Schott, Gaspar
,
Mechanica hydraulico-pneumatica. Pars I. Mechanicae Hydraulico-pnevmaticae Theoriam continet.
,
1657
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<
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>DAtum ſit foramen AB, & latus
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DC, in eodem vaſe;
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oporteatq;
">oporteatque</
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deſcribere foramen, cujus latus ſit
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DC, & è quo effluat eodem tempore
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aqua ut ab AB. </
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>Ductis CN, & DF ho
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rizontalibus, & p̨ducta BE, reperiatur
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ratio
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aquarũ
">aquarum</
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fluentiũ
">fluentium</
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ex AB, & FE,
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per Propoſit. 9. hujus Capitis, quæ ſit
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ut G ad H; & fiat, ut H ad G, ita
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FI ad FK, per decimam tertiam Sex
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ti Euclid. & Propoſit. 3. Parergi Capitis 3; & à K erigatur
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perpendicularis KL, & tandem fiat foramen, cujus latus DC,
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æquale & ſimile ipſi FL foramini, & ſit DM. </
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>Dico, è foramine
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DM fluere aquam, ut ex AB foramine. </
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>Quoniam enim aqua
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fluens ex AB, ad aquam fluentem ex FE, eſtut G ad H, per con
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ſtructionem; item aqua fluens per FL, ſeu ei æquale DM, ad
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fluentem per idem FE, eſt itidem ut G ad H, per Propoſit. 2.
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hujus Capitis; erunt aquæ fluentes per AB, & per DM, inter ſe
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æquales, per nonam Quinti Euclidis. </
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<
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>Igitur DM erit foramen
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quæſitum. </
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Proproſitio XIII. Problema VIII.
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Dato foramine, reperire aliud æquale in eodem vaſe, è
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quo fluat aqua in ratione data.
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<
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>DEtur in vaſe AB foramen C, & da
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ta ſit ratio aquarum D, E, quarum
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D fluat in dato tempore per foramen C;
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reperiendum verò ſit, ubi fiat æquale
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foramen, è quo fluat in æquali tempore
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aqua E. </
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<
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>Fiat ad D, E, AC, quarta pro
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portionalis AF, per duodecimam Sexti
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Euclid. aut Propoſit. 8. Parergi Capitis
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tertij præcedentis; & ad AC, AF, ter
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tia proportionalis AG, per vndecimam </
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