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

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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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            rum dato tempore affundendarum ſequi rationem ſeſquiplicatam altitudinum,
              <lb/>
            ad quas aquæ à fundo cylindri aſcendunt: </s>
            <s xml:id="echoid-s3054" xml:space="preserve">aut viciſſim altitudines ſequi ra-
              <lb/>
            tionem ſubtriplicatam quadratorum quantitatum, quibus aquæ dato tempore
              <lb/>
            affunduntur.</s>
            <s xml:id="echoid-s3055" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s3056" xml:space="preserve">§. </s>
            <s xml:id="echoid-s3057" xml:space="preserve">19. </s>
            <s xml:id="echoid-s3058" xml:space="preserve">Soluto hoc problemate venio ad alterum Cl. </s>
            <s xml:id="echoid-s3059" xml:space="preserve">Poleno conſide-
              <lb/>
            ratum.</s>
            <s xml:id="echoid-s3060" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3061" xml:space="preserve">Sit idem cylindrus, ſed aquis in foſſa veluti vaſe infinito ſtagnantibus,
              <lb/>
            ſubmerſus; </s>
            <s xml:id="echoid-s3062" xml:space="preserve">dicaturque altitudo ſubmerſionis = a, quæritur nunc iiſdem po-
              <lb/>
            ſitis, ut antea, rurſus æquatio inter altitudinem α ſuperficiei aqueæ internæ ſu-
              <lb/>
            pra externam, & </s>
            <s xml:id="echoid-s3063" xml:space="preserve">quantitatem q dato tempore affundendam.</s>
            <s xml:id="echoid-s3064" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s3065" xml:space="preserve">Quod ad illam rimæ partem α, quæ aquas ejicit & </s>
            <s xml:id="echoid-s3066" xml:space="preserve">ſupra aquam exter-
              <lb/>
            nam eminet, illam jam vidimus dato tempore erogare quantitatem {2/3} n α √ α:
              <lb/>
            </s>
            <s xml:id="echoid-s3067" xml:space="preserve">reſidua autem rimæ pars ſubmerſa aquas ubique communi velocitate tranſimit-
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            tit, ut ex infra dicendis patebit, & </s>
            <s xml:id="echoid-s3068" xml:space="preserve">quidem velocitate √ α, ita, ut multiplica-
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            ta hâc velocitate per magnitudinem rimæ ſubmerſæ n a, habeatur quantitas,
              <lb/>
            quam dato tempore ejicit = n a √ α. </s>
            <s xml:id="echoid-s3069" xml:space="preserve">Si utraque quantitas in ſummam conji-
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            ciatur, habebitur ({2/3} α + a)n√α = q.</s>
            <s xml:id="echoid-s3070" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s3071" xml:space="preserve">Ope hujus æquationis cognoſcitur q ex datis altitudinibus a & </s>
            <s xml:id="echoid-s3072" xml:space="preserve">α: </s>
            <s xml:id="echoid-s3073" xml:space="preserve">aut
              <lb/>
            viciſſim altitudo α ex cognitis quantitatibus a & </s>
            <s xml:id="echoid-s3074" xml:space="preserve">q.</s>
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            <s xml:id="echoid-s3076" xml:space="preserve">Convenire autem hanc æquationem admodum accurate cum experi-
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            mentis, ipſe oſtendit celeberrimus eorum auctor, cujus ſolutio ab hâc no-
              <lb/>
            ſtra non differt. </s>
            <s xml:id="echoid-s3077" xml:space="preserve">Sequitur ex iſta æquatione, elevationes α eo majores eſſe pro
              <lb/>
            iiſdem aquarum affuſionibus, quo minor eſt altitudo ſubmerſionis a.</s>
            <s xml:id="echoid-s3078" xml:space="preserve"/>
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        <div xml:id="echoid-div115" type="section" level="1" n="88">
          <head xml:id="echoid-head113" style="it" xml:space="preserve">Experimenta quæ ad Sectionem V. pertinent.</head>
          <head xml:id="echoid-head114" xml:space="preserve">Ad §. 5.</head>
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            <s xml:id="echoid-s3079" xml:space="preserve">VAſe uſus ſum §. </s>
            <s xml:id="echoid-s3080" xml:space="preserve">5. </s>
            <s xml:id="echoid-s3081" xml:space="preserve">deſcripto cum tubulo vitreo (Fig. </s>
            <s xml:id="echoid-s3082" xml:space="preserve">30.) </s>
            <s xml:id="echoid-s3083" xml:space="preserve">Primo autem
              <lb/>
            obturavi orificium L M, tubumque R N aqua implevi, donec ſuper-
              <lb/>
            ficies ejus raderet foraminulum in a: </s>
            <s xml:id="echoid-s3084" xml:space="preserve">aquam tunc tubo ingreſſam ob-
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            fervavi extremitate attigiſſe punctum f: </s>
            <s xml:id="echoid-s3085" xml:space="preserve">poſtea reſerato orificio L M, & </s>
            <s xml:id="echoid-s3086" xml:space="preserve">aquis ef-
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            fluentibus novas affundebam in vas ſuperius E F P Q adhibita diligentia, ut
              <lb/>
            extremitas aquæ in f interea nec aſcenderet nec deſcenderet. </s>
            <s xml:id="echoid-s3087" xml:space="preserve">Hæc dum </s>
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