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

Table of Notes

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            <s xml:id="echoid-s6899" xml:space="preserve">An vero iſta vis viva aëri inhæreat proprie externo an interno, logoma@
              <lb/>
            chia eſt; </s>
            <s xml:id="echoid-s6900" xml:space="preserve">ſufficit quod à ſublato æquilibrio inter utrumque aërem talis vis viva
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            obtineri poteſt, dum reſtitutio permittitur.</s>
            <s xml:id="echoid-s6901" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6902" xml:space="preserve">Habeatur v. </s>
            <s xml:id="echoid-s6903" xml:space="preserve">gr. </s>
            <s xml:id="echoid-s6904" xml:space="preserve">pes cubicus aëris naturali duplo rarioris, cui hypotheſi
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            quadrabunt poſitiones p = 2240 lib. </s>
            <s xml:id="echoid-s6905" xml:space="preserve">a = {1/2} ped. </s>
            <s xml:id="echoid-s6906" xml:space="preserve">& </s>
            <s xml:id="echoid-s6907" xml:space="preserve">x = {1/2} ped. </s>
            <s xml:id="echoid-s6908" xml:space="preserve">& </s>
            <s xml:id="echoid-s6909" xml:space="preserve">erit vis viva, de
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            qua ſermo eſt, = 1120 - 1120 log. </s>
            <s xml:id="echoid-s6910" xml:space="preserve">2 = 344, id eſt, ea quæ generatur lapſu li-
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            bero 344 lib. </s>
            <s xml:id="echoid-s6911" xml:space="preserve">ab altitudine unius pedis.</s>
            <s xml:id="echoid-s6912" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6913" xml:space="preserve">Si pes cubicus ſit aëre repletus, qui naturali ſit quadruplo rarior, erit
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            jam vis viva quæſita (poſito nempe p = 2240, & </s>
            <s xml:id="echoid-s6914" xml:space="preserve">a = {1/4}, x = {3/4}) = 1680 -
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            560. </s>
            <s xml:id="echoid-s6915" xml:space="preserve">log. </s>
            <s xml:id="echoid-s6916" xml:space="preserve">4 = 904, ſeu talis quæ oritur lapſu libero ponderis 904 lib. </s>
            <s xml:id="echoid-s6917" xml:space="preserve">per altit.
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            </s>
            <s xml:id="echoid-s6918" xml:space="preserve">unius pedis.</s>
            <s xml:id="echoid-s6919" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6920" xml:space="preserve">Si denique habeatur pes cubicus ab aëre omnino vacuus, ponendum
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            eſt p = 2240; </s>
            <s xml:id="echoid-s6921" xml:space="preserve">a = 0, & </s>
            <s xml:id="echoid-s6922" xml:space="preserve">x = 1: </s>
            <s xml:id="echoid-s6923" xml:space="preserve">atque ſic erit vis viva quæſita = 2240 X
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            (1 - 0 log. </s>
            <s xml:id="echoid-s6924" xml:space="preserve">{1/0}) conſtat autem eſſe 0 log. </s>
            <s xml:id="echoid-s6925" xml:space="preserve">{1/0} infinite parvum præ unitate; </s>
            <s xml:id="echoid-s6926" xml:space="preserve">eſt igitur
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            numerus iſte = 2240, qui indicat poſſe hac vi viva 2240 libras ad altitudinem
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            unius pedis elevari.</s>
            <s xml:id="echoid-s6927" xml:space="preserve"/>
          </p>
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            <s xml:id="echoid-s6928" xml:space="preserve">§. </s>
            <s xml:id="echoid-s6929" xml:space="preserve">46. </s>
            <s xml:id="echoid-s6930" xml:space="preserve">Pertinet ad præſens argumentum ſtupenda vis aëris admodum
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            condenſati, ſed præſertim auræ pulveris pyrii accenſi in uſu ſclopetorum pneu-
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            maticorum & </s>
            <s xml:id="echoid-s6931" xml:space="preserve">tormentorum bellicorum. </s>
            <s xml:id="echoid-s6932" xml:space="preserve">De his quæ ſeorſim commentatus ſum
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            huic ſectioni adjiciam.</s>
            <s xml:id="echoid-s6933" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div252" type="section" level="1" n="194">
          <head xml:id="echoid-head245" style="it" xml:space="preserve">De vi aëris condenſati & auræ pulveris pyrii ac-
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          cenſi ad globos projiciendos in uſu ſclopetorum
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          pneumaticorum & tormentorum bellicorum.</head>
          <p>
            <s xml:id="echoid-s6934" xml:space="preserve">(I) Sit A G (Fig. </s>
            <s xml:id="echoid-s6935" xml:space="preserve">64.) </s>
            <s xml:id="echoid-s6936" xml:space="preserve">longitudo animæ in tormento ſclopetove hori-
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              <note position="left" xlink:label="note-0248-01" xlink:href="note-0248-01a" xml:space="preserve">Fig. 64.</note>
            zontaliter poſito, voceturque = a: </s>
            <s xml:id="echoid-s6937" xml:space="preserve">denotet A C longitudinem ſpatii, quod
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            aër condenſatus ſeu aura pulveris pyrii accenſi occupat ab initio exploſionis,
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            ſitque A C = b: </s>
            <s xml:id="echoid-s6938" xml:space="preserve">pondus globi ejiciendi E = 1; </s>
            <s xml:id="echoid-s6939" xml:space="preserve">ponimus autem, globum ca-
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            vitatem animæ exacte replere & </s>
            <s xml:id="echoid-s6940" xml:space="preserve">liberrime in illa moveri: </s>
            <s xml:id="echoid-s6941" xml:space="preserve">denſitas aëris con-
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            denſati in ſpatio A D ſe habeat ad denſitatem aëris naturalis ut n ad 1: </s>
            <s xml:id="echoid-s6942" xml:space="preserve"/>
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