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

Table of contents

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[Item 1.]
[2.] DANIELIS BERNOULLI Joh. Fil. Med. Prof. Basil. ACAD. SCIENT. IMPER. PETROPOLITANÆ, PRIUS MATHESEOS SUBLIMIORIS PROF. ORD. NUNC MEMBRI ET PROF. HONOR. HYDRODYNAMICA, SIVE DE VIRIBUS ET MOTIBUS FLUIDORUM COMMENTARII. OPUS ACADEMICUM AB AUCTORE, DUM PETROPOLI AGERET, CONGESTUM.
[3.] ARGENTORATI, Sumptibus JOHANNIS REINHOLDI DULSECKERI, Anno M D CC XXXVIII. Typis Joh. Henr. Deckeri, Typographi Baſilienſis.
[4.] CELSISSIMO ATQUE SERENISSIMO PRINCIPI ET DOMINO DOMINO ERNESTO JOHANNI DEI GRATIA IN LIVONIA CURLANDIÆ ET SEM - GALLIÆ DUCI.
[5.] CELSISSIME ATQUE SERENISSIME PRINCEPS, DOMINE GRATIOSISSIME.
[6.] SERENISSIME & CELSISSIME PRINCEPS DOMINE GRATIOSISSIME
[7.] PRÆFATIO.
[8.] HYDRODYNAMICÆ SECTIO PRIMA. Quæ introitus eſt, variaque continet prænotanda. §. 1.
[9.] HYDRODYNAMICÆ SECTIO SECUNDA, Quæ agit de fluidis ſtagnantibus eorundemque æquilibrio tum inter ſe, tum ad alias po-tentias relato. Theorema 1. §. 1.
[10.] Demonſtratio.
[11.] Corollarium.
[12.] Theorema 2.
[13.] Demonſtratio.
[14.] Scholium 1.
[15.] Scholium 2.
[16.] Lemma.
[17.] Demonſtratio.
[18.] Theorema 3.
[19.] Demonſtratio.
[20.] Scholion.
[21.] Caſus I.
[22.] Caſus II.
[23.] Sequuntur Experimenta quæ ad Sectionem pertinent Secundam. Ad §. 5.
[24.] HYDRODYNAMICÆ SECTIO TERTIA. De velocitatibus fluidorum ex vaſe utcumque for-mato per lumen qualecunque effluentium. §. 1.
[25.] Problema.
[26.] Solutio.
[27.] Problema.
[28.] Solutio.
[29.] Scholion.
[30.] Problema.
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        <div xml:id="echoid-div69" type="section" level="1" n="49">
          <head xml:id="echoid-head61" style="it" xml:space="preserve">De Velocitatibus maximis fluidorum per foramina
            <lb/>
          valde ampla effluentium.</head>
          <head xml:id="echoid-head62" xml:space="preserve">Ad §. 16. & 20.</head>
          <head xml:id="echoid-head63" xml:space="preserve">Experimentum Primum.</head>
          <p>
            <s xml:id="echoid-s1392" xml:space="preserve">TUbum Cylindricum F A (Fig. </s>
            <s xml:id="echoid-s1393" xml:space="preserve">22.) </s>
            <s xml:id="echoid-s1394" xml:space="preserve">longitudinis quatuor pollicum
              <lb/>
              <note position="left" xlink:label="note-0068-01" xlink:href="note-0068-01a" xml:space="preserve">Fig. 22.</note>
            oblique ad horizontem poſui, in eoque ſitu firmavi, erat autem
              <lb/>
            amplitudo tubi ad amplitudinem luminis in A ut 2 ad 1. </s>
            <s xml:id="echoid-s1395" xml:space="preserve">& </s>
            <s xml:id="echoid-s1396" xml:space="preserve">quidem dia-
              <lb/>
            meter tubi præter propter ſeptem lineas exæquabat; </s>
            <s xml:id="echoid-s1397" xml:space="preserve">Dein menſuris acceptis
              <lb/>
            in particulis æqualibus linearum F E, A B & </s>
            <s xml:id="echoid-s1398" xml:space="preserve">B D (quarum lex ex ipſa figura per
              <lb/>
            ſe patet) illas inveni 81. </s>
            <s xml:id="echoid-s1399" xml:space="preserve">619. </s>
            <s xml:id="echoid-s1400" xml:space="preserve">& </s>
            <s xml:id="echoid-s1401" xml:space="preserve">740.</s>
            <s xml:id="echoid-s1402" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1403" xml:space="preserve">His ita præparatis, tubum aquâ replevi, digito interim obturato ori-
              <lb/>
            ficio A, eoque confeſtim remoto aquæ breviſſimo tempuſculo effluxere om-
              <lb/>
            nes: </s>
            <s xml:id="echoid-s1404" xml:space="preserve">obſervare tamen potui, primas & </s>
            <s xml:id="echoid-s1405" xml:space="preserve">ultimas propius ad verticalem AB,
              <lb/>
            quam medias cecidiſſe; </s>
            <s xml:id="echoid-s1406" xml:space="preserve">guttas autem longiſſime projectas incidiſſe in locum
              <lb/>
            C invenique poſt ſæpius repetitum experimentum BC particularum, qui-
              <lb/>
            bus antea uſus fueram, 235.</s>
            <s xml:id="echoid-s1407" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1408" xml:space="preserve">Jam vero ſi per præmiſſum lemma quæratur altitudo E G, ad quam guttæ
              <lb/>
            maxima velocitate ejectæ aſcendere poſſint, reperitur E G = 56. </s>
            <s xml:id="echoid-s1409" xml:space="preserve">part. </s>
            <s xml:id="echoid-s1410" xml:space="preserve">de-
              <lb/>
            beret autem vi §. </s>
            <s xml:id="echoid-s1411" xml:space="preserve">§. </s>
            <s xml:id="echoid-s1412" xml:space="preserve">16. </s>
            <s xml:id="echoid-s1413" xml:space="preserve">& </s>
            <s xml:id="echoid-s1414" xml:space="preserve">20. </s>
            <s xml:id="echoid-s1415" xml:space="preserve">eſſe.</s>
            <s xml:id="echoid-s1416" xml:space="preserve">
              <unsure/>
            = 62. </s>
            <s xml:id="echoid-s1417" xml:space="preserve">niſi attritus aquæ ejusquæ adhæ-
              <lb/>
            ſio ad latera tubi impedimentum motui afferret: </s>
            <s xml:id="echoid-s1418" xml:space="preserve">majorem conſenſum non
              <lb/>
            expectavi.</s>
            <s xml:id="echoid-s1419" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1420" xml:space="preserve">II. </s>
            <s xml:id="echoid-s1421" xml:space="preserve">Poſitis quæ prius, diminuto tantum ad dimidium foramine A,
              <lb/>
            ita ut amplitudo tubi eſſet quadrupla amplitudinis ad lumen pertinentis, ob-
              <lb/>
            ſervavi B C = 252; </s>
            <s xml:id="echoid-s1422" xml:space="preserve">Hinc deducitur E G = 68 per experimentum; </s>
            <s xml:id="echoid-s1423" xml:space="preserve">per
              <lb/>
            theoriam autem debuiſſet eſſe = 70; </s>
            <s xml:id="echoid-s1424" xml:space="preserve">numeri hi minus differunt quam
              <lb/>
            præcedentes, quia hîc multo minus fuit attritus impedimentum ob diminu-
              <lb/>
            tam velocitatem internæ aquæ. </s>
            <s xml:id="echoid-s1425" xml:space="preserve">Utrumque autem experimentum egregie
              <lb/>
            profecto theoriam confirmat.</s>
            <s xml:id="echoid-s1426" xml:space="preserve"/>
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