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

Page concordance

< >
Scan Original
61 47
62 48
63 49
64 50
65 51
66 52
67 53
68 54
69 55
70 56
71 57
72 58
73 59
74 60
75
76 62
77 63
78 64
79 65
80 66
81 67
82 68
83 69
84 70
85 71
86 72
87 73
88 74
89 75
90 76
< >
page |< < (53) of 361 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div65" type="section" level="1" n="46">
          <pb o="53" file="0067" n="67" rhead="SECTIO TERTIA."/>
        </div>
        <div xml:id="echoid-div66" type="section" level="1" n="47">
          <head xml:id="echoid-head58" style="it" xml:space="preserve">Experimenta quæ ad Sect. 3. pertinent.</head>
          <head xml:id="echoid-head59" xml:space="preserve">Prænotanda.</head>
          <p>
            <s xml:id="echoid-s1369" xml:space="preserve">PLurima quidem ſunt in hâc Sectione eaque fere præcipua, quæ vix
              <lb/>
            ad experimenta revocari immediate poſſunt; </s>
            <s xml:id="echoid-s1370" xml:space="preserve">Etenim cum Auctores ha-
              <lb/>
            ctenus motum in fluidis effluentibus alium non conſideraverint,
              <lb/>
            quam qui fiunt per foramina valde parva, cumque proin nova ſit theoria
              <lb/>
            quam dedimus pro amplitudinibus foraminum qualibuscunque, hæc ipſa
              <lb/>
            eſt, cujus confirmatio maxime juvaret. </s>
            <s xml:id="echoid-s1371" xml:space="preserve">At non video, quomodo in Cy-
              <lb/>
            lindris verticalibus, de quibus potiſſimum egimus, velocitas aquæ effluen-
              <lb/>
            tis obſervari poſſit, præſertim cum foramen eſt valde amplum (ſecus enim
              <lb/>
            ex tempore depletionis aliquod de velocitatibus judicium ferri poteſt.) </s>
            <s xml:id="echoid-s1372" xml:space="preserve">Hæc
              <lb/>
            ita perpendens cogitavi demum ſcopo noſtro inſervire poſſe paragraphos 16.
              <lb/>
            </s>
            <s xml:id="echoid-s1373" xml:space="preserve">& </s>
            <s xml:id="echoid-s1374" xml:space="preserve">20. </s>
            <s xml:id="echoid-s1375" xml:space="preserve">in quorum priore determinata fuit velocitas maxima aquæ effluentis
              <lb/>
            ex cylindris verticaliter poſitis, in altero autem demonſtratum eſt, eundem
              <lb/>
            eſſe motum ex cylindris oblique poſitis & </s>
            <s xml:id="echoid-s1376" xml:space="preserve">verticalibus, ſi utrobique altitudi-
              <lb/>
            nes verticales ſimiles aſſumantur: </s>
            <s xml:id="echoid-s1377" xml:space="preserve">Commode igitur utemur cylindris oblique
              <lb/>
            poſitis, ut ex maxima amplitudine jactus aquei poſſit velocitas maxima aquæ
              <lb/>
            ſeu altitudo eidem debita experimento haberi: </s>
            <s xml:id="echoid-s1378" xml:space="preserve">& </s>
            <s xml:id="echoid-s1379" xml:space="preserve">hâc quidem ratione accu-
              <lb/>
            rate velocitas illa maxima, qualis revera eſt, explorari poteſt, etiamſi ſo-
              <lb/>
            ramina ſint quantumlibet magna, quæ proin ſi convenire obſervetur cum re-
              <lb/>
            gulis noſtris, de integra theoria dubium ſupereſſe nullum poterit.</s>
            <s xml:id="echoid-s1380" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1381" xml:space="preserve">Priusquam vero rem ipſam aggrediar, præmittendum erit theore
              <unsure/>
            ma
              <lb/>
            mechanicum, quod ſequitur.</s>
            <s xml:id="echoid-s1382" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div67" type="section" level="1" n="48">
          <head xml:id="echoid-head60" xml:space="preserve">Lemma.</head>
          <p>
            <s xml:id="echoid-s1383" xml:space="preserve">Sit A B (Fig. </s>
            <s xml:id="echoid-s1384" xml:space="preserve">21.) </s>
            <s xml:id="echoid-s1385" xml:space="preserve">linea verticalis, B D horizontalis; </s>
            <s xml:id="echoid-s1386" xml:space="preserve">linea autem A D
              <lb/>
              <note position="right" xlink:label="note-0067-01" xlink:href="note-0067-01a" xml:space="preserve">Fig. 21.</note>
            directionem habeat qualemcunque, ſub cujus directione corpus in A proje-
              <lb/>
            ctum intelligatur, arcum deſcribens parabolium A C, cujus nempe tangens
              <lb/>
            in A eſt recta A D, erit altitudo debita velocitati, qua corpus in A proje-
              <lb/>
            ctum fuit, = {BC
              <emph style="super">2</emph>
            X AD
              <emph style="super">2</emph>
            /4AB.</s>
            <s xml:id="echoid-s1387" xml:space="preserve">BD.</s>
            <s xml:id="echoid-s1388" xml:space="preserve">CD} atque ſi AD fuerit horizontalis ſive angulus B A D
              <lb/>
            rectus, erit eadem illa altitudo = {BC
              <emph style="super">2</emph>
            /4AB}.</s>
            <s xml:id="echoid-s1389" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1390" xml:space="preserve">Jam vero quæ mihi obſervata fuerint exponam.</s>
            <s xml:id="echoid-s1391" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum