Borelli, Giovanni Alfonso, De motionibus naturalibus a gravitate pendentibus, 1670

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<archimedes>
<text>
<body>
<chap>
<p type="main">
<s id="s.000082">
<arrow.to.target n="marg15"/>
<lb/>
Y in ſecundo & ſubleuata vſque ad V; tunc quidem̨
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centrum grauitatis prædictæ aquæ horizontaliter
<expan abbr="cõ-ſtitutæ">con­
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ſtitutæ</expan>
præcisè incidet in
<expan abbr="cẽtro">centro</expan>
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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<lb/>
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. </s>
<s id="s.000083">quia moles aquæ
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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 </s>
</p>
</chap>
</body>
</text>
</archimedes>