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

Table of handwritten notes

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            <s xml:id="echoid-s530" xml:space="preserve">
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            plenus usque in C. </s>
            <s xml:id="echoid-s531" xml:space="preserve">Si nunc fingatur vas perforatum in G; </s>
            <s xml:id="echoid-s532" xml:space="preserve">erit utrumque flui-
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            dum in æquilibrio (per §. </s>
            <s xml:id="echoid-s533" xml:space="preserve">3.) </s>
            <s xml:id="echoid-s534" xml:space="preserve">tantum ergo premit fluidum tubuli C G ver-
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            ſus interiora, quantum premit fluidum vaſis verſus exteriora. </s>
            <s xml:id="echoid-s535" xml:space="preserve">Sed prior
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            preſſio convenit propoſitioni (per §. </s>
            <s xml:id="echoid-s536" xml:space="preserve">6.) </s>
            <s xml:id="echoid-s537" xml:space="preserve">ergo & </s>
            <s xml:id="echoid-s538" xml:space="preserve">altera.</s>
            <s xml:id="echoid-s539" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s540" xml:space="preserve">II. </s>
            <s xml:id="echoid-s541" xml:space="preserve">Si vero loco puncti G ſumatur aliud H tale, ut linea, quæ eo in
              <lb/>
            loco vaſi perpendiculariter inſiſtit, cadat intra vas; </s>
            <s xml:id="echoid-s542" xml:space="preserve">tunc poteſt vas integrum
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            concipi R H S O N, priori unitum in H, & </s>
            <s xml:id="echoid-s543" xml:space="preserve">aqua repletum usque in P O. </s>
            <s xml:id="echoid-s544" xml:space="preserve">Sic
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            enim apparet, ſi particula H, quæ utrique vaſi communis eſt, perforetur,
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            fluida ſic fore in æquilibrio (§. </s>
            <s xml:id="echoid-s545" xml:space="preserve">3.) </s>
            <s xml:id="echoid-s546" xml:space="preserve">adeoque utriusque preſſionem in H eſſe
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            æqualem. </s>
            <s xml:id="echoid-s547" xml:space="preserve">Preſſio autem fluidi in R S N ea eſt, quæ indicatur in propoſi-
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            tione (per partem primam hujus demonſtrationis) ergo & </s>
            <s xml:id="echoid-s548" xml:space="preserve">preſſio fluidi,
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            quod eſt in vaſe A M B. </s>
            <s xml:id="echoid-s549" xml:space="preserve">Q. </s>
            <s xml:id="echoid-s550" xml:space="preserve">E. </s>
            <s xml:id="echoid-s551" xml:space="preserve">D.</s>
            <s xml:id="echoid-s552" xml:space="preserve"/>
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        <div xml:id="echoid-div24" type="section" level="1" n="20">
          <head xml:id="echoid-head26" xml:space="preserve">Scholion.</head>
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            <s xml:id="echoid-s553" xml:space="preserve">§. </s>
            <s xml:id="echoid-s554" xml:space="preserve">8. </s>
            <s xml:id="echoid-s555" xml:space="preserve">Ex his propoſitionibus facile deducuntur æquilibria flui-
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            dorum ſtagnantium in caſibus magis compoſitis. </s>
            <s xml:id="echoid-s556" xml:space="preserve">Nolo autem omnia
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            proſequi, neque enim inſtituti noſtri ratio id poſtulat, contentus demon-
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            ſtrationibus, quas modo dedi, propoſitionum fundamentalium in hydroſtatica.
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            </s>
            <s xml:id="echoid-s557" xml:space="preserve">Quod vero attinet ad preſſiones fluidorum non ſtagnantium, funt certe hæ
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            altioris indaginis. </s>
            <s xml:id="echoid-s558" xml:space="preserve">Nec dum à quoquam recte determinata fuit preſſio fluido-
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            rum, par canales ſeu tubos dato velocitatis gradu fluentium, quamvis id ar-
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            gumenti genus tam in rebus aquariis, quam multis aliis ſit utiliſſimum. </s>
            <s xml:id="echoid-s559" xml:space="preserve">
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            De his vero prius agere non licet, quam de motu fluidorum commentati
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            ſimus.</s>
            <s xml:id="echoid-s560" xml:space="preserve"/>
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            <s xml:id="echoid-s561" xml:space="preserve">§. </s>
            <s xml:id="echoid-s562" xml:space="preserve">9. </s>
            <s xml:id="echoid-s563" xml:space="preserve">Patet ex præcedentibus ratio potentiarum veſicularium, qui-
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            bus ingentia pondera ſuperari poſſunt: </s>
            <s xml:id="echoid-s564" xml:space="preserve">Inde etiam noſcitur vis, quam ſu-
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            ſtinent latera tubi, in quo aquæ ſtagnant; </s>
            <s xml:id="echoid-s565" xml:space="preserve">quod argumentum, quoniam
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            pertractari ſolet ab hydroſtaticæ ſcriptoribus, nunc percurremus, præſer-
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            tim cum multa alia eo innitantur, de quibus nobis dicendum erit.</s>
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            <s xml:id="echoid-s567" xml:space="preserve">Sit Primo veſicaonmp, (Fig. </s>
            <s xml:id="echoid-s568" xml:space="preserve">5.) </s>
            <s xml:id="echoid-s569" xml:space="preserve">pavimento & </s>
            <s xml:id="echoid-s570" xml:space="preserve">ponderi B interpoſita, in
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              <note position="right" xlink:label="note-0035-01" xlink:href="note-0035-01a" xml:space="preserve">Fig. 5.</note>
            quam aqua infundatur per tubum FRo, cujus crus verticale FR brevitatis
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            gratia incomparabiliter longius ponemus, quam diametrum veſicæ: </s>
            <s xml:id="echoid-s571" xml:space="preserve">Non ele-
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            vabitur ſtatim pondus B; </s>
            <s xml:id="echoid-s572" xml:space="preserve">Atſi aqua porro infundatur usque v. </s>
            <s xml:id="echoid-s573" xml:space="preserve">gr. </s>
            <s xml:id="echoid-s574" xml:space="preserve">in </s>
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