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[29. Figure]

we will ſet before you the preſent Contemplation. Suppoſe, there-

fore, that A B, C D, and E F are three Leavers; and that on the

middle points of them G, H, and I the Weight K doth hang in

common, ſo that every one of them ſhall ſuſtain the third part of

[Figure 16]

it: And becauſe the Power in

B, ſuſtaining with the Leaver

B A thependent Weight in G,

hapneth to be the half of the

ſaid Weight, and it hath been

already ſaid, that it ſuſtaineth

the third part of the Weight

K: Therefore the Moment of

the Force B is equal to half of

the third part of the Weight K; that is, to the ſixth part of it:

And the ſame ſhall be demonſtrated of the other Forces D and F:

From whence we may eaſily gather, that putting three Gyrils or

Rundles into the inferiour Pulley, and two or three into the upper-

[Figure 17]

moſt, we may multiply the Force accor-

ding to our ^{*} Senarius. And if we would

encreaſe it according to any other even

Number, the Gyrils of the Pulley below

muſt be multiplyed according to the half

of that Number, according to which the

Force is to be multiplyed, circumpoſing

the Rope about the Pulleys, ſo as that one

of the ends be faſtned to the upper Pul-

ley, and let the Force be in the other; as

in this Figure adjoyning may manifeſtly

be gathered.

fore, that A B, C D, and E F are three Leavers; and that on the

middle points of them G, H, and I the Weight K doth hang in

common, ſo that every one of them ſhall ſuſtain the third part of

[Figure 16]

it: And becauſe the Power in

B, ſuſtaining with the Leaver

B A thependent Weight in G,

hapneth to be the half of the

ſaid Weight, and it hath been

already ſaid, that it ſuſtaineth

the third part of the Weight

K: Therefore the Moment of

the Force B is equal to half of

the third part of the Weight K; that is, to the ſixth part of it:

And the ſame ſhall be demonſtrated of the other Forces D and F:

From whence we may eaſily gather, that putting three Gyrils or

Rundles into the inferiour Pulley, and two or three into the upper-

[Figure 17]

moſt, we may multiply the Force accor-

ding to our ^{*} Senarius. And if we would

encreaſe it according to any other even

Number, the Gyrils of the Pulley below

muſt be multiplyed according to the half

of that Number, according to which the

Force is to be multiplyed, circumpoſing

the Rope about the Pulleys, ſo as that one

of the ends be faſtned to the upper Pul-

ley, and let the Force be in the other; as

in this Figure adjoyning may manifeſtly

be gathered.

* Or in Sexcuple

proportion.

proportion.

Now paſſing to the Declaration of the

manner how to multiply the Force ac-

cording to the odd Numbers, and begin-

[Figure 18]

ning at the triple proportion: firſt, let us

propoſe the preſent Contemplation, as

that, on the underſtanding of which the

knowledge of all the Work in hand

doth depend. Let therefore the Leaver

be A B, its Fulciment A, and from the

middle of it, that is, at the point C let

the Grave D be hanged; and let it be ſu-

ſtained by two equal Forces; and let one of them be applied to the

point C, and the other to the term B. I ſay, that each of thoſe Powers

have Moment equal to the third part of the Weight D. For the

Force in C ſuſtaineth a Weight equal to it ſelf, being placed in the

ſame Line in which the Weight D doth hang & Gravitate: But the

manner how to multiply the Force ac-

cording to the odd Numbers, and begin-

[Figure 18]

ning at the triple proportion: firſt, let us

propoſe the preſent Contemplation, as

that, on the underſtanding of which the

knowledge of all the Work in hand

doth depend. Let therefore the Leaver

be A B, its Fulciment A, and from the

middle of it, that is, at the point C let

the Grave D be hanged; and let it be ſu-

ſtained by two equal Forces; and let one of them be applied to the

point C, and the other to the term B. I ſay, that each of thoſe Powers

have Moment equal to the third part of the Weight D. For the

Force in C ſuſtaineth a Weight equal to it ſelf, being placed in the

ſame Line in which the Weight D doth hang & Gravitate: But the