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

Table of Notes

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            <s xml:id="echoid-s8631" xml:space="preserve">
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            plana totas excipiant, non autem de fluidis corpora ambientibus in eademque
              <lb/>
            impetum facientibus, veluti de Ventis aut fluminibus: </s>
            <s xml:id="echoid-s8632" xml:space="preserve">dico enim hos dupli-
              <lb/>
            cis generis impetus quos auctores adhuc confuderunt, probe à ſe invicem di-
              <lb/>
            ſtinguendos eſſe, ob rationes infra breviter exponendas.</s>
            <s xml:id="echoid-s8633" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8634" xml:space="preserve">§. </s>
            <s xml:id="echoid-s8635" xml:space="preserve">16. </s>
            <s xml:id="echoid-s8636" xml:space="preserve">Ratione venæ aqueæ ſic cenſeo: </s>
            <s xml:id="echoid-s8637" xml:space="preserve">aquas velocitate uniformi ex
              <lb/>
            cylindro infinite amplo verticali A B M (Fig. </s>
            <s xml:id="echoid-s8638" xml:space="preserve">84.) </s>
            <s xml:id="echoid-s8639" xml:space="preserve">per foramen laterale C M
              <lb/>
              <note position="left" xlink:label="note-0304-01" xlink:href="note-0304-01a" xml:space="preserve">Fig. 84.</note>
            horizontaliter effluere pono, venamque perpendiculariter impingere in lami-
              <lb/>
            nam E F: </s>
            <s xml:id="echoid-s8640" xml:space="preserve">ita facile video, quia particulæ inſequentes priores impediunt ne
              <lb/>
            reſilire poſſint, fore ut ſingulæ ad latera deflectantur, idque motu laminæ E F
              <lb/>
            (ſi modo hæc ſat magna fuerit, ut vena tota quamvis diſperſa excipiatur) pa-
              <lb/>
            rallelo vel tantum non tali: </s>
            <s xml:id="echoid-s8641" xml:space="preserve">Et quia omnia ſunt in ſtatu permanentiæ, fingere
              <lb/>
            licet laminam E F vaſi eſſe affirmatam, venamque lateribus C H D G L M
              <lb/>
            circumdatam, ita, ut aquæ per hiatum circularem D E G F effluere ex vaſe
              <lb/>
            A B C H D E F G L M cenſeri poſſint. </s>
            <s xml:id="echoid-s8642" xml:space="preserve">Hoc ſi ita fuerit, demonſtravimus
              <lb/>
            §. </s>
            <s xml:id="echoid-s8643" xml:space="preserve">13. </s>
            <s xml:id="echoid-s8644" xml:space="preserve">guttulas in D E effluentes vim repellentem quidem producere ſecun-
              <lb/>
            dum E F; </s>
            <s xml:id="echoid-s8645" xml:space="preserve">ſed ſimul apparet vim repellentem eſſe in G F priori contrariam
              <lb/>
            ita ut ad hanc virium repellentium claſſem hic non ſit attendendum. </s>
            <s xml:id="echoid-s8646" xml:space="preserve">Quod
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            vero ad directionem, laminæ E F vel cylindro B C, perpendicularem atti-
              <lb/>
            net, demonſtravimus in fine ejuſdem §. </s>
            <s xml:id="echoid-s8647" xml:space="preserve">13. </s>
            <s xml:id="echoid-s8648" xml:space="preserve">ſub ea directione plane nullam
              <lb/>
            fieri repulſionem: </s>
            <s xml:id="echoid-s8649" xml:space="preserve">Igitur tantum lamina E F propellitur, quantum cylindrus
              <lb/>
            repellitur. </s>
            <s xml:id="echoid-s8650" xml:space="preserve">Idque eſt quod demonſtrare volui: </s>
            <s xml:id="echoid-s8651" xml:space="preserve">Atque inde jam ſequitur, preſ-
              <lb/>
            ſionem venæ aqueæ, quæ tota in laminam incurrit, tantam eſſe quanta pon-
              <lb/>
            dus cylindri aquei, qui pro baſe habeat ſectionem venæ (poſtquam hæc unifor-
              <lb/>
            mem acquiſivit amplitudinem) & </s>
            <s xml:id="echoid-s8652" xml:space="preserve">pro altitudine duplam altitudinem velocita-
              <lb/>
            ti aquarum (poſtquam hæc ſimiliter uniformis facta eſt) debitam.</s>
            <s xml:id="echoid-s8653" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8654" xml:space="preserve">§. </s>
            <s xml:id="echoid-s8655" xml:space="preserve">17. </s>
            <s xml:id="echoid-s8656" xml:space="preserve">Non dubito multos fore, quibus propoſitio hæc plane nova
              <lb/>
            ſuſpecta videatur atque experimentis contraria: </s>
            <s xml:id="echoid-s8657" xml:space="preserve">Hos vero perpendere velim,
              <lb/>
            experimenta hactenus ſumta nequaquam regulæ communi accurate reſponde-
              <lb/>
            re, & </s>
            <s xml:id="echoid-s8658" xml:space="preserve">in pleriſque caſibus noſtram Regulam parum differre à communi, quam-
              <lb/>
            vis in theoria maxime ſint diverſæ: </s>
            <s xml:id="echoid-s8659" xml:space="preserve">tum etiam eos in anteceſſum monitos cu-
              <lb/>
            pio, alia me inſtituiſſe experimenta, quæ ſingula meam ſententiam exactiſſime
              <lb/>
            confirmant, veteremque plane refellunt! experimenta a me ſumpta in fine Se-
              <lb/>
            ctionis recenſebo. </s>
            <s xml:id="echoid-s8660" xml:space="preserve">Demonſtrandi modus quo uſus fui, fortaſſe etiam </s>
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