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

Table of contents

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[171.] Scholium Generale.
Page: 194 (180)
[172.] Commentationes ſpeciales de Cochlea Archimedis.
Page: 197 (183)
[173.] Problema.
Page: 200 (186)
[174.] Solutio.
Page: 200 (186)
[175.] Scholium 1.
Page: 200 (186)
[176.] Scholium 2.
Page: 201 (187)
[177.] Scholium 3.
Page: 202 (188)
[178.] Scholium 4.
Page: 202 (188)
[179.] Problema.
Page: 203 (189)
[180.] Solutio.
Page: 203 (189)
[181.] Scholium 1.
Page: 205 (191)
[182.] Scholium 2.
Page: 205 (191)
[183.] (C) De Machinis, quæ ab impetu fluidi, veluti vi venti moventur.
Page: 207 (193)
[184.] HYDRODYNAMICÆ SECTIO DECIMA. De affectionibus atque motibus fluidorum elaſti-corum, præcipue autem aëris. §. 1.
Page: 214 (200)
[185.] Digreſsio de refractione radiorum per atmoſphæ-ram transeuntium.
Page: 233 (219)
[186.] Problema.
Page: 238 (224)
[187.] Solutio.
Page: 238 (224)
[188.] Problema.
Page: 240 (226)
[189.] Solutio.
Page: 240 (226)
[190.] Corollarium 1.
Page: 241 (227)
[191.] Corollarium 2.
Page: 241 (227)
[192.] Problema.
Page: 241 (227)
[193.] Solutio.
Page: 242 (228)
[194.] De vi aëris condenſati & auræ pulveris pyrii ac-cenſi ad globos projiciendos in uſu ſclopetorum pneumaticorum & tormentorum bellicorum.
Page: 248 (234)
[195.] HYDRODYNAMICÆ SECTIO UNDECIMA. De fluidis in vorticem actis, tum etiam de iis, quæ in vaſis motis continentur. §. 1.
Page: 258 (244)
[196.] HYDRODYNAMICÆ SECTIO DUODECIMA. Quæ ſtaticam fluidorum motorum, quam hy-draulico - ſtaticam voco, exhibet. § 1.
Page: 270 (256)
[197.] Problema.
Page: 272 (258)
[198.] Solutio.
Page: 272 (258)
[199.] Corollarium 1.
Page: 274 (260)
[200.] Corollarium 2.
Page: 274 (260)
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          <head xml:id="echoid-head239" xml:space="preserve">Problema.</head>
          <p>
            <s xml:id="echoid-s6639" xml:space="preserve">§. </s>
            <s xml:id="echoid-s6640" xml:space="preserve">35. </s>
            <s xml:id="echoid-s6641" xml:space="preserve">Quæritur motus aëris denſioris in aërem externum rariorem
              <lb/>
            infinitum ex vaſe per foramen valde parvum erumpentis, poſito in utroque
              <lb/>
            aëre eodem caloris gradu.</s>
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          <head xml:id="echoid-head240" xml:space="preserve">Solutio.</head>
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            <s xml:id="echoid-s6643" xml:space="preserve">Sit denſitas aëris interni initialis = D; </s>
            <s xml:id="echoid-s6644" xml:space="preserve">denfitas aëris externi = δ:
              <lb/>
            </s>
            <s xml:id="echoid-s6645" xml:space="preserve">denſitas aëris interni poſt datum tempus t reſidui = x, altitudo aëris homo-
              <lb/>
            genei, (ſive ratione aëris interni ſive externi, nec enim diverſa eſſe poteſt,
              <lb/>
            ſi uterque aër eodem calore præditus ſit, ſicque denſitates & </s>
            <s xml:id="echoid-s6646" xml:space="preserve">elaſticitates in
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            pari ratione decreſcant) = A. </s>
            <s xml:id="echoid-s6647" xml:space="preserve">Quæratur ubique altitudo aëris homogenei,
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            qui habeat eandem preſſionem ſeu elaterem cum aëre externo & </s>
            <s xml:id="echoid-s6648" xml:space="preserve">cujus den-
              <lb/>
            ſitas eadem ſit cum aëre interno: </s>
            <s xml:id="echoid-s6649" xml:space="preserve">hæc altitudo ab initio erit {δA/D}, & </s>
            <s xml:id="echoid-s6650" xml:space="preserve">poſt
              <lb/>
            tempus t erit {δA/x}. </s>
            <s xml:id="echoid-s6651" xml:space="preserve">Patet autem velocitatem aëris erumpentis talem ubique
              <lb/>
            fore, quæ reſpondeat differentiæ definitarum altitudinum A & </s>
            <s xml:id="echoid-s6652" xml:space="preserve">{δA/x}; </s>
            <s xml:id="echoid-s6653" xml:space="preserve">eſt itaque
              <lb/>
            poſt tempus t velocitas aëris erumpentis = √(A - {δA/x}).</s>
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          </p>
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            <s xml:id="echoid-s6655" xml:space="preserve">Sunt porro decrementa denſitatum (- d x) proportionalia quantitati-
              <lb/>
            bus aëris erumpentis, quæ rationem habent compoſitam ex velocitate
              <lb/>
            (√(A - {δA/x})) ex denſitate (x) & </s>
            <s xml:id="echoid-s6656" xml:space="preserve">ex tempuſculo (d t): </s>
            <s xml:id="echoid-s6657" xml:space="preserve">ſic igitur eſt - d x
              <lb/>
            = a (√(A - {δA/x})) x d t, ubi a eſt numerus conſtans qui per metho-
              <lb/>
            dum præcedentis paragraphi fit = {1/L}, retenta ſignificatione hujus litteræ
              <lb/>
            ibidem adhibita; </s>
            <s xml:id="echoid-s6658" xml:space="preserve">hocque valore ſubſtituto oritur
              <lb/>
            - d x = {dt/L} X √ (Axx - δAx) ſeu {- dx/√ (xx - δx)} = {dt√A/L}:
              <lb/>
            </s>
            <s xml:id="echoid-s6659" xml:space="preserve">Factaque debita integratione fit: </s>
            <s xml:id="echoid-s6660" xml:space="preserve">
              <lb/>
            log.</s>
            <s xml:id="echoid-s6661" xml:space="preserve">{[√x - √(x - δ)] x [√D + √(D - δ)]/[√x + √(x - δ)] x [√D - √(D - δ)]} = {t√A/L}, aut poſito rurſus, ut in
              <lb/>
            præcedente paragragho, t = 2 n √ s, </s>
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