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

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            <s xml:id="echoid-s3029" xml:space="preserve">
              <pb o="134" file="0194" n="212" rhead="CHRISTIANI HUGENII"/>
            nempe rectangulum fit à diſtantia centri gravitatis
              <lb/>
              <note position="left" xlink:label="note-0194-01" xlink:href="note-0194-01a" xml:space="preserve">
                <emph style="sc">De centro</emph>
                <lb/>
                <emph style="sc">OSCILLA-</emph>
                <lb/>
                <emph style="sc">TIONIS.</emph>
              </note>
            figuræ ab eadem recta, & </s>
            <s xml:id="echoid-s3030" xml:space="preserve">à ſubcentrica cunei, qui
              <lb/>
            per illam ſuper figura abſcinditur.</s>
            <s xml:id="echoid-s3031" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3032" xml:space="preserve">Poſitis enim cæteris omnibus quæ in conſtructione præce-
              <lb/>
              <note position="left" xlink:label="note-0194-02" xlink:href="note-0194-02a" xml:space="preserve">TAB. XIX.
                <lb/>
              Fig. 4.</note>
            denti, ſit L A cunei A B D ſubcentrica in rectam E E. </s>
            <s xml:id="echoid-s3033" xml:space="preserve">O-
              <lb/>
            portet igitur oſtendere, ſummam quadratorum omnium à di-
              <lb/>
            ſtantiis particularum figuræ A C B æquari rectangulo ab
              <lb/>
            F A, L A, multiplici ſecundum particularum numerum.</s>
            <s xml:id="echoid-s3034" xml:space="preserve"/>
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            <s xml:id="echoid-s3035" xml:space="preserve">Et conſtat quidem ex demonſtratione præcedenti, altitu-
              <lb/>
            dines parallelepipedorum ſingulorum, ut G K, æquales eſ-
              <lb/>
            ſe diſtantiis particularum, quæ ipſorum baſes ſunt, ut G,
              <lb/>
            ab recta A E. </s>
            <s xml:id="echoid-s3036" xml:space="preserve">Quare, ſi jam parallelepipedum G K ducamus
              <lb/>
            in diſtantiam G H, perinde eſt ac ſi particula G ducatur in
              <lb/>
            quadratum diſtantiæ G H. </s>
            <s xml:id="echoid-s3037" xml:space="preserve">Eodemque modo ſe res habet in
              <lb/>
            reliquis omnibus. </s>
            <s xml:id="echoid-s3038" xml:space="preserve">Atqui producta omnia parallelepipedorum
              <lb/>
            in diſtantias ſuas ab recta A E, æquantur ſimul producto ex
              <lb/>
            cuneo A B D in diſtantiam L A , quia cuneus gravitat
              <note symbol="*" position="left" xlink:label="note-0194-03" xlink:href="note-0194-03a" xml:space="preserve">Prop. 1.
                <lb/>
              huj.</note>
            per puncto L. </s>
            <s xml:id="echoid-s3039" xml:space="preserve">Ergo etiam ſumma productorum à particulis
              <lb/>
            ſingulis G, in quadrata ſuarum diſtantiarum ab recta A E,
              <lb/>
            æquabitur producto ex cuneo A B D in rectam L A, hoc
              <lb/>
            eſt, producto ex figura A C B in rectangulum ab F A, L A.
              <lb/>
            </s>
            <s xml:id="echoid-s3040" xml:space="preserve">Nam cuneus A B D, æqualis eſt producto ex figura A C B
              <lb/>
            in rectam F A . </s>
            <s xml:id="echoid-s3041" xml:space="preserve">Rurſus quia figura A C B æqualis eſt
              <note symbol="*" position="left" xlink:label="note-0194-04" xlink:href="note-0194-04a" xml:space="preserve">Prop.
                <lb/>
              præced.</note>
            ducto ex particula una G, in numerum ipſarum particula-
              <lb/>
            rum; </s>
            <s xml:id="echoid-s3042" xml:space="preserve">ſequitur, dictum productum ex figura A C B in re-
              <lb/>
            ctangulum ab F A, L A, æquari producto ex particula G
              <lb/>
            in rectangulum ab F A, L A, multiplici ſecundum nume-
              <lb/>
            rum particularum G. </s>
            <s xml:id="echoid-s3043" xml:space="preserve">Cui proinde etiam æqualis erit dicta
              <lb/>
            ſumma productorum, à particulis ſingulis G in quadrata
              <lb/>
            ſuarum diſtantiarum ab recta A E, ſive à particula una G in
              <lb/>
            ſummam omnium horum quadratorum. </s>
            <s xml:id="echoid-s3044" xml:space="preserve">Quare, omiſſa utrin-
              <lb/>
            que multiplicatione in particulam G, neceſſe eſt ſummam
              <lb/>
            @andem quadratorum æquari rectangulo ab F A, L A, mul-
              <lb/>
            tiplici ſecundum numerum particularum in quas figura A C B
              <lb/>
            diviſa intelligitur. </s>
            <s xml:id="echoid-s3045" xml:space="preserve">quod erat demonſtrandum.</s>
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