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

Table of Notes

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          <p>
            <s xml:id="echoid-s4996" xml:space="preserve">
              <pb o="172" file="0186" n="186" rhead="HYDRODYNAMICÆ"/>
            nis n, & </s>
            <s xml:id="echoid-s4997" xml:space="preserve">alterutrum foraminum o, p, quibus ſingulis ſit amplitudo α; </s>
            <s xml:id="echoid-s4998" xml:space="preserve">ita erit
              <lb/>
            diſpendium potentiæ abſolutæ = {nn/αα}, poſita potentiâ integra = 1 + {nn/aα},
              <lb/>
            quæ quantitates ſunt ut n n ad n n + α α. </s>
            <s xml:id="echoid-s4999" xml:space="preserve">Conſiderabile certe eſt hoc diſpen-
              <lb/>
            dium, ſi iconibus harum machinarum fidere licet, in quibus fæpe orificia
              <lb/>
            o & </s>
            <s xml:id="echoid-s5000" xml:space="preserve">p minora ſunt orificio effluxus H, quod ſi foret plus quam dimidium
              <lb/>
            perderetur potentiæ abſolutæ. </s>
            <s xml:id="echoid-s5001" xml:space="preserve">Erunt autem canales A B & </s>
            <s xml:id="echoid-s5002" xml:space="preserve">D E per totum tra-
              <lb/>
            ctum, quantum id licet, amplificandi, ut machina parum de ſuâ præſtantia
              <lb/>
            perdat.</s>
            <s xml:id="echoid-s5003" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5004" xml:space="preserve">Ceterum fuit hæc machina excogitata, ut jactus fieret continuus per H.
              <lb/>
            </s>
            <s xml:id="echoid-s5005" xml:space="preserve">Quia tamen fieri non poteſt, quin aliquod temporis intervallum intercedat
              <lb/>
            inter ultimum emboli elevationis punctum, inſtantisque ejusdem depreſſio-
              <lb/>
            nis initium, non poterit jactus omnino eſſe continuus & </s>
            <s xml:id="echoid-s5006" xml:space="preserve">æquabilis. </s>
            <s xml:id="echoid-s5007" xml:space="preserve">Huic
              <lb/>
            vero incommodo optimum remedium attulit auctor machinæ illius, cujus
              <lb/>
            mentionem facit D. </s>
            <s xml:id="echoid-s5008" xml:space="preserve">Perrault in Comment. </s>
            <s xml:id="echoid-s5009" xml:space="preserve">ad Vitruvium pag. </s>
            <s xml:id="echoid-s5010" xml:space="preserve">318. </s>
            <s xml:id="echoid-s5011" xml:space="preserve">edit. </s>
            <s xml:id="echoid-s5012" xml:space="preserve">2. </s>
            <s xml:id="echoid-s5013" xml:space="preserve">Paris. </s>
            <s xml:id="echoid-s5014" xml:space="preserve">
              <lb/>
            quamque in Bibliotheca Regia Paris. </s>
            <s xml:id="echoid-s5015" xml:space="preserve">aſſervari dicit; </s>
            <s xml:id="echoid-s5016" xml:space="preserve">inſerviet nobis hæc ma-
              <lb/>
            china alterius exempli loco: </s>
            <s xml:id="echoid-s5017" xml:space="preserve">figuram autem deſumam una cùm ejusdem de-
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            ſcriptione ex ipſo Perraultio.</s>
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        <div xml:id="echoid-div204" type="section" level="1" n="159">
          <head xml:id="echoid-head206" xml:space="preserve">Exemplum 2.</head>
          <p>
            <s xml:id="echoid-s5019" xml:space="preserve">„ Machina eſt referente præfato Perraultio, in quâ aqua expellitur ex
              <lb/>
            modiolo A (Fig. </s>
            <s xml:id="echoid-s5020" xml:space="preserve">51.) </s>
            <s xml:id="echoid-s5021" xml:space="preserve">mediante embolo B in catinum F G, ex quo aër,
              <lb/>
              <note position="left" xlink:label="note-0186-01" xlink:href="note-0186-01a" xml:space="preserve">Fig. 51.</note>
            ſi modo aliquid aquæ jam adſit, egredi non valet; </s>
            <s xml:id="echoid-s5022" xml:space="preserve">quia tubus E F us-
              <lb/>
            que ad fundum fere deſcendit: </s>
            <s xml:id="echoid-s5023" xml:space="preserve">ſic enim fit, ut aqua propulſa ex modio-
              <lb/>
            lo A per diabeten D, imumque catini occupans claudat orificium tubæ in
              <lb/>
            F, aërique tranſitum neget. </s>
            <s xml:id="echoid-s5024" xml:space="preserve">Igitur cum embolus novas intrudit aquas
              <lb/>
            in mediolum, partim aëre partim aqua, repletum, hæ aquæ de novo af-
              <lb/>
            fuſæ vim exerunt in utrumque fluidum, & </s>
            <s xml:id="echoid-s5025" xml:space="preserve">cum aqua non poſſit exilire
              <lb/>
            per tubum F E eadem velocitate qua irruit ex antlia per diabeten D, quia
              <lb/>
            ſcilicet (ſunt verba Perraultii) tubus F E in extremitate ſua E orificio per-
              <lb/>
            forata eſt multo minori, quam eſt orificium tubi D, aqua in catino ac-
              <lb/>
            cumulata aërem comprimit, ab eodemque reciproce preſſa, etiam dum
              <lb/>
            embolus elevatur, per tubam F E exilit.”</s>
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          </p>
          <p>
            <s xml:id="echoid-s5026" xml:space="preserve">Perditur in hâc machina magna potentiæ abſolutæ pars à tranſitu aquæ per dia-
              <lb/>
            beten D, hocque diſpendium eo majus erit, quo anguſtior eſt iſte tubulus:</s>
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