Galilei, Galileo, Mechanics, 1665

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Force 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.
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

Figure: /permanent/archimedes/galil_mecha_070_en_1665/figures/ not scanned
[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.
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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