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

Table of contents

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[111.] Problema.
[112.] Solutio.
[113.] Scholium.
[114.] Corollarium 1.
[115.] Corollarium 2.
[116.] Scholion Generale.
[117.] HYDRODYNAMICÆ SECTIO SEPTIMA. De motu aquarum per vaſa ſubmerſa, ubi exem-plis oſtenditur, quam inſigniter utile ſit princi-pium conſervationis virium vivarum, veliis in caſibus, quibus continue aliquid de illis perdi cenſendum eſt. PARS PRIMA. De deſcenſu aquarum. §. 1.
[118.] PARS SECUNDA. De aſcenſu aquarum.
[119.] Corollarium.
[120.] Scholium Generale.
[121.] EXPERIMENTA Ad ſect. ſept. referenda. Experimentum 1.
[122.] Experimentum 2.
[123.] Experimentum 3.
[124.] De iſto tubo experimentum ita ſumſi:
[125.] Experimentum 4.
[126.] Experimentum 5.
[127.] HYDRODYNAMICÆ SECTIO OCTAVA. De motu fluidorum cum homogeneorum tum hetero-geneorum per vaſa irregularis & præruptæ ſtru-cturæ, ubi ex theoria virium vivarum, quarum pars continue abſorbeatur, explicantur præcipue Phæno-mena ſingularia fluidorum, per plurima foramina trajecto-rum, præmiſsis regulis generalibus pro motibus fluido-rum ubique definiendis. §. 1.
[128.] Regula 1.
[129.] Regula 2.
[130.] Problema.
[131.] Solutio.
[132.] Scholium 1.
[133.] Scholium 2.
[134.] Corollarium.
[135.] EXPERIMENTA Ad ſectionem octavam pertinentia. Experimentum 1.
[136.] Experimentum 2.
[137.] HYDRODYNAMICÆ SECTIO NONA. De motu fluidorum, quæ non proprio pondere, ſed potentia aliena ejiciuntur, ubi præſertim de Machinis Hydraulicis earundemque ultimo qui da-ri poteſt perfectionis gradu, & quomodo mecha-nica tam ſolidorum quam fluidorum ulterius perſici poſsit. §. 1.
[138.] Definitiones.
[139.] (A) De machinis aquas cum impetu in altum projicientibus. Regula 1.
[140.] Demonſtratio.
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            erit diſpendium potentiæ abſolutæ ad integram hanc potentiam ut F G ad alti-
              <lb/>
            tudinem G ſupra A B.</s>
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        <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-
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            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-
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            bilis, exprimetur potentia movens per altitudinem F ſupra A B, cum antea po-
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            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-
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            dem ſit velocitas potentiæ moventis, erunt potentiæ abſolutæ pro iiſdem tempori-
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            bus ut altitudo G ad altitudinem F ſupra communem A B. </s>
            <s xml:id="echoid-s4908" xml:space="preserve">Igitur differentia
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            altitudinum G & </s>
            <s xml:id="echoid-s4909" xml:space="preserve">F exprimet diſpendium, cum integra altitudo G ſupra A B
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            repræſentat totam potentiam abſolutam.</s>
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            <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-
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            ties nempe aquæ in locum, ad quem elevandæ ſunt, evectæ notabilem habent
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            velocitatem, magnum fit potentiæ abſolutæ diſpendium: </s>
            <s xml:id="echoid-s4915" xml:space="preserve">poſita enim altitudine
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            elevationis = A; </s>
            <s xml:id="echoid-s4916" xml:space="preserve">altitudine debita velocitati aquarum in loco quo effundun-
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            tur = B, integra potentia abſoluta = P, perdetur {B/A + B} X P.</s>
            <s xml:id="echoid-s4917" xml:space="preserve"/>
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            <s xml:id="echoid-s4918" xml:space="preserve">Notari etiam poteſt, cum aquæ trans altitudinem aliquam, cujus cul-
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            men in F poſitum ſit, fundi debent ope antliæ tubo inſtructæ, continuandum
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            eſſe tubum D F inferiora verſus quantum id liceat, nec abrumpendum in F,
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            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-
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            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>
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          <head xml:id="echoid-head200" xml:space="preserve">Regula 6.</head>
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            <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
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            ſeu potius emboli non bene lateribus machinarum reſpondent, hiatus relin-
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            quitur, & </s>
            <s xml:id="echoid-s4928" xml:space="preserve">ab hoc aliud diſpendii genus in potentiis abſolutis oritur, quod
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            in antliis, in quibus altitudo orificii ſuprà embolum negligi </s>
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