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

Table of contents

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[141.] Scholium.
[142.] Regula 2.
[143.] Demonſtratio.
[144.] Scholium.
[145.] Regula 3.
[146.] Demonſtratio.
[147.] Scholium.
[148.] Regula 4.
[149.] Demonſtratio.
[150.] Scholium.
[151.] Regula 5.
[152.] Demonſtratio.
[153.] Regula 6.
[154.] Demonſtratio.
[155.] Scholium.
[156.] Regula 7.
[157.] Scholium.
[158.] Exemplum 1.
[159.] Exemplum 2.
[160.] Digreſſus continens aliquas commentationes in Ma-chinam Hydraulicam quam repræſent at figura 51.
[161.] Regula 8.
[162.] Scholium.
[163.] Regula 9.
[164.] Scholium.
[165.] Scholium Generale.
[166.] (B) De machinis hydraulicis aquas ſine not abili impetu ex loco humiliori in altiorem tranſportantibus. Regula 10.
[167.] Demonſtratio.
[168.] Corollarium.
[169.] Scholium 1.
[170.] Scholium 2.
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            <s xml:id="echoid-s4928" xml:space="preserve">
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            ſic determinatur. </s>
            <s xml:id="echoid-s4929" xml:space="preserve">Ut aggregatum ex foramine effluxus & </s>
            <s xml:id="echoid-s4930" xml:space="preserve">prædicto hiatu,
              <lb/>
            ad eundem hiatum, ita potentia abſoluta, quæ impenditur, ad partem illius
              <lb/>
            quæ inutilis eſt, ſeu ad ejusdem diſpendium.</s>
            <s xml:id="echoid-s4931" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div198" type="section" level="1" n="154">
          <head xml:id="echoid-head201" xml:space="preserve">Demonſtratio.</head>
          <p>
            <s xml:id="echoid-s4932" xml:space="preserve">Nam aquæ per foramen & </s>
            <s xml:id="echoid-s4933" xml:space="preserve">hiatum æqualiter premuntur, & </s>
            <s xml:id="echoid-s4934" xml:space="preserve">æqualive-
              <lb/>
            locitate fluunt; </s>
            <s xml:id="echoid-s4935" xml:space="preserve">perditur autem omnis potentia abſoluta, quæaquas per hiatum
              <lb/>
            cogit, & </s>
            <s xml:id="echoid-s4936" xml:space="preserve">hæc ſe habet ad integram potentiam abſolutam, ut hiatus ad ſum-
              <lb/>
            mam foraminis & </s>
            <s xml:id="echoid-s4937" xml:space="preserve">hiatus.</s>
            <s xml:id="echoid-s4938" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div199" type="section" level="1" n="155">
          <head xml:id="echoid-head202" xml:space="preserve">Scholium.</head>
          <p>
            <s xml:id="echoid-s4939" xml:space="preserve">§. </s>
            <s xml:id="echoid-s4940" xml:space="preserve">14. </s>
            <s xml:id="echoid-s4941" xml:space="preserve">Convenit utique embolis uti bene formatis & </s>
            <s xml:id="echoid-s4942" xml:space="preserve">politis; </s>
            <s xml:id="echoid-s4943" xml:space="preserve">neceſſe
              <lb/>
            quoque eſt ut cavitas antliæ ſit plane cylindrica, ejusdemque latera pariter
              <lb/>
            perpolita. </s>
            <s xml:id="echoid-s4944" xml:space="preserve">Vix autem crediderim, niſi id fiat alio fine, è re eſſe, ut embo-
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            li cavitates@ultima accuratione expleant, quia fortaſſe ſic majus oritur virium
              <lb/>
            diſpendium à frictionibus, quam ſi circumcirca parvulus relictus fuiſſet hia-
              <lb/>
            tus: </s>
            <s xml:id="echoid-s4945" xml:space="preserve">Si enim hiatus ille centeſimam v. </s>
            <s xml:id="echoid-s4946" xml:space="preserve">gr. </s>
            <s xml:id="echoid-s4947" xml:space="preserve">partem foraminis effluxus efficiat,
              <lb/>
            vix amplius locus erit frictionibus & </s>
            <s xml:id="echoid-s4948" xml:space="preserve">non niſi centeſima præterpropter poten-
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            tiæ abſolutæ pars inde perditur, & </s>
            <s xml:id="echoid-s4949" xml:space="preserve">fortaſſe à frictione emboli cavitatem antliæ
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            exacte occupantis majus diſpendium oritur. </s>
            <s xml:id="echoid-s4950" xml:space="preserve">Igitur hoc reſpectu non eſt quod
              <lb/>
            nimis ſollicite evitemus tranſitum aquæ per hiatum ab embolo relictum. </s>
            <s xml:id="echoid-s4951" xml:space="preserve">Non
              <lb/>
            reſpicit autem hæc animadverſio illas machinas, in quibus emboli retractio-
              <lb/>
            ne aquæ in antliam attrahendæ ſunt. </s>
            <s xml:id="echoid-s4952" xml:space="preserve">Hic enim juſta & </s>
            <s xml:id="echoid-s4953" xml:space="preserve">plena emboli ma-
              <lb/>
            gnitudo omnino eſt neceſſaria.</s>
            <s xml:id="echoid-s4954" xml:space="preserve"/>
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          <head xml:id="echoid-head203" xml:space="preserve">Regula 7.</head>
          <p>
            <s xml:id="echoid-s4955" xml:space="preserve">§. </s>
            <s xml:id="echoid-s4956" xml:space="preserve">15. </s>
            <s xml:id="echoid-s4957" xml:space="preserve">In machinis quæ plura habent foramina aquas transmittentia ex una
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            cavitate in alteram, aliquid de potentia abſoluta perditur, cujus rei rationem
              <lb/>
            in præcedente ſectione eſſe diximus, quod ſingularum guttularum ex una
              <lb/>
            cavitate in alteram per foramen commune fluentium aſcenſus potentialis perit.</s>
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            <s xml:id="echoid-s4959" xml:space="preserve">Quo plura ſunt & </s>
            <s xml:id="echoid-s4960" xml:space="preserve">quo minora hujusmodi foramina, eo majus oritur
              <lb/>
            potentiæ abſolutæ diſpendium, quod magni momenti eſſe ſolet, idque fortaſſe
              <lb/>
            præter communem opinionem, in machinis, quas Vitruvius ab </s>
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