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

Table of contents

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[21.] Caſus I.
[22.] Caſus II.
[23.] Sequuntur Experimenta quæ ad Sectionem pertinent Secundam. Ad §. 5.
[24.] HYDRODYNAMICÆ SECTIO TERTIA. De velocitatibus fluidorum ex vaſe utcumque for-mato per lumen qualecunque effluentium. §. 1.
[25.] Problema.
[26.] Solutio.
[27.] Problema.
[28.] Solutio.
[29.] Scholion.
[30.] Problema.
[31.] Solutio.
[32.] Problema.
[33.] Solutio.
[34.] Problema.
[35.] Solutio.
[36.] Corollarium 1.
[37.] Corollarium 2.
[38.] Corollarium 3.
[39.] Scholium Generale.
[40.] De his quæ pertinent ad effluxum aquarum ex Cy-lindris verticaliter poſitis, per Lumen quod-cunque, quod eſt in fundo horizontali. §. 13.
[41.] De Effluxu Aquarum ex Cylindris verticaliter po-ſitis, qui in alios tubos ſtrictiores pariter verticales deſinunt. §. 21.
[42.] Problema.
[43.] Solutio.
[44.] Problema.
[45.] Solutio.
[46.] Scholium.
[47.] Experimenta quæ ad Sect. 3. pertinent. Prænotanda.
[48.] Lemma.
[49.] De Velocitatibus maximis fluidorum per foramina valde ampla effluentium. Ad §. 16. & 20. Experimentum Primum.
[50.] De velocitate aquæ ex vaſe ampliſſimo erumpentis. Ad §. 17.
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          <p>
            <s xml:id="echoid-s426" xml:space="preserve">
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            quæ particulis heterogeneis ſunt imprægnata, tempore congelationis fit quæ-
              <lb/>
            dam partium ex poris expulſio, ſeu ſecretio atque præcipitatio. </s>
            <s xml:id="echoid-s427" xml:space="preserve">Infinita ſunt
              <lb/>
            alia corporum tum ſolidorum tum fluidorum phænomena, quæ mire admo-
              <lb/>
            dum cum principio mutuæ gravitationis conveniunt, ita, ut dolendum ſit,
              <lb/>
            principium ipſum tam alte ſupra mentem humanam poſitum eſſe, ut nemi-
              <lb/>
            nem eſſe putem, qui id ullo modo intelligere poſſit.</s>
            <s xml:id="echoid-s428" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s429" xml:space="preserve">§. </s>
            <s xml:id="echoid-s430" xml:space="preserve">25. </s>
            <s xml:id="echoid-s431" xml:space="preserve">Denique hic monuiſſe conveniet, tractatum hunc ut Phyſicum
              <lb/>
            potius quam Mathematicum mihi conſiderari, nec proin conſultum me duxif-
              <lb/>
            ſe, methodum Geometricam in hypotheſibus, definitionibus cæterisque ap-
              <lb/>
            paratibus præmittendis nimium affectare, & </s>
            <s xml:id="echoid-s432" xml:space="preserve">ubique ordinem ſermonemque
              <lb/>
            Geometrarum ſequi, qui ſolent ab ovo ordiri, propoſitionibus complecti, & </s>
            <s xml:id="echoid-s433" xml:space="preserve">
              <lb/>
            eo ordine omnia pertractare, ut ex primis præmiſſis ſingula rite deducantur,
              <lb/>
            nihilque indemonſtratum poſt ſe relinquant, quamvis id a tot aliis jam de-
              <lb/>
            monſtratum fuerit. </s>
            <s xml:id="echoid-s434" xml:space="preserve">Non mihi hæc cura fuit ratione eorum, quæ ab aliis
              <lb/>
            tradita ſunt, ſive definitiones fuerint & </s>
            <s xml:id="echoid-s435" xml:space="preserve">axiomata, ſive etiam theoremata, non
              <lb/>
            omiſi tamen demonſtrationes eorum, quæ nova ſunt, imo etiam in prima
              <lb/>
            ſectione apponuntur demonſtrationes Theorematum, ab aliis paſſim demon-
              <lb/>
            ſtratorum; </s>
            <s xml:id="echoid-s436" xml:space="preserve">& </s>
            <s xml:id="echoid-s437" xml:space="preserve">cum quidam occurrant termini, ab aliis non explicati nec uſi-
              <lb/>
            tati, horum definitiones in ipſo textu exhibebo. </s>
            <s xml:id="echoid-s438" xml:space="preserve">Cætera modo ſub forma
              <lb/>
            Propoſitionum, Theorematum, Problematum, Corollariorum, Scholiorum-
              <lb/>
            que pro more Geometrarum proponam, modo etiam ſermone continuo ex-
              <lb/>
            plicata dabo.</s>
            <s xml:id="echoid-s439" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s440" xml:space="preserve">Unum ſupereſt, de quo Lectorem præmonitum potiſſimum volo: </s>
            <s xml:id="echoid-s441" xml:space="preserve">non
              <lb/>
            potuiſſe me huic operi eam adhibere ſive diligentiam ſive attentionem, quam
              <lb/>
            debuiſſem, & </s>
            <s xml:id="echoid-s442" xml:space="preserve">quam ipſe deſideravi. </s>
            <s xml:id="echoid-s443" xml:space="preserve">Nullus adeoque dubito, quin nonnul-
              <lb/>
            li irrepſerint errores, dum calculos ponerem, quos, ſpero, nemo ſiniſtre
              <lb/>
            explicabit: </s>
            <s xml:id="echoid-s444" xml:space="preserve">aliquos, qui in oculos incurrerunt, dum tractatum leviter relege-
              <lb/>
            rem, ipſe correxi; </s>
            <s xml:id="echoid-s445" xml:space="preserve">alios tamen etiamnum ſupereſſe mihi perſuadeo.</s>
            <s xml:id="echoid-s446" xml:space="preserve"/>
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