Bernoulli, Daniel, Hydrodynamica, sive De viribus et motibus fluidorum commentarii

Table of contents

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[91.] Exemplum 1.
Page: 126 (112)
[92.] Exemplum 2.
Page: 126 (112)
[93.] De oſcillationibus fluidorum in tubisrecurvis. Caſus II.
Page: 128 (114)
[94.] Lemma.
Page: 129 (115)
[95.] Solutio.
Page: 129 (115)
[96.] Problema.
Page: 130 (116)
[97.] Solutio.
Page: 130 (116)
[98.] Corollarium 1.
Page: 131 (117)
[99.] Corollarium 2.
Page: 131 (117)
[100.] Corollarium 3.
Page: 131 (117)
[101.] Corollarium 4.
Page: 131 (117)
[102.] Theorema.
Page: 132 (118)
[103.] Demonſtratio.
Page: 132 (118)
[104.] Problema.
Page: 132 (118)
[105.] Solutio.
Page: 132 (118)
[106.] Corollarium. 1.
Page: 133 (119)
[107.] Corollarium 2.
Page: 133 (119)
[108.] Scholion.
Page: 133 (119)
[109.] Theorema.
Page: 134 (120)
[110.] Demonſtratio.
Page: 134 (120)
[111.] Problema.
Page: 134 (120)
[112.] Solutio.
Page: 134 (120)
[113.] Scholium.
Page: 134 (120)
[114.] Corollarium 1.
Page: 135 (121)
[115.] Corollarium 2.
Page: 135 (121)
[116.] Scholion Generale.
Page: 136 (122)
[117.] HYDRODYNAMICÆ SECTIO SEPTIMA. De motu aquarum per vaſa ſubmerſa, ubi exem-plis oſtenditur, quam inſigniter utile ſit princi-pium conſervationis virium vivarum, veliis in caſibus, quibus continue aliquid de illis perdi cenſendum eſt. PARS PRIMA. De deſcenſu aquarum. §. 1.
Page: 138
[118.] PARS SECUNDA. De aſcenſu aquarum.
Page: 146 (132)
[119.] Corollarium.
Page: 152 (138)
[120.] Scholium Generale.
Page: 153 (139)
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          <head xml:id="echoid-head78" xml:space="preserve">Experimentum 2.</head>
          <p>
            <s xml:id="echoid-s2186" xml:space="preserve">Deinde experimento explorare volui, an in omnibus jactibus ſub qua-
              <lb/>
            cunque directione contractio eadem ſit, & </s>
            <s xml:id="echoid-s2187" xml:space="preserve">hunc in finem exiſtimavi rem ſic
              <lb/>
            eſſe aggrediendam, ut præter directionis iſtius mutationem circumſtantiæ cæ-
              <lb/>
            ræ omnes eſſent prorſus ſimiles. </s>
            <s xml:id="echoid-s2188" xml:space="preserve">Id vero ſic obtinui.</s>
            <s xml:id="echoid-s2189" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2190" xml:space="preserve">Eodem ſcilicet, quo antea cylindro uſus ſum, eum autem arcæ pris-
              <lb/>
            maticæ verticaliter poſitæ implantavi, ita, ut axis cylindri eſſet horizontalis,
              <lb/>
            ſicque implantatum circumverti, ut centrum foraminis, aqua@um effluxui de-
              <lb/>
            ſtinati, modo locum ſummum, modo medium, modo imum occuparet: </s>
            <s xml:id="echoid-s2191" xml:space="preserve">in
              <lb/>
            primo caſu aquæ verticaliter ſurſum effluebant, in ſecundo horizontaliter, in
              <lb/>
            tertio verticaliter deorſum ejiciebantur; </s>
            <s xml:id="echoid-s2192" xml:space="preserve">in ſingulis vero feci ut altitudines aquæ
              <lb/>
            in arca ſupra centrum foraminis eſſent perfecte æquales: </s>
            <s xml:id="echoid-s2193" xml:space="preserve">ſucceſſus hic fuit.</s>
            <s xml:id="echoid-s2194" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2195" xml:space="preserve">Obſervavi æqualibus temporibus ſuperficiem aquæ in ſingulis caſibus per
              <lb/>
            ſpatia æqualia in arca deſcendere. </s>
            <s xml:id="echoid-s2196" xml:space="preserve">Igitur in venis ſurſum projectis aqua uperior
              <lb/>
            non reſiſtit ſenſibiliter aquæ inferiori ſubſequenti, quod idem alio intellexi modo,
              <lb/>
            quod ſcilicet, ſi ad parvam à foramine diſtantiam veluti 3. </s>
            <s xml:id="echoid-s2197" xml:space="preserve">linearum nummo
              <lb/>
            aliquo venam aqueam cujuſcunque directionis excipiebam, ita ut vena in num-
              <lb/>
            mum perpendiculariter incideret, effluxus aquarum non fuerit retardatus.
              <lb/>
            </s>
            <s xml:id="echoid-s2198" xml:space="preserve">Porro nec aqua in venis verticaliter deſcendentibus anterior poſteriorem poſt ſe
              <lb/>
            trahit; </s>
            <s xml:id="echoid-s2199" xml:space="preserve">ipſaque venæ contractio ſimilis ubique eſt, non conſiderata retarda-
              <lb/>
            tione accelerationeque aquarum ſurſum vel deorſum ejectarum, quæ faciunt
              <lb/>
            ut vena in aliqua à foramine diſtantia vel intumeſcat, vel gracileſcat. </s>
            <s xml:id="echoid-s2200" xml:space="preserve">Hic
              <lb/>
            enim ſermo eſt de illa modo contractione, quæ oritur à motu particularum
              <lb/>
            obliquo in regione foraminis.</s>
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          <head xml:id="echoid-head79" xml:space="preserve">Experimentum 3.</head>
          <p>
            <s xml:id="echoid-s2202" xml:space="preserve">Eadem machina prædicto modo præparata uſus ſum ad explorandum,
              <lb/>
            num contractio venæ cæteris paribus mutaretur ab aucta altitudine aquæ ſupra
              <lb/>
            foramen. </s>
            <s xml:id="echoid-s2203" xml:space="preserve">Hunc in finem duas acus infixi lateribus internis arcæ ad perpen-
              <lb/>
            diculum ſibi reſpondentes, prior eminebat ſupra centrum foraminis 13 poll.
              <lb/>
            </s>
            <s xml:id="echoid-s2204" xml:space="preserve">cum 10. </s>
            <s xml:id="echoid-s2205" xml:space="preserve">lineis, altera 12. </s>
            <s xml:id="echoid-s2206" xml:space="preserve">poll. </s>
            <s xml:id="echoid-s2207" xml:space="preserve">1 {3/5} lin. </s>
            <s xml:id="echoid-s2208" xml:space="preserve">menſ. </s>
            <s xml:id="echoid-s2209" xml:space="preserve">Angl. </s>
            <s xml:id="echoid-s2210" xml:space="preserve">amplitudo arcæ erat ad am-
              <lb/>
            plitudinem foraminis ut 404. </s>
            <s xml:id="echoid-s2211" xml:space="preserve">ad 1. </s>
            <s xml:id="echoid-s2212" xml:space="preserve">vidi autem ſuperficiem aquæ à </s>
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