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Theſe things determined and ſuppoſed, we come to the explica-

tion of a Principle, the moſt common and materiall of the greater

part of Mechanick Inſtruments: demonſtrating, that unequall

Weights weigh equally when ſuſpended by [or at] unequal Diſtan-

ces, which have contrary proportion to that which thoſe weights

are found to have, See the Demonſtration in the beginning of the

ſecond Dialogue of Local-Motions.

tion of a Principle, the moſt common and materiall of the greater

part of Mechanick Inſtruments: demonſtrating, that unequall

Weights weigh equally when ſuſpended by [or at] unequal Diſtan-

ces, which have contrary proportion to that which thoſe weights

are found to have, See the Demonſtration in the beginning of the

ſecond Dialogue of Local-Motions.

Now being that Weights unequall come to acquire equall

Moment, by being alternately ſuſpended at Diſtances that

have the ſame proportion with them; I think it not fit to

over paſſe with ſilence another congruicy and probability, which

may confirm the ſame truth; for let the Ballance A B, be conſide-

red, as it is divided into unequal parts in the point C, and let the

Weights be of the ſame propor-

[Figure 2]

tion that is between the Diſtan-

ces B C, and C A, alternately

ſuſpended by the points A, and

B: It is already manifeſt, that

the one will counterpoiſe the

other, and conſequently, that

were there added to one of them

a very ſmall Moment of Gravity, it would preponderate, raiſing

the other, ſo that an inſenſible Weight put to the Grave B, the

Ballance would move and deſcend from the point B towards E,

and the other extream A would aſcend into D, and in regard that

to weigh down B, every ſmall Gravity is ſufficient, therefore not

keeping any accompt of this inſenſible Moment, we will put no

difference between one Weights ſuſtaining, and one Weights

moving another. Now, let us conſider the Motion which the

Weight B makes, deſcending into E, and that which the other

A makes in aſcending into D, we ſhall without doubt find the

Space B E to be ſo much greater than the Space A D, as the Di-

ſtance B C is greater than C A, forming in the Center C two an-

gles D C A, and E C B, equall as being at the Cock, and conſe-

quently two Circumferences A D and B E alike; and to have the

ſame proportion to one another, as have the Semidiameters B C,

and C A, by which they are deſcribed: ſo that then the Velocity

of the Motion of the deſcending Grave B cometh to be ſo much

Superiour to the Velocity of the other aſcending Moveable A, as

the Gravity of this exceeds the Gravity of that; and it not being

Moment, by being alternately ſuſpended at Diſtances that

have the ſame proportion with them; I think it not fit to

over paſſe with ſilence another congruicy and probability, which

may confirm the ſame truth; for let the Ballance A B, be conſide-

red, as it is divided into unequal parts in the point C, and let the

Weights be of the ſame propor-

[Figure 2]

tion that is between the Diſtan-

ces B C, and C A, alternately

ſuſpended by the points A, and

B: It is already manifeſt, that

the one will counterpoiſe the

other, and conſequently, that

were there added to one of them

a very ſmall Moment of Gravity, it would preponderate, raiſing

the other, ſo that an inſenſible Weight put to the Grave B, the

Ballance would move and deſcend from the point B towards E,

and the other extream A would aſcend into D, and in regard that

to weigh down B, every ſmall Gravity is ſufficient, therefore not

keeping any accompt of this inſenſible Moment, we will put no

difference between one Weights ſuſtaining, and one Weights

moving another. Now, let us conſider the Motion which the

Weight B makes, deſcending into E, and that which the other

A makes in aſcending into D, we ſhall without doubt find the

Space B E to be ſo much greater than the Space A D, as the Di-

ſtance B C is greater than C A, forming in the Center C two an-

gles D C A, and E C B, equall as being at the Cock, and conſe-

quently two Circumferences A D and B E alike; and to have the

ſame proportion to one another, as have the Semidiameters B C,

and C A, by which they are deſcribed: ſo that then the Velocity

of the Motion of the deſcending Grave B cometh to be ſo much

Superiour to the Velocity of the other aſcending Moveable A, as

the Gravity of this exceeds the Gravity of that; and it not being