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

Table of Notes

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            quæ axi viciniores ſunt, breviores & </s>
            <s xml:id="echoid-s4817" xml:space="preserve">frequentiores vibrationes
              <lb/>
            peragent quam remotiores, ſi arcus ſimiles deſcribant, & </s>
            <s xml:id="echoid-s4818" xml:space="preserve">aër non
              <lb/>
            reſiſtat.</s>
            <s xml:id="echoid-s4819" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s4820" xml:space="preserve">Cujus rei ratio eſt, quod viciniores deſcribant arcus mi-
              <lb/>
            nores & </s>
            <s xml:id="echoid-s4821" xml:space="preserve">acquirant celeritates majores reſpectu arcuum quam
              <lb/>
            remotiores: </s>
            <s xml:id="echoid-s4822" xml:space="preserve">nam arcus ſunt proportionales quadratis, & </s>
            <s xml:id="echoid-s4823" xml:space="preserve">
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            velocitates radicibus eorum; </s>
            <s xml:id="echoid-s4824" xml:space="preserve">quo autem radices minores ſunt
              <lb/>
            inter ſe, eo majores ſunt reſpectu quadratorum ſuorum.</s>
            <s xml:id="echoid-s4825" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4826" xml:space="preserve">Cum in Pendulo omnes partes niſi ſimul, propter earum
              <lb/>
            conjunctionem, moveri nequeant, vibratio minus diſtantium
              <lb/>
            ab axe ita retardata eſt a vibratione remotiorum, & </s>
            <s xml:id="echoid-s4827" xml:space="preserve">vibratio
              <lb/>
            remotiorum ita accelerata eſt a vibratione aliarum, ut inter
              <lb/>
            illas detur compenſatio velocitatum proportionalis arcubus
              <lb/>
            quos deſcribunt; </s>
            <s xml:id="echoid-s4828" xml:space="preserve">ita ut tempus vibrationis totius Penduli
              <lb/>
            medium ſit inter tempus, quo Oſcillationem peragunt ejus
              <lb/>
            partes a ſe invicem ſolutæ, ut ſit æquale ſummæ illorum
              <lb/>
            temporum, diviſæ per numerum partium, quas ut Mathema-
              <lb/>
            tice & </s>
            <s xml:id="echoid-s4829" xml:space="preserve">exactiſſime procedamus conſideramus, ac ſi reductæ
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            eſſent in puncta.</s>
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            <s xml:id="echoid-s4831" xml:space="preserve">Conſtat experimentis, & </s>
            <s xml:id="echoid-s4832" xml:space="preserve">per Philoſophiam Carteſianam
              <lb/>
            demonſtrari poteſt, omnia gravia tellurem verſus cadere in
              <lb/>
            temporibus quæ ſunt in ratione ſubduplicatâ, vel ſicuti radi-
              <lb/>
            ces, altitudinum, unde deſcendunt, ſi verticaliter deſcendant,
              <lb/>
            quod etiam & </s>
            <s xml:id="echoid-s4833" xml:space="preserve">ex principiis Galilæi demonſtrari poteſt, ſi cadant per
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            arcus ſimiles, qui incipiunt omnes in eodem plano.</s>
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          </p>
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            <s xml:id="echoid-s4835" xml:space="preserve">Hæ altitudines in Pendulis, quæ deſcribunt arcus ſimiles cir-
              <lb/>
            ca axem, quocum forrmant idem planum, ſunt inter ſe ut diſtantiæ
              <lb/>
            ab axe, circa quem moventur.</s>
            <s xml:id="echoid-s4836" xml:space="preserve"/>
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            <s xml:id="echoid-s4837" xml:space="preserve">Propoſita ergo quæſtio eo redit, ut dividamus, per nume-
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            rum partium Penduli, ſummam radicum diſtantiarum partium
              <lb/>
            ab axe. </s>
            <s xml:id="echoid-s4838" xml:space="preserve">vel generaliter ſummam linearum rectarum quæ repræſentant
              <lb/>
            tempora vibrationium partium ſeparatim ſumtarum, ut habeamus lineam
              <lb/>
            rectam, quæ ſit menſura temporis, quo vibrationes ſuas per-
              <lb/>
            agit Pendulum, cujus conſequenter quadratum vel 3a. </s>
            <s xml:id="echoid-s4839" xml:space="preserve">propor-
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            tionalis erit diſtantia inter axem & </s>
            <s xml:id="echoid-s4840" xml:space="preserve">centrum Oſcillationis.</s>
            <s xml:id="echoid-s4841" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4842" xml:space="preserve">Applicatio hujus principii tribus magnitudinibus quas ha-
              <lb/>
            bet Geometria pro objecto ſatis facilis eſt.</s>
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