Borelli, Giovanni Alfonso
,
De motionibus naturalibus a gravitate pendentibus
,
1670
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Y in ſecundo & ſubleuata vſque ad V; tunc quidem̨
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centrum grauitatis prædictæ aquæ horizontaliter
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cõ-ſtitutæ
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ſtitutæ</
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præcisè incidet in
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ſuſpenſionis M, prop
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terea quòd vt baſis V ad baſim A ſeù vt cylindrus a
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queus GLV ad equè altum cy
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lindrum AEF in primo caſu vel
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ad CEF in ſecundo, ita fuit reci
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procè diſtantia EM ad ML. o
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ſtendendum modò eſt punctą
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A, Q, R, S, M in eadèm linea pa
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rabolica eſſe. </
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<
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TX æqualis eſt æquæ moli GH
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I, ergo, XBF vnà cum GHI æ
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qualis eſt moli aqueæ TAF; e
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rat verò moles aquæ XBF vnà
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cum GHI ad GHI vt linea HB
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ad BQ ſeu (ducta QN parallel
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là AE) vt LE ad EN, ergo FAT
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ad TX atque ſemiſſis illius FA
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ad huius ſemiſſem AB eamdem
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proportionem habebit quam̨
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LE ad EN, eſt verò EA ad AF vt MA ad AG, ſeù vt
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ME ad EL, ergo ex æqualitate ordinata EA ad AB
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eamdem proportionem habebit quam ME ad EN, &
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per conuerſionem rationis EA ad EB erit vt EM ad
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MN, ſeù vt EB ad NQ, erunt igitur tres continuæ pro
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portionales EA, EB, & NQ in eadem ratione quam̨
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habet EM ad MN, quare quadratum ex EM ad qua
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dratum ex MN eam proportionem habebit, quam̨ </
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