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.