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

Table of figures

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              tubicos æquè craſſos, & deſcendunt cylindri AC, &
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              DF; ergo (ex prop. 223) tempus V ad tempus T e­
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              rit vt altitudo GB ad DE, quod erat &c. </s>
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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.</s>
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              PROP. CCXXVIII.
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              Iiſdem datis, ſi aſcenſus, vel deſcenſus fiant æqualibus
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                poribus</expan>
              , ſpatia ab eis exacta habebunt ſubduplicatam
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              proportionem altitudinum.
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              <s id="s.002492">EOdem tempore T primo ſolidum AC aſcenden­
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              do percurrat ſpatium X, atque
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              DF per­
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              tranſeat ſpatium Z; dico, quod ſpatium X ad Z eam­
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              dem proportionem habebit, quam
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              GB ad DE; quia eodem tempore T
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              per orificium ſiphonis
                <expan abbr="ambiẽtis">ambientis</expan>
              cy­
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              lindrum AC cuius foramen æquale
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              eſt baſi BC, defluit cylindrus aqueus
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              cuius baſis æqualis eſt ipſi BC, alti­
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              tudo verò X, quantum ſcilicèt
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                dit</expan>
              prædictus cylindrus, atque tem­
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              pore T per ſiphonem
                <expan abbr="ambiẽtem">ambientem</expan>
              cy­
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              lindrum DF, cuius foramen æquale eſt EF, ſeu BC,
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              defluit cylindrus aqueus ſub eadem baſi, & altitudi­
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              ne Z contentus; igitur moles aquæ defluxa ex priori
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              cylindro altiori ad molem aquæ egreſſam ex minori
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              cylindro, ſcilicèt altitudo X ad Z ſubduplicatam̨
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                <expan abbr="proportionẽ">proportionem</expan>
              habebit altitudinis AB ad DE, & proin­
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              de ſpatium X aſcenſus cylindri AC ad ſpatium Z ele­
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              uationis cylindri DF eodem tempore T eamdem pro­
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              portionem habet, quam altitudo GB ad DE; quod
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              erat &c. </s>
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