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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              <pb o="189" file="0203" n="203" rhead="SECTIO NONA."/>
            angulum quam Vitruvius, & </s>
            <s xml:id="echoid-s5447" xml:space="preserve">cum eo pauciores ſuper eodem nucleo circum-
              <lb/>
            flecti poſſint canales, quo obliquius ſunt inſerti, Vitruvius octo, Cardanus
              <lb/>
            tres tantum ponendos ſtatuit: </s>
            <s xml:id="echoid-s5448" xml:space="preserve">ſunt autem canales longiores in cochlea Car-
              <lb/>
            dani, ita ut longitudinibus accedat, quod numero canalium decedit. </s>
            <s xml:id="echoid-s5449" xml:space="preserve">Ra-
              <lb/>
            tione alterius anguli N M G obſervari meretur, aquam altius elevari poſſe,
              <lb/>
            quo major iſte fiat angulus, ſed e contrario minorem aquæ quantitatem
              <lb/>
            ſingulis ejici revolutionibus. </s>
            <s xml:id="echoid-s5450" xml:space="preserve">Juſtum fortaſſe tenebunt medium, qui angu-
              <lb/>
            lum iſtum 60. </s>
            <s xml:id="echoid-s5451" xml:space="preserve">facient gradum.</s>
            <s xml:id="echoid-s5452" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5453" xml:space="preserve">(XI.) </s>
            <s xml:id="echoid-s5454" xml:space="preserve">Subducemus nunc hujus noſtræ quoque ad normam præceden-
              <lb/>
            tis articuli conſtructæ cochleæ calculum, prouti fecimus de cochlea ad Vi-
              <lb/>
            truvii præceptum conſtructa, art. </s>
            <s xml:id="echoid-s5455" xml:space="preserve">VIII. </s>
            <s xml:id="echoid-s5456" xml:space="preserve">Quia vero per hypotheſin angulus
              <lb/>
            s a o eſt 5
              <emph style="super">0</emph>
            & </s>
            <s xml:id="echoid-s5457" xml:space="preserve">angulus N M G = 60
              <emph style="super">0</emph>
            ; </s>
            <s xml:id="echoid-s5458" xml:space="preserve">reperietur per art. </s>
            <s xml:id="echoid-s5459" xml:space="preserve">IV. </s>
            <s xml:id="echoid-s5460" xml:space="preserve">arcus a g 8
              <emph style="super">0</emph>
            , 43
              <emph style="super">1</emph>
            ,
              <lb/>
            & </s>
            <s xml:id="echoid-s5461" xml:space="preserve">linea verticalis o r = 1, 00574, cui æqualis erit altera verticalis q x, ſi
              <lb/>
            dentur arcui a g h M s 284
              <emph style="super">0</emph>
            , 57
              <emph style="super">1</emph>
            , a quo ſi ſubtrahatur arcus a g, remanet ar-
              <lb/>
            cus g h M s 276
              <emph style="super">0</emph>
            , 14
              <emph style="super">1</emph>
            : </s>
            <s xml:id="echoid-s5462" xml:space="preserve">qui reſpondet arcui helicis aquam retinere valenti: </s>
            <s xml:id="echoid-s5463" xml:space="preserve">eſt
              <lb/>
            igitur hæc pars ad totam helicem ut 16574 ad 21600 vel ut 8287 ad 10800,
              <lb/>
            ſic ut ſingulis revolutioniqus ejici poſſint plus quam quatuor quintæ partes
              <lb/>
            integræ helicis capacitatis, duplumque cum triente præterpropter hac ma-
              <lb/>
            china efficiatur, quam obtinetur ſimili machinatione ad mentem Vitruvii fa-
              <lb/>
            bricata: </s>
            <s xml:id="echoid-s5464" xml:space="preserve">altius quoque eodem nucleo elevantur aquæ in ratione ut √3 ad √2.
              <lb/>
            </s>
            <s xml:id="echoid-s5465" xml:space="preserve">Venio jam ad potentiam tum moventem tum abſolutam, quæ in elevandis aquis
              <lb/>
            impenditur.</s>
            <s xml:id="echoid-s5466" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div226" type="section" level="1" n="179">
          <head xml:id="echoid-head227" xml:space="preserve">Problema.</head>
          <p>
            <s xml:id="echoid-s5467" xml:space="preserve">(XII.) </s>
            <s xml:id="echoid-s5468" xml:space="preserve">Dato pondere aquæ in helice quieſcentis, invenire potentiam
              <lb/>
            tangentialem in f in æquilibrio cum illo pondere poſitam.</s>
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          </p>
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        <div xml:id="echoid-div227" type="section" level="1" n="180">
          <head xml:id="echoid-head228" xml:space="preserve">Solutio.</head>
          <p>
            <s xml:id="echoid-s5470" xml:space="preserve">Vidimus quomodo problema hoc geometrice ſolvendum ſit ratione
              <lb/>
            globi in puncto infimo p quieſcentis. </s>
            <s xml:id="echoid-s5471" xml:space="preserve">In præſenti vero caſu paullo aliter ſe
              <lb/>
            res habet, quod pondus aquæ per magnum helicis arcum eſt diſtributum,
              <lb/>
            neque in puncto aliquo dato concentratum. </s>
            <s xml:id="echoid-s5472" xml:space="preserve">Facile quidem eſt in anteceſ-
              <lb/>
            ſum prævidere, in utroque caſu easdem fore potentias ex regulis </s>
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