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

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            - {2 Adx/ds}, quia in S eſt dx = d s: </s>
            <s xml:id="echoid-s8558" xml:space="preserve">Nunc ut habeatur vis in directione
              <lb/>
            tangentis S B pro tota fiſtula, ponendum eſt {RB/RA} pro {dx/ds}, ergo tota vis ſe-
              <lb/>
            cundum tangentem SB = 2A - {2A x RB/RA}. </s>
            <s xml:id="echoid-s8559" xml:space="preserve">Hæc vero oritur à vi centrifu-
              <lb/>
            ga cujusvis guttulæ: </s>
            <s xml:id="echoid-s8560" xml:space="preserve">ſed alia vis ſupereſt conſideranda; </s>
            <s xml:id="echoid-s8561" xml:space="preserve">nempe dum aqua
              <lb/>
            ex vaſe infinite amplo continue in fiſtulam influit velocitate uniformi reſpon-
              <lb/>
            dente altitudini A, vas repellitur ſecundum directionem R A vi 2 A (per §. </s>
            <s xml:id="echoid-s8562" xml:space="preserve">4.)
              <lb/>
            </s>
            <s xml:id="echoid-s8563" xml:space="preserve">quâ reſoluta in tangentialem ſecundum S B eique perpendicularem ſecundum
              <lb/>
            B A, prior {2A x RB/RA} erit ſola conſideranda; </s>
            <s xml:id="echoid-s8564" xml:space="preserve">& </s>
            <s xml:id="echoid-s8565" xml:space="preserve">quia habet directionem com-
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            munem cum vi 2A - {2A x RB/RA} à vi centrifuga oriunda & </s>
            <s xml:id="echoid-s8566" xml:space="preserve">modo definita, erit
              <lb/>
            eidem addenda: </s>
            <s xml:id="echoid-s8567" xml:space="preserve">ſicque ſumma 2A - {2A x RB/RA} + {2A x RB/RA} vel 2A expri-
              <lb/>
            met vim repellentem ſecundum directionem S B.</s>
            <s xml:id="echoid-s8568" xml:space="preserve"/>
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            <s xml:id="echoid-s8569" xml:space="preserve">Ut porro demonſtremus ſub nulla alia directione vas repelli, recurre-
              <lb/>
            mus ad vim elementarem eo, quam vidimus = {2Addy/ds}, cujus integrale =
              <lb/>
            {2A x AB/AR}, quæ præciſe annihilatur à vi 2A vas repellente ſecundum directio-
              <lb/>
            nem R A, poſtquam hæc debite reſoluta fuit. </s>
            <s xml:id="echoid-s8570" xml:space="preserve">Q. </s>
            <s xml:id="echoid-s8571" xml:space="preserve">E. </s>
            <s xml:id="echoid-s8572" xml:space="preserve">D.</s>
            <s xml:id="echoid-s8573" xml:space="preserve"/>
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            <s xml:id="echoid-s8574" xml:space="preserve">§. </s>
            <s xml:id="echoid-s8575" xml:space="preserve">14. </s>
            <s xml:id="echoid-s8576" xml:space="preserve">Hæc theorematis generaliſſimi ſimplicitas, quâ nempe vis re-
              <lb/>
            pellens in directione aquis uniformiter effluentibus contraria indicatur con-
              <lb/>
            ſtanter = 2A, argumentum eſſe poteſt, quod dicitur ad hominem pro ejus-
              <lb/>
            dem bonitate, iis qui ratiocinium noſtrum aut non aſſequentur aut exami-
              <lb/>
            nare non cupient ſufficienti attentione. </s>
            <s xml:id="echoid-s8577" xml:space="preserve">Si vero vim repellentem aquæ ex
              <lb/>
            vaſe infinito in fiſtulam influentis ſub directione A R ſtatuas = A, vides ſy-
              <lb/>
            ſtema repelli in directione S B vi quæ ſit = 2A - {A x RB/RA}, quod abſurdum
              <lb/>
            eſſe vel ipſa mihi indicare videtur formula. </s>
            <s xml:id="echoid-s8578" xml:space="preserve">Neque in hâc opinione nulla eſ-
              <lb/>
            ſet vis in directione ad priorem perpendiculari: </s>
            <s xml:id="echoid-s8579" xml:space="preserve">Nam vas deberet reprimi ſe-
              <lb/>
            cundum directionem B A vi {A x AB/AR}, quod iterum mihi eſt abſurdum & </s>
            <s xml:id="echoid-s8580" xml:space="preserve">cu-
              <lb/>
            jus falſitatem experimento cognovi, in caſu quo angulus A R S erat rectus & </s>
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            A B = A R.</s>
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