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

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              <pb o="137" file="0199" n="218" rhead="HOROLOG. OSCILLATOR."/>
            tis figuræ A B C; </s>
            <s xml:id="echoid-s3100" xml:space="preserve">erit ſumma quadratorum à di-
              <lb/>
              <note position="right" xlink:label="note-0199-01" xlink:href="note-0199-01a" xml:space="preserve">
                <emph style="sc">De centro</emph>
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                <emph style="sc">OSCILLA-</emph>
                <lb/>
                <emph style="sc">TIONIS</emph>
              .</note>
            ſtantiis particularum, in quas figura diviſa intel-
              <lb/>
            ligitur, ab recta E D, æqualis rectangulo ſoli
              <lb/>
            A G H, multiplici ſecundum ipſarum particula-
              <lb/>
            rum numerum.</s>
            <s xml:id="echoid-s3101" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3102" xml:space="preserve">Hoc enim manifeſtum eſt, quum nullum tunc ſit quadra-
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            tum E G.</s>
            <s xml:id="echoid-s3103" xml:space="preserve"/>
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        <div xml:id="echoid-div271" type="section" level="1" n="101">
          <head xml:id="echoid-head127" xml:space="preserve">PROPOSITIO XI.</head>
          <p style="it">
            <s xml:id="echoid-s3104" xml:space="preserve">POſitis rurſus cæteris ut in præcedentium penul-
              <lb/>
              <note position="right" xlink:label="note-0199-02" xlink:href="note-0199-02a" xml:space="preserve">TAB. XX.
                <lb/>
              Fig. 4.</note>
            tima; </s>
            <s xml:id="echoid-s3105" xml:space="preserve">ſi D E ſit axis figuræ planæ A B C, in
              <lb/>
            duas æquales ſimilesque portiones eam dividens, ſit-
              <lb/>
            que inſuper V G diſtantia centri gravitatis dimi-
              <lb/>
            diæ figuræ D A D ab recta E D, cunei vero, ſu-
              <lb/>
            per ipſam abſciſſi per ipſam E D, ſubcentrica G X;
              <lb/>
            </s>
            <s xml:id="echoid-s3106" xml:space="preserve">erit rectangulum X G V æquale rectangulo A G H.</s>
            <s xml:id="echoid-s3107" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3108" xml:space="preserve">Eſt enim rectangulum X G V, multiplex ſecundum nu-
              <lb/>
            merum particularum figuræ D A D, æquale quadratis omni-
              <lb/>
            bus perpendicularium à particulis ejusdem figuræ dimidiæ in
              <lb/>
            rectam E D cadentium . </s>
            <s xml:id="echoid-s3109" xml:space="preserve">Ac proinde idem
              <note symbol="*" position="right" xlink:label="note-0199-03" xlink:href="note-0199-03a" xml:space="preserve">Prop. @.
                <lb/>
              huj.</note>
            X G V, multiplex ſecundum numerum particularum totius
              <lb/>
            figuræ A B C, æquale erit quadratis perpendicularium, ab
              <lb/>
            omnibus particulis figuræ hujus in rectam E D demiſſarum;
              <lb/>
            </s>
            <s xml:id="echoid-s3110" xml:space="preserve">hoc eſt, rectangulo A G H multiplici ſecundum eundem
              <lb/>
            particularum numerum, ut conſtat ex propoſ. </s>
            <s xml:id="echoid-s3111" xml:space="preserve">præcedenti. </s>
            <s xml:id="echoid-s3112" xml:space="preserve">
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            Unde ſequitur rectangula X G V, A G H inter ſe æqualia
              <lb/>
            eſſe. </s>
            <s xml:id="echoid-s3113" xml:space="preserve">quod erat demonſtrandum.</s>
            <s xml:id="echoid-s3114" xml:space="preserve"/>
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        <div xml:id="echoid-div274" type="section" level="1" n="102">
          <head xml:id="echoid-head128" xml:space="preserve">PROPOSITIO XII.</head>
          <p style="it">
            <s xml:id="echoid-s3115" xml:space="preserve">DAtis in plano punctis quotlibet; </s>
            <s xml:id="echoid-s3116" xml:space="preserve">ſi ex centro
              <lb/>
            gravitatis eorum circulus quilibet deſcribatur;</s>
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