Borelli, Giovanni Alfonso
,
De motionibus naturalibus a gravitate pendentibus
,
1670
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mo loco debemus velocitates
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inter ſe hete
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rogeneorum, quæ contingunt in eodem, vel diuerſis
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fluidis; hæc verò requirunt lemmata aliqua mechani
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ca, quorum primum erit. </
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Cap. 11. gra
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uia in fluido
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velocitati
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bus inæqua
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libus ferri
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debere.</
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PROP. CCXXXVI.
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Si in libra radiorum æqualium duo pondera in æqualia
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ſuſpẽ-dantur
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dantur</
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, ſumma inæqualium ponderum ad eorum diffe
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rentiam eamdem proportionem habebit, quam libræ ra
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dius ad pendulum, quod constituit eadem libra.
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">ATerminis eiuſdem libræ AB ſuſpenſæ in puncto
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eius intermedio C
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pendeãt
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pondera inæqualia
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D maius, & E minus, ſit
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que F centrum grauita
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tis libræ cum ponderi
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bus appenſis, patet CF
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eſſe longitudinem pen
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duli. </
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">dico D plus, E ad D minus E eamdem propor
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tionem habere, quam libræ radius AC ad penduli
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longitudinem CF. quia F eſt centrum grauitatis librę
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cum ponderibus ſuſpenſis D & E, ergo D ad E
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eamdẽ
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proportionem habet (ex mechanicis) quàm BF ad FA,
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& componendo D plus E ad E, pariterque duplum̨
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ſummæ D & E ad duplum E eamdem proportionem
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habebit, quàm BA ad AF, igitur antecedentium ſe
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miſſes ad conſequentes eamdem proportionem ha
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bebunt, ſcilicèt D plus E ad duplum E erit vt ſemi
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BA, ſeu CA ad AF, & per conuerſionem rationis D
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plus E ad D minus E eamdem
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proportionẽ
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habebit,
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quàm CA, ad CF, quod erat, &c. </
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