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

Table of contents

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[151.] Regula 5.
Page: 182 (168)
[152.] Demonſtratio.
Page: 183 (169)
[153.] Regula 6.
Page: 183 (169)
[154.] Demonſtratio.
Page: 184 (170)
[155.] Scholium.
Page: 184 (170)
[156.] Regula 7.
Page: 184 (170)
[157.] Scholium.
Page: 185 (171)
[158.] Exemplum 1.
Page: 185 (171)
[159.] Exemplum 2.
Page: 186 (172)
[160.] Digreſſus continens aliquas commentationes in Ma-chinam Hydraulicam quam repræſent at figura 51.
Page: 187 (173)
[161.] Regula 8.
Page: 190 (176)
[162.] Scholium.
Page: 191 (177)
[163.] Regula 9.
Page: 191 (177)
[164.] Scholium.
Page: 191 (177)
[165.] Scholium Generale.
Page: 192 (178)
[166.] (B) De machinis hydraulicis aquas ſine not abili impetu ex loco humiliori in altiorem tranſportantibus. Regula 10.
Page: 192 (178)
[167.] Demonſtratio.
Page: 193 (179)
[168.] Corollarium.
Page: 193 (179)
[169.] Scholium 1.
Page: 193 (179)
[170.] Scholium 2.
Page: 194 (180)
[171.] Scholium Generale.
Page: 194 (180)
[172.] Commentationes ſpeciales de Cochlea Archimedis.
Page: 197 (183)
[173.] Problema.
Page: 200 (186)
[174.] Solutio.
Page: 200 (186)
[175.] Scholium 1.
Page: 200 (186)
[176.] Scholium 2.
Page: 201 (187)
[177.] Scholium 3.
Page: 202 (188)
[178.] Scholium 4.
Page: 202 (188)
[179.] Problema.
Page: 203 (189)
[180.] Solutio.
Page: 203 (189)
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          <p>
            <s xml:id="echoid-s3989" xml:space="preserve">
              <pb o="138" file="0152" n="152" rhead="HYDRODYNAMICÆ"/>
            tionis; </s>
            <s xml:id="echoid-s3990" xml:space="preserve">deinde quod ibi longitudo penduli ſit æqualis dimidiæ longitudini tubi,
              <lb/>
            cum hîc ſit æqualis integræ, quamvis ſi recte res perpendatur, hic potius ſit con-
              <lb/>
            ſenſus quam diſſenſus dicendus ob tubi, quæ in priori caſu eſt, duplicationem.</s>
            <s xml:id="echoid-s3991" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s3992" xml:space="preserve">§. </s>
            <s xml:id="echoid-s3993" xml:space="preserve">20. </s>
            <s xml:id="echoid-s3994" xml:space="preserve">Utroque oſcillationum genere illuſtratur natura undarum ven-
              <lb/>
            to agitatarum: </s>
            <s xml:id="echoid-s3995" xml:space="preserve">neque enim aliter moventur, quam quod aquæ in illis conti-
              <lb/>
            nue aſcendant rurſuſque deſcendant. </s>
            <s xml:id="echoid-s3996" xml:space="preserve">Ita patet quod dicit Newtonus, tem-
              <lb/>
            pora undulationum eſſe in ratione dimidiata latitudinum undarum, quia ponit
              <lb/>
            undarum formam ſibi conſtanter eſſe ſimilem & </s>
            <s xml:id="echoid-s3997" xml:space="preserve">proinde earum latitudinem
              <lb/>
            proportionalem profunditati, ad quam aquæ agitantur. </s>
            <s xml:id="echoid-s3998" xml:space="preserve">Veriſimile autem eſt
              <lb/>
            profunditatem eam eſſe, quæ pendulo ſimplici cum undis tautochrono, nempe
              <lb/>
            v.</s>
            <s xml:id="echoid-s3999" xml:space="preserve">gr. </s>
            <s xml:id="echoid-s4000" xml:space="preserve">60 {1/3} ped. </s>
            <s xml:id="echoid-s4001" xml:space="preserve">Pariſ. </s>
            <s xml:id="echoid-s4002" xml:space="preserve">ſi ſingulis binis ſecundis fiat undarum aſcenſus deſcenſuſve.</s>
            <s xml:id="echoid-s4003" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s4004" xml:space="preserve">§. </s>
            <s xml:id="echoid-s4005" xml:space="preserve">21. </s>
            <s xml:id="echoid-s4006" xml:space="preserve">Quamvis noluerim ad prolixitatem calculi evitandam, hoc ar-
              <lb/>
            gumentum in omni ſua extenſione proſequi, propterque ea de cylindricis va-
              <lb/>
            ſis tantum egerim, attamen quia in caſu ſubmerſionis infinitæ, enunciationes
              <lb/>
            & </s>
            <s xml:id="echoid-s4007" xml:space="preserve">theoremata parum de ſua concinnitate perdunt, ſuperaddam theorema ge-
              <lb/>
            nerale pro oſcillationibus aquæ in tubo utcunque inæquali, omiſſa tamen de-
              <lb/>
            monſtratione, quæ ex alibi dictis unicuique obvia erit, præſertim vero ex iis
              <lb/>
            quæ in Sect. </s>
            <s xml:id="echoid-s4008" xml:space="preserve">6. </s>
            <s xml:id="echoid-s4009" xml:space="preserve">§. </s>
            <s xml:id="echoid-s4010" xml:space="preserve">§. </s>
            <s xml:id="echoid-s4011" xml:space="preserve">6. </s>
            <s xml:id="echoid-s4012" xml:space="preserve">7. </s>
            <s xml:id="echoid-s4013" xml:space="preserve">& </s>
            <s xml:id="echoid-s4014" xml:space="preserve">ſeqq. </s>
            <s xml:id="echoid-s4015" xml:space="preserve">uſque ad 20. </s>
            <s xml:id="echoid-s4016" xml:space="preserve">expoſita fuerunt. </s>
            <s xml:id="echoid-s4017" xml:space="preserve">Faciendum au-
              <lb/>
            tem eſt, ut cylindricæ ſit ſtructuræ pars illa vaſis ſuperior, in quâ excurſiones
              <lb/>
            fiunt.</s>
            <s xml:id="echoid-s4018" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s4019" xml:space="preserve">§. </s>
            <s xml:id="echoid-s4020" xml:space="preserve">22. </s>
            <s xml:id="echoid-s4021" xml:space="preserve">Fuerit igitur bd longitudo vaſis ſubmerſi (Fig. </s>
            <s xml:id="echoid-s4022" xml:space="preserve">35. </s>
            <s xml:id="echoid-s4023" xml:space="preserve">b) Repræſentet
              <lb/>
            b F ejus amplitudinem in loco ſuperficiei, ponaturque vas ita formatum, ut ſit
              <lb/>
            curva FGH ſcala amplitudinum: </s>
            <s xml:id="echoid-s4024" xml:space="preserve">ſumatur linea b c fiatque curva L M N,
              <lb/>
            cujus applicata c M ſit ubique = {bF
              <emph style="super">2</emph>
            /cG}, & </s>
            <s xml:id="echoid-s4025" xml:space="preserve">erit longitudo penduli iſochro-
              <lb/>
            ni cum oſcillationibus aqueæ ſuperficiei = ſpatio bd NL diviſo per b L.</s>
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          <head xml:id="echoid-head155" xml:space="preserve">Corollarium.</head>
          <p>
            <s xml:id="echoid-s4027" xml:space="preserve">§. </s>
            <s xml:id="echoid-s4028" xml:space="preserve">23. </s>
            <s xml:id="echoid-s4029" xml:space="preserve">Ex præcedente paragrapho ſequitur, ſi tubus ſubmerſus coni-
              <lb/>
            cus fuerit, habeatque amplitudinem in regione aquæ ſuperficiei, quæ ſit ad
              <lb/>
            orificium ſubmerſum ut m ad n, fore longitudinem penduli Iſochroni cum
              <lb/>
            vibrante aqua ad longitudinem ſubmerſi tubi, ut √m ad √n, id eſt, ut ra-
              <lb/>
            dices prædictarum amplitudinum, atque ſi tubus idem ſitu, modo recto </s>
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