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

Page concordance

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              mo loco debemus velocitates
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              inter ſe hete­
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              rogeneorum, quæ contingunt in eodem, vel diuerſis
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              fluidis; hæc verò requirunt lemmata aliqua mechani­
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              ca, quorum primum erit. </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. CCXXXVI.
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              Si in libra radiorum æqualium duo pondera in æqualia
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                dantur</expan>
              , ſumma inæqualium ponderum ad eorum diffe­
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              rentiam eamdem proportionem habebit, quam libræ ra­
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              dius ad pendulum, quod constituit eadem libra.
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              <s id="s.002579">ATerminis eiuſdem libræ AB ſuſpenſæ in puncto
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              eius intermedio C
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              pondera inæqualia
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              D maius, & E minus, ſit­
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              que F centrum grauita­
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              tis libræ cum ponderi­
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              bus appenſis, patet CF
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              eſſe longitudinem pen­
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              duli. </s>
              <s id="s.002580">dico D plus, E ad D minus E eamdem propor­
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              tionem habere, quam libræ radius AC ad penduli
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              longitudinem CF. quia F eſt centrum grauitatis librę
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              cum ponderibus ſuſpenſis D & E, ergo D ad E
                <expan abbr="eamdẽ">eamdem</expan>
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              proportionem habet (ex mechanicis) quàm BF ad FA,
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              & componendo D plus E ad E, pariterque duplum̨
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              ſummæ D & E ad duplum E eamdem proportionem
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              habebit, quàm BA ad AF, igitur antecedentium ſe­
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              miſſes ad conſequentes eamdem proportionem ha­
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              bebunt, ſcilicèt D plus E ad duplum E erit vt ſemi
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              BA, ſeu CA ad AF, & per conuerſionem rationis D
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              plus E ad D minus E eamdem
                <expan abbr="proportionẽ">proportionem</expan>
              habebit,
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              quàm CA, ad CF, quod erat, &c. </s>
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