Galilei, Galileo - Mechanics

Galilei, Galileo, Mechanics, 1665

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of the Members and Muſcles, and as we uſe to ſay, by Force of
Armes, beſides the extern Weight, we are to lift up the Weight of
our own Armes, in which greater pains is required. Conclude we,
therefore, that this upper Pulley doth not bring any Facility to the
Force ſimply conſidered, but onely to the manner of applying it:
but if we ſhall make uſe of the like Machine

[Figure 12]

in another manner, as we are now about to
declare; we may raiſe the Weight with di-
minution of Forces: For let the Pulley
B D C be voluble about the Center E placed
in it's Frame B L C, at which hang the
Grave G; and let the Rope A B D C F
paſſe about the Pulley; of which let the end
A be faſtned to ſome fixed ſtay, and in the
other F let the Force be placed; which
moving to wards H ſhall raiſe the Machine
B L C, and conſequently the Weight G:
and in this operation I ſay, that the Force in
F is the half of the Weight ſuſtained by it.
For the ſaid Weight being kept to Rights by the two ^{*} Ropes A B

and F C, it is manifeſt, that the Labour is equally ſhared betwixt
the Force F and the Fulciment A: and more ſubtilly examining the
nature of this Inſtrument, if we but continue forth the Diameter
B E C, we ſhall ſee a Leaver to be made, at the midſt of which, that
is at the point E, the Grave doth hang, and the Fulciment cometh
to be at the end B, and the Force in the Term C: whereupon, by
what hath been above demonſtrated, the Force ſhall have the ſame
proportion to the Weight, that the Diſtance E B hath to the Di-
ſtance; Therefore it ſhall be the half of the ſaid Weight: And
becauſe the Force riſing towards A, the Pulley turneth round,
therefore that Reſpect or Conſtitution which the Fulciment B and
Center E, on which the Weight and Term C, in which the Force
is employed do depend, ſhall not change all the while; but yet in
the Circuinduction the Terms B and C happen to vary in number,
but not in vertue, others and others continually ſucceeding in their
place, whereby the Leaver B C cometh to be perpetuated. And
here (as hath been done in the other Inſtruments, and ſhall be in
thoſe that follow) we will not paſſe without conſidering how that
the journey that the Force maketh, is double to the Moment of the
Weight. For in caſe the Weight ſhall be moved ſo far, till that
the Line B C come to arrive with it's points B and C, at the points
A and F, it is neceſſary that the two equal Ropes be diſtended in
one ſole Line F H, and conſequently, when the Weight ſhall have
aſcended along the Intervall B A, the Force ſhall have been moved
twice as far, that is, from F unto H. Then conſidering that the

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