Borelli, Giovanni Alfonso
,
De motionibus naturalibus a gravitate pendentibus
,
1670
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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. CCXL.
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In ijſdem trutinis datis quatuor ponderibus in illis
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ſuſpẽſis
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,
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reperire proportionem velocitatum quibus libræ reuol
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uuntur.
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">IN eadem figura ſint data pondera inæqualia D, &
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G, nec non præcognita ſint pondera æqualia E,
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& M, quæ minora prioribus ſint: reperiri debet pro
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portio velocitatum qui
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bus prædictæ libræ
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reuol-uũtur
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uuntur</
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; fiat CI media pro
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portionalis inter CF, &
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KH; quia duo pondera D,
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& E ſuam vim compreſſi
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uam exercent in F centro
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grauitatis communis eo
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rumdem ponderum, ergo ea velocitate flectetur li
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bra AB circa centrum fixum C, quæ competit longi
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tudini penduli CF; eadem ratione ea velocitate fle
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ctetur libra NO cum ponderibus G, M circa centrum
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K, quæ competit longitudini penduli KH; & quią
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velocitas penduli CF ad velocitatem penduli KH
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eã-dem
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dem</
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rationem habet quam CF ad CI; & CF ad KH
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compoſitam proportionem habet ex ratione diffe
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rentiæ ponderum D, & E ad eorum ſummam, & ex
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ratione ſummæ ponderum G, M ad eorum differen
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tiam, ergo reperire debemus
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ſubduplicatã
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propor
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tionem prædictæ compoſitæ proportionis, vt quæſi
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to ſatisfaciamus. </
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<
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E ad R, vt ſumma ponderum G, & M ad eorumdem̨ </
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