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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            <s xml:id="echoid-s5106" xml:space="preserve">
              <pb o="177" file="0191" n="191" rhead="SECTIO NONA."/>
            diverſis temporibus fiant emboli elevatio & </s>
            <s xml:id="echoid-s5107" xml:space="preserve">depreſſio, ſunt velocitates recipro-
              <lb/>
            ce ut tempora & </s>
            <s xml:id="echoid-s5108" xml:space="preserve">aſcenſus potentiales reciproce ut quadrata temporum. </s>
            <s xml:id="echoid-s5109" xml:space="preserve">Eſt igi-
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            tur aſcenſus potentialis aquæ influxu generatus ad aſcenſum potent. </s>
            <s xml:id="echoid-s5110" xml:space="preserve">qui ab effluxu
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            oritur ſolusque intenditur, in ratione reciproca quadrata compoſita ex ratio-
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            ne foraminis influxus ad foramen effluxus & </s>
            <s xml:id="echoid-s5111" xml:space="preserve">temporis, quo hauriuntur aquæ ad
              <lb/>
            tempus quo expelluntur.</s>
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        <div xml:id="echoid-div208" type="section" level="1" n="162">
          <head xml:id="echoid-head209" xml:space="preserve">Scholium.</head>
          <p>
            <s xml:id="echoid-s5113" xml:space="preserve">§. </s>
            <s xml:id="echoid-s5114" xml:space="preserve">18. </s>
            <s xml:id="echoid-s5115" xml:space="preserve">Ex utraque æſ
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            timandi ratione ſequitur lente embolum eſſe ele-
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            vandum: </s>
            <s xml:id="echoid-s5116" xml:space="preserve">ita enim parva fit potentia movens ratione primæ methodi aut magnum
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            fit tempus elevationis ratione ſecundæ, atque ſic operarii ſingulis elevationis
              <lb/>
            emboli intervallis à conatu præcedentis depreſſionis exantlato reficientur. </s>
            <s xml:id="echoid-s5117" xml:space="preserve">Po-
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            ſterior porro methodus indicat foramina, per quæ aquæ attrahuntur amplian-
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            da & </s>
            <s xml:id="echoid-s5118" xml:space="preserve">multiplicanda eſſe; </s>
            <s xml:id="echoid-s5119" xml:space="preserve">id vero etiam priori conforme eſt methodo, quia
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            ſic ſufficiens fere aquæ quantitas ſua ſponte influit, minorique adeo potentia mo-
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            vente opus eſt.</s>
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          <head xml:id="echoid-head210" xml:space="preserve">Regula 9.</head>
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            <s xml:id="echoid-s5121" xml:space="preserve">§. </s>
            <s xml:id="echoid-s5122" xml:space="preserve">19. </s>
            <s xml:id="echoid-s5123" xml:space="preserve">Denique jactum aqueum verticaliter aſſurgentem nunquam
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            eam attingere altitudinem obſervandum eſt, quæ debeatur aquæ velocitati ini-
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            tiali, id eſt, ſi vena fluidi verticaliter aſſurgere incipiat ab ſua origine veloci-
              <lb/>
            tate tali, quam grave libere cadendo ex altitudine a acquirat, non poterit flui-
              <lb/>
            dum aſcendere ad totam altitudinem a, etiamſi aëris reſiſtentiam removeas, aut
              <lb/>
            quicquid excogitare velis, quod caſu motum retardare queat. </s>
            <s xml:id="echoid-s5124" xml:space="preserve">Ipſa enim rei na-
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            tura defectum aliquem exigit neceſſario, cujus rei ratio phyſica hæc eſt: </s>
            <s xml:id="echoid-s5125" xml:space="preserve">Nem-
              <lb/>
            pe quælibet guttula etiamſi aſcenſum incipiens verticalem, non poteſt tamen,
              <lb/>
            quin ſenſim ad latera deflectatur & </s>
            <s xml:id="echoid-s5126" xml:space="preserve">tandem, cum ad ſummum pervenit, motu
              <lb/>
            feratur horizontali, qui notabilis eſſe debet, quia per ſupremum limbum vel
              <lb/>
            ſectionem venæ aqueæ omnis aqua tranſit, quæ per foramen effluxit: </s>
            <s xml:id="echoid-s5127" xml:space="preserve">fac igi-
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            tur unicuique guttulæ eo temporis puncto quo horizontaliter movetur veloci-
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            tatem ineſſe, quam grave lapſu libero per altitudinem b acquirit: </s>
            <s xml:id="echoid-s5128" xml:space="preserve">ita vides non
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            poſſe venam ultra altitudinem a - b aſſurgere: </s>
            <s xml:id="echoid-s5129" xml:space="preserve">Atque hoc titulo diſpendium
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            oritur ratione potentiæ abſolutæ totius ut b ad a.</s>
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        <div xml:id="echoid-div210" type="section" level="1" n="164">
          <head xml:id="echoid-head211" xml:space="preserve">Scholium.</head>
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            <s xml:id="echoid-s5131" xml:space="preserve">§. </s>
            <s xml:id="echoid-s5132" xml:space="preserve">20. </s>
            <s xml:id="echoid-s5133" xml:space="preserve">Obſervatum fuit inter aquas communi velocitate ex tubulis </s>
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