Galilei, Galileo
,
Mechanics
,
1665
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[Figure 21]
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[Figure 29]
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and in the Velocity: which peradventure, might not have ſeemed
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to ſome ſo true and manifeſt in the preſent Contemplation; nay,
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rather it ſeems, that in this caſe the Force is multiplied without the
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Movers moving a longer way than the Moveable: In regard, that
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if we ſhall in the Triangle A B C ſuppoſe the Line A B to be the
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Plane of the Horizon, A C the elevated Plane, whoſe Altitude is
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meaſured by the Perpendicular C B, a Moveable placed upon the
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Plane A C, and the Cord E D
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F
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tyed to it, and a
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F
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orce or Weight
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applyed in
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F
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that hath to the
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Gravity of the Weight E the
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ſame proportion that the Line
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B C hath to C A; by what
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hath been demonſtrated, the
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Weight
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F
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ſhall deſcend
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downwards, drawing the
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Moveable E along the eleva
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ted Plane; nor ſhall the Move
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able E meaſure a greater Space
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when it ſhall have paſſed the
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whole Line A
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C,
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than that which the ſaid Grave
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F
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meaſureth in its
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deſcent downwards. </
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<
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>But here yet it muſt be advertiſed, that al
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though the Moveable E ſhall have paſſed the whole Line A C, in
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the ſame Time that the other Grave
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F
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ſhall have been abaſed the
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like Space, nevertheleſs the Grave E ſhall not have retired from the
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common Center of things Grave more than the Space of the Per
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pendicular
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C
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B. but yet the Grave
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F
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deſcending Perpendicularly ſhall
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be abaſed a Space equal to the whole Line A
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C.
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And becauſe Grave
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Bodies make no Reſiſtance to Tranſverſal Motions, but only ſo
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far as they happen to recede from the
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C
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enter of the Earth; There
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fore the Moveable E in all the Motion A
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C
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being raiſed no more
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than the length of the Line
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C
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B, but the other
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F
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being abaſed per
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pendicularly the quantity of all the Line A
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C
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: Therefore we may
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deſervedly affirm that Way of the
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F
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orce E maintaineth the ſame
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proportion to the
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F
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orce
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F
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that the
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L
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ine A
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C
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hath to
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C
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B; that is,
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the Weight E to the Weight
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F.
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It very much importeth, therefore,
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to conſider by [
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or along
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] what
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L
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ines the Motions are made, eſpe
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cially in exanimate Grave Bodies, the Moments of which have their
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total Vigour, and entire Reſiſtance in the
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L
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ine Perpendicular to
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the Horizon; and in the others tranſverſally Elevated and Inclined
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they feel the more or leſs Vigour,
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Impetus,
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or Reſiſtance, the more
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or leſs thoſe Inclinations approach unto the Perpendicular Inclina
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tion.</
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