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

Page concordance

< >
Scan Original
131 117
132 118
133 119
134 120
135 121
136 122
137 123
138
139 125
140 126
141 127
142 128
143 129
144 130
145 131
146 132
147 133
148 134
149 135
150 136
151 137
152 138
153 139
154 140
155 141
156 142
157
158 144
159 145
160 146
< >
page |< < (176) of 361 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div206" type="section" level="1" n="160">
          <p>
            <s xml:id="echoid-s5088" xml:space="preserve">
              <pb o="176" file="0190" n="190" rhead="HYDRODYNAMICÆ"/>
            mmθθ + μμtt ad m m θ θ, ex qua ratione artifices judicabunt de firmitate
              <lb/>
            laterum, quæ pro utroque requiritur.</s>
            <s xml:id="echoid-s5089" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div207" type="section" level="1" n="161">
          <head xml:id="echoid-head208" xml:space="preserve">Regula 8.</head>
          <p>
            <s xml:id="echoid-s5090" xml:space="preserve">§. </s>
            <s xml:id="echoid-s5091" xml:space="preserve">17. </s>
            <s xml:id="echoid-s5092" xml:space="preserve">Quando embolus in antliis retrahitur & </s>
            <s xml:id="echoid-s5093" xml:space="preserve">aqua in modiolum in-
              <lb/>
            fluit, non ſolum proprio pondere ſolicitata ſed maximam partem ab embo-
              <lb/>
            lo attracta, tunc omnis potentia abſoluta in hanc attractionem impenſa caſu
              <lb/>
            ſupervenit, quia antlia, ſub aquis, ut fit, poſita, ſua ſponte impleretur ſi ſuf-
              <lb/>
            ficiens huic impletioni tempus concederetur; </s>
            <s xml:id="echoid-s5094" xml:space="preserve">nec adeoque attractio illa ita
              <lb/>
            pertinet ad ejiciendas aquas certa cum velocitate, quin tota vitari poſſit, hoc-
              <lb/>
            que nomine labor in illam impenſus mihi inutilis dicitur.</s>
            <s xml:id="echoid-s5095" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5096" xml:space="preserve">Quia vero influxus aquarum partim proprio pondere fit, partim
              <lb/>
            etiam elevatione emboli, non poteſt diſpendium potentiæ abſolutæ ab effectu
              <lb/>
            æſtimari: </s>
            <s xml:id="echoid-s5097" xml:space="preserve">Quin potius calculus ita eſt ponendus, ut poſitis potentia embo-
              <lb/>
            lum in certo ſitu elevante = π, velocitate emboli = v, tempuſculoque
              <lb/>
            quantitatibus π & </s>
            <s xml:id="echoid-s5098" xml:space="preserve">v reſpondente d t, dicatur omnis potentia abſoluta in eleva-
              <lb/>
            tionem emboli impenſa = ſ π v d t vel = ſ π d x, ſi per d x intelligatur ele-
              <lb/>
            mentum ſpatioli tempuſculo d t percurſi. </s>
            <s xml:id="echoid-s5099" xml:space="preserve">Sequitur inde, ſi conſtantis mag-
              <lb/>
            nitudinis ſit, uti fere eſt conatus, quo embolus elevatur, fore potentiam abſo-
              <lb/>
            lutam æqualem potentiæ moventi ductæ in ſpatium percurſum: </s>
            <s xml:id="echoid-s5100" xml:space="preserve">ſimile autem ra-
              <lb/>
            tiocinium cum valeat etiam pro depreſſione emboli ſimulque tantum eleve-
              <lb/>
            tur embolus quantum deprimitur, apparet potenti{as} abſolut{as}, quæ in attrahen-
              <lb/>
            das expellendaſque alternatim aquas impenduntur, proxime eſſe ut potentiæ
              <lb/>
            utrobique moventes; </s>
            <s xml:id="echoid-s5101" xml:space="preserve">unde diſpendium oritur quod eſt = {π/π + p} X P, factis ſci-
              <lb/>
            licet potentia elevante = π, potentia deprimente = p & </s>
            <s xml:id="echoid-s5102" xml:space="preserve">potentia abſoluta in
              <lb/>
            elevationem depreſſionemque emboli impenſa = P.</s>
            <s xml:id="echoid-s5103" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5104" xml:space="preserve">Poteſt aliter diſpendium potentiœ abſolutæ proxime æſtimari ex eo, quod
              <lb/>
            omnis aſcenſ{us} potentialis aquæ in antliam influentis inutiliter generatus cenſeri
              <lb/>
            debeat. </s>
            <s xml:id="echoid-s5105" xml:space="preserve">Sed ſi iiſdem temporibus, ſive eadem velocitate embolus ſurſum de-
              <lb/>
            orſumque movetur, erit velocitas quâ aquæ admittuntur ad velocitatem quâ
              <lb/>
            ejiciuntur reciproce ut foramina reſpondentia, ipſique aſcenſus potentiales utro-
              <lb/>
            bique erunt in ratione quadrata inverſa foraminum reſpondentium. </s>
            <s xml:id="echoid-s5106" xml:space="preserve">Si </s>
          </p>
        </div>
      </text>
    </echo>
Impressum