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

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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. CCXXXIX.
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              Si à terminis duarum librarum æqualium, & æqualium
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              radiorum duo pondera æqualia pendeant, ſed oppoſitis
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              minora, pendulum prioris libræ ad pendulum poſterioris
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              proportionem compoſitam habebit ex ratione differentiæ
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              priorum ponderum ad eorum ſummam, & ex ratione
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              ſummæ posteriorum ad differentiam eorumdem
                <expan abbr="ponderũ">ponderum</expan>
              .
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              <s id="s.002584">SInt duæ libræ æquales AB, & NO bifariàm ſectæ
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              in fulci mentis C, & K, atque ex A pendeat ma­
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              ius pondus D, ex N verò minus pondus G, atque iņ
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              B, & O ſuſpendantur duo
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                dera</expan>
              æqualia E, & M,
                <expan abbr="quorũ">quorum</expan>
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              ſingula minora ſint quàm D,
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              vel G;
                <expan abbr="reperiãturque">reperianturque</expan>
              duo ea­
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              rum centra grauitatum F, &
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              H; dico pendulum CF ad K
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              H proportionem
                <expan abbr="compoſitã">compoſitam</expan>
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              habere ex ratione ponderis D minus E ad D plus E,
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              & ex ratione G plus M ad G minus M;
                <expan abbr="quoniã">quoniam</expan>
              AC ad
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              CF eſt vt D plus E ad D minus E (ex præcedenti) er­
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              go inuertendo FC ad CA, ſeu ad ei æqualem KN
                <expan abbr="eã-dem">ean­
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                dem</expan>
              proportionem habet
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              D minus E ad D plus
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              E, & NK ad KH eamdem proportionem habet,
                <expan abbr="quã">quam</expan>
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              G plus M ad G minus M; habet verò FC ad HK pro­
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              portionem compoſitam ex ratione FC ad CA, ſeu ad
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              NK, & ex ratione KN ad KH, ergo FC ad KH com­
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              poſitam proportionem habebit ex ijſdem proportio­
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              nibus D minus E ad D plus E, & ex G plus M ad G
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              minus M. </s>
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