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

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          <p>
            <s xml:id="echoid-s1230" xml:space="preserve">
              <pb o="48" file="0062" n="62" rhead="HYDRODYNAMICÆ."/>
            dente, quod de aqua deſcendente: </s>
            <s xml:id="echoid-s1231" xml:space="preserve">hæc autem in fig. </s>
            <s xml:id="echoid-s1232" xml:space="preserve">18. </s>
            <s xml:id="echoid-s1233" xml:space="preserve">eo celerius effluit per
              <lb/>
            orificium M N, quo amplius eſt, & </s>
            <s xml:id="echoid-s1234" xml:space="preserve">quo humilius poſitum: </s>
            <s xml:id="echoid-s1235" xml:space="preserve">ergo etiam fumus
              <lb/>
            eo celerius caminum tranſibit, eoque magis ignis in foco accendetur, quo
              <lb/>
            altius ducetur caminus, & </s>
            <s xml:id="echoid-s1236" xml:space="preserve">quo magis ſuperiora verſus divergit, ſi modo non
              <lb/>
            nimis divergat; </s>
            <s xml:id="echoid-s1237" xml:space="preserve">quod utrumque experientia confirmat; </s>
            <s xml:id="echoid-s1238" xml:space="preserve">Ipſe deinde inſuper
              <lb/>
            expertusſum, ſi caminus alicubi perforetur, tantum abeſſe, ut fumus per fora-
              <lb/>
            men iſtud exitum tentet, quin potius aër magno impetu irruat, ſeque fumo
              <lb/>
            miſcens per caminum aſcendat, non ſecus atque aërem per foraminulum e in
              <lb/>
            tubum F G N M (Fig. </s>
            <s xml:id="echoid-s1239" xml:space="preserve">18. </s>
            <s xml:id="echoid-s1240" xml:space="preserve">& </s>
            <s xml:id="echoid-s1241" xml:space="preserve">19.) </s>
            <s xml:id="echoid-s1242" xml:space="preserve">irrumpere indicavimus. </s>
            <s xml:id="echoid-s1243" xml:space="preserve">Ita vero fumus mino-
              <lb/>
            ri certe copia, aut ſaltem difficilius aſcendet ignisque remittet.</s>
            <s xml:id="echoid-s1244" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1245" xml:space="preserve">Cæterum duæ ſunt potiſſimum cauſæ, altera aliena altera naturæ rei
              <lb/>
            propria, quæ motum aquæ valde retardare poſſunt in fig. </s>
            <s xml:id="echoid-s1246" xml:space="preserve">18. </s>
            <s xml:id="echoid-s1247" xml:space="preserve">& </s>
            <s xml:id="echoid-s1248" xml:space="preserve">19. </s>
            <s xml:id="echoid-s1249" xml:space="preserve">Prior eſt
              <lb/>
            adhæſio aquæ ad latera tubi, & </s>
            <s xml:id="echoid-s1250" xml:space="preserve">altera, quod cum tubus amplitudine creſcit
              <lb/>
            velocitas aquæ, nullibi ſibi conſtans in quovis tubi loco mutetur, quæ mutatio
              <lb/>
            ſi oriri cenſeatur ab impulſibus infinite parvis aquæ velocius motæ in aquam
              <lb/>
            minus velociter motam, apparet ſingulis momentis ab impulſibus his corpo-
              <lb/>
            rum mollium aliquid de aſcenſu potentiali perdi, unde neceſſario aquarum ef-
              <lb/>
            fluxus notabiliter diminuitur.</s>
            <s xml:id="echoid-s1251" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1252" xml:space="preserve">§. </s>
            <s xml:id="echoid-s1253" xml:space="preserve">26 Loco ultimo nunc dicam quædam de vaſis recurvis, ex quibus
              <lb/>
            aquæ non omnes effluunt: </s>
            <s xml:id="echoid-s1254" xml:space="preserve">brevitatis autem gratiâ canalem conſiderabimus
              <lb/>
            cylindricum, & </s>
            <s xml:id="echoid-s1255" xml:space="preserve">cujus quidem pars, quam ſuperficies aquea non tranſgreditur,
              <lb/>
            ſit recta.</s>
            <s xml:id="echoid-s1256" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div62" type="section" level="1" n="44">
          <head xml:id="echoid-head55" xml:space="preserve">
            <emph style="bf">Problema.</emph>
          </head>
          <p>
            <s xml:id="echoid-s1257" xml:space="preserve">Sit nempe canalis cylindricus C E D B (Fig. </s>
            <s xml:id="echoid-s1258" xml:space="preserve">20.) </s>
            <s xml:id="echoid-s1259" xml:space="preserve">cujus pars C E quan-
              <lb/>
            ta ſufficit eſt recta, reliqua E D B utcunque incurvata; </s>
            <s xml:id="echoid-s1260" xml:space="preserve">fuerit canalis totus aqua
              <lb/>
              <note position="left" xlink:label="note-0062-01" xlink:href="note-0062-01a" xml:space="preserve">Fig. 20.</note>
            plenus effluxura per foramen B, perveneritque ſuperficies aquæ ex C in F,
              <lb/>
            quæritur altitudo reſpondens velocitati aquæ in F.</s>
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        <div xml:id="echoid-div64" type="section" level="1" n="45">
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            <emph style="bf">Solutio.</emph>
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            <s xml:id="echoid-s1262" xml:space="preserve">Ducantur verticalis B H & </s>
            <s xml:id="echoid-s1263" xml:space="preserve">horizontales C H, F G, A B, ſitque ſinus
              <lb/>
            anguli H C E ad ſinum totum ut 1 ad g: </s>
            <s xml:id="echoid-s1264" xml:space="preserve">Jam vero ſi rem recte perpendamus,
              <lb/>
            videbimus contineri problema præſens in altero generaliori, quod ſuprà pa-
              <lb/>
            ragrapho 20. </s>
            <s xml:id="echoid-s1265" xml:space="preserve">tractavimus, ubi habuimus hanc æquationem:
              <lb/>
            </s>
            <s xml:id="echoid-s1266" xml:space="preserve">v = ξ
              <emph style="super">{mm/nn - 1}</emph>
            ſ - xξ
              <emph style="super">{- mm/nn}</emph>
            </s>
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