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

Page concordance

< >
Scan Original
41 27
42 28
43 29
44 30
45 31
46 32
47 33
48 34
49 35
50 36
51 37
52 38
53 39
54 40
55 41
56 42
57 43
58 44
59 45
60 46
61 47
62 48
63 49
64 50
65 51
66 52
67 53
68 54
69 55
70 56
< >
page |< < (201) of 361 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div234" type="section" level="1" n="184">
          <p>
            <s xml:id="echoid-s5804" xml:space="preserve">
              <pb o="201" file="0215" n="215" rhead="SECTIO DECIMA."/>
            dus P operculum detinens in ſitu E F non differt à preſſione Atmoſphæræ ſuper-
              <lb/>
            incumbentis, quam proinde per P in ſequentibus deſignabimus.</s>
            <s xml:id="echoid-s5805" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5806" xml:space="preserve">Notetur autem hanc preſſionem minime æqualem eſſe ponderi abſo-
              <lb/>
            luto cylindri verticalis aërei operculo E F in atmoſphæra ſuperincumbentis,
              <lb/>
            quod hactenus inconſiderate affirmarunt auctores: </s>
            <s xml:id="echoid-s5807" xml:space="preserve">ſed eſt preſſio iſta æqualis
              <lb/>
            quartæ proportionali ad ſuperficiem terræ, magnitudinem operculi E F & </s>
            <s xml:id="echoid-s5808" xml:space="preserve">pon-
              <lb/>
            deri totius atmoſphæræ in ſuperficiem terræ.</s>
            <s xml:id="echoid-s5809" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5810" xml:space="preserve">§. </s>
            <s xml:id="echoid-s5811" xml:space="preserve">4. </s>
            <s xml:id="echoid-s5812" xml:space="preserve">Quæratur jam pondus π, quod aërem E C D F in ſpatium e C
              <lb/>
            D f condenſare valeat, poſitis velocitatibus particularum in utroque aëre,
              <lb/>
            naturali ſcilicet & </s>
            <s xml:id="echoid-s5813" xml:space="preserve">condenſato, iisdem: </s>
            <s xml:id="echoid-s5814" xml:space="preserve">ſit autem E C = 1 & </s>
            <s xml:id="echoid-s5815" xml:space="preserve">e C = s: </s>
            <s xml:id="echoid-s5816" xml:space="preserve">Cum
              <lb/>
            vero operculum E F transponitur in e f, majorem à fluido patitur niſum duplici
              <lb/>
            modo: </s>
            <s xml:id="echoid-s5817" xml:space="preserve">primo quod numerus particularum ratione ſpatii, cui includuntur,
              <lb/>
            major nunc eſt, & </s>
            <s xml:id="echoid-s5818" xml:space="preserve">ſecundo quod quævis particula ſæpius impulſum repetit:
              <lb/>
            </s>
            <s xml:id="echoid-s5819" xml:space="preserve">ut recte calculum ponamus incrementi, quod à prima pendet cauſa, parti-
              <lb/>
            culas conſiderabimus ceu quieſcentes, atque numerum earum, quæ opercu-
              <lb/>
            lo in ſitu E F ſunt contiguæ, faciemus = n, & </s>
            <s xml:id="echoid-s5820" xml:space="preserve">erit numerus ſimilis pro ſi-
              <lb/>
            tu operculi in e f = n: </s>
            <s xml:id="echoid-s5821" xml:space="preserve">({eC/EC})
              <emph style="super">{2/3}</emph>
            , ſeu = n: </s>
            <s xml:id="echoid-s5822" xml:space="preserve">s
              <emph style="super">{2/3}</emph>
            :</s>
            <s xml:id="echoid-s5823" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5824" xml:space="preserve">Notetur autem fluid
              <unsure/>
            um à nobis conſiderari non magis condenſatum
              <lb/>
            in parte inferiori, quam in ſuperiori, quale eſt, cum pondus P veluti infi-
              <lb/>
            nitè majus eſt pondere proprio fluidi: </s>
            <s xml:id="echoid-s5825" xml:space="preserve">Perſpicuum hinc eſt, hoc nomine
              <lb/>
            vim fluidi eſſe, ut ſunt numeri n & </s>
            <s xml:id="echoid-s5826" xml:space="preserve">n: </s>
            <s xml:id="echoid-s5827" xml:space="preserve">s
              <emph style="super">{2/3}</emph>
            , id eſt, ut s
              <emph style="super">{2/3}</emph>
            ad 1. </s>
            <s xml:id="echoid-s5828" xml:space="preserve">Quod vero
              <lb/>
            attinet ad alterum incrementum à ſecunda proveniens cauſa, invenitur id re-
              <lb/>
            ſpiciendo motum particularum; </s>
            <s xml:id="echoid-s5829" xml:space="preserve">atque ſic apparet impulſus eo ſæpius fieri,
              <lb/>
            quo propius ad ſe invicem ſitæ ſunt particulæ: </s>
            <s xml:id="echoid-s5830" xml:space="preserve">Erunt ſcilicet impulſuum nu-
              <lb/>
            meri reciproce ut diſtantiæ mediæ inter ſuperficies particularum: </s>
            <s xml:id="echoid-s5831" xml:space="preserve">Iſtæque di-
              <lb/>
            ſtantiæ mediæ ita determinabuntur.</s>
            <s xml:id="echoid-s5832" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5833" xml:space="preserve">Particulas ponemus eſſe ſphæricas, diſtantiamque mediam inter cen-
              <lb/>
            tra globulorum pro ſitu operculi E F vocabimus D; </s>
            <s xml:id="echoid-s5834" xml:space="preserve">diametrumque globuli
              <lb/>
            deſignabimus per d: </s>
            <s xml:id="echoid-s5835" xml:space="preserve">ita erit diſtantia media inter ſuperficies globulorum =
              <lb/>
            D - d: </s>
            <s xml:id="echoid-s5836" xml:space="preserve">patet vero in ſitu operculi e f fore diſtantiam mediam inter centra
              <lb/>
            globulorum = D ∛ s, atque proinde diſtantiam mediam inter ſuperficies
              <lb/>
            globulorum = D ∛ s - d. </s>
            <s xml:id="echoid-s5837" xml:space="preserve">Igitur reſpectu ſecundæ cauſæ erit vis aëris </s>
          </p>
        </div>
      </text>
    </echo>
Impressum