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
198[Figure 198]
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.
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
198[Figure 198]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.