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

Table of contents

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[111.] Problema.
[112.] Solutio.
[113.] Scholium.
[114.] Corollarium 1.
[115.] Corollarium 2.
[116.] Scholion Generale.
[117.] HYDRODYNAMICÆ SECTIO SEPTIMA. De motu aquarum per vaſa ſubmerſa, ubi exem-plis oſtenditur, quam inſigniter utile ſit princi-pium conſervationis virium vivarum, veliis in caſibus, quibus continue aliquid de illis perdi cenſendum eſt. PARS PRIMA. De deſcenſu aquarum. §. 1.
[118.] PARS SECUNDA. De aſcenſu aquarum.
[119.] Corollarium.
[120.] Scholium Generale.
[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.
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            tionis; </s>
            <s xml:id="echoid-s3990" xml:space="preserve">deinde quod ibi longitudo penduli ſit æqualis dimidiæ longitudini tubi,
              <lb/>
            cum hîc ſit æqualis integræ, quamvis ſi recte res perpendatur, hic potius ſit con-
              <lb/>
            ſenſus quam diſſenſus dicendus ob tubi, quæ in priori caſu eſt, duplicationem.</s>
            <s xml:id="echoid-s3991" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s3992" xml:space="preserve">§. </s>
            <s xml:id="echoid-s3993" xml:space="preserve">20. </s>
            <s xml:id="echoid-s3994" xml:space="preserve">Utroque oſcillationum genere illuſtratur natura undarum ven-
              <lb/>
            to agitatarum: </s>
            <s xml:id="echoid-s3995" xml:space="preserve">neque enim aliter moventur, quam quod aquæ in illis conti-
              <lb/>
            nue aſcendant rurſuſque deſcendant. </s>
            <s xml:id="echoid-s3996" xml:space="preserve">Ita patet quod dicit Newtonus, tem-
              <lb/>
            pora undulationum eſſe in ratione dimidiata latitudinum undarum, quia ponit
              <lb/>
            undarum formam ſibi conſtanter eſſe ſimilem & </s>
            <s xml:id="echoid-s3997" xml:space="preserve">proinde earum latitudinem
              <lb/>
            proportionalem profunditati, ad quam aquæ agitantur. </s>
            <s xml:id="echoid-s3998" xml:space="preserve">Veriſimile autem eſt
              <lb/>
            profunditatem eam eſſe, quæ pendulo ſimplici cum undis tautochrono, nempe
              <lb/>
            v.</s>
            <s xml:id="echoid-s3999" xml:space="preserve">gr. </s>
            <s xml:id="echoid-s4000" xml:space="preserve">60 {1/3} ped. </s>
            <s xml:id="echoid-s4001" xml:space="preserve">Pariſ. </s>
            <s xml:id="echoid-s4002" xml:space="preserve">ſi ſingulis binis ſecundis fiat undarum aſcenſus deſcenſuſve.</s>
            <s xml:id="echoid-s4003" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s4004" xml:space="preserve">§. </s>
            <s xml:id="echoid-s4005" xml:space="preserve">21. </s>
            <s xml:id="echoid-s4006" xml:space="preserve">Quamvis noluerim ad prolixitatem calculi evitandam, hoc ar-
              <lb/>
            gumentum in omni ſua extenſione proſequi, propterque ea de cylindricis va-
              <lb/>
            ſis tantum egerim, attamen quia in caſu ſubmerſionis infinitæ, enunciationes
              <lb/>
            & </s>
            <s xml:id="echoid-s4007" xml:space="preserve">theoremata parum de ſua concinnitate perdunt, ſuperaddam theorema ge-
              <lb/>
            nerale pro oſcillationibus aquæ in tubo utcunque inæquali, omiſſa tamen de-
              <lb/>
            monſtratione, quæ ex alibi dictis unicuique obvia erit, præſertim vero ex iis
              <lb/>
            quæ in Sect. </s>
            <s xml:id="echoid-s4008" xml:space="preserve">6. </s>
            <s xml:id="echoid-s4009" xml:space="preserve">§. </s>
            <s xml:id="echoid-s4010" xml:space="preserve">§. </s>
            <s xml:id="echoid-s4011" xml:space="preserve">6. </s>
            <s xml:id="echoid-s4012" xml:space="preserve">7. </s>
            <s xml:id="echoid-s4013" xml:space="preserve">& </s>
            <s xml:id="echoid-s4014" xml:space="preserve">ſeqq. </s>
            <s xml:id="echoid-s4015" xml:space="preserve">uſque ad 20. </s>
            <s xml:id="echoid-s4016" xml:space="preserve">expoſita fuerunt. </s>
            <s xml:id="echoid-s4017" xml:space="preserve">Faciendum au-
              <lb/>
            tem eſt, ut cylindricæ ſit ſtructuræ pars illa vaſis ſuperior, in quâ excurſiones
              <lb/>
            fiunt.</s>
            <s xml:id="echoid-s4018" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s4019" xml:space="preserve">§. </s>
            <s xml:id="echoid-s4020" xml:space="preserve">22. </s>
            <s xml:id="echoid-s4021" xml:space="preserve">Fuerit igitur bd longitudo vaſis ſubmerſi (Fig. </s>
            <s xml:id="echoid-s4022" xml:space="preserve">35. </s>
            <s xml:id="echoid-s4023" xml:space="preserve">b) Repræſentet
              <lb/>
            b F ejus amplitudinem in loco ſuperficiei, ponaturque vas ita formatum, ut ſit
              <lb/>
            curva FGH ſcala amplitudinum: </s>
            <s xml:id="echoid-s4024" xml:space="preserve">ſumatur linea b c fiatque curva L M N,
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            cujus applicata c M ſit ubique = {bF
              <emph style="super">2</emph>
            /cG}, & </s>
            <s xml:id="echoid-s4025" xml:space="preserve">erit longitudo penduli iſochro-
              <lb/>
            ni cum oſcillationibus aqueæ ſuperficiei = ſpatio bd NL diviſo per b L.</s>
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          <head xml:id="echoid-head155" xml:space="preserve">Corollarium.</head>
          <p>
            <s xml:id="echoid-s4027" xml:space="preserve">§. </s>
            <s xml:id="echoid-s4028" xml:space="preserve">23. </s>
            <s xml:id="echoid-s4029" xml:space="preserve">Ex præcedente paragrapho ſequitur, ſi tubus ſubmerſus coni-
              <lb/>
            cus fuerit, habeatque amplitudinem in regione aquæ ſuperficiei, quæ ſit ad
              <lb/>
            orificium ſubmerſum ut m ad n, fore longitudinem penduli Iſochroni cum
              <lb/>
            vibrante aqua ad longitudinem ſubmerſi tubi, ut √m ad √n, id eſt, ut ra-
              <lb/>
            dices prædictarum amplitudinum, atque ſi tubus idem ſitu, modo recto </s>
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