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

Table of figures

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            <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
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              <note position="right" xlink:label="note-0309-01" xlink:href="note-0309-01a" xml:space="preserve">TAB. XXVIII.
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              Fig. 4.</note>
            diſtantia ab Axe quadruplo major ſit alterius diſtantiâ.</s>
            <s xml:id="echoid-s5050" xml:space="preserve"/>
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            <s xml:id="echoid-s5051" xml:space="preserve">Adeoque ſi altitudo perpendicularis B I, ex qua deſcendit
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            corpus B deſcribendo arcum B G, ponatur quatuor pedum,
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            altera A H, unde corpus A delabitur, unius pedis erit.
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            </s>
            <s xml:id="echoid-s5052" xml:space="preserve">Celeritates igitur, quas ſeparatim cadendo acquirunt, quo-
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            niam ſunt ut radices altitudinum, ſe habent ut 2 ad 1. </s>
            <s xml:id="echoid-s5053" xml:space="preserve">Summa
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            3, quæ totalem Penduli celeritatem manifeſtat, quando pro-
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            portionaliter ad altitudines, ſive ad arcus B G & </s>
            <s xml:id="echoid-s5054" xml:space="preserve">A F divi-
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            ditur, dat gradus celeritatis, quos obtinent pondera, quan-
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            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,
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            ſane a ſumma altitudinum, e quibus pondera dimittuntur,
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            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
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            reſiliunt, adſcendunt, non ipſas altitudines exprimunt; </s>
            <s xml:id="echoid-s5059" xml:space="preserve">quas
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            inter ratio quidem eſſe poteſt, quæ eſt inter {144/25} & </s>
            <s xml:id="echoid-s5060" xml:space="preserve">{9/25}, hoc eſt
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            inter 16 & </s>
            <s xml:id="echoid-s5061" xml:space="preserve">1, dum ipſa ſumma eſt quinque, quæ eſt ſum-
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            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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            <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
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            commune ponderum A & </s>
            <s xml:id="echoid-s5069" xml:space="preserve">B, ubi in L, M pervenere, erit
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            ad eandem altitudinem, quam obtinebat ante Oſcillationis ini-
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            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-
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            tum L infra eam deprimitur, videlicet {12/17} unius pedis; </s>
            <s xml:id="echoid-s5072" xml:space="preserve">ſe-
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            quitur hinc in triangulis ſimilibus M P Q & </s>
            <s xml:id="echoid-s5073" xml:space="preserve">L Q R latera
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            M Q & </s>
            <s xml:id="echoid-s5074" xml:space="preserve">Q L eſſe æqualia, hoc eſt medium lineæ M L, quæ
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            duo pondera conjungit, eſſe in interſectione lineæ Horizon-
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            talis.</s>
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