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

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          <pb o="297" file="0311" n="311" rhead="SECTIO DECIMA TERTIA."/>
        </div>
        <div xml:id="echoid-div305" type="section" level="1" n="229">
          <head xml:id="echoid-head291" xml:space="preserve">Scholium.</head>
          <p>
            <s xml:id="echoid-s8842" xml:space="preserve">§. </s>
            <s xml:id="echoid-s8843" xml:space="preserve">26. </s>
            <s xml:id="echoid-s8844" xml:space="preserve">In quavis nave aquæ ad aliam atque aliam altitudinem ſunt ele-
              <lb/>
            vandæ, ut eadem potentia, quæ in hauriendis aquis inſumitur, vis navem
              <lb/>
            promovens maxima obtineatur & </s>
            <s xml:id="echoid-s8845" xml:space="preserve">duo requiruntur ad altitudinem illam uti-
              <lb/>
            liſſimam definiendam pro certo operariorum numero. </s>
            <s xml:id="echoid-s8846" xml:space="preserve">Primo ut cognitum
              <lb/>
            ſit quamnam velocitatem propoſita navis à data potentia acquirat: </s>
            <s xml:id="echoid-s8847" xml:space="preserve">ratione
              <lb/>
            hujus poſtulati, ponemus navem à preſſione, quæ ſit æqualis ponderi unius
              <lb/>
            pedis cubici aquæ ſeu circiter 72 librarum acquirere velocitatem, quæ gene-
              <lb/>
            retur lapſu libero per altitudinem C, & </s>
            <s xml:id="echoid-s8848" xml:space="preserve">quia deinceps ſemper in pedibus
              <lb/>
            menſuras omnes exprimemus, erit pondus unius pedis cubici aquæ expri-
              <lb/>
            mendum per unitatem. </s>
            <s xml:id="echoid-s8849" xml:space="preserve">Secundo pro cognita aſſumenda eſt relatio inter ce-
              <lb/>
            leritates navis & </s>
            <s xml:id="echoid-s8850" xml:space="preserve">potentias navem propellents: </s>
            <s xml:id="echoid-s8851" xml:space="preserve">ſtatuitur hic vulgo velocita-
              <lb/>
            tes habere rationem ſubduplicatam virium propellentium, experimenta qui-
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            dem hanc hypotheſin non exactè confirmant in motibus lentis; </s>
            <s xml:id="echoid-s8852" xml:space="preserve">interim ta-
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            men eam reliquis omnibus præferendam cenſemus. </s>
            <s xml:id="echoid-s8853" xml:space="preserve">Si quis velit rem ſub alia
              <lb/>
            hypotheſi explorare, is poterit eodem modo, quo nunc utemur, calculum
              <lb/>
            inſtituere.</s>
            <s xml:id="echoid-s8854" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div306" type="section" level="1" n="230">
          <head xml:id="echoid-head292" xml:space="preserve">Problema.</head>
          <p>
            <s xml:id="echoid-s8855" xml:space="preserve">§. </s>
            <s xml:id="echoid-s8856" xml:space="preserve">27. </s>
            <s xml:id="echoid-s8857" xml:space="preserve">Invenire altitudinem, ad quam aquæ continue elevandæ ſunt,
              <lb/>
            inſtituto utiliſſimam, nempe talem, ut eadem potentia in elevandis aquis
              <lb/>
            adhibenda vis navem promovens maxima oriatur.</s>
            <s xml:id="echoid-s8858" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div307" type="section" level="1" n="231">
          <head xml:id="echoid-head293" xml:space="preserve">Solutio.</head>
          <p>
            <s xml:id="echoid-s8859" xml:space="preserve">Serventur denominationes omnes in hoc argumento adhibitæ: </s>
            <s xml:id="echoid-s8860" xml:space="preserve">erit an-
              <lb/>
            te omnia inquirenda velocitas navis ſeu altitudo huic velocitati debita quam
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            vocavimus B. </s>
            <s xml:id="echoid-s8861" xml:space="preserve">Quia vero velocitates navis ponuntur proportionales radici-
              <lb/>
            bus potentiarum navem urgentium, erunt altitudines velocitatum ipſis po-
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            tentiis proportionales. </s>
            <s xml:id="echoid-s8862" xml:space="preserve">Erit igitur talis analogia inſtituenda.</s>
            <s xml:id="echoid-s8863" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8864" xml:space="preserve">Sicuti pondus unius pedis cubici ad altitudinem C (conf. </s>
            <s xml:id="echoid-s8865" xml:space="preserve">§. </s>
            <s xml:id="echoid-s8866" xml:space="preserve">26.) </s>
            <s xml:id="echoid-s8867" xml:space="preserve">ita
              <lb/>
            preſſio navem urgens ſeu 2MA - 2M√AB (vid. </s>
            <s xml:id="echoid-s8868" xml:space="preserve">§. </s>
            <s xml:id="echoid-s8869" xml:space="preserve">23.) </s>
            <s xml:id="echoid-s8870" xml:space="preserve">ad altitudinem ve-
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            locitati navis reſpondentem, quæ proinde erit 2MC X (A - √AB): </s>
            <s xml:id="echoid-s8871" xml:space="preserve">Hanc
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            vero altitudinem vocavimus B: </s>
            <s xml:id="echoid-s8872" xml:space="preserve">Eſt itaque</s>
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