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

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[71.] Caſus 1.
Page: 105 (91)
[72.] Caſus II.
Page: 107 (93)
[73.] Scholion 1.
Page: 108 (94)
[74.] Scholion 2.
Page: 110 (96)
[75.] Scholion 3.
Page: 111 (97)
[76.] Scholion 4.
Page: 111 (97)
[77.] Corollarium 1.
Page: 112 (98)
[78.] Corollarium 3.
Page: 113 (99)
[79.] Corollarium 4.
Page: 113 (99)
[80.] Problema.
Page: 113 (99)
[81.] Solutio.
Page: 114 (100)
[82.] Scholium.
Page: 114 (100)
[83.] Problema.
Page: 116 (102)
[84.] Solutio.
Page: 117 (103)
[85.] Corollarium 1.
Page: 118 (104)
[86.] Corollarium 2.
Page: 119 (105)
[87.] Scholium.
Page: 120 (106)
[88.] Experimenta quæ ad Sectionem V. pertinent. Ad §. 5.
Page: 122 (108)
[89.] HYDRODYNAMICÆ SECTIO SEXTA. De fluidis non effluentibus ſeu intra latera vaſorum motis. §. 1.
Page: 125 (111)
[90.] De motu aquarum per canales indefinite longos. Caſus 1.
Page: 125 (111)
[91.] Exemplum 1.
Page: 126 (112)
[92.] Exemplum 2.
Page: 126 (112)
[93.] De oſcillationibus fluidorum in tubisrecurvis. Caſus II.
Page: 128 (114)
[94.] Lemma.
Page: 129 (115)
[95.] Solutio.
Page: 129 (115)
[96.] Problema.
Page: 130 (116)
[97.] Solutio.
Page: 130 (116)
[98.] Corollarium 1.
Page: 131 (117)
[99.] Corollarium 2.
Page: 131 (117)
[100.] Corollarium 3.
Page: 131 (117)
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page |< < (93) of 361 > >|
10793SECTIO QUINTA.
Debet vero iſtud incrementum æquari deſcenſui actuali centri gravitatis;
Atqui iſte deſcenſus, poſita D L = a, eſt per paragraphum ſeptimum ſect. 3.
= {nadx/M}; habetur igitur talis æquatio
{N/M}dv - {n3/mmM}vdx + {n/M}vdx = {nadx/M}, ſeu
dx = Ndv: (na - nv + {n3/mm} v);
Hæc vero ſi ita integretur, ut v & x ſimul evaneſcant, dat
x = {mmN/n3 - nmm} log. {mma - mmv + nnv/mma}
quæ æquatio, poſito c pro numero cujus logarithmus eſt unitas, æquivalet
huic @alteri
v = {mma/mm - nn} X (1 - c{n3 - nmm/mmN} x)
Hæc vero ſolutio quadrat pro caſu primo, ubi aqua ſuperne motu af-
ſunditur communi cum deſcenſu ſuperficiei proximæ.

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