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

Table of Notes

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            titudinis aquarum in vaſe ſupra foramen poſitarum: </s>
            <s xml:id="echoid-s8763" xml:space="preserve">fuerit enim quantitas
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            aquarum dato tempore effluentium = Q; </s>
            <s xml:id="echoid-s8764" xml:space="preserve">altitudo earum = A, erit ma-
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            gnitudo foraminis aquas eructantis proportionalis cenſenda quantitati {Q/√ A}
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            pro eodem tempore: </s>
            <s xml:id="echoid-s8765" xml:space="preserve">at vero vis repellens, quæ hic navem promovet, æqualis
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            eſt magnitudini foraminis ductæ in duplam altitudinem aquarum (per §. </s>
            <s xml:id="echoid-s8766" xml:space="preserve">4.)
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            </s>
            <s xml:id="echoid-s8767" xml:space="preserve">id eſt, æqualis quantitati {Q/√ A} X
              <emph style="bf">2</emph>
            A ſeu 2 Q √ A. </s>
            <s xml:id="echoid-s8768" xml:space="preserve">Ex comparatione utrius-
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            que propoſitionis ſequitur laborem hominum in elevandis aquis exantlatum
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            eſſe ad vim naves propellentem inde obtinendam, ut Q A ad 2 Q √ A ſive ut
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            √ A ad quantitatem aliquam conſtantem: </s>
            <s xml:id="echoid-s8769" xml:space="preserve">igitur quo minor eſt altitudo ad
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            quam aquæ elevantur, eò major vis naves promovens ab eodem labore obti-
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            netur, ita ut labore hominum quantumvis parvo vis naves propellens utcun-
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            que magna obtineri poßit. </s>
            <s xml:id="echoid-s8770" xml:space="preserve">Verum etiam inertia aquarum, quæ hauriuntur,
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            (de qua ab initio hujus paragraphi diximus) naves retardans eo majorem
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            obtinet rationem ad vim naves propellentem, quo minor aſſumitur altitudo
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            A, ad quod animus hic probe eſt advertendus.</s>
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            <s xml:id="echoid-s8772" xml:space="preserve">§. </s>
            <s xml:id="echoid-s8773" xml:space="preserve">22. </s>
            <s xml:id="echoid-s8774" xml:space="preserve">Perſpicuum eſt ex præcedente paragrapho, altitudinem ad quam
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            aquæ ſunt elevandæ eſſe ex earum claſſe, quæ alicubi maximæ ſunt. </s>
            <s xml:id="echoid-s8775" xml:space="preserve">Ut ve-
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            ro altitudo maxime ad propoſitum proficua determinetur, aliæ nobis ſe of-
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            ferunt quæſtiones prius examinandæ.</s>
            <s xml:id="echoid-s8776" xml:space="preserve"/>
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        <div xml:id="echoid-div298" type="section" level="1" n="222">
          <head xml:id="echoid-head284" xml:space="preserve">Problema.</head>
          <p>
            <s xml:id="echoid-s8777" xml:space="preserve">Ponatur navis uniformi progredi velocitate, quæ generatur lapſu li-
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            bero per altitudinem B, fingaturque aquas continue affluere in navem, ve-
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            luti ſub forma pluviarum, & </s>
            <s xml:id="echoid-s8778" xml:space="preserve">quidem tanta quantitate, quantam remotis om-
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            nibus impedimentis alienis ſuppeditaret cylindrus conſtanter plenus ad alti-
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            tudinem A per orificium magnitudinis M. </s>
            <s xml:id="echoid-s8779" xml:space="preserve">Quæritur quantam reſiſtentiam
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            navis ab iſto perpetuo & </s>
            <s xml:id="echoid-s8780" xml:space="preserve">uniformi aquarum affluxu earundemque inertia pa-
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            tiatur.</s>
            <s xml:id="echoid-s8781" xml:space="preserve"/>
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        <div xml:id="echoid-div299" type="section" level="1" n="223">
          <head xml:id="echoid-head285" xml:space="preserve">Solutio.</head>
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            <s xml:id="echoid-s8782" xml:space="preserve">Aſſumatur tempus quodcunque t, quod ſi æſtimetur ex ſpatio, quod
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            fluidum affluens ſua velocitate percurrit, diviſo per eandem velocitatem, </s>
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