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

Table of Notes

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          <head xml:id="echoid-head148" style="it" xml:space="preserve">Centrum oſcillationis in Pyramide.</head>
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            <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-
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            bentes O.</s>
            <s xml:id="echoid-s3774" xml:space="preserve"/>
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          <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"/>
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          <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>
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            <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>
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