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

Table of handwritten notes

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            <s xml:id="echoid-s6661" xml:space="preserve">
              <pb o="227" file="0241" n="241" rhead="SECTIO DECIMA."/>
            log.</s>
            <s xml:id="echoid-s6662" xml:space="preserve">{[√x - √(x - δ)] x [√D + √(D - δ)]/[√x + √(x - δ)] X [√D - √(D - δ)]} = {2n√As/L}</s>
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        <div xml:id="echoid-div246" type="section" level="1" n="190">
          <head xml:id="echoid-head241" xml:space="preserve">Corollarium 1.</head>
          <p>
            <s xml:id="echoid-s6663" xml:space="preserve">§. </s>
            <s xml:id="echoid-s6664" xml:space="preserve">36. </s>
            <s xml:id="echoid-s6665" xml:space="preserve">Omnis effluxus fit tempore finito quâ in re iſta quæſtio ab alte-
              <lb/>
            ra præcedente differt: </s>
            <s xml:id="echoid-s6666" xml:space="preserve">Ceſſat autem aër effluere, cum eſt x = δ, & </s>
            <s xml:id="echoid-s6667" xml:space="preserve">tunc fit
              <lb/>
            n = {L/2√As} X log. </s>
            <s xml:id="echoid-s6668" xml:space="preserve">{√D + √(D - δ)/√D - √(D - δ)}.</s>
            <s xml:id="echoid-s6669" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6670" xml:space="preserve">Sit v. </s>
            <s xml:id="echoid-s6671" xml:space="preserve">gr. </s>
            <s xml:id="echoid-s6672" xml:space="preserve">A = 26000 ped. </s>
            <s xml:id="echoid-s6673" xml:space="preserve">Paris. </s>
            <s xml:id="echoid-s6674" xml:space="preserve">contineat vas propoſitum unum pedem
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            cubicum, foramen autèm habeat amplitudinem unius lineæ quadratæ, erit
              <lb/>
            L = 20736; </s>
            <s xml:id="echoid-s6675" xml:space="preserve">ponatur inſuper aërem intèrnum ab initio duplo fuiſſe den-
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            ſiorem externo; </s>
            <s xml:id="echoid-s6676" xml:space="preserve">eſt autem ut conſtat s = 15 {1/12} ped. </s>
            <s xml:id="echoid-s6677" xml:space="preserve">Paris. </s>
            <s xml:id="echoid-s6678" xml:space="preserve">Fiet igitur
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            n = {20736√3/√(181.</s>
            <s xml:id="echoid-s6679" xml:space="preserve">26000)} log. </s>
            <s xml:id="echoid-s6680" xml:space="preserve">{√2 + 1/√2 - 1} = 29, 2,
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            quod ſignificat aërem utrumque ad æquilibrium compoſitum iri tempore
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            paullo majori quam viginti novem minutorum ſecundorum, poſt idque
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            omnem effluxum ceſſaturum. </s>
            <s xml:id="echoid-s6681" xml:space="preserve">Fieri autèm poteſt à contractione, quam flui-
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            da præ foramine patiuntur (vid. </s>
            <s xml:id="echoid-s6682" xml:space="preserve">ſect. </s>
            <s xml:id="echoid-s6683" xml:space="preserve">IV.) </s>
            <s xml:id="echoid-s6684" xml:space="preserve">& </s>
            <s xml:id="echoid-s6685" xml:space="preserve">ad quam nullam fecimus in com-
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            puto attentionem, ut tempus iſtud augeatur fere in in ratione ut 1 ad √ 2.</s>
            <s xml:id="echoid-s6686" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div247" type="section" level="1" n="191">
          <head xml:id="echoid-head242" xml:space="preserve">Corollarium 2.</head>
          <p>
            <s xml:id="echoid-s6687" xml:space="preserve">§. </s>
            <s xml:id="echoid-s6688" xml:space="preserve">37. </s>
            <s xml:id="echoid-s6689" xml:space="preserve">Si fingatur aërem non immediate per foramen effluere, ſed
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            per longum tubum, non mutabitur propterea velocitas, ſi modo totius tubi
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            capacitas ſit veluti infinite parva ratione capacitatis, quæ in vaſe ipſo eſt;
              <lb/>
            </s>
            <s xml:id="echoid-s6690" xml:space="preserve">Videtur autem denſitatem aëris, quamdiu in tubo eſt, eandem eſſe cum denſitate
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            aëris vaſi incluſi, nectamen, quod demonſtrabo inferius, elaſticitas aëris in tubo
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            major eſt elaſticitate aëris externi, qui tubum circumdat. </s>
            <s xml:id="echoid-s6691" xml:space="preserve">Conſequens inde
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            eſt, ventum aërem eſſe denſiorem aëre quieſcente, ſed non magis elaſticum: </s>
            <s xml:id="echoid-s6692" xml:space="preserve">
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            attamen denſitatum differentia parvula quoque erit; </s>
            <s xml:id="echoid-s6693" xml:space="preserve">ventus enim, qui vel
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            30. </s>
            <s xml:id="echoid-s6694" xml:space="preserve">pedes ſingulis minutis ſecundis conficit, aërem vicinum, æque calidum
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            & </s>
            <s xml:id="echoid-s6695" xml:space="preserve">quietum, vix una milleſima ſeptingentiſſima parte denſitate ſuperabit.</s>
            <s xml:id="echoid-s6696" xml:space="preserve"/>
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        <div xml:id="echoid-div248" type="section" level="1" n="192">
          <head xml:id="echoid-head243" xml:space="preserve">Problema.</head>
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            <s xml:id="echoid-s6697" xml:space="preserve">§. </s>
            <s xml:id="echoid-s6698" xml:space="preserve">38. </s>
            <s xml:id="echoid-s6699" xml:space="preserve">Definire influxum aëris per foramen valde parvum in vas aëre
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            rariore plenum, poſito rurſus utrobique eodem caloris gradu.</s>
            <s xml:id="echoid-s6700" xml:space="preserve"/>
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