1the Weight to be at one extream, and the Force at the other, and

the Fulciment placed in ſome point between the extreams: but we

may make uſe of the Leaver another way, yet, placing, as we ſee,

the Fulciment in the extream A, the Force in the other extream C,

and ſuppoſing the Weight D to hang by ſome point in the midſt,

189[Figure 189]

as here we ſee by the point B, in

this example it's manifeſt, that if

the Weight did hang at a point

Equi-diſtant from the two ex

treams A and C, as at the point F,

the labour of ſuſtaining it would

be equally divided betwixt the

two points A and C, ſo that half

the Weight would be felt by the

Force C, the other half being ſu

ſtained by the Fulciment A: but if the Grave Body ſhall be hanged

at another place, as at B, we ſhall ſhew that the Force in C is ſuffi

cient to ſuſtain the Weight in B, as it hath the ſame proportion

to it, that the Diſtance, A B hath to the Diſtance A C. For De

monſtration of which, let us imagine the Line B A to be continued

right out unto G, and let the Diſtance B A be equall to A G, and

let the Weight hanging at G, be ſuppoſed equall to D: It is ma

nifeſt, that by reaſon of the equality of the Weights D and E, and

of the Diſtances G A and A B, the Moment of the Weight E

ſhall equalize the Moment of the Weight D, and is ſufficient to

ſuſtain it: Therefore whatever Force ſhall have Moment equall to

that of the Weight E, and that ſhall be able to ſuſtain it, ſhall be

ſufficient likewiſe to ſuſtain the Weight D: But for ſuſtaining the

Weight E, let there be placed in the point C ſuch a Force, whoſe

Moment hath that proportion to the Weight E, that the Diſtance

G A hath to the Diſtance A C, it ſhall be ſufficient to ſuſtain it:

Therefore the ſame Force ſhall likewiſe be able to ſuſtain the

Weight D, whoſe Moment is equall to the of E: But look what

Proportion the Line G A hath to the Line A C; and A B alſo hath

the ſame to the ſaid A C, G A having been ſuppoſed equall to A B:

And becauſe the Weights E and D are equall, each of them ſhall

have the ſame proportion to the Force placed in C: Therefore the

Force in C is concluded to equall the Moment of the Weight D,

as often as it hath unto it the ſame proportion that the Diſtance B A

hath to the Diſtance C A. And by moving the Weight, with the

Leaver uſed in this manner, it is gathered in this alſo, as well as in

the other Inſtruments, that what is gained in Force is loſt in Velo

city: for the Force C raiſing the Leaver, and transferring it to A I,

the Weight is moved the Space B H, which is as much leſſer than

the Space C I paſſed by the Force, as the Diſtance A B is leſſer

the Fulciment placed in ſome point between the extreams: but we

may make uſe of the Leaver another way, yet, placing, as we ſee,

the Fulciment in the extream A, the Force in the other extream C,

and ſuppoſing the Weight D to hang by ſome point in the midſt,

189[Figure 189]

as here we ſee by the point B, in

this example it's manifeſt, that if

the Weight did hang at a point

Equi-diſtant from the two ex

treams A and C, as at the point F,

the labour of ſuſtaining it would

be equally divided betwixt the

two points A and C, ſo that half

the Weight would be felt by the

Force C, the other half being ſu

ſtained by the Fulciment A: but if the Grave Body ſhall be hanged

at another place, as at B, we ſhall ſhew that the Force in C is ſuffi

cient to ſuſtain the Weight in B, as it hath the ſame proportion

to it, that the Diſtance, A B hath to the Diſtance A C. For De

monſtration of which, let us imagine the Line B A to be continued

right out unto G, and let the Diſtance B A be equall to A G, and

let the Weight hanging at G, be ſuppoſed equall to D: It is ma

nifeſt, that by reaſon of the equality of the Weights D and E, and

of the Diſtances G A and A B, the Moment of the Weight E

ſhall equalize the Moment of the Weight D, and is ſufficient to

ſuſtain it: Therefore whatever Force ſhall have Moment equall to

that of the Weight E, and that ſhall be able to ſuſtain it, ſhall be

ſufficient likewiſe to ſuſtain the Weight D: But for ſuſtaining the

Weight E, let there be placed in the point C ſuch a Force, whoſe

Moment hath that proportion to the Weight E, that the Diſtance

G A hath to the Diſtance A C, it ſhall be ſufficient to ſuſtain it:

Therefore the ſame Force ſhall likewiſe be able to ſuſtain the

Weight D, whoſe Moment is equall to the of E: But look what

Proportion the Line G A hath to the Line A C; and A B alſo hath

the ſame to the ſaid A C, G A having been ſuppoſed equall to A B:

And becauſe the Weights E and D are equall, each of them ſhall

have the ſame proportion to the Force placed in C: Therefore the

Force in C is concluded to equall the Moment of the Weight D,

as often as it hath unto it the ſame proportion that the Diſtance B A

hath to the Diſtance C A. And by moving the Weight, with the

Leaver uſed in this manner, it is gathered in this alſo, as well as in

the other Inſtruments, that what is gained in Force is loſt in Velo

city: for the Force C raiſing the Leaver, and transferring it to A I,

the Weight is moved the Space B H, which is as much leſſer than

the Space C I paſſed by the Force, as the Diſtance A B is leſſer