Galilei, Galileo - Mechanics

Galilei, Galileo, Mechanics, 1665

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

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