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

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          <pb o="244" file="0322" n="349" rhead="DE CENTRO OSCILL"/>
          <p>
            <s xml:id="echoid-s5333" xml:space="preserve">Si addamus ad pendulum compoſitum D A B novum pon-
              <lb/>
              <note position="left" xlink:label="note-0322-01" xlink:href="note-0322-01a" xml:space="preserve">TAB. XXVIII.
                <lb/>
              Fig. 7.</note>
            dus C æquale cuivis ponderi A & </s>
            <s xml:id="echoid-s5334" xml:space="preserve">B, ita ut D C duplum
              <lb/>
            ſit D A, conſiderari debent pondera A & </s>
            <s xml:id="echoid-s5335" xml:space="preserve">B tanquam ap-
              <lb/>
            penſa ad G commune ſuum Oſcillationis centrum, in extre-
              <lb/>
            mitate penduli ſimplicis D G; </s>
            <s xml:id="echoid-s5336" xml:space="preserve">& </s>
            <s xml:id="echoid-s5337" xml:space="preserve">tunc ponendo x, quanti-
              <lb/>
            tatem motus corporis C in pendulo compoſito D C G, ha-
              <lb/>
            bebimus C-x pro reſiduo exceſſu quantitatis motus corporis
              <lb/>
            C. </s>
            <s xml:id="echoid-s5338" xml:space="preserve">Quantitas hæc reſidua applicata in C exercet vim in pun-
              <lb/>
            ctum fixum D, & </s>
            <s xml:id="echoid-s5339" xml:space="preserve">punctum G, quod conſidero ut fixum
              <lb/>
            ipſius reſpectu; </s>
            <s xml:id="echoid-s5340" xml:space="preserve">habebimus ergo D G, {17/5}, eſt ad D C, 2, ut C-x
              <lb/>
            eſt ad {10 C - 10 x/17}, portionem ejus exceſſus, quæ diſtribuitur in
              <lb/>
            G; </s>
            <s xml:id="echoid-s5341" xml:space="preserve">unde ſequitur, quantitatem motus corporum A & </s>
            <s xml:id="echoid-s5342" xml:space="preserve">B in
              <lb/>
            pendulo compoſito D A C B futuram {5/17} A + {20/17} B + {10 C - 10 x/17}
              <lb/>
            id eſt {35 C - 10 x/17}; </s>
            <s xml:id="echoid-s5343" xml:space="preserve">Ob virgam autem inflexilem D B, velocitas
              <lb/>
            corporis A in pendulo compoſito erit neceſſario dimidia ve-
              <lb/>
            locitatis corporis C, & </s>
            <s xml:id="echoid-s5344" xml:space="preserve">velocitas corporis B erit dupla ve-
              <lb/>
            locitatis corporis C, & </s>
            <s xml:id="echoid-s5345" xml:space="preserve">eædem quoque inter motus quanti-
              <lb/>
            tates rationes dantur, cum tria corpora ſint æqualia inter ſe;
              <lb/>
            </s>
            <s xml:id="echoid-s5346" xml:space="preserve">datur ergo æqualitas inter 2 x + {1/2} x & </s>
            <s xml:id="echoid-s5347" xml:space="preserve">{35 C - 10 x/17}, unde de-
              <lb/>
            ducitur quantitas {2/7} x = C, exprimens quantitatem motus
              <lb/>
            corporis C in pendulo compoſito D A C B. </s>
            <s xml:id="echoid-s5348" xml:space="preserve">Jam ſi fiat, ut
              <lb/>
            {2/3}, velocitas corporis C in pendulo compoſito, eſt ad 1, ve-
              <lb/>
            locitatem cujusvis corporis gravis in extremitate penduli ſim-
              <lb/>
            plicis; </s>
            <s xml:id="echoid-s5349" xml:space="preserve">ita D C, 2. </s>
            <s xml:id="echoid-s5350" xml:space="preserve">eſt ad D E, 3, erit hæc longitudo pen-
              <lb/>
            duli ſimplicis iſochroni.</s>
            <s xml:id="echoid-s5351" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5352" xml:space="preserve">Si pondera A, B, C eſſent inæqualia, inveniretur ſemper,
              <lb/>
            ſequendo hoc ratiocinium, centrum Oſcillationis. </s>
            <s xml:id="echoid-s5353" xml:space="preserve">ita ut hæc
              <lb/>
            methodus ſit generalis, quicunque ſit ponderum numerus,
              <lb/>
            & </s>
            <s xml:id="echoid-s5354" xml:space="preserve">quæcunque eorundem inæqualitas. </s>
            <s xml:id="echoid-s5355" xml:space="preserve">Oſtendendum nunc,
              <lb/>
            methodum hanc etiam uſu venire, ſi pondera ſint ad puncti
              <lb/>
            fixi partem utramque diſpoſita.</s>
            <s xml:id="echoid-s5356" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5357" xml:space="preserve">Sit pendulum compoſitum A D B mobile circa punctum
              <lb/>
            fixum D, & </s>
            <s xml:id="echoid-s5358" xml:space="preserve">oneratum ponderibus æqualibus A & </s>
            <s xml:id="echoid-s5359" xml:space="preserve">B, ſitque
              <lb/>
            D B quadrupla ipſius D A, patet quod corpus A debeat
              <lb/>
            retardare motum corporis B in pendulo compoſito; </s>
            <s xml:id="echoid-s5360" xml:space="preserve">& </s>
            <s xml:id="echoid-s5361" xml:space="preserve"/>
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