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

Table of Notes

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            id ſecat in duas partes, centrum gravitatis plani ſic onerati
              <lb/>
            erit in ipſa lineâ rectâ.</s>
            <s xml:id="echoid-s6168" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s6169" xml:space="preserve">Sit planum Horizontale A B oneratum ponderibus C C,
              <lb/>
              <note position="left" xlink:label="note-0368-01" xlink:href="note-0368-01a" xml:space="preserve">TAB. XXXII.
                <lb/>
              Fig. 6.</note>
            D D & </s>
            <s xml:id="echoid-s6170" xml:space="preserve">quod manet in æquilibrio, impoſitum rectæ E F;
              <lb/>
            </s>
            <s xml:id="echoid-s6171" xml:space="preserve">dico centrum ejus gravitatis eſſe in illa linea E F; </s>
            <s xml:id="echoid-s6172" xml:space="preserve">nam poſi-
              <lb/>
            to, ſi fieri poteſt, centrum gravitatis eſſe alibi in puncto G,
              <lb/>
            ducatur per id punctum recta H K parallela ipſi E F.</s>
            <s xml:id="echoid-s6173" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s6174" xml:space="preserve">Tunc ergo, quia planum fultum in puncto G, manet
              <lb/>
            in ſuo ſitu Horizontali, debent, ducta linea recta qua-
              <lb/>
            cunque in plano per punctum G, pondera ad utramque par-
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            tem lineæ eſſe in æquilibrio.</s>
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            <s xml:id="echoid-s6176" xml:space="preserve">Idcirco pondera C C facient æquilibrium cum ponderibus
              <lb/>
            D D, quando planum fulcitur a recta H K: </s>
            <s xml:id="echoid-s6177" xml:space="preserve">id quod fieri
              <lb/>
            nequit, quoniam manet in æquilibrio fultum a recta E F;
              <lb/>
            </s>
            <s xml:id="echoid-s6178" xml:space="preserve">nam patet, omnes diſtantias ponderum ad unam partem eſſe
              <lb/>
            diminutas, ſcilicet ponderum C C, & </s>
            <s xml:id="echoid-s6179" xml:space="preserve">conſequenter etiam
              <lb/>
            effectus gravitatis eorum; </s>
            <s xml:id="echoid-s6180" xml:space="preserve">& </s>
            <s xml:id="echoid-s6181" xml:space="preserve">diſtantias ponderum oppoſito-
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            rum D D eſſe auctas, & </s>
            <s xml:id="echoid-s6182" xml:space="preserve">eodem tempore effectum eorum
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            gravitatis, adeo ut ultima pondera deflexura ſint planum ad
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            ſuam partem, & </s>
            <s xml:id="echoid-s6183" xml:space="preserve">multo magis ſi unum vel plura pondera
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            C C ſint ad alteram partem lineæ H K; </s>
            <s xml:id="echoid-s6184" xml:space="preserve">Centrum ergo gra-
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            vitatis plani onerati erit in linea E F. </s>
            <s xml:id="echoid-s6185" xml:space="preserve">Q. </s>
            <s xml:id="echoid-s6186" xml:space="preserve">E. </s>
            <s xml:id="echoid-s6187" xml:space="preserve">D.</s>
            <s xml:id="echoid-s6188" xml:space="preserve"/>
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            <s xml:id="echoid-s6189" xml:space="preserve">PROP. </s>
            <s xml:id="echoid-s6190" xml:space="preserve">III. </s>
            <s xml:id="echoid-s6191" xml:space="preserve">Duo gravia commenſur abilia appenſa ad extre-
              <lb/>
            mitates brachiorum Libræ erunt in æquilibrio, ſi brachia ſint
              <lb/>
            in ratione reciproca gravium.</s>
            <s xml:id="echoid-s6192" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s6193" xml:space="preserve">Sint gravia commenſurabilia A & </s>
            <s xml:id="echoid-s6194" xml:space="preserve">B, quorum A ſit ma-
              <lb/>
              <note position="left" xlink:label="note-0368-02" xlink:href="note-0368-02a" xml:space="preserve">TAB. XXXII.
                <lb/>
              Fig. 7.</note>
            jus; </s>
            <s xml:id="echoid-s6195" xml:space="preserve">& </s>
            <s xml:id="echoid-s6196" xml:space="preserve">libra C D E, cujus brachium D E ſit ad D C, ut
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            grave A ad grave B; </s>
            <s xml:id="echoid-s6197" xml:space="preserve">dico, libram eſſe in æquilibrio appenſo
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            A ad extremum C, & </s>
            <s xml:id="echoid-s6198" xml:space="preserve">B ad extremum E, ſi C E ſuſtineatur in D.</s>
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            <s xml:id="echoid-s6200" xml:space="preserve">Concipiatur planum parallelum ad horizontem tranſiens
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            per lineam C E, in eo plano ſint ductæ per puncta E
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            & </s>
            <s xml:id="echoid-s6201" xml:space="preserve">C rectæ L E G, K C M perpendiculares ad C E; </s>
            <s xml:id="echoid-s6202" xml:space="preserve">fiat
              <lb/>
            ulterius E F æquale C D, & </s>
            <s xml:id="echoid-s6203" xml:space="preserve">ducantur G F K, M D L
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            quæ cum C E angulos ſemirectos efficiunt & </s>
            <s xml:id="echoid-s6204" xml:space="preserve">ſeſe mutuò ad
              <lb/>
            angulos rectos ſecant in N; </s>
            <s xml:id="echoid-s6205" xml:space="preserve">illæ lineæ neceſſario occurrunt
              <lb/>
            duabus prioribus, quas duximus per E & </s>
            <s xml:id="echoid-s6206" xml:space="preserve">C; </s>
            <s xml:id="echoid-s6207" xml:space="preserve">ponamus </s>
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