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

List of thumbnails

< >
101
101 (87) 		102
102 (88)
103
103 (89) 		104
104
105
105 (91) 		106
106 (92)
107
107 (93) 		108
108 (94)
109
109 (95) 		110
110 (96)
< >
page |< < (63) of 361 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div77" type="section" level="1" n="54">
          <p>
            <s xml:id="echoid-s1702" xml:space="preserve">
              <pb o="63" file="0077" n="77" rhead="SECTIO QUARTA."/>
            primatur, atque ſic gracileſcat. </s>
            <s xml:id="echoid-s1703" xml:space="preserve">Et ab iſta compreſſione fit, quod alias con-
              <lb/>
            tradictionem involveret, ut aqua jam jam egreſſa, etiamnum præ foramine ac-
              <lb/>
            celeretur, & </s>
            <s xml:id="echoid-s1704" xml:space="preserve">ſic aſcenſ{us} potentialis creſcat, etiamſi ad alteram accelerationem
              <lb/>
            omnibus corporibus cadentibus communem non attendamus, ceu huc non
              <lb/>
            pertinentem, & </s>
            <s xml:id="echoid-s1705" xml:space="preserve">cujus deinceps mentionem non faciemus. </s>
            <s xml:id="echoid-s1706" xml:space="preserve">Hæc autem niſi me
              <lb/>
            fallat opinio, res erit porro hunc in modum tractanda.</s>
            <s xml:id="echoid-s1707" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1708" xml:space="preserve">(I.) </s>
            <s xml:id="echoid-s1709" xml:space="preserve">Eouſque vena aquæ conſideranda eſt, donec particularum velo-
              <lb/>
            citates amplius non mutentur, quod quamvis nunquam fiat omni rigore, at-
              <lb/>
            tamen non procul à foramine fieri cenſendum eſt, veluti in d e. </s>
            <s xml:id="echoid-s1710" xml:space="preserve">Hoc
              <lb/>
            autem ſi ita fuerit & </s>
            <s xml:id="echoid-s1711" xml:space="preserve">aquæ ex vaſe A B C D per foramen a c effluere
              <lb/>
            ponantur, erit loco vaſis ſimplicis A B C D concipiendum aliud com-
              <lb/>
            poſitum A B a d e c C D.</s>
            <s xml:id="echoid-s1712" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1713" xml:space="preserve">Quicquid igitur in præcedente ſectione præmiſſum fuit, pro determi-
              <lb/>
            nandis ubique velocitatibus, id omnino locum habebit, ſi loco vaſis ſubjecti
              <lb/>
            concipiatur vas, quod dixi tubulo contracto inſtructum. </s>
            <s xml:id="echoid-s1714" xml:space="preserve">Nec tamen hæc cor-
              <lb/>
            rectio, ratione præmiſſæ noſtræ methodi velocitatum aquæ effluentis determi-
              <lb/>
            nandarum, ſenſibilem mutationem producere poteſt ob brevitatem tubuli a d c e,
              <lb/>
            poteſt autem valde notabilem ratione quantitatis, quia aquæ non tam per ori-
              <lb/>
            ficium a c, quam per d e effluere cenſendæ ſunt.</s>
            <s xml:id="echoid-s1715" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1716" xml:space="preserve">(II.) </s>
            <s xml:id="echoid-s1717" xml:space="preserve">Sic erunt velocitates in diverſis locis ipſius venæ reciproce ut
              <lb/>
            amplitudines ſectionum reſpondentium & </s>
            <s xml:id="echoid-s1718" xml:space="preserve">cum in vaſis ampliſſimis velocitas
              <lb/>
            in d e talis ſit quæ toti altitudini aquæ conveniat, ſimulque experimentis con-
              <lb/>
            ſtet, amplitudines a c & </s>
            <s xml:id="echoid-s1719" xml:space="preserve">d e proxime eſſe ut √ 2 ad 1, putavit Newtonus ſic
              <lb/>
            confirmari poſſe theoriam ſuam, qua ſtatuit aquam ex foramine vero veloci-
              <lb/>
            tate effluere quæ debeatur dimidiæ altitudini aquæ ſupra foramen, quamvis in
              <lb/>
            progreſſu velocitas aquæ creſcat: </s>
            <s xml:id="echoid-s1720" xml:space="preserve">quâ in re mihi videtur nimium adhæſiſſe præ-
              <lb/>
            conceptæ opinioni: </s>
            <s xml:id="echoid-s1721" xml:space="preserve">neque enim ratio orificii a c ad d e ſemper eadem eſt, ne-
              <lb/>
            que ſic explicari poteſt motus aquarum ex vaſe, cui tubulus adhæret: </s>
            <s xml:id="echoid-s1722" xml:space="preserve">verbo!
              <lb/>
            attenuatio venæ prorſus accidentalis eſt, poteſt enim tota impediri, apponen-
              <lb/>
            do foramini parvulum tubulum cylindricum vel augendo tantum craſſitiem la-
              <lb/>
            minæ, cui foramen ineſt, & </s>
            <s xml:id="echoid-s1723" xml:space="preserve">tunc ſine ulla correctione locum habent tam </s>
          </p>
        </div>
      </text>
    </echo>
Impressum