Galilei, Galileo, Mechanics, 1665

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1Force in B ſuſtaineth a part of the Weight D double to it ſelf, its
Diſtance
from the Fulciment A, that is, the Line B A being dou­
ble
to the Diſtance A C at which the Grave hangeth: But becauſe
the
two Forces in B and C are ſuppoſed to be equal to each other:
Therefore
the part of the Weight D, which is ſuſtained by the
Force
in B, is double to the part ſuſtained by the Force in C.
If
therefore
, of the Grave D two parts be made, the one double to
the
remainder, the greater is ſuſtained by the Force in B, and the
leſſer
by the Force in C: But this leſſer is the third part of the
Weight
D: Therefore the Moment of the Force in C is equal to
the
Moment of the third part of the Weight D; to which, of
conſequence
, the Force B ſhall be equal, we having ſuppoſed it
equal
to the other Force C: Wherefore our intention is manifell,
which
we were to demonſtrate, how that each of the two Powers
C
and B is equal to the third part of the Weight D.
Which be­
ing
demonſtrated, we will paſs forwards to the Pulleys, and will
deſcribe
the inferiour Gyrils of A C B, voluble about the Center
G
, and the Weight H hanging thereat, we will draw the other up­
per
one E F, winding about them both the Rope D F E A C B I,
of
which let the end D be faſtned to the inferiour Pulley, and to
19[Figure 19]
the
other I let the Force be applyed:
Which
, I ſay, ſuſtaining or moving the
Weight
H, ſhall feele no more than the
third
part of the Gravity of the ſame.
For
conſidering
the contrivance of this Ma­
chine
, we ſhall find that the Diameter A B
ſupplieth
the place of a Leaver, in whoſe
term
B the Force I is applied, and in the
other
A the Fuiciment is placed, at the mid­
dle
G the Grave H is hanged, and another
Force D applied at the ſame place: ſo that

the
Weight is faſtned to the ^{*} three Ropes
I
B, F D, and E A, which with equal Labour
ſuſtain
the Weight.
Now, by what hath
already
been contemplated, the two Forces
D
and B being applied, one, to the midſt of the Leaver A B, and
the
other to the extream term B, it is manifeſt, that each of them
holdeth
no more but the third part of the Weight H: Therefore
the
Power I, having a Moment equal to the third part of the
Weight
H, ſhall be able to ſuſtain and move it: but yet the Way
of
the Force in I ſhall be triple to the Way that the Weight ſhall
paſs
; the ſaid Force being to diſtend it ſelf according to the
Length
of the three Ropes I B, F D, and E A, of which one alone
meaſureth
the Way of the Weight H.

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