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[29. Figure]

Weight G hanging at F, it hath been already demonſtrated, that

the ſaid Force D hath to the Weight ſo by it ſuſtained, that ſame

proportion which the Diſtance F C hath to the Diſtance C D:

Which is ſubduple proportion: Therefore the Moment D is ſub-

duple to the Moment of half of the Weight G ſuſtained by it:

Wherefore it followeth, that it is the fourth part of the Moment

of the whole Weight. And in the ſame manner the ſame thing is

demonſtrated, of the Moment B; and it is but reaſonable, that the

Weight G being ſuſtained by the four points, A, B, C, D, each of

them ſhould feel an equall part of the Labour.

the ſaid Force D hath to the Weight ſo by it ſuſtained, that ſame

proportion which the Diſtance F C hath to the Diſtance C D:

Which is ſubduple proportion: Therefore the Moment D is ſub-

duple to the Moment of half of the Weight G ſuſtained by it:

Wherefore it followeth, that it is the fourth part of the Moment

of the whole Weight. And in the ſame manner the ſame thing is

demonſtrated, of the Moment B; and it is but reaſonable, that the

Weight G being ſuſtained by the four points, A, B, C, D, each of

them ſhould feel an equall part of the Labour.

Let us come now to apply this Conſideration to Pullies, and let

the Weight X be ſuppoſed to hang at the two Pullies A B and D E

entwining about them, and about the uppermoſt Pulley G H, the

Rope, as we ſee, I D E H G A B, ſuſtaining the whole Machine in

the point K. Now I ſay, that placing the Force in L, it ſhall be able

to ſuſtain the Weight X, if ſo be, it be equal to the fourth part of

it. For if we do imagine the two Diameters D E and A B, and the

Weights hanging at the middle points F and C, we ſhall have two

Leavers like to thoſe before deſcribed, the Fulciments of which an-

ſwer to the points D and A. Whereupon the Force placed in B,

[Figure 15]

or if you will, in L, ſhall be able to ſu-

ſtain the Weight X, being the fourth

part of it: And if we adde another Pul-

ley above the other two, making the

Rope or Cord to paſs along L M N, trans-

ferring the Force L into N, it ſhall be

able to bear the ſame Weight gravitating

downwards, the upper Pulley neither aug-

menting or diminiſhing the Force, as hath

been declared. And we will likewiſe

note, that to make the: Weight aſcend the

four Ropes B L, E H, D I, and A G

ought to paſs, whereupon the Mover will

be to begin, as much as thoſe Ropes are

long; and yet nevertheleſs the Weight

ſhall move but only as much as the length

of one of them: So that we may ſay by

way of advertiſement, and for confirma-

tion of what hatn been many times ſpo-

ken, namely, that look with what proportion the Labour of the

Mover is diminiſhed, the length of the Way, on the contrary, is

encreaſed with the ſame proportion

the Weight X be ſuppoſed to hang at the two Pullies A B and D E

entwining about them, and about the uppermoſt Pulley G H, the

Rope, as we ſee, I D E H G A B, ſuſtaining the whole Machine in

the point K. Now I ſay, that placing the Force in L, it ſhall be able

to ſuſtain the Weight X, if ſo be, it be equal to the fourth part of

it. For if we do imagine the two Diameters D E and A B, and the

Weights hanging at the middle points F and C, we ſhall have two

Leavers like to thoſe before deſcribed, the Fulciments of which an-

ſwer to the points D and A. Whereupon the Force placed in B,

[Figure 15]

or if you will, in L, ſhall be able to ſu-

ſtain the Weight X, being the fourth

part of it: And if we adde another Pul-

ley above the other two, making the

Rope or Cord to paſs along L M N, trans-

ferring the Force L into N, it ſhall be

able to bear the ſame Weight gravitating

downwards, the upper Pulley neither aug-

menting or diminiſhing the Force, as hath

been declared. And we will likewiſe

note, that to make the: Weight aſcend the

four Ropes B L, E H, D I, and A G

ought to paſs, whereupon the Mover will

be to begin, as much as thoſe Ropes are

long; and yet nevertheleſs the Weight

ſhall move but only as much as the length

of one of them: So that we may ſay by

way of advertiſement, and for confirma-

tion of what hatn been many times ſpo-

ken, namely, that look with what proportion the Labour of the

Mover is diminiſhed, the length of the Way, on the contrary, is

encreaſed with the ſame proportion