Galilei, Galileo
,
Mechanics
,
1665
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[Figure 11]
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[Figure 12]
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[Figure 13]
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[Figure 27]
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[Figure 28]
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[Figure 29]
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Weight G hanging at
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F,
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it hath been already demonſtrated, that
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the ſaid
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F
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orce D hath to the Weight ſo by it ſuſtained, that ſame
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proportion which the Diſtance
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F
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C hath to the Diſtance C D:
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Which is ſubduple proportion: Therefore the Moment D is ſub
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duple to the Moment of half of the Weight G ſuſtained by it:
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Wherefore it followeth, that it is the fourth part of the Moment
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of the whole Weight. </
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>And in the ſame manner the ſame thing is
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demonſtrated, of the Moment
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B
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; and it is but reaſonable, that the
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Weight G being ſuſtained by the four points, A,
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B,
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C, D, each of
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them ſhould feel an equall part of the Labour.</
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>Let us come now to apply this Conſideration to Pullies, and let
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the Weight X be ſuppoſed to hang at the two Pullies A B and D E
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entwining about them, and about the uppermoſt Pulley G H, the
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Rope, as we ſee, I D E H G A B, ſuſtaining the whole Machine in
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the point K. </
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>Now I ſay, that placing the Force in L, it ſhall be able
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to ſuſtain the Weight X, if ſo be, it be equal to the fourth part of
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it. </
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>For if we do imagine the two Diameters D E and A B, and the
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Weights hanging at the middle points F and C, we ſhall have two
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Leavers like to thoſe before deſcribed, the Fulciments of which an
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ſwer to the points D and A. </
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<
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>Whereupon the Force placed in B,
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or if you will, in L, ſhall be able to ſu
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ſtain the Weight X, being the fourth
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part of it: And if we adde another Pul
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ley above the other two, making the
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Rope or Cord to paſs along L M N, trans
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ferring the Force L into N, it ſhall be
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able to bear the ſame Weight gravitating
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downwards, the upper Pulley neither aug
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menting or diminiſhing the Force, as hath
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been declared. </
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>And we will likewiſe
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note, that to make the: Weight aſcend the
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four Ropes B L, E H, D I, and A G
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ought to paſs, whereupon the Mover will
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be to begin, as much as thoſe Ropes are
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long; and yet nevertheleſs the Weight
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ſhall move but only as much as the length
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of one of them: So that we may ſay by
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way of advertiſement, and for confirma
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tion of what hatn been many times ſpo
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ken, namely, that look with what proportion the Labour of the
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Mover is diminiſhed, the length of the Way, on the contrary, is
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encreaſed with the ſame proportion</
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* Or four parts
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of the ſame Rope</
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* The word
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Gy
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rilla
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ſignifieth a
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Shiver, Rundle,
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or ſmall Wheel
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of a Pulley, tran
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ſlated by we
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ſometimes Pul
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ley, ſometimes
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Nut or Girill.</
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<
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>But if we would encreaſe the Force in ſexcuple proportion, it
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will be requiſite that we adjoyn another ^{*} ſmall Pulley or Gyrill
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to the inferiour Pulley which that you may the better underſtand </
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