectione per axem, centrum agitationis invenire licebit. </s>
            <s xml:id="echoid-s3852" xml:space="preserve">Ut
              <lb/>
            ſi ſit conus dimidiatus A B C, verticem habens A, diame-
              <lb/>
            trum ſemicirculi baſeos B C: </s>
            <s xml:id="echoid-s3853" xml:space="preserve">ejus quidem centrum gravita-
              <lb/>
            tis D notum eſt, quoniam A D eſt {3/4} rectæ A E, ita divi-
              <lb/>
            dentis B C in E, ut, ſicut quadrans circumferentiæ </s>
          </p>
        </div>
      </text>
    </echo>
Impressum