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

Table of contents

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[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.
[141.] Scholium.
[142.] Regula 2.
[143.] Demonſtratio.
[144.] Scholium.
[145.] Regula 3.
[146.] Demonſtratio.
[147.] Scholium.
[148.] Regula 4.
[149.] Demonſtratio.
[150.] Scholium.
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            <s xml:id="echoid-s4781" xml:space="preserve">
              <pb o="165" file="0179" n="179" rhead="SECTIO NONA."/>
            nempe duplus ab utraque parte. </s>
            <s xml:id="echoid-s4782" xml:space="preserve">Finge pondus P deſcenſu ſuo aquam per ori-
              <lb/>
            ficium F ejicere ad altitudinem F G: </s>
            <s xml:id="echoid-s4783" xml:space="preserve">deinde manentibus reliquis duplica-
              <lb/>
            tum puta orificium F, & </s>
            <s xml:id="echoid-s4784" xml:space="preserve">vides ad eandem altitudinem F G eodemque tem-
              <lb/>
            pore duplam aquæ quantitatem ejectum iri ab eadem potentia movente P, ſed
              <lb/>
            ea duplo celerius deſcendente. </s>
            <s xml:id="echoid-s4785" xml:space="preserve">Pariter quantitas aquæ manentibus reliquis
              <lb/>
            duplicabitur, ſi & </s>
            <s xml:id="echoid-s4786" xml:space="preserve">orificium F & </s>
            <s xml:id="echoid-s4787" xml:space="preserve">amplitudinem A B & </s>
            <s xml:id="echoid-s4788" xml:space="preserve">pondus ſeu potent. </s>
            <s xml:id="echoid-s4789" xml:space="preserve">mo-
              <lb/>
            vent. </s>
            <s xml:id="echoid-s4790" xml:space="preserve">P duplices, tunc vero velocitas hujus potentiæ duplicatæ invariata ma-
              <lb/>
            net. </s>
            <s xml:id="echoid-s4791" xml:space="preserve">Igitur utroque modo effectus geminatur. </s>
            <s xml:id="echoid-s4792" xml:space="preserve">Q. </s>
            <s xml:id="echoid-s4793" xml:space="preserve">E. </s>
            <s xml:id="echoid-s4794" xml:space="preserve">D.</s>
            <s xml:id="echoid-s4795" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div181" type="section" level="1" n="141">
          <head xml:id="echoid-head188" xml:space="preserve">Scholium.</head>
          <p>
            <s xml:id="echoid-s4796" xml:space="preserve">§. </s>
            <s xml:id="echoid-s4797" xml:space="preserve">4. </s>
            <s xml:id="echoid-s4798" xml:space="preserve">Propoſitio præcedens non ſenſu phyſiologico ſed morali eſt in-
              <lb/>
            terpretanda: </s>
            <s xml:id="echoid-s4799" xml:space="preserve">moraliter neque plus neque minus æſtimo laborem hominis, qui
              <lb/>
            eadem celeritate conatum duplum exercet, quam ejus qui eodem conatu ce-
              <lb/>
            leritatem duplicat, quia nempe uterque eundem edit effectum, fieri tamen po-
              <lb/>
            teſt, ut alterius labor, quamvis altero non minus robuſti, ſenſu phyſiologi-
              <lb/>
            co ſit admodum major. </s>
            <s xml:id="echoid-s4800" xml:space="preserve">Si quis conatu 20. </s>
            <s xml:id="echoid-s4801" xml:space="preserve">librarum ſingulis minutis primis ſpa-
              <lb/>
            tium 200. </s>
            <s xml:id="echoid-s4802" xml:space="preserve">ped. </s>
            <s xml:id="echoid-s4803" xml:space="preserve">faciat, is facile conatum geminabit, difficillime vero velocita-
              <lb/>
            tem. </s>
            <s xml:id="echoid-s4804" xml:space="preserve">Ex hoc conſequens eſt in omni machinarum genere diſpiciendum præ-
              <lb/>
            ſertim eſſe, quomodo debeant eſſe conſtitutæ, ut pro eodem tempore minima
              <lb/>
            hominum defatigatione productum ex conatu eorum in velocitatem omnium
              <lb/>
            maximum ſit: </s>
            <s xml:id="echoid-s4805" xml:space="preserve">atque exinde patebit, quænam in ergatis longitudo vectibus
              <lb/>
            ſit tribuenda, quantus in rotis ſeu tympanis calcatoriis radius ſit faciendus,
              <lb/>
            quanta remis longitudo ſit concilianda, & </s>
            <s xml:id="echoid-s4806" xml:space="preserve">ſic de aliis machinis.</s>
            <s xml:id="echoid-s4807" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4808" xml:space="preserve">Ratione uſus autem tympanorum calcatoriorum, quæ frequentiſſime
              <lb/>
            adhibentur ut momentum noſtræ animadverſionis eo magis fiat perſpicuum,
              <lb/>
            hoc experimentum intelligatur:</s>
            <s xml:id="echoid-s4809" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s4810" xml:space="preserve">Ponamus in Fig. </s>
            <s xml:id="echoid-s4811" xml:space="preserve">46. </s>
            <s xml:id="echoid-s4812" xml:space="preserve">altitudinem verticalem multorum milliarum, ad
              <lb/>
              <note position="right" xlink:label="note-0179-01" xlink:href="note-0179-01a" xml:space="preserve">Fig. 46.</note>
            quam homo dato tempore aſcendere debeat: </s>
            <s xml:id="echoid-s4813" xml:space="preserve">tempus autem ſumemus decem
              <lb/>
            horarum, quia talis laboribus diurnis terminus eſſe ſolet, dein fingamus plu-
              <lb/>
            res vias, A C, A D &</s>
            <s xml:id="echoid-s4814" xml:space="preserve">c. </s>
            <s xml:id="echoid-s4815" xml:space="preserve">diverſe ad horizontalem B D inclinatas: </s>
            <s xml:id="echoid-s4816" xml:space="preserve">His poſitis
              <lb/>
            intelligimus eò celerius viatori progrediendum eſſe, quo viam ſelegerit mi-
              <lb/>
            nus inclinatam, ut eodem tempore culmen montis A attingat, & </s>
            <s xml:id="echoid-s4817" xml:space="preserve">patet viam
              <lb/>
            aliquam fore veluti A C, ſuper quâ minima defatigatione iter abſolvet, </s>
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