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

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          <p>
            <s xml:id="echoid-s5288" xml:space="preserve">
              <pb o="242" file="0320" n="347" rhead="DE CENTRO OSCILL."/>
            que obſtaculorum; </s>
            <s xml:id="echoid-s5289" xml:space="preserve">prout ipſa quoque hæc aëris reſiſtentia
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            in cauſa eſt, cur ſimplex pendulum motum ſuum non con-
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            tinuet, ut maxime in Hypotheſi Hugeniana ad eandem
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            aſcendere debeat altitudinem, a qua deſcendit.</s>
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        <div xml:id="echoid-div439" type="section" level="1" n="180">
          <head xml:id="echoid-head226" style="it" xml:space="preserve">XI.
            <lb/>
          Litteræ D
            <emph style="super">ni</emph>
          Marchionis de l’Hôpital ad D
            <emph style="super">um</emph>
          Huge-
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          nium, in quibus contendit, ſeregulam hujus Au-
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          ctoris de Centro oſcillationis penduli compoſiti
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          demonſtrare per cauſam Phyſicam, & re-
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          ſpondere ſimul D
            <emph style="super">no</emph>
          Bernoulli.</head>
          <p>
            <s xml:id="echoid-s5291" xml:space="preserve">Ante aliquot annos, cum admiratione legi eruditum tuum
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            de centris Oſcillationis tractatum, & </s>
            <s xml:id="echoid-s5292" xml:space="preserve">pleniſſime mihi
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            perſuaſum eſt veras eſſe demonſtrationes tuas. </s>
            <s xml:id="echoid-s5293" xml:space="preserve">Interea cum
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            Acta Lipſienſia nuper mihi ad manus venerint, inveni in actis
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            menſis Julii anni 1686. </s>
            <s xml:id="echoid-s5294" xml:space="preserve">relationem tuæ hac de re cum D
              <emph style="super">no</emph>
              <lb/>
            Abbate Cateleno controverſiæ, à D
              <emph style="super">no</emph>
            Bernoulli factam, qui
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            tuam ſententiam amplectitur, uti certe debent, quicunque
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            aliquem inter Geometras locum ſe tenere contendunt. </s>
            <s xml:id="echoid-s5295" xml:space="preserve">Sed
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            attonitus vidi, finem ratiocinii quo utitur, contrarium eſſe
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            tuis demonſtrationibus: </s>
            <s xml:id="echoid-s5296" xml:space="preserve">unde ad illud ſedulo examinandum
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            perductus fui, & </s>
            <s xml:id="echoid-s5297" xml:space="preserve">cognovi, quod utatur principio veriſſimo,
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            licet in eodem applicando fallatur; </s>
            <s xml:id="echoid-s5298" xml:space="preserve">illud enim principium,
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            uti demonſtrabo, ducit ad eandem veritatem, quam probaſti
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            in 5
              <emph style="super">a</emph>
            tua propoſitione.</s>
            <s xml:id="echoid-s5299" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5300" xml:space="preserve">Sit D A B virga inflexilis & </s>
            <s xml:id="echoid-s5301" xml:space="preserve">ſine gravitate, mobilis circa
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              <note position="left" xlink:label="note-0320-01" xlink:href="note-0320-01a" xml:space="preserve">TAB. XXVIII.
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              Fig. 6.</note>
            punctum fixum D, ad quam annexa ſint 2 pondera æqualia
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            A & </s>
            <s xml:id="echoid-s5302" xml:space="preserve">B; </s>
            <s xml:id="echoid-s5303" xml:space="preserve">& </s>
            <s xml:id="echoid-s5304" xml:space="preserve">ſit diſtantia B D a puncto fixo quadrupla di-
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            ſtantiæ A D, quæritur longitudo D G penduli ſimplicis
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            iſochroni, id eſt, quod movetur cum eâdem celeritate ac pen-
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            dulum compoſitum.</s>
            <s xml:id="echoid-s5305" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5306" xml:space="preserve">Ad ſolvendum hoc problema, conſidero velocitates, cum
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            quibus corpora A & </s>
            <s xml:id="echoid-s5307" xml:space="preserve">B incipiunt deſcendere in primo </s>
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