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

Table of contents

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[121.] EXPERIMENTA Ad ſect. ſept. referenda. Experimentum 1.
[122.] Experimentum 2.
[123.] Experimentum 3.
[124.] De iſto tubo experimentum ita ſumſi:
[125.] Experimentum 4.
[126.] Experimentum 5.
[127.] HYDRODYNAMICÆ SECTIO OCTAVA. De motu fluidorum cum homogeneorum tum hetero-geneorum per vaſa irregularis & præruptæ ſtru-cturæ, ubi ex theoria virium vivarum, quarum pars continue abſorbeatur, explicantur præcipue Phæno-mena ſingularia fluidorum, per plurima foramina trajecto-rum, præmiſsis regulis generalibus pro motibus fluido-rum ubique definiendis. §. 1.
[128.] Regula 1.
[129.] Regula 2.
[130.] Problema.
[131.] Solutio.
[132.] Scholium 1.
[133.] Scholium 2.
[134.] Corollarium.
[135.] EXPERIMENTA Ad ſectionem octavam pertinentia. Experimentum 1.
[136.] Experimentum 2.
[137.] HYDRODYNAMICÆ SECTIO NONA. De motu fluidorum, quæ non proprio pondere, ſed potentia aliena ejiciuntur, ubi præſertim de Machinis Hydraulicis earundemque ultimo qui da-ri poteſt perfectionis gradu, & quomodo mecha-nica tam ſolidorum quam fluidorum ulterius perſici poſsit. §. 1.
[138.] Definitiones.
[139.] (A) De machinis aquas cum impetu in altum projicientibus. Regula 1.
[140.] Demonſtratio.
[141.] Scholium.
[142.] Regula 2.
[143.] Demonſtratio.
[144.] Scholium.
[145.] Regula 3.
[146.] Demonſtratio.
[147.] Scholium.
[148.] Regula 4.
[149.] Demonſtratio.
[150.] Scholium.
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        <div xml:id="echoid-div119" type="section" level="1" n="92">
          <p>
            <s xml:id="echoid-s3250" xml:space="preserve">
              <pb o="114" file="0128" n="128" rhead="HYDRODYNAMICÆ"/>
            ximas hanc legem ſervare. </s>
            <s xml:id="echoid-s3251" xml:space="preserve">Cum itaque talis caſus occurrit, eo magis con-
              <lb/>
            veniet motus realis cum theoria, quo longior fuerit pars b m & </s>
            <s xml:id="echoid-s3252" xml:space="preserve">quo paucio-
              <lb/>
            ra adfuerint obſtacula.</s>
            <s xml:id="echoid-s3253" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3254" xml:space="preserve">§. </s>
            <s xml:id="echoid-s3255" xml:space="preserve">3. </s>
            <s xml:id="echoid-s3256" xml:space="preserve">Quod ſi nunc canalis fuerit non horizontaliter ſed oblique ad
              <lb/>
            horizontem poſitus, apparet omnia ſimiliter ſe habere, niſi quod aſcenſus potent.
              <lb/>
            </s>
            <s xml:id="echoid-s3257" xml:space="preserve">aquæ in omni ſitu æquandus ſit aſcenſui potent. </s>
            <s xml:id="echoid-s3258" xml:space="preserve">initiali aucto deſcenſu actuali, id
              <lb/>
            eſt, deſcenſui verticali centri gravitatis. </s>
            <s xml:id="echoid-s3259" xml:space="preserve">Atque ſi nullo impulſu aqua ſua ſponte
              <lb/>
            ſe movere incipiat, erit ſimpliciter deſcenſus actualis æqualis aſcenſui potent.</s>
            <s xml:id="echoid-s3260" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3261" xml:space="preserve">Igitur aqua continue progredi perget, quamdiu centrum gravitatis lo-
              <lb/>
            co humiliori poſitum eſt, ac fuit ab initio motus. </s>
            <s xml:id="echoid-s3262" xml:space="preserve">At vero cum tubus ita
              <lb/>
            fuerit formatus & </s>
            <s xml:id="echoid-s3263" xml:space="preserve">inflexus eaque fluidi quantitate repletus, ut centrum gravi-
              <lb/>
            tatis priſtinam altitudinem reaſſumere poſſit, tunc fluidum motum obtinebit
              <lb/>
            retrogradum & </s>
            <s xml:id="echoid-s3264" xml:space="preserve">ſine fine oſcillabitur. </s>
            <s xml:id="echoid-s3265" xml:space="preserve">De iſto motu præcipuam huj
              <unsure/>
            us ſectionis
              <lb/>
            partem faciente mox dicemus. </s>
            <s xml:id="echoid-s3266" xml:space="preserve">Interea obſervare licet, fieri poſſe, ut aqua
              <lb/>
            omnis ex loco humiliore per altiorem ſua ſponte ſine prævia ſuctione præter-
              <lb/>
            fluat, ſi modo omnia debito modo ſe habeant.</s>
            <s xml:id="echoid-s3267" xml:space="preserve"/>
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        </div>
        <div xml:id="echoid-div121" type="section" level="1" n="93">
          <head xml:id="echoid-head122" style="it" xml:space="preserve">De oſcillationibus fluidorum in tubisrecurvis.</head>
          <head xml:id="echoid-head123" xml:space="preserve">Caſus II.</head>
          <p>
            <s xml:id="echoid-s3268" xml:space="preserve">§. </s>
            <s xml:id="echoid-s3269" xml:space="preserve">4. </s>
            <s xml:id="echoid-s3270" xml:space="preserve">Dedit Pater meus in Comm. </s>
            <s xml:id="echoid-s3271" xml:space="preserve">Acad. </s>
            <s xml:id="echoid-s3272" xml:space="preserve">Scient. </s>
            <s xml:id="echoid-s3273" xml:space="preserve">Petrop. </s>
            <s xml:id="echoid-s3274" xml:space="preserve">tom. </s>
            <s xml:id="echoid-s3275" xml:space="preserve">2. </s>
            <s xml:id="echoid-s3276" xml:space="preserve">theore-
              <lb/>
            mata quædam, quæ inſignem manifeſtant uſum quem theoria virium vivarum
              <lb/>
            habet in rebus mechanicis. </s>
            <s xml:id="echoid-s3277" xml:space="preserve">Illud vero quod tertio loco poſitum eſt ita ſe
              <lb/>
            habet.</s>
            <s xml:id="echoid-s3278" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s3279" xml:space="preserve">Sit tubus cylindricus A B C H (Fig. </s>
            <s xml:id="echoid-s3280" xml:space="preserve">33.) </s>
            <s xml:id="echoid-s3281" xml:space="preserve">utrobi{q́ue} apertus at{q́ue} infle-
              <lb/>
              <note position="left" xlink:label="note-0128-01" xlink:href="note-0128-01a" xml:space="preserve">Fig. 33.</note>
            xus in duo crura B A & </s>
            <s xml:id="echoid-s3282" xml:space="preserve">C H ad partem horizontalem B C; </s>
            <s xml:id="echoid-s3283" xml:space="preserve">ſit ſinus anguli
              <lb/>
            A B C = p, & </s>
            <s xml:id="echoid-s3284" xml:space="preserve">ſinus anguli H C B = q; </s>
            <s xml:id="echoid-s3285" xml:space="preserve">exiſtente nimirum ſinu toto = 1;
              <lb/>
            </s>
            <s xml:id="echoid-s3286" xml:space="preserve">ſit porro ille tubus aqua plenus uſ{q́ue} ad horizontalem M N; </s>
            <s xml:id="echoid-s3287" xml:space="preserve">vocetur{q́ue} L longi-
              <lb/>
            tudo partis tubi M B C N aqua plenæ: </s>
            <s xml:id="echoid-s3288" xml:space="preserve">Erunt agitati liquoris in hoc tubo oſ-
              <lb/>
            cillationes tam majores, quam minores omnes tautochronæ at{q́ue} ejuſdem duratio-
              <lb/>
            nis cum oſcillationibus minimis penduli alicujus ſimplicis, cujus longitudo
              <lb/>
            = {L/p + q}.</s>
            <s xml:id="echoid-s3289" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3290" xml:space="preserve">Huic theoremati eodem auctore ſubnectitur tale corollarium.</s>
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