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

Table of handwritten notes

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            <s xml:id="echoid-s5675" xml:space="preserve">
              <pb o="196" file="0210" n="210" rhead="HYDRODYNAMICÆ"/>
            ad √ 3; </s>
            <s xml:id="echoid-s5676" xml:space="preserve">Si vero vena fluidi eadem atque tota excipiatur ab ala, modo ſic mo-
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            do aliter ad directionem fluidi inclinatâ, maximam preſſionem ſuſtinebit in
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            directione rotationis ala, quæ facit angulum ſemirectum cum directione fluidi.</s>
            <s xml:id="echoid-s5677" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5678" xml:space="preserve">Prima Regula pertinet ad machinas quæ à vento omnia ambiente cir-
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            cumaguntur: </s>
            <s xml:id="echoid-s5679" xml:space="preserve">altera ad illas, quæ à vena ſolitaria & </s>
            <s xml:id="echoid-s5680" xml:space="preserve">à certa determinataque flui-
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            di quantitate moventur. </s>
            <s xml:id="echoid-s5681" xml:space="preserve">Utraque vero hypotheſi innititur, quod motus ala-
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            rum admodum parvus ſit reſpectu motus fluidi, ſi enim ad motum alarum re-
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            ſpicias, ambæ regulæ falſæ ſunt; </s>
            <s xml:id="echoid-s5682" xml:space="preserve">neque profecto iſte motus negligendus eſt, in
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            moletrinis enim ſæpe obſervavi, extremitates alarum velocitate ferri, ipſam
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            fere venti velocitatem exæquante.</s>
            <s xml:id="echoid-s5683" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5684" xml:space="preserve">Hæc cum ita ſint, calculum nunc ita ponemus, ut utriuſque motus
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            rationem habeamus.</s>
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            <s xml:id="echoid-s5686" xml:space="preserve">§. </s>
            <s xml:id="echoid-s5687" xml:space="preserve">39. </s>
            <s xml:id="echoid-s5688" xml:space="preserve">Sit igitur fluidum D E B A (Fig. </s>
            <s xml:id="echoid-s5689" xml:space="preserve">55.) </s>
            <s xml:id="echoid-s5690" xml:space="preserve">quod ſub directione E B
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              <note position="left" xlink:label="note-0210-01" xlink:href="note-0210-01a" xml:space="preserve">Fig. 55.</note>
            impingit in totum planum A B: </s>
            <s xml:id="echoid-s5691" xml:space="preserve">moveri autem ponitur planum motu paral-
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            lelo in directione B b ad E B perpendiculari: </s>
            <s xml:id="echoid-s5692" xml:space="preserve">Sint porro velocitates ejusmo-
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            di, ut dum particula fluidi percurrit lineam E B, punctum plani B abſol-
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            vat lineam B b. </s>
            <s xml:id="echoid-s5693" xml:space="preserve">His poſitis fingere licet totum ſyſtema, fluidum nempe
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            cum plano moveri à b verſus B & </s>
            <s xml:id="echoid-s5694" xml:space="preserve">quidem velocitate b B: </s>
            <s xml:id="echoid-s5695" xml:space="preserve">Ita vero fiet, ut
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            planum A B quieſcat, particula autem fluidi in punctum B incidens cenſen-
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            da ſit veniſſe expuncto e, ſumta E e = B b, & </s>
            <s xml:id="echoid-s5696" xml:space="preserve">ſic de omnibus guttulis.
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            </s>
            <s xml:id="echoid-s5697" xml:space="preserve">Igitur loco fluidi D E B A in planum motum A B incidentis velocitate E B
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            concipiendum erit fluidum d e B A in idem planum A B ſed immotum inci-
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            dens velocitate e B: </s>
            <s xml:id="echoid-s5698" xml:space="preserve">Producatur jam A B usque in b agaturque D E d e b per-
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            pendicularis ad E B, erit motus particulæ fluidi repræſentatus per e B reſol-
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            vendus in e g & </s>
            <s xml:id="echoid-s5699" xml:space="preserve">g B, ſibi invicem perpendiculariter inſiſtentes, quorum po-
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            ſterior nihil in planum A B agit, alter vero e g rurſus ex duobus compoſi-
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            tus eſt motibus e f & </s>
            <s xml:id="echoid-s5700" xml:space="preserve">f g, quorum poſterior f g planum A B inutiliter in di-
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            rectione E B propellere tentat; </s>
            <s xml:id="echoid-s5701" xml:space="preserve">dum prior e f ſolus idem planum in dire-
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            ctione B b propellit. </s>
            <s xml:id="echoid-s5702" xml:space="preserve">Demonſtratum itaque eſt, quamlibet particulam face-
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            re impulſum proportionalem lineæ e f: </s>
            <s xml:id="echoid-s5703" xml:space="preserve">Dein patet quoque, ſi linea A B
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            repræſentet totum planum, fore numerum particularum dato tempore in
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            planum impingentium repræſentandum per lineam B N perpendicularem ad
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            A d ſeu B e. </s>
            <s xml:id="echoid-s5704" xml:space="preserve">Unde tandem niſus aquarum ad movendum planum in dire-
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            ctione B b eſt proportionalis lineæ e f ductæ in B N.</s>
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