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

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          <pb o="292" file="0306" n="306" rhead="HYDRODYNAMICÆ"/>
          <p>
            <s xml:id="echoid-s8687" xml:space="preserve">§. </s>
            <s xml:id="echoid-s8688" xml:space="preserve">18. </s>
            <s xml:id="echoid-s8689" xml:space="preserve">Sequitur porro ex præfata affectione probe intellecta, eundem
              <lb/>
            oriri à preſſionibus effectum ſive lamina aquas ad latera deflectat, ſive cauſa
              <lb/>
            fingatur motum omnem, quem particulæ aqueæ cylindrum egreſſæ acquiſive-
              <lb/>
            runt, abſorbens: </s>
            <s xml:id="echoid-s8690" xml:space="preserve">Inde intelligitur quid futurum ſit, ſi orificium C M (Fig. </s>
            <s xml:id="echoid-s8691" xml:space="preserve">85.)
              <lb/>
            </s>
            <s xml:id="echoid-s8692" xml:space="preserve">
              <note position="left" xlink:label="note-0306-01" xlink:href="note-0306-01a" xml:space="preserve">Fig. 85.</note>
            per quod aquæ ex cylindro A B M effluunt, aliis aquis in vaſe P Q F E ſtagnan-
              <lb/>
            tibus ſubmerſum fuerit: </s>
            <s xml:id="echoid-s8693" xml:space="preserve">repelletur nempe cylindrus A B M verſus P Q intra vas
              <lb/>
            P Q F E, ſi hoc cum cylindro non cohæreat; </s>
            <s xml:id="echoid-s8694" xml:space="preserve">At ſi vaſa inter ſe fuerint firmata,
              <lb/>
            nullam patietur ſyſtema preſſionem prævalentem; </s>
            <s xml:id="echoid-s8695" xml:space="preserve">quanta enim eſt preſſio ver-
              <lb/>
            ſus P Q ab effluentibus aquis, tanta quoque oritur preſſio contraria verſus E F
              <lb/>
            à continua deſtructione motus, quem particulæ cylindrum egreſſæ acquiſivere.</s>
            <s xml:id="echoid-s8696" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8697" xml:space="preserve">§. </s>
            <s xml:id="echoid-s8698" xml:space="preserve">19. </s>
            <s xml:id="echoid-s8699" xml:space="preserve">Dixi de preſſione venæ, quam lamina totam etiamſi expanſam
              <lb/>
            excipit: </s>
            <s xml:id="echoid-s8700" xml:space="preserve">Venio ad alteram ſpeciem impetus aquarum, quem ſcilicet ſuſtinent
              <lb/>
            laminæ fluido undique ſubmerſæ: </s>
            <s xml:id="echoid-s8701" xml:space="preserve">puto autem hanc non poſſe abſolute defini-
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            ri, quia ſingulæ particulæ in laminam impingentes aliter deflectuntur. </s>
            <s xml:id="echoid-s8702" xml:space="preserve">Si vero
              <lb/>
            cujuslibet particulæ deviatio cognita ponatur, non difficilis erit amplius quæ-
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            ſtionis ſolutio, mutato paullum theoremate, quo §. </s>
            <s xml:id="echoid-s8703" xml:space="preserve">17. </s>
            <s xml:id="echoid-s8704" xml:space="preserve">uſi ſumus eoque ge-
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            neraliori reddito, nempe tali: </s>
            <s xml:id="echoid-s8705" xml:space="preserve">ſi angulus mutatæ in corpore moto directionis non
              <lb/>
            fuerit rectus, ſed recto minor, tunc quoque minor erit ſumma productorum (de
              <lb/>
            quâ antea ſermo fuit) in ratione ut ſinus verſus mutatæ directionis ad ſinum
              <lb/>
            totum.</s>
            <s xml:id="echoid-s8706" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8707" xml:space="preserve">Igitur pro quâvis guttula indagandum eſſet, quantum directionem mo-
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            tus ab obice, ſeu lamina curſui oppoſita mutare cogatur. </s>
            <s xml:id="echoid-s8708" xml:space="preserve">At in theoria hu-
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            juſmodi definitiones exhiberi accurate vix poſſunt; </s>
            <s xml:id="echoid-s8709" xml:space="preserve">nec experientia probattheo-
              <lb/>
            remata hanc in rem exhiberi ſolita; </s>
            <s xml:id="echoid-s8710" xml:space="preserve">veluti quod conatus fluminis directe con-
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            tra circulum impingentis duplo ſit major conatu ejuſdem fluminis contra ſphæ-
              <lb/>
            ram ejuſdem diametri, & </s>
            <s xml:id="echoid-s8711" xml:space="preserve">quæ ſunt ſimilia: </s>
            <s xml:id="echoid-s8712" xml:space="preserve">quod autem quantitas preſſionis
              <lb/>
            pro ſphæra, qualis dari ſolet ab auctoribus, cum experimentis à Newtono
              <lb/>
            aliiſque inſtitutis & </s>
            <s xml:id="echoid-s8713" xml:space="preserve">in princ. </s>
            <s xml:id="echoid-s8714" xml:space="preserve">math. </s>
            <s xml:id="echoid-s8715" xml:space="preserve">phil. </s>
            <s xml:id="echoid-s8716" xml:space="preserve">nat. </s>
            <s xml:id="echoid-s8717" xml:space="preserve">recenſitis, ſatis accurate conveniat,
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            id omnibus bene perpenſis caſui fortuito tribuendum eſſe cenſeo.</s>
            <s xml:id="echoid-s8718" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8719" xml:space="preserve">Theoremata quæ ad motum in mediis reſiſtentibus theoretice conſideratum
              <lb/>
            faciunt, tum etiam varias obſervationes phyſicas dedi in tom. </s>
            <s xml:id="echoid-s8720" xml:space="preserve">II. </s>
            <s xml:id="echoid-s8721" xml:space="preserve">Comm. </s>
            <s xml:id="echoid-s8722" xml:space="preserve">Acad. </s>
            <s xml:id="echoid-s8723" xml:space="preserve">Sc.
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            </s>
            <s xml:id="echoid-s8724" xml:space="preserve">Petrop. </s>
            <s xml:id="echoid-s8725" xml:space="preserve">& </s>
            <s xml:id="echoid-s8726" xml:space="preserve">ſeqq. </s>
            <s xml:id="echoid-s8727" xml:space="preserve">Neque proinde ea hic repetam, quamvis ad inſtitutum no-
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            ſtrum pertineant; </s>
            <s xml:id="echoid-s8728" xml:space="preserve">diutius meditationibus hiſce hydrodynamicis immorari </s>
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