Bernoulli, Daniel
,
Hydrodynamica, sive De viribus et motibus fluidorum commentarii
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HYDRODYNAMICÆ
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tudinem orificii pertinere ad motum aquæ internæ, cujus rei originem jam
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ſupra (§. </
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<
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<
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">In ſequentibus autem demonſtrabimus, non differre hunc motum à
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ſubſequente motu refluo, hincque oſcillationes fieri tautochronas. </
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<
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quam vero ad alia pergam monendum duxi, in iſto calculo quantitates
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{c/a} & </
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<
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">{z/a} non ſolum præ unitate, ſed & </
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<
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">præ {1/nn} ceu infinite parvas poſitas fuiſ-
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ſe, ad quod animus probe eſt advertendus in inſtituendis experimentis;
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</
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<
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">licet utique theoriam infinite parvorum ad experimenta, ſine notabili erro-
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re revocare diminuendo admodum quantitates, quæ in theoria ceu infinite
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parvæ conſideratæ fuerunt, ſed faciendum eſt, ut in experimento omnia
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huic legi ſint ſubjecta. </
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">ſi in cylindro omne fundum abſit, poſito
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n = 1, idque ſubmerſum ponatur ad altitudinem triginta quinque pollicum,
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ſatis accurate ſumetur experimentum, cum aqua ante oſcillationes elevata
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tantum fuerit ad altitudinem unius pollicis ſupra ſuperficiem aquæ circum-
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fluæ nec dum error notabilis erit, ſi vel orificiium inferius ad dimidium
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obſtruatur exiſtente tunc {c/a} ad {1/nn} ut 1. </
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">9, quæ ratio in noſtro experimento
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tuto adhuc negligi poteſt: </
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">at ſi jam diametrum tubi duplam ponas diame-
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tri orificii, occluſis tribus quartis aperturæ integræ partibus, jam fiet n = 4
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& </
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<
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">{c/a} ad {1/nn} ut 4 ad 9, quæ ratio non ſatis parva amplius erit, ut experimentum
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conditionibus theoriæ cum ſufficienti præciſione ſatisfacere affirmari poſſit.</
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<
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">Hic itaque jam porro inquirere conveniet, quid de his caſibus ſtatuen-
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dum ſit, quibus {c/a} & </
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">{1/nn} notabilem quidem inter ſe habent rationem, utra-
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que vero quantitas fit admodum exigua, quod nimirum fit, cum cylindrus
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profundiſſime ſubmergitur, ſimul autem fundum parvulo eſt pertuſum fo-
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ramine.</
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<
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">Sed iſte, quem modo finximus, caſus melius ex æquatione
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differentiali paragraphi tertii, quam ex integrali, ut antea factum, deduci-
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tur: </
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">poteſt autem pro his circumſtantiis rejici terminus - v d x præ n n v d x,
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atque ſic aſſumi - x d v + n n v d x = (x - b) d x, in quâ ſi rurſus ponitur
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a - b = c & </
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adv + zdv + nnvdz = (c - z) </
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