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

Table of figures

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              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
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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. </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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              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>
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