Galilei, Galileo
,
Mechanics
,
1665
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Axis, ſo that they ſhall conſtantly maintain alike Site and Poſition
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in reſpect of the Diſtances B A and A C, the Motion ſhall be
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perpetuated, the Weight I deſcending, and forcing the other G
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to aſcend. </
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>Where we are to obſerve the neceſſity of be-laying
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or winding the Rope about the Wheel, that ſo the Weight I may
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hang according to the Line that is tangent to the ſaid Wheel: for
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if one ſhould ſuſpend the ſaid Weight, ſo as that it did hang by the
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point F, cutting the ſaid Wheel, as is ſeen along the Line F N M,
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the Motion would ceaſe, the Moment of the Weight M being di
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miniſhed; which would weigh no more then if it did hang by the
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point N: becauſe the Diſtance of its Suſpenſion from the Center
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A, cometh to be determined by the Line A N, which falleth per
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pendicularly upon the Rope F M, and is no longer terminated by
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the Semidiameter of the Wheel A F, which falleth at unequall
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Angles upon the ſaid Line F M. </
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>A violence therefore being offered
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in the Circumference of the Wheel by a Grave and Exanimate
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Body that hath no other
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Impetus
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then that of Deſcending, it is
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neceſſary that it be ſuſtained by a Line that is contingent with
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the Wheel, and not by one that cutteth it. </
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>But if in the ſame
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Circumference an Animate Force were employed, that had a Mo
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ment or Faculty of making an
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Impulſe
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on all ſides, the work might
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be effected in any whatever place of the ſaid Circumference. </
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>And
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thus being placed in F, it would draw up the Weight by turning
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the Wheel about, pulling not according to the Line F M down
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wards, but ſide-waies according to the Contingent Line F L, which
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maketh a Right Angle, with that which is drawn from the Center
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A unto the point of Contact F: ſo, that if in this manner one do
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meaſure the Diſtance from the Center A to the Force placed in
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F, according to the Line A F perpendicular to F L, along which
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the
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Impetus
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is made, a man ſhall not in any part have altered the
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uſe of the ordinary Leaver. </
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>And we muſt note, that the ſame
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would be poſſible to be done likewiſe with an Exanimate Force,
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in caſe that a way were found out to cauſe that its Moment might
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make Impulſe in the point F, drawing according to the Contingent
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Line F L: which would be done by adjoyning beneath the Line F L
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a turning Pulley, making the Rope wound about the Wheel to
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paſſe along upon it, as it is ſeen to do by the Line F L X, ſuſpending
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at the end thereof the Weight X equall to the other I, which ex
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erciſing its Force according to the Line F L, ſhall alwaies keep a
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Diſtance from the Center A equall unto the Semidiameter of the
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Wheel. </
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>And from what hath been declared we will gather for a
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Concluſion, That in this Inſtrument the Force hath alwaies the
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ſame proportion to the Weight, as the Semidiameter of the Axis
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or Barrell hath to the Semidiameter of the Wheel.</
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