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

Page concordance

< >
Scan Original
151 137
152 138
153 139
154 140
155 141
156 142
157
158 144
159 145
160 146
161 147
162 148
163 149
164 150
165 151
166 152
167 153
168 154
169 155
170 156
171 157
172 158
173 159
174 160
175 161
176 162
177
178 164
179 165
180 166
< >
page |< < (197) of 361 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div231" type="section" level="1" n="183">
          <pb o="197" file="0211" n="211" rhead="SECTIO NONA."/>
          <p>
            <s xml:id="echoid-s5706" xml:space="preserve">Ut jam determinetur inclinatio plani ad fluidum ſub his circumſtantiis
              <lb/>
            maxime favorabilis ut motus plani in directione B b promoveatur: </s>
            <s xml:id="echoid-s5707" xml:space="preserve">ponemus
              <lb/>
            A B = 1, D E ſeu A C = x, B C = √1 - xx; </s>
            <s xml:id="echoid-s5708" xml:space="preserve">lineam E B, quæ repræ-
              <lb/>
            ſentat motum fluidi, = v, & </s>
            <s xml:id="echoid-s5709" xml:space="preserve">B b ceu menſuram motus plani = V; </s>
            <s xml:id="echoid-s5710" xml:space="preserve">atque
              <lb/>
            ſic inſtituto calculo invenitur
              <lb/>
            ef = xv √ (1 - xx) - (1 - xx) V, atque BN = [xv - V √ (1 - xx]:
              <lb/>
            </s>
            <s xml:id="echoid-s5711" xml:space="preserve">√ (vv + VV); </s>
            <s xml:id="echoid-s5712" xml:space="preserve">unde e f X B N = [xv - V √ (1 - xx)]
              <emph style="super">2</emph>
            X {√ (1 - xx)/√ (vv + VV)}, quæ
              <lb/>
            quantitas maxima erit, cum fit
              <lb/>
            (9v
              <emph style="super">4</emph>
            + 18vvVV + 9V
              <emph style="super">4</emph>
            )x
              <emph style="super">6</emph>
            - (12v
              <emph style="super">4</emph>
            + 30vvVV + 18V
              <emph style="super">4</emph>
            ) x
              <emph style="super">4</emph>
              <lb/>
            + (4v
              <emph style="super">4</emph>
            + 16vvVV + 9V
              <emph style="super">4</emph>
            ) xx - 4vvVV = o.</s>
            <s xml:id="echoid-s5713" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5714" xml:space="preserve">§. </s>
            <s xml:id="echoid-s5715" xml:space="preserve">40. </s>
            <s xml:id="echoid-s5716" xml:space="preserve">Calculus ratione inclinationis alarum in moletrinis alius eſt,
              <lb/>
            quia velocitates in diverſis alarum locis variæ ſunt; </s>
            <s xml:id="echoid-s5717" xml:space="preserve">ſunt enim proportiona-
              <lb/>
            les diſtantiis à centro, facile autem nunc cuivis erit computum pro mole-
              <lb/>
            trinis inſtituere, huic caſui non ulterius inſiſtam, ſufficiat id notaſſe, quod
              <lb/>
            non ſatis accurate ſtatuatur ab auctoribus x x = {2/3}, & </s>
            <s xml:id="echoid-s5718" xml:space="preserve">quod verus valor ip-
              <lb/>
            ſius x ſemper minor ſit quam √ {2/3}. </s>
            <s xml:id="echoid-s5719" xml:space="preserve">Si fuerit v. </s>
            <s xml:id="echoid-s5720" xml:space="preserve">gr. </s>
            <s xml:id="echoid-s5721" xml:space="preserve">V = v, & </s>
            <s xml:id="echoid-s5722" xml:space="preserve">omnia alæ
              <lb/>
            puncta ſimili velocitate moveri cenſeantur, fiet x = √ {1/2}, quod indicat in-
              <lb/>
            clinandam eſſe alam ad directionem venti ſub angulo ſemirecto. </s>
            <s xml:id="echoid-s5723" xml:space="preserve">Optima
              <lb/>
            alarum conſtructio foret, ſi incurvarentur, ita, ut ſub angulo minori ventus
              <lb/>
            in illas impingat ſuperius quam inferius, aut ſi fiat ut alæ ubique ventum
              <lb/>
            ſub angulo medio quinquaginta præterpropter graduum excipiant.</s>
            <s xml:id="echoid-s5724" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5725" xml:space="preserve">§. </s>
            <s xml:id="echoid-s5726" xml:space="preserve">41. </s>
            <s xml:id="echoid-s5727" xml:space="preserve">Pergo ad alterum caſum, quo omne fluidum à plano, utcun-
              <lb/>
            que id inclinatum ſit, excipi ponitur. </s>
            <s xml:id="echoid-s5728" xml:space="preserve">Hic autem patet; </s>
            <s xml:id="echoid-s5729" xml:space="preserve">quia numerus
              <lb/>
            particularum dato tempore impellentium ſemper idem eſt, nullam eſſe at-
              <lb/>
            tentionem faciendam ad linem B N, atque ſic niſum quem aquæ faciunt ad
              <lb/>
            movendum planum A B in directione B b ſimpliciter repræſentari per e f ſeu
              <lb/>
            xv√1 - xx - (1 - xx) V. </s>
            <s xml:id="echoid-s5730" xml:space="preserve">Igitur niſus iſte maximus obtinebitur ſumendo
              <lb/>
            xx = {1/2} + {V/2√(vv + VV)}, atque erit ipſe niſus tunc = {1/2}√(vv + VV)
              <lb/>
            - {1/2} V, ſi per v intelligatur preſſio directa, quam vena exerit in planum cui
              <lb/>
            perpendiculariter occurrit.</s>
            <s xml:id="echoid-s5731" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5732" xml:space="preserve">§. </s>
            <s xml:id="echoid-s5733" xml:space="preserve">42. </s>
            <s xml:id="echoid-s5734" xml:space="preserve">Conſideremus nunc venam D E B A tanquam immediate ex </s>
          </p>
        </div>
      </text>
    </echo>
Impressum