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

Page concordance

< >
Scan Original
191 119
192 120
193 121
194 122
195
196
197
198 123
199 124
200 125
201 126
202 127
203 128
204
205
206
207 129
208 130
209 131
210 132
211 133
212 134
213 135
214 136
215
216
217
218 137
219 138
220 139
< >
page |< < (166) of 434 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div342" type="section" level="1" n="121">
          <pb o="166" file="0238" n="262" rhead="CHRISTIANI HUGENII"/>
        </div>
        <div xml:id="echoid-div344" type="section" level="1" n="122">
          <head xml:id="echoid-head148" style="it" xml:space="preserve">Centrum oſcillationis in Pyramide.</head>
          <note position="left" xml:space="preserve">
            <emph style="sc">Decentro</emph>
            <lb/>
            <emph style="sc">OSCILLA-</emph>
            <lb/>
            <emph style="sc">TIONIS</emph>
          .</note>
          <p>
            <s xml:id="echoid-s3770" xml:space="preserve">Sit primum A B C pyramis, verticem habens A, axem
              <lb/>
              <note position="left" xlink:label="note-0238-02" xlink:href="note-0238-02a" xml:space="preserve">TAB.XXVI.
                <lb/>
              Fig. 1.</note>
            A D, baſin vero quadratum, cujus latus B C. </s>
            <s xml:id="echoid-s3771" xml:space="preserve">ponaturque
              <lb/>
            agitari circa axem qui, per verticem A, ſit hujus paginæ
              <lb/>
            plano ad angulos rectos.</s>
            <s xml:id="echoid-s3772" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3773" xml:space="preserve">Hic figura plana proportionalis O V V, à latere adpo-
              <lb/>
            nenda, ſecundum propoſitionem 14, conſtabit ex reſiduis
              <lb/>
            parabolicis O P V, quæ nempe ſuperſunt, cum, à rectan-
              <lb/>
            gulis Ω P, auferuntur ſemiparabolæ O V Ω, verticem ha-
              <lb/>
            bentes O.</s>
            <s xml:id="echoid-s3774" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3775" xml:space="preserve">Sicut enim inter ſe ſectiones pyramidis B C, N N, ita
              <lb/>
            quoque rectæ V V, R R, ipſis in figura plana reſponden-
              <lb/>
            tes. </s>
            <s xml:id="echoid-s3776" xml:space="preserve">& </s>
            <s xml:id="echoid-s3777" xml:space="preserve">ſicut centrum gravitatis E diſtat, à vertice pyrami-
              <lb/>
            dis, tribus quartis axis A D, ita quoque centrum gravita-
              <lb/>
            tis F, figuræ O V V, diſtabit tribus quartis diametri O P
              <lb/>
            à vertice O.</s>
            <s xml:id="echoid-s3778" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3779" xml:space="preserve">Intellecto porro horizontali plano N E, per centrum gra-
              <lb/>
            vitatis pyramidis A B C, quod idem figuram O V V ſecet
              <lb/>
            ſecundum R F; </s>
            <s xml:id="echoid-s3780" xml:space="preserve">inventâque ſubcentricâ cunei, ſuper figura
              <lb/>
            O V V abſciſſi plano per O Ω, quæ ſubcentrica ſit O G,
              <lb/>
            (eſt autem {4/5} diametri O P) erit rectangulum O F G, mul-
              <lb/>
            tiplex per numerum particularum figuræ O V V, æquale
              <lb/>
            quadratis diſtantiarum ab recta R F , ac proinde
              <note symbol="*" position="left" xlink:label="note-0238-03" xlink:href="note-0238-03a" xml:space="preserve">Prop. 10.
                <lb/>
              huj.</note>
            quadratis diſtantiarum à plano N E, particularum ſolidi
              <lb/>
            A B C. </s>
            <s xml:id="echoid-s3781" xml:space="preserve">Fit autem rectangulum O F G æquale {3/80} quadrati
              <lb/>
            O P, vel quadrati A D.</s>
            <s xml:id="echoid-s3782" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3783" xml:space="preserve">Deinde, ad inveniendam ſummam quadratorum à diſtan-
              <lb/>
            tiis à plano A D, noſcenda primo ſubcentrica cunei, ſuper
              <lb/>
            quadratâ baſi pyramidis B C abſciſſi, plano per rectam quæ
              <lb/>
            in B intelligitur axi A parallela; </s>
            <s xml:id="echoid-s3784" xml:space="preserve">quæ ſubcentrica ſit B K;
              <lb/>
            </s>
            <s xml:id="echoid-s3785" xml:space="preserve">eſtque {2/3} B C. </s>
            <s xml:id="echoid-s3786" xml:space="preserve">Noſcenda item diſtantia centr. </s>
            <s xml:id="echoid-s3787" xml:space="preserve">gr. </s>
            <s xml:id="echoid-s3788" xml:space="preserve">dimidiæ fi-
              <lb/>
            guræ O P V ab O P; </s>
            <s xml:id="echoid-s3789" xml:space="preserve">quæ ſit Φ P; </s>
            <s xml:id="echoid-s3790" xml:space="preserve">eſtque {3/10} P V. </s>
            <s xml:id="echoid-s3791" xml:space="preserve">Inde,
              <lb/>
            diviſà bifariam P V in Δ, ſi fiat ut Δ P ad P Φ, hoc eſt,
              <lb/>
            ut 5 ad 3, ita rectangulum B D K, quod eſt {1/12} quadrati
              <lb/>
            B C, ad aliud ſpatium Z; </s>
            <s xml:id="echoid-s3792" xml:space="preserve">erit hoc, multiplex </s>
          </p>
        </div>
      </text>
    </echo>
Impressum