Schott, Gaspar
,
Mechanica hydraulico-pneumatica. Pars I. Mechanicae Hydraulico-pnevmaticae Theoriam continet.
,
1657
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Leges aquæ
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effluentis
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per
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tubi ſemper
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pleni.
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Corollarium II.
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>COlligitur ſecundò, Aquam apud B, in utroque tubo, hoc eſt,
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ſemper & non ſemper pleno, tantâ ſolùm vi premi prope
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foramen B, quanta eſt vis ſeu pondus aquæ à B uſque ad ſu
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premam aquæ ſuperficiem, id eſt, columnæ aqueæ habentis
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pro baſi latitudinem foraminis B, pro altitudine perpendicu
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larem à B ad dictam ſuperficiem. </
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>Ratio eſt, quia ſolùm illa
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columna premit ſupra B, per dicta Propoſit. 1. </
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>Intellige, niſi
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illa aliunde impetum recipiat, ut ſi ipſi affunderetur aqua ex
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tubo inclinato, ſive conjuncto, ſive diſiuncto. </
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Corollarium. III.
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>COlligitur tertiò, Leges prædictas deſcenſus gravium ſervari
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ab aqua in tubo ſemper pleno, deſcendendo ab A ad B, ſo
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lùm in primo deſcenſu, non verò in deſcenſu continuato; item
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ſolùm à prima parte aquæ deſcendentis,
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nõ
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à partibusipſi conti
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guis & ſubſequentibus. </
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>Explico Deſcendat aqua ab A ad B, effi
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ciatque deſcenſus columnam aqueam AB, quæ dividatur in vi
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ginti
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quinq;
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æquales partes ſecundùm longitudinem ſeu altitu
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dinem ab A ad B. </
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>Dico, ſolùmvigeſimam quintam partem, quæ
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eſt apud B, ſervare prædictam legem deſcenſus gravium cre
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ſcentis in velocitate ſecundùm numeros impares ab unitate
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numeratos; & quidem illam ſolam vigeſimam quintam par
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tem, quæ eſt in prima columna aquea à deſcenſu aquæ for
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mata, non verò quæ eſt in reliquis columnis ſubſequentibus. </
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Ratio eſt, quia cùm nulla pars ex viginti quinque egrediatur
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è foramine B, quin ingrediatur alia per orificium A priori
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æqualis; & nulla tranſeat vigeſimum quintum & ultimum ſpa
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tiolum lateris AB, quin eodem tempore tranſeat alia æqualis
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primum ſpatiolum, & alia ſecundum, & alia tertium, ac reli
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qua omma; neceſsè eſt ut omnes reliquæ partes eâdem velo
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citate conficiant ſingula ſpatiola, qua velocitate ultima con
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ficit ultimum; & eâdem velocitate unaquæque pertranſeat
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ſpatiolum ſibi correſpondens, qua velocitate ultima pars per
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tranſit ultimum ſpatiolum. </
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<
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>Patet ergo propoſitum. </
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