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

Page concordance

< >
Scan Original
201 187
202 188
203 189
204 190
205 191
206 192
207 193
208 194
209 195
210 196
211 197
212 198
213 199
214 200
215 201
216 202
217 203
218 204
219 205
220 206
221 207
222 208
223 209
224 210
225 211
226 212
227 213
228 214
229 215
230 216
< >
page |< < (196) of 361 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div231" type="section" level="1" n="183">
          <p>
            <s xml:id="echoid-s5675" xml:space="preserve">
              <pb o="196" file="0210" n="210" rhead="HYDRODYNAMICÆ"/>
            ad √ 3; </s>
            <s xml:id="echoid-s5676" xml:space="preserve">Si vero vena fluidi eadem atque tota excipiatur ab ala, modo ſic mo-
              <lb/>
            do aliter ad directionem fluidi inclinatâ, maximam preſſionem ſuſtinebit in
              <lb/>
            directione rotationis ala, quæ facit angulum ſemirectum cum directione fluidi.</s>
            <s xml:id="echoid-s5677" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5678" xml:space="preserve">Prima Regula pertinet ad machinas quæ à vento omnia ambiente cir-
              <lb/>
            cumaguntur: </s>
            <s xml:id="echoid-s5679" xml:space="preserve">altera ad illas, quæ à vena ſolitaria & </s>
            <s xml:id="echoid-s5680" xml:space="preserve">à certa determinataque flui-
              <lb/>
            di quantitate moventur. </s>
            <s xml:id="echoid-s5681" xml:space="preserve">Utraque vero hypotheſi innititur, quod motus ala-
              <lb/>
            rum admodum parvus ſit reſpectu motus fluidi, ſi enim ad motum alarum re-
              <lb/>
            ſpicias, ambæ regulæ falſæ ſunt; </s>
            <s xml:id="echoid-s5682" xml:space="preserve">neque profecto iſte motus negligendus eſt, in
              <lb/>
            moletrinis enim ſæpe obſervavi, extremitates alarum velocitate ferri, ipſam
              <lb/>
            fere venti velocitatem exæquante.</s>
            <s xml:id="echoid-s5683" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5684" xml:space="preserve">Hæc cum ita ſint, calculum nunc ita ponemus, ut utriuſque motus
              <lb/>
            rationem habeamus.</s>
            <s xml:id="echoid-s5685" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5686" xml:space="preserve">§. </s>
            <s xml:id="echoid-s5687" xml:space="preserve">39. </s>
            <s xml:id="echoid-s5688" xml:space="preserve">Sit igitur fluidum D E B A (Fig. </s>
            <s xml:id="echoid-s5689" xml:space="preserve">55.) </s>
            <s xml:id="echoid-s5690" xml:space="preserve">quod ſub directione E B
              <lb/>
              <note position="left" xlink:label="note-0210-01" xlink:href="note-0210-01a" xml:space="preserve">Fig. 55.</note>
            impingit in totum planum A B: </s>
            <s xml:id="echoid-s5691" xml:space="preserve">moveri autem ponitur planum motu paral-
              <lb/>
            lelo in directione B b ad E B perpendiculari: </s>
            <s xml:id="echoid-s5692" xml:space="preserve">Sint porro velocitates ejusmo-
              <lb/>
            di, ut dum particula fluidi percurrit lineam E B, punctum plani B abſol-
              <lb/>
            vat lineam B b. </s>
            <s xml:id="echoid-s5693" xml:space="preserve">His poſitis fingere licet totum ſyſtema, fluidum nempe
              <lb/>
            cum plano moveri à b verſus B & </s>
            <s xml:id="echoid-s5694" xml:space="preserve">quidem velocitate b B: </s>
            <s xml:id="echoid-s5695" xml:space="preserve">Ita vero fiet, ut
              <lb/>
            planum A B quieſcat, particula autem fluidi in punctum B incidens cenſen-
              <lb/>
            da ſit veniſſe expuncto e, ſumta E e = B b, & </s>
            <s xml:id="echoid-s5696" xml:space="preserve">ſic de omnibus guttulis.
              <lb/>
            </s>
            <s xml:id="echoid-s5697" xml:space="preserve">Igitur loco fluidi D E B A in planum motum A B incidentis velocitate E B
              <lb/>
            concipiendum erit fluidum d e B A in idem planum A B ſed immotum inci-
              <lb/>
            dens velocitate e B: </s>
            <s xml:id="echoid-s5698" xml:space="preserve">Producatur jam A B usque in b agaturque D E d e b per-
              <lb/>
            pendicularis ad E B, erit motus particulæ fluidi repræſentatus per e B reſol-
              <lb/>
            vendus in e g & </s>
            <s xml:id="echoid-s5699" xml:space="preserve">g B, ſibi invicem perpendiculariter inſiſtentes, quorum po-
              <lb/>
            ſterior nihil in planum A B agit, alter vero e g rurſus ex duobus compoſi-
              <lb/>
            tus eſt motibus e f & </s>
            <s xml:id="echoid-s5700" xml:space="preserve">f g, quorum poſterior f g planum A B inutiliter in di-
              <lb/>
            rectione E B propellere tentat; </s>
            <s xml:id="echoid-s5701" xml:space="preserve">dum prior e f ſolus idem planum in dire-
              <lb/>
            ctione B b propellit. </s>
            <s xml:id="echoid-s5702" xml:space="preserve">Demonſtratum itaque eſt, quamlibet particulam face-
              <lb/>
            re impulſum proportionalem lineæ e f: </s>
            <s xml:id="echoid-s5703" xml:space="preserve">Dein patet quoque, ſi linea A B
              <lb/>
            repræſentet totum planum, fore numerum particularum dato tempore in
              <lb/>
            planum impingentium repræſentandum per lineam B N perpendicularem ad
              <lb/>
            A d ſeu B e. </s>
            <s xml:id="echoid-s5704" xml:space="preserve">Unde tandem niſus aquarum ad movendum planum in dire-
              <lb/>
            ctione B b eſt proportionalis lineæ e f ductæ in B N.</s>
            <s xml:id="echoid-s5705" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum