Galilei, Galileo, Mechanics, 1665

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1the Weight to be at one extream, and the Force at the other, and
the
Fulciment placed in ſome point between the extreams: but we
may
make uſe of the Leaver another way, yet, placing, as we ſee,
the
Fulciment in the extream A, the Force in the other extream C,
and
ſuppoſing the Weight D to hang by ſome point in the midſt,
10[Figure 10]
as
here we ſee by the point B, in
this
example it's manifeſt, that if
the
Weight did hang at a point
Equi-diſtant
from the two ex­
treams
A and C, as at the point F,
the
labour of ſuſtaining it would
be
equally divided betwixt the
two
points A and C, ſo that half
the
Weight would be felt by the
Force
C, the other half being ſu­
ſtained
by the Fulciment A: but if the Grave Body ſhall be hanged
at
another place, as at B, we ſhall ſhew that the Force in C is ſuffi­
cient
to ſuſtain the Weight in B, as it hath the ſame proportion
to
it, that the Diſtance, A B hath to the Diſtance A C.
For De­
monſtration
of which, let us imagine the Line B A to be continued
right
out unto G, and let the Diſtance B A be equall to A G, and
let
the Weight hanging at G, be ſuppoſed equall to D: It is ma­
nifeſt
, that by reaſon of the equality of the Weights D and E, and
of
the Diſtances G A and A B, the Moment of the Weight E
ſhall
equalize the Moment of the Weight D, and is ſufficient to
ſuſtain
it: Therefore whatever Force ſhall have Moment equall to
that
of the Weight E, and that ſhall be able to ſuſtain it, ſhall be
ſufficient
likewiſe to ſuſtain the Weight D: But for ſuſtaining the
Weight
E, let there be placed in the point C ſuch a Force, whoſe
Moment
hath that proportion to the Weight E, that the Diſtance
G
A hath to the Diſtance A C, it ſhall be ſufficient to ſuſtain it:
Therefore
the ſame Force ſhall likewiſe be able to ſuſtain the
Weight
D, whoſe Moment is equall to the of E: But look what
Proportion
the Line G A hath to the Line A C; and A B alſo hath
the
ſame to the ſaid A C, G A having been ſuppoſed equall to A B:
And
becauſe the Weights E and D are equall, each of them ſhall
have
the ſame proportion to the Force placed in C: Therefore the
Force
in C is concluded to equall the Moment of the Weight D,
as
often as it hath unto it the ſame proportion that the Diſtance B A
hath
to the Diſtance C A.
And by moving the Weight, with the
Leaver
uſed in this manner, it is gathered in this alſo, as well as in
the
other Inſtruments, that what is gained in Force is loſt in Velo­
city
: for the Force C raiſing the Leaver, and transferring it to A I,
the
Weight is moved the Space B H, which is as much leſſer than
the
Space C I paſſed by the Force, as the Diſtance A B is leſſer

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