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

Table of Notes

< >
< >
page |< < (169) of 361 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div194" type="section" level="1" n="151">
          <p>
            <s xml:id="echoid-s4901" xml:space="preserve">
              <pb o="169" file="0183" n="183" rhead="SECTIO NONA."/>
            erit diſpendium potentiæ abſolutæ ad integram hanc potentiam ut F G ad alti-
              <lb/>
            tudinem G ſupra A B.</s>
            <s xml:id="echoid-s4902" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div195" type="section" level="1" n="152">
          <head xml:id="echoid-head199" xml:space="preserve">Demonſtratio.</head>
          <p>
            <s xml:id="echoid-s4903" xml:space="preserve">Fingamus augeri admodum orificium F diminuta in eadem ratione ve-
              <lb/>
            locitate aquarum effluentium in F; </s>
            <s xml:id="echoid-s4904" xml:space="preserve">ſic non mutabitur quantitas aquæ dato
              <lb/>
            tempore effluentis, ſi velocitas potentiæ moventis eadem ſit, atque proinde idem
              <lb/>
            erit effectus. </s>
            <s xml:id="echoid-s4905" xml:space="preserve">Sed ſi velocitas ita diminuatur, ut altitudo ipſi debita ſit inſenſi-
              <lb/>
            bilis, exprimetur potentia movens per altitudinem F ſupra A B, cum antea po-
              <lb/>
            tentia movens erat æqualis altitudini G ſupra A B; </s>
            <s xml:id="echoid-s4906" xml:space="preserve">& </s>
            <s xml:id="echoid-s4907" xml:space="preserve">cum in utroque caſu ea-
              <lb/>
            dem ſit velocitas potentiæ moventis, erunt potentiæ abſolutæ pro iiſdem tempori-
              <lb/>
            bus ut altitudo G ad altitudinem F ſupra communem A B. </s>
            <s xml:id="echoid-s4908" xml:space="preserve">Igitur differentia
              <lb/>
            altitudinum G & </s>
            <s xml:id="echoid-s4909" xml:space="preserve">F exprimet diſpendium, cum integra altitudo G ſupra A B
              <lb/>
            repræſentat totam potentiam abſolutam.</s>
            <s xml:id="echoid-s4910" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4911" xml:space="preserve">§. </s>
            <s xml:id="echoid-s4912" xml:space="preserve">12. </s>
            <s xml:id="echoid-s4913" xml:space="preserve">Idem ratiocinium valet pro omni machinationum genere: </s>
            <s xml:id="echoid-s4914" xml:space="preserve">Quo-
              <lb/>
            ties nempe aquæ in locum, ad quem elevandæ ſunt, evectæ notabilem habent
              <lb/>
            velocitatem, magnum fit potentiæ abſolutæ diſpendium: </s>
            <s xml:id="echoid-s4915" xml:space="preserve">poſita enim altitudine
              <lb/>
            elevationis = A; </s>
            <s xml:id="echoid-s4916" xml:space="preserve">altitudine debita velocitati aquarum in loco quo effundun-
              <lb/>
            tur = B, integra potentia abſoluta = P, perdetur {B/A + B} X P.</s>
            <s xml:id="echoid-s4917" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4918" xml:space="preserve">Notari etiam poteſt, cum aquæ trans altitudinem aliquam, cujus cul-
              <lb/>
            men in F poſitum ſit, fundi debent ope antliæ tubo inſtructæ, continuandum
              <lb/>
            eſſe tubum D F inferiora verſus quantum id liceat, nec abrumpendum in F,
              <lb/>
            prouti id apparet ex Fig. </s>
            <s xml:id="echoid-s4919" xml:space="preserve">49. </s>
            <s xml:id="echoid-s4920" xml:space="preserve">Nam ſi v. </s>
            <s xml:id="echoid-s4921" xml:space="preserve">gr. </s>
            <s xml:id="echoid-s4922" xml:space="preserve">punctum F duplo altius poſitum ſit,
              <lb/>
              <note position="right" xlink:label="note-0183-01" xlink:href="note-0183-01a" xml:space="preserve">Fig. 49</note>
            quam extremitas tubi G, duplo major potentia abſoluta requiritur pro transfun-
              <lb/>
            dendis aquis per canalem abruptum in F, quam per continuatum uſque in G;
              <lb/>
            </s>
            <s xml:id="echoid-s4923" xml:space="preserve">ſi parvula utrobique velocitate effluant, cujus nempe altitudo genitrix parva
              <lb/>
            ſit ratione altitudinum F D vel G D.</s>
            <s xml:id="echoid-s4924" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div197" type="section" level="1" n="153">
          <head xml:id="echoid-head200" xml:space="preserve">Regula 6.</head>
          <p>
            <s xml:id="echoid-s4925" xml:space="preserve">§. </s>
            <s xml:id="echoid-s4926" xml:space="preserve">13. </s>
            <s xml:id="echoid-s4927" xml:space="preserve">Cum in antliis quas hucusque conſideravimus opercula A B
              <lb/>
            ſeu potius emboli non bene lateribus machinarum reſpondent, hiatus relin-
              <lb/>
            quitur, & </s>
            <s xml:id="echoid-s4928" xml:space="preserve">ab hoc aliud diſpendii genus in potentiis abſolutis oritur, quod
              <lb/>
            in antliis, in quibus altitudo orificii ſuprà embolum negligi </s>
          </p>
        </div>
      </text>
    </echo>
Impressum