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

List of thumbnails

< >
51
51 (37) 		52
52 (38)
53
53 (39) 		54
54 (40)
55
55 (41) 		56
56 (42)
57
57 (43) 		58
58 (44)
59
59 (45) 		60
60 (46)
< >
page |< < (40) of 361 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div55" type="section" level="1" n="40">
          <p>
            <s xml:id="echoid-s1076" xml:space="preserve">
              <pb o="40" file="0054" n="54" rhead="HYDRODYNAMICÆ."/>
            mina in inſtrumentis hydraulicis raro occurrere ſolent, & </s>
            <s xml:id="echoid-s1077" xml:space="preserve">fingamus ſuperfi-
              <lb/>
            ciem aquæ per centeſimam partem deſcendiſſe tantum totius altitudinis ini-
              <lb/>
            tialis (deſcendiſſe autem aliquantulum aſſumo, quia à primo initio motus
              <lb/>
            aquæ nullus ineſſe poteſt, nedum tantus, ut aqua effluens ad totam alti-
              <lb/>
            tudinem aſcendere motu ſuo poſſit) hæ poſitiones faciunt m = 16n & </s>
            <s xml:id="echoid-s1078" xml:space="preserve">mm =
              <lb/>
            256nn, atque x = {99/100}a, unde prodit
              <lb/>
            z = {128/127}({99/100} - ({99/100})
              <emph style="super">255</emph>
            )a = {92/100}a,
              <lb/>
            quæ quidem aliquantulum differt à quantitate x, ſeu {99/100}a, ſed tamen non
              <lb/>
            multum admodum, fitque differentia multo minor, cum minus eſt foramen,
              <lb/>
            & </s>
            <s xml:id="echoid-s1079" xml:space="preserve">paullo magis deſcendit ſuperficies aquæ. </s>
            <s xml:id="echoid-s1080" xml:space="preserve">Igitur differt hæc Theoria à vul-
              <lb/>
            gari potiſſimum circa fluxus initium, quo minor eſt motus, quam ſtatutum
              <lb/>
            fuit: </s>
            <s xml:id="echoid-s1081" xml:space="preserve">è contrario circa fluxus finem majori velocitate aqua ejicitur, quam ſe-
              <lb/>
            cundum principia ſolita deberet.</s>
            <s xml:id="echoid-s1082" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1083" xml:space="preserve">§. </s>
            <s xml:id="echoid-s1084" xml:space="preserve">18. </s>
            <s xml:id="echoid-s1085" xml:space="preserve">Hactenus conſideravimus motum aquæ à propria ſua gravitate
              <lb/>
            ortum; </s>
            <s xml:id="echoid-s1086" xml:space="preserve">ponamus nunc vi aliena aquam ejectam fuiſſe præter vim gravitatis,
              <lb/>
            talemque aquæ effluenti communicatam fuiſſe velocitatem, qua ad altitudi-
              <lb/>
            nem multo majorem aſcendere poſſit, quam ſi ſola aquæ gravitas motum
              <lb/>
            produxiſſet; </s>
            <s xml:id="echoid-s1087" xml:space="preserve">dein ſubito vim illam alienam evaneſcere, & </s>
            <s xml:id="echoid-s1088" xml:space="preserve">aquam ſibi relin-
              <lb/>
            qui; </s>
            <s xml:id="echoid-s1089" xml:space="preserve">Id autem ſi fiat, experientia docet citiſſime aquæ velocitatem decreſce-
              <lb/>
            re & </s>
            <s xml:id="echoid-s1090" xml:space="preserve">mox talem eſſe, ut notabililer non ſuperet velocitatem eam, quæ ex
              <lb/>
            ſola aquæ gravitate oritura fuiſſet. </s>
            <s xml:id="echoid-s1091" xml:space="preserve">Ita videmus fieri aliquando in fontibus
              <lb/>
            ſalientibus (de cujus rei cauſa vera atque menſura alibi dicam) ut aquæ ad
              <lb/>
            triplam vel quadruplam majoremve altitudinem aſſiliat, quam eſt ordinaria;
              <lb/>
            </s>
            <s xml:id="echoid-s1092" xml:space="preserve">quod cum ita contingit, ſaltus iſte protinus ceſſat ſolitamque altitudinem,
              <lb/>
            quantum id ſenſibus percipi poteſt, non excedit: </s>
            <s xml:id="echoid-s1093" xml:space="preserve">loquor autem de tubis
              <lb/>
            foraminibus non valde magnis perforatis; </s>
            <s xml:id="echoid-s1094" xml:space="preserve">nam cum foramen eſt ali-
              <lb/>
            quanto majus, non ita cito decreſcit aquæ ſaltus. </s>
            <s xml:id="echoid-s1095" xml:space="preserve">Jam itaque examinabi-
              <lb/>
            mus, quousque theoria cum iſtis phænomenis conveniat, accuratasque
              <lb/>
            menſuras eorum, quales inde ſequuntur, ſubjungemus. </s>
            <s xml:id="echoid-s1096" xml:space="preserve">Ut vero rem ge-
              <lb/>
            neraliter proſequamur, ponemus rurſus amplitudinem cylindri ad amplitu-
              <lb/>
            dinem foraminis ut m ad n: </s>
            <s xml:id="echoid-s1097" xml:space="preserve">aquam ea explodi velocitate qua aſſurgere poſſit
              <lb/>
            ad altitudinem a, eoque ipſo temporis puncto altitudinem aquæ ſupra </s>
          </p>
        </div>
      </text>
    </echo>
Impressum