Bernoulli, Daniel
,
Hydrodynamica, sive De viribus et motibus fluidorum commentarii
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196
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HYDRODYNAMICÆ
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ad √ 3; </
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<
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xml:space
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">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.</
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<
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">Prima Regula pertinet ad machinas quæ à vento omnia ambiente cir-
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cumaguntur: </
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<
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">altera ad illas, quæ à vena ſolitaria & </
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<
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xml:space
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">à certa determinataque flui-
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di quantitate moventur. </
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<
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xml:space
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">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; </
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<
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">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.</
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<
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">Hæc cum ita ſint, calculum nunc ita ponemus, ut utriuſque motus
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rationem habeamus.</
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<
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<
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">Sit igitur fluidum D E B A (Fig. </
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">quod ſub directione E B
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impingit in totum planum A B: </
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">moveri autem ponitur planum motu paral-
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lelo in directione B b ad E B perpendiculari: </
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<
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">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. </
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<
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">His poſitis fingere licet totum ſyſtema, fluidum nempe
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cum plano moveri à b verſus B & </
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">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, & </
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<
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</
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<
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">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: </
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<
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">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 & </
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<
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">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 & </
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<
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">f g, quorum poſterior f g planum A B inutiliter in di-
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rectione E B propellere tentat; </
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<
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ctione B b propellit. </
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<
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">Demonſtratum itaque eſt, quamlibet particulam face-
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re impulſum proportionalem lineæ e f: </
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">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. </
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">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.</
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