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

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        <div xml:id="echoid-div261" type="section" level="1" n="98">
          <pb o="135" file="0195" n="213" rhead="HOROLOG. OSCILLATOR."/>
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        <div xml:id="echoid-div265" type="section" level="1" n="99">
          <head xml:id="echoid-head125" xml:space="preserve">PROPOSITIO IX.</head>
          <note position="right" xml:space="preserve">
            <emph style="sc">De centro-</emph>
            <lb/>
            <emph style="sc">OSCILLA-</emph>
            <lb/>
            <emph style="sc">TIONIS.</emph>
          </note>
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            <s xml:id="echoid-s3047" xml:space="preserve">DAtâ figurâ planâ & </s>
            <s xml:id="echoid-s3048" xml:space="preserve">in eodem plano lineâ re-
              <lb/>
            ctâ, quæ vel ſecet figuram vel non, ad quam
              <lb/>
            perpendiculares cadant à particulis ſingulis minimis
              <lb/>
            & </s>
            <s xml:id="echoid-s3049" xml:space="preserve">æqualibus, in quas figura diviſa intelligitur;
              <lb/>
            </s>
            <s xml:id="echoid-s3050" xml:space="preserve">invenire ſummam quadratorum ab omnibus iſtis per-
              <lb/>
            pendicularibus; </s>
            <s xml:id="echoid-s3051" xml:space="preserve">ſive planum, cujus multiplex, ſe-
              <lb/>
            cundum particularum numerum, dictæ quadrato-
              <lb/>
            rum ſummæ æquale ſit.</s>
            <s xml:id="echoid-s3052" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3053" xml:space="preserve">Sit data figura plana A B C, & </s>
            <s xml:id="echoid-s3054" xml:space="preserve">in eodem plano recta
              <lb/>
              <note position="right" xlink:label="note-0195-02" xlink:href="note-0195-02a" xml:space="preserve">TAB. XIX.
                <lb/>
              Fig. 5. 6.</note>
            E D; </s>
            <s xml:id="echoid-s3055" xml:space="preserve">divisâque figurâ cogitatu in particulas minimas æqua-
              <lb/>
            les, intelligantur ab unaquaque earum perpendiculares du-
              <lb/>
            ctæ in rectam E D, ſicut à particula F ducta eſt F K. </s>
            <s xml:id="echoid-s3056" xml:space="preserve">O-
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            porteatque invenire ſummam quadratorum ab omnibus iſtis
              <lb/>
            perpendicularibus.</s>
            <s xml:id="echoid-s3057" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3058" xml:space="preserve">Sit datæ E D parallela recta A L, quæ figuram tangat,
              <lb/>
            ac tota extra eam poſita ſit. </s>
            <s xml:id="echoid-s3059" xml:space="preserve">Poteſt autem figuram vel ab ea-
              <lb/>
            dem parte ex qua eſt E D, vel à parte oppoſita contingere.
              <lb/>
            </s>
            <s xml:id="echoid-s3060" xml:space="preserve">Diſtantia vero centri gravitatis figuræ ab recta A L ſit recta
              <lb/>
            G A, ſecans E D in E; </s>
            <s xml:id="echoid-s3061" xml:space="preserve">& </s>
            <s xml:id="echoid-s3062" xml:space="preserve">ſubcentrica cunei, ſuper figura
              <lb/>
            abſciſſi plano per rectam A L, ſit H A. </s>
            <s xml:id="echoid-s3063" xml:space="preserve">Dico ſummam qua-
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            dratorum quæſitam æquari rectangulo A G H una cum qua-
              <lb/>
            drato E G, multiplicibus ſecundum particularum numerum,
              <lb/>
            in quas figura diviſa intelligitur.</s>
            <s xml:id="echoid-s3064" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3065" xml:space="preserve">Occurrat enim F K, ſi opus eſt producta, tangenti A L
              <lb/>
            in L puncto. </s>
            <s xml:id="echoid-s3066" xml:space="preserve">Itaque primum, eo caſu quo recta E D à ſi-
              <lb/>
            gura diſtat, & </s>
            <s xml:id="echoid-s3067" xml:space="preserve">tangens A L ad eandem figuræ partem ducta
              <lb/>
            eſt, ſic propoſitum oſtendetur. </s>
            <s xml:id="echoid-s3068" xml:space="preserve">Summa omnium quadrato-
              <lb/>
            rum F K æquatur totidem quadratis K L, una cum bis to-
              <lb/>
            tidem rectangulis K L F, & </s>
            <s xml:id="echoid-s3069" xml:space="preserve">totidem inſuper quadratis L F.
              <lb/>
            </s>
            <s xml:id="echoid-s3070" xml:space="preserve">Sed quadrata K L æquantur totidem quadratis E A. </s>
            <s xml:id="echoid-s3071" xml:space="preserve">Et re-
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            ctangula K L F æqualia eſſe conſtat totidem </s>
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