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

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          <p>
            <s xml:id="echoid-s5048" xml:space="preserve">Sint A & </s>
            <s xml:id="echoid-s5049" xml:space="preserve">B duo corpora ex Axe D ſuſpenſa ita, ut unius
              <lb/>
              <note position="right" xlink:label="note-0309-01" xlink:href="note-0309-01a" xml:space="preserve">TAB. XXVIII.
                <lb/>
              Fig. 4.</note>
            diſtantia ab Axe quadruplo major ſit alterius diſtantiâ.</s>
            <s xml:id="echoid-s5050" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5051" xml:space="preserve">Adeoque ſi altitudo perpendicularis B I, ex qua deſcendit
              <lb/>
            corpus B deſcribendo arcum B G, ponatur quatuor pedum,
              <lb/>
            altera A H, unde corpus A delabitur, unius pedis erit.
              <lb/>
            </s>
            <s xml:id="echoid-s5052" xml:space="preserve">Celeritates igitur, quas ſeparatim cadendo acquirunt, quo-
              <lb/>
            niam ſunt ut radices altitudinum, ſe habent ut 2 ad 1. </s>
            <s xml:id="echoid-s5053" xml:space="preserve">Summa
              <lb/>
            3, quæ totalem Penduli celeritatem manifeſtat, quando pro-
              <lb/>
            portionaliter ad altitudines, ſive ad arcus B G & </s>
            <s xml:id="echoid-s5054" xml:space="preserve">A F divi-
              <lb/>
            ditur, dat gradus celeritatis, quos obtinent pondera, quan-
              <lb/>
            do conjunctim in tabulam D G decidunt, videlicet {12/5} & </s>
            <s xml:id="echoid-s5055" xml:space="preserve">{3/5},
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            quorum quadrata ſunt {144/25} & </s>
            <s xml:id="echoid-s5056" xml:space="preserve">{9/25}, unde quæ prodit ſumma,
              <lb/>
            ſane a ſumma altitudinum, e quibus pondera dimittuntur,
              <lb/>
            differt. </s>
            <s xml:id="echoid-s5057" xml:space="preserve">Veruntamen hæc quadrata proportionem ſolummodo
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            altitudinum O M & </s>
            <s xml:id="echoid-s5058" xml:space="preserve">N L, ad quas pondera, dum a tabula
              <lb/>
            reſiliunt, adſcendunt, non ipſas altitudines exprimunt; </s>
            <s xml:id="echoid-s5059" xml:space="preserve">quas
              <lb/>
            inter ratio quidem eſſe poteſt, quæ eſt inter {144/25} & </s>
            <s xml:id="echoid-s5060" xml:space="preserve">{9/25}, hoc eſt
              <lb/>
            inter 16 & </s>
            <s xml:id="echoid-s5061" xml:space="preserve">1, dum ipſa ſumma eſt quinque, quæ eſt ſum-
              <lb/>
            ma altitudinum B I & </s>
            <s xml:id="echoid-s5062" xml:space="preserve">A H unde pondera delapſa ſunt.</s>
            <s xml:id="echoid-s5063" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s5064" xml:space="preserve">Nam ſi ponamus altitudinem O M 4{17/1@} pedum eſſe, & </s>
            <s xml:id="echoid-s5065" xml:space="preserve">alte-
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            ram N L {5/17}, O M ſe habebit ad N L, ut 16 ad 1; </s>
            <s xml:id="echoid-s5066" xml:space="preserve">& </s>
            <s xml:id="echoid-s5067" xml:space="preserve">O M
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            † N L erit æqualis B I † A H. </s>
            <s xml:id="echoid-s5068" xml:space="preserve">Idcirco centrum gravitatis
              <lb/>
            commune ponderum A & </s>
            <s xml:id="echoid-s5069" xml:space="preserve">B, ubi in L, M pervenere, erit
              <lb/>
            ad eandem altitudinem, quam obtinebat ante Oſcillationis ini-
              <lb/>
            tium. </s>
            <s xml:id="echoid-s5070" xml:space="preserve">Id clare ex inſpectione figuræ apparet. </s>
            <s xml:id="echoid-s5071" xml:space="preserve">Pondus enim
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            M tantum ſupra lineam Horizontalem B D elevatur, quan-
              <lb/>
            tum L infra eam deprimitur, videlicet {12/17} unius pedis; </s>
            <s xml:id="echoid-s5072" xml:space="preserve">ſe-
              <lb/>
            quitur hinc in triangulis ſimilibus M P Q & </s>
            <s xml:id="echoid-s5073" xml:space="preserve">L Q R latera
              <lb/>
            M Q & </s>
            <s xml:id="echoid-s5074" xml:space="preserve">Q L eſſe æqualia, hoc eſt medium lineæ M L, quæ
              <lb/>
            duo pondera conjungit, eſſe in interſectione lineæ Horizon-
              <lb/>
            talis.</s>
            <s xml:id="echoid-s5075" xml:space="preserve"/>
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          <figure number="135">
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