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

Table of contents

< >
[151.] Regula 5.
Page: 182 (168)
[152.] Demonſtratio.
Page: 183 (169)
[153.] Regula 6.
Page: 183 (169)
[154.] Demonſtratio.
Page: 184 (170)
[155.] Scholium.
Page: 184 (170)
[156.] Regula 7.
Page: 184 (170)
[157.] Scholium.
Page: 185 (171)
[158.] Exemplum 1.
Page: 185 (171)
[159.] Exemplum 2.
Page: 186 (172)
[160.] Digreſſus continens aliquas commentationes in Ma-chinam Hydraulicam quam repræſent at figura 51.
Page: 187 (173)
[161.] Regula 8.
Page: 190 (176)
[162.] Scholium.
Page: 191 (177)
[163.] Regula 9.
Page: 191 (177)
[164.] Scholium.
Page: 191 (177)
[165.] Scholium Generale.
Page: 192 (178)
[166.] (B) De machinis hydraulicis aquas ſine not abili impetu ex loco humiliori in altiorem tranſportantibus. Regula 10.
Page: 192 (178)
[167.] Demonſtratio.
Page: 193 (179)
[168.] Corollarium.
Page: 193 (179)
[169.] Scholium 1.
Page: 193 (179)
[170.] Scholium 2.
Page: 194 (180)
[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)
< >
page |< < (186) of 361 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div218" type="section" level="1" n="172">
          <p>
            <s xml:id="echoid-s5362" xml:space="preserve">
              <pb o="186" file="0200" n="200" rhead="HYDRODYNAMICÆ"/>
            alii ex principio alieno petere ſolent. </s>
            <s xml:id="echoid-s5363" xml:space="preserve">Præmiſſis iſtis præmittendis uſum ma-
              <lb/>
            chinæ conſiderare nunc incipiemus, quem habet pro elevandis aquis.</s>
            <s xml:id="echoid-s5364" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div220" type="section" level="1" n="173">
          <head xml:id="echoid-head221" xml:space="preserve">Problema.</head>
          <p>
            <s xml:id="echoid-s5365" xml:space="preserve">(VI) Quæritur quænam maxima ſit aquæ quantitas quam cochlea qua-
              <lb/>
            vis revolutione ejicere poteſt.</s>
            <s xml:id="echoid-s5366" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div221" type="section" level="1" n="174">
          <head xml:id="echoid-head222" xml:space="preserve">Solutio.</head>
          <p>
            <s xml:id="echoid-s5367" xml:space="preserve">Conſideremus helicem integram a 1 b, ſitque quantitas aquæ quam
              <lb/>
            plena continet = q: </s>
            <s xml:id="echoid-s5368" xml:space="preserve">Notandum autem eſt non poſſe helicem eſſe totam aqua re-
              <lb/>
            pletam, ſi enim totus canalis plenus eſſet, effluerent aquæ per orificium
              <lb/>
            inferius, igitur quivis ramus, qualis eſt a 1 b, partim aëre partim aqua oc-
              <lb/>
            cupatur, erit autem altera aquæ extremitas in o ceu puncto ſupremo, alte-
              <lb/>
            ra in q, ceu puncto ad libellam cum priori compoſito: </s>
            <s xml:id="echoid-s5369" xml:space="preserve">pars igitur aqua ple-
              <lb/>
            na eſt o p q, atque ſi hæc pars ponatur ad longitudinem totius helicis a 1 b
              <lb/>
            ut g ad h, erit maxima aquæ quantitas una revolutione ejicienda = {g q/h}. </s>
            <s xml:id="echoid-s5370" xml:space="preserve">Q.</s>
            <s xml:id="echoid-s5371" xml:space="preserve">E.</s>
            <s xml:id="echoid-s5372" xml:space="preserve">I.</s>
            <s xml:id="echoid-s5373" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div222" type="section" level="1" n="175">
          <head xml:id="echoid-head223" xml:space="preserve">Scholium 1.</head>
          <p>
            <s xml:id="echoid-s5374" xml:space="preserve">(VII) Quoniam, ut diximus, fieri non poteſt ut aq
              <unsure/>
            a per totum ca-
              <lb/>
            nalis tractum ſit contigua, cavendum eſt, ne ſeparatio aquæ impediatur,
              <lb/>
            quod facile fieri poteſt cum totum cylindri fundum aquæ immergitur, quia
              <lb/>
            ſic aëri prohibetur ingreſſus per orificium inferius canalis: </s>
            <s xml:id="echoid-s5375" xml:space="preserve">Neque faciendum
              <lb/>
            eſt, ut nimia fundi pars extra aquam promineat, quia ſic cochlea non om-
              <lb/>
            nem, quam una revolutione alias poſſet, aquam haurit; </s>
            <s xml:id="echoid-s5376" xml:space="preserve">imo nihil hauriet,
              <lb/>
            ſi immerſio punctum h non attingat: </s>
            <s xml:id="echoid-s5377" xml:space="preserve">Debita autem fiet immerſio usque ad
              <lb/>
            punctum g, quia ſic arcus helicis o p q, qui aquam retinere valet, maximus
              <lb/>
            fit. </s>
            <s xml:id="echoid-s5378" xml:space="preserve">Etſi enim nunquam rei periculum fecerim, & </s>
            <s xml:id="echoid-s5379" xml:space="preserve">plerique auctores aliter
              <lb/>
            de illa loqui videantur, malim tamen rationi, quam auctoritati illorum, qui
              <lb/>
            ad immerſionem hanc animum non adverterunt, credere.</s>
            <s xml:id="echoid-s5380" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5381" xml:space="preserve">Regula igitur ratione immerſionis hæc obſervabitur, fundum nempe ſub-
              <lb/>
            mergetur, donec chorda arcus extra aquam eminentis ſit = {2mN/Mn}, ubi lit-
              <lb/>
            teræ m, N, M, & </s>
            <s xml:id="echoid-s5382" xml:space="preserve">n idem ſignificant, quod in articulo quarto.</s>
            <s xml:id="echoid-s5383" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum