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

Table of figures

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              <pb o="130" file="0144" n="144" rhead="HYDRODYNAMICÆ"/>
            tudinem orificii pertinere ad motum aquæ internæ, cujus rei originem jam
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            ſupra (§. </s>
            <s xml:id="echoid-s3741" xml:space="preserve">7.) </s>
            <s xml:id="echoid-s3742" xml:space="preserve">indicavi.</s>
            <s xml:id="echoid-s3743" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3744" xml:space="preserve">In ſequentibus autem demonſtrabimus, non differre hunc motum à
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            ſubſequente motu refluo, hincque oſcillationes fieri tautochronas. </s>
            <s xml:id="echoid-s3745" xml:space="preserve">Prius-
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            quam vero ad alia pergam monendum duxi, in iſto calculo quantitates
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            {c/a} & </s>
            <s xml:id="echoid-s3746" xml:space="preserve">{z/a} non ſolum præ unitate, ſed & </s>
            <s xml:id="echoid-s3747" xml:space="preserve">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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            </s>
            <s xml:id="echoid-s3748" xml:space="preserve">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. </s>
            <s xml:id="echoid-s3749" xml:space="preserve">Ita v. </s>
            <s xml:id="echoid-s3750" xml:space="preserve">gr. </s>
            <s xml:id="echoid-s3751" xml:space="preserve">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. </s>
            <s xml:id="echoid-s3752" xml:space="preserve">9, quæ ratio in noſtro experimento
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            tuto adhuc negligi poteſt: </s>
            <s xml:id="echoid-s3753" xml:space="preserve">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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            & </s>
            <s xml:id="echoid-s3754" xml:space="preserve">{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.</s>
            <s xml:id="echoid-s3755" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s3756" xml:space="preserve">Hic itaque jam porro inquirere conveniet, quid de his caſibus ſtatuen-
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            dum ſit, quibus {c/a} & </s>
            <s xml:id="echoid-s3757" xml:space="preserve">{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.</s>
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            <s xml:id="echoid-s3759" xml:space="preserve">§. </s>
            <s xml:id="echoid-s3760" xml:space="preserve">11. </s>
            <s xml:id="echoid-s3761" xml:space="preserve">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: </s>
            <s xml:id="echoid-s3762" xml:space="preserve">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 & </s>
            <s xml:id="echoid-s3763" xml:space="preserve">a - x = z, prodit
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            adv + zdv + nnvdz = (c - z) </s>
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