Bernoulli, Daniel
,
Hydrodynamica, sive De viribus et motibus fluidorum commentarii
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HYDRODYNAMICÆ
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qui ſi vocetur X, ejuſque coſinus x, ſit o, 60000X + o, 80000 (1 + x)
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= or = 1, 83800: </
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">pro iſta conditione invenitur arcus a g h M s proxime
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175 {1/2} grad. </
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,
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35
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, erit tandem arcus g h M s 126
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, 55
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, qui proinde erit ad circumfe-
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rentiam circuli præterpropter ut 10 ad 29: </
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cum helicis o p q integramque helicem.</
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">Conſequens inde eſt, ſingulis revolutionibus cochlea à Vitruvio de-
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ſcripta proxime ejici {10/29} illius quantitatis, quam helix integra & </
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<
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tinet, ſeu paullulum ultra trientem.</
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">(IX) Notandum tamen eſt, quæcunque ſit aquæ quantitas, quæ qua-
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libet cochleæ revolutione canalem inferius ingreditur, ſuperiuſque ex eodem
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eſſluit, nullum nec detrimentum nec lucrum propterea cadere in potentiam ab-
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ſolutam ſi nulla habeatur frictionum ration, quia potentia movens cæteris paribus
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illi quantitati proportionalis eſt. </
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">At vero quia frictiones ſemper obſtant, eædem-
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que fere ſunt ob pondus machinæ proprium, ſive major ſive minor quantitas
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aquæ hauriatur, opera utique danda eſt, ut iſta quantitas cæteris paribus fiat
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maxima: </
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">(X) Jam innui ſuprà, creſcere rationem arcus g h M s ad circumferen-
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tiam circuli decreſcentibus angulis s a o & </
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">uterque igitur minimus eſſet
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conſtruendus, niſi alia obſtarent incommoda, præſertim ratione anguli N M G.
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<
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">Quod ad angulum s a o attinet, poteſt is fere ad lubitum diminui, neque aliud
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inde incommodum reſultat, niſi quod latera canalis circumflectendi nimis ad
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ſe invicem accedere poſſunt: </
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">E contrario à diminutione iſtius anguli aliud ob-
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tinetur compendium, nempe quod tunc eo verticalius poſſit erigi machina ip-
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ſaque aqua eo altius elevari, etenim angulus a M H ſemper major eſſe debet
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angulo s a o: </
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<
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">à verticaliori autem cochleæ poſitione ſimul obtinetur, ut mino-
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ri incommodo ſit machinæ proprium pondus eaque facilius ſuſtineatur.</
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<
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">Hæc ita perpendens crediderim fere ſufficere poſſe angulum 5 graduum,
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quem faciat canalis cum baſe nuclei. </
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