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

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          <pb o="148" file="0212" n="232" rhead="CHRISTIANI HUGENII"/>
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        <div xml:id="echoid-div291" type="section" level="1" n="106">
          <head xml:id="echoid-head132" xml:space="preserve">PROPOSITIO XVI.</head>
          <note position="left" xml:space="preserve">
            <emph style="sc">De centro</emph>
            <lb/>
            <emph style="sc">OSCILLA-</emph>
            <lb/>
            <emph style="sc">TIONIS</emph>
          .</note>
          <p style="it">
            <s xml:id="echoid-s3347" xml:space="preserve">FIgura quævis, ſive linea fuerit, ſive ſuperſi-
              <lb/>
            cies, ſive ſolidum; </s>
            <s xml:id="echoid-s3348" xml:space="preserve">ſi aliter at que aliter ſuſpen-
              <lb/>
            datur, agiteturque ſuper axibus inter ſe paralle-
              <lb/>
            lis, quique à centro gravitatis figuræ æqualiter di-
              <lb/>
            ſtent, ſibi ipſi iſochrona eſt.</s>
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          </p>
          <p>
            <s xml:id="echoid-s3350" xml:space="preserve">Proponatur magnitudo quævis, cujus centrum gravitatis
              <lb/>
            E punctum, ſitque primo ſuſpenſa ab axe, qui per F intel-
              <lb/>
              <note position="left" xlink:label="note-0212-02" xlink:href="note-0212-02a" xml:space="preserve">TAB. XXI.
                <lb/>
              Fig. 3.</note>
            ligitur hujus paginæ plano ad angulos rectos. </s>
            <s xml:id="echoid-s3351" xml:space="preserve">Itaque idem
              <lb/>
            planum erit & </s>
            <s xml:id="echoid-s3352" xml:space="preserve">planum oſcillationis. </s>
            <s xml:id="echoid-s3353" xml:space="preserve">In quo ſi centro E, ra-
              <lb/>
            dio E F, deſcribatur circumferentia F H G, ſumptoque in
              <lb/>
            illa puncto quovis, ut H, magnitudo ſecundò ſuſpendi intel-
              <lb/>
            ligatur ab axe in hoc puncto infixo, atque agitari, manente
              <lb/>
            eodem oſcillationis plano. </s>
            <s xml:id="echoid-s3354" xml:space="preserve">Dico iſochronam fore ſibi ipſi agi-
              <lb/>
            tatæ circa axem in F.</s>
            <s xml:id="echoid-s3355" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3356" xml:space="preserve">Intelligatur enim dividi magnitudo propoſita in particu-
              <lb/>
            las minimas æquales. </s>
            <s xml:id="echoid-s3357" xml:space="preserve">Itaque, quia in utraque illa ſuſpenſio-
              <lb/>
            ne idem manet oſcillationis planum, reſpectu partium ma-
              <lb/>
            gnitudinis; </s>
            <s xml:id="echoid-s3358" xml:space="preserve">manifeſtum eſt, ſi ab omnibus particulis, in quas
              <lb/>
            diviſa eſt magnitudo, perpendiculares cadere concipiantur
              <lb/>
            in dictum oſcillationis planum, illas utraque ſuſpenſione oc-
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            currere ipſi in punctis iisdem. </s>
            <s xml:id="echoid-s3359" xml:space="preserve">Sint autem hæc puncta ea
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            quæ apparent in ſpatio A B C D.</s>
            <s xml:id="echoid-s3360" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s3361" xml:space="preserve">Quum igitur E ſit centrum gravitatis magnitudinis pro-
              <lb/>
            poſitæ, ipſaque proinde circa axem, qui per E punctum
              <lb/>
            erectus eſt ad planum A B C D, quovis ſitu æquilibrium
              <lb/>
            ſervet; </s>
            <s xml:id="echoid-s3362" xml:space="preserve">facile perſpicitur, quod ſi punctis omnibus ante di-
              <lb/>
            ctis, quæ in ſpatio A B C D ſignantur, æqualis gravitas
              <lb/>
            tribuatur, eorum quoque omnium centrum gravitatis futu-
              <lb/>
            rum eſt punctum E. </s>
            <s xml:id="echoid-s3363" xml:space="preserve">Quod ſi vero, ut fieri poteſt, in pun-
              <lb/>
            cta aliqua plures perpendiculares coincidant, illa puncta
              <lb/>
            quaſi toties geminata intelligenda ſunt, gravitatesque toties
              <lb/>
            multiplices accipiendæ. </s>
            <s xml:id="echoid-s3364" xml:space="preserve">Atque ita conſideratorum, patet
              <lb/>
            rurſus centrum gravitatis eſſe E punctum.</s>
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