1Weight 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,
15[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,
15[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