Bernoulli, Daniel
,
Hydrodynamica, sive De viribus et motibus fluidorum commentarii
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SECTIO SEXTA.
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quantitates M & </
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rei eo magis unicuique pateat.</
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<
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xml:space
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a & b.</
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que in B & </
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<
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">ponatur ſinus totus = 1, ſinus anguli D B C = {b/a} = m,
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ſinus anguli B D C = {β/α} = n, erit longitudo penduli tautochroni = {γMN/mgγ + ngg},
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ubi g denotat amplitudinem canalis in B & </
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<
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<
s
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">Concipiatur nunc longitudo canalis B C D fluido plena in rectam ex-
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tenſa bcd, ſuper qua ceu axe fiat curva F G H, quæ ſit ſcala amplitudinum
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in locis homologis, ita, ut poſita bc = B C ſit c G ad b F, ut amplitudo in
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C ad amplitudinem in B. </
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<
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ſpatium bd H F repræſentabit magnitudinem M. </
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<
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conſtruatur alia curva L M N, cujus applicata c M ſit ubique {bF
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/cG} & </
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(per §. </
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">N = ſpatio b d N L diviſo per ſpatium bd H F, ita ut ſit
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M X N = ſpatio b d N L, quod multiplicatum per {γ/mgγ + ngg} dabit longitu-
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dinem penduli tautochroni.</
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gitudo dicatur l, erit F H linea recta ipſi bd parallela, pariter atque L N:
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<
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= ({x/l}[√γ - √g] + √g)
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; </
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;
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proinde totum ſpatium bdN L = {ggl/√gγ - g} + {ggl/√gγ - γ} = {ggl/√gγ}: </
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igitur longitudo penduli tautochroni cum oſcillante aqua = {l√gγ/mγ + ng}.</
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<
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