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

Table of handwritten notes

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          <pb o="228" file="0242" n="242" rhead="HYDRODYNAMICÆ"/>
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          <head xml:id="echoid-head244" xml:space="preserve">Solutio.</head>
          <p>
            <s xml:id="echoid-s6701" xml:space="preserve">Fuerit vas ab initio omnino vacuum, & </s>
            <s xml:id="echoid-s6702" xml:space="preserve">poſt tempus t ponatur denſitas
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            aëris interni = x; </s>
            <s xml:id="echoid-s6703" xml:space="preserve">ſic reperietur iiſdem fere veſtigiis inſiſtendo, quibus in tri-
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            geſimo quinto paragrapho uſi ſumus retentisque iisdem denominationibus
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            {dx/√(δ - x)} = {dt√AD/L} ſive t = 2n√s = {2L/√A} - {2L√(D - x)/√AD}.</s>
            <s xml:id="echoid-s6704" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s6705" xml:space="preserve">Numerus igitur minutorum ſecundorum, quo totum vas impletur,
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            donec inter utrumque aërem æquilibrium ſit exprimitur per {L/√As}: </s>
            <s xml:id="echoid-s6706" xml:space="preserve">& </s>
            <s xml:id="echoid-s6707" xml:space="preserve">eſt tem-
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            pus repletionis duplum illius quo repleretur ſi velocitate initiali conſtanter in-
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            flueretaër. </s>
            <s xml:id="echoid-s6708" xml:space="preserve">In caſu quo capacitas vaſis pedem cubicum continet & </s>
            <s xml:id="echoid-s6709" xml:space="preserve">foramen lineam
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            quadratam æquat, fit repletio tempore propemodum triginta trium minutorum
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            ſecundorum, niſi contractione venæ aëreæ influentis repletio retardetur.</s>
            <s xml:id="echoid-s6710" xml:space="preserve"/>
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            <s xml:id="echoid-s6711" xml:space="preserve">§. </s>
            <s xml:id="echoid-s6712" xml:space="preserve">39. </s>
            <s xml:id="echoid-s6713" xml:space="preserve">Expoſuimus varias fluidorum elaſticorum ſive motorum ſive
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            quieſcentium proprietates: </s>
            <s xml:id="echoid-s6714" xml:space="preserve">Unum ſupereſt non omittendum, quo fluida ela-
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            ſtica differunt à non - elaſticis, hoc ſcilicet, quod fluido elaſtico vel quieſ-
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            centi vis viva inſita ſit, non quod inſtar aliorum corporum motorum ſe ad cer-
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            tam altitudinem elevare poſſit, neque enim motum localem in illo hic conſi-
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            deramus, ſed quod elatere ſuo talem aſcenſum in aliis corporibus gravibus ge-
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            nerare poſſit. </s>
            <s xml:id="echoid-s6715" xml:space="preserve">Licebit autem, quod ſpero, in ſequentibus uti vocabulo vis vi-
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            væ corpori elaſtico compreſſo inſitæ, quando nihil aliud eo intelligitur quam aſcen-
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            ſus potentialis, quem corpus elaſticum aliis corporibus communicare poteſt
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            priuſquam totam ſuam vim elaſticam perdiderit.</s>
            <s xml:id="echoid-s6716" xml:space="preserve"/>
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            <s xml:id="echoid-s6717" xml:space="preserve">Meretur hic in anteceſſum notari, quod ſicut deſcenſus corporis dati
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            per datam altitudinem, utcunque fiat, eandem conſtanter vim vivam in cor-
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            pore producit, ita quoque elaſtrum ſive fluidum elaſticum poſtquam à dato
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            tenſionis ſeu condenſationis gradu ad datum alium gradum fuit reductum ut-
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            cunque, id ſemper eandem vim vivam in ſe recipiat rurſuſque contraria muta-
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            tione alii corpori communicare poſſit.</s>
            <s xml:id="echoid-s6718" xml:space="preserve"/>
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            <s xml:id="echoid-s6719" xml:space="preserve">De hujuſmodi viribus vivis fluido elaſtico compreſſo inſitis earundem-
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            que menſuris paucis nunc agam: </s>
            <s xml:id="echoid-s6720" xml:space="preserve">dignum attentione argumentum eſt, quod
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            eo reducantur menſuræ virium prò machinis aëre, aut igne aut aliis </s>
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