Bernoulli, Daniel
,
Hydrodynamica, sive De viribus et motibus fluidorum commentarii
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SECTIO SECUNDA.
"/>
ſus ſimpliciſſimus hujus rei eſt, cum ſupponitur f = m = o, tunc enim fit
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- dx = {-gydy/√(4nnhh - ggyy)} ſeu facta integratione cum additione debitæ conſtan-
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tis, x = - √({4nnhh/gg} - yy) + {2nh/g}, quæ eſt æquatio ad ſemicirculum, ad
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quem nempe ſe linteum accommodabit in ſequenti hypotheſi: </
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<
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xml:space
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tei gravis AEG (Fig. </
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<
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xml:space
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">cujus diameter AG
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ad libellam poſita ſit; </
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">ſuperincumbat ſilo fluidum usque ad AG, dico ſi
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fluidi pondus ſit æquale ponderi fili, fore ut filum perfecte flexile & </
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<
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xml:space
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">uni-
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formis craſſitiei figuram ſemicircularem conſervet. </
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<
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xml:space
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">Quomodo autem pon-
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dera fili & </
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<
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xml:space
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">fluidi, ut æqualia fiant, efficiendum ſit ex elementis Geometriæ
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conſtat. </
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<
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xml:space
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">Denique ſi ſtatuatur tam potentias A quam C eſſe ubique applica-
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tæ reſpondenti y proportionales (quæ hypotheſis ſane maxime convenire vi-
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detur cum vera figura veſicæ in figura ſexta) poterit rurſus æquatio canoni-
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ca, quæ continet differentialia tertii Ordinis, reduci ad æquationem ſimpli-
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citer differentialem eamque per quadraturas facile conſtruendam. </
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<
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xml:space
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pe A = my & </
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<
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">C = ny, dico naturam curvæ A D G in fig. </
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">exprimi hâc æquatione
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dx = (g
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+ {1/2} myy) dy: </
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">√[(f
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+ {1/2} nyy)
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- (g
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+ {1/2} myy)
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]
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in qua literæ conſtantis magnitudinis f & </
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">g rurſus ab integrationibus pro-
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dierunt: </
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">fit autem valor literæ n negativus, cum æquatio ad veſicæ inflatæ
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figuram determinandam adhibetur.</
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<
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">Nolui his nimis inſiſtere, quod non proxime pertinent ad Hy-
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drodynamicam: </
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<
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">Nihil etiam addo de fluidis elaſticis, quia horum theoriam
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ſeorſim tradere conſtitui; </
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<
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">attamen quod ad preſſiones fluidorum elaſtico-
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rum attinet, poterunt illæ ex natura fluidorum ſimpliciter gravium ſupra ex-
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poſita facile deduci & </
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<
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">demonſtrari, fingendo fluidum elaſticitate eſſe deſti-
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tutum, cylindrumque fluidi ſimilis altitudinis infinitæ vel quaſi infinitæ ſu-
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perimcumbere; </
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<
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">hæc autem quomodo intelligenda ſint ſuo loco dicemus:
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</
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<
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">Nunc quidem pergo ad id, quod in rebus aquariis potiſſimum quæri ſolet,
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quanta nempe debeat eſſe firmitas canalium, ut preſſioni aquæ reſiſtere poſ-
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ſint, ubi præſertim conſiderantur canales, qui aquas ad fontes vehunt, de
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quibus ego quoque pauca monebo.</
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<
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