1of Direction A D H and A E I are Right Angles, we ſuppoſe that

theſe two Forces I and H weigh alike upon the Center A as if they

were nearer to the Center, at the equal Diſtances A B and A C,

and we alſo ſuppoſe the ſame if theſe very Forces were ſuſpended

both together in A, the Angles of Directions being ſtill Right

Angles.

theſe two Forces I and H weigh alike upon the Center A as if they

were nearer to the Center, at the equal Diſtances A B and A C,

and we alſo ſuppoſe the ſame if theſe very Forces were ſuſpended

both together in A, the Angles of Directions being ſtill Right

Angles.

PROPOSITION I.

Theſe Principles agreed upon, we will eaſily demonſtrate,

in Imitation of Archimedes, that upon a ſtraight Balance

the Forces, of which and of all their parts the Lines of Dire

ction are parallel to one another, and perpendicular to the Balance,

ſhall couuterpoiſe and make an Equilibrium, when the ſaid Forces

ſhall be to one another in Reciprocal proportion of their Arms,

which we think to be ſo manifeſt to you, that we thence ſhall de

rive the Demonſtration of this Univerſal Propoſition to which we

haſten.

in Imitation of Archimedes, that upon a ſtraight Balance

the Forces, of which and of all their parts the Lines of Dire

ction are parallel to one another, and perpendicular to the Balance,

ſhall couuterpoiſe and make an Equilibrium, when the ſaid Forces

ſhall be to one another in Reciprocal proportion of their Arms,

which we think to be ſo manifeſt to you, that we thence ſhall de

rive the Demonſtration of this Univerſal Propoſition to which we

haſten.

PROPOS. II.

In every Balance or Leaver, if the proportion of the Forces is

reciprocal to that of the Perpendicular Lines drawn from the

Center or Point of the Fulciment unto the Lines of Direction

of the Forces, drawing the one againſt the other, they ſhall make

an Equilibrium, and drawing on one and the ſame ſide, they ſhall

have a like Effect, that is to ſay, that they ſhall have as much Force

the one as the other, to move the Balance.

reciprocal to that of the Perpendicular Lines drawn from the

Center or Point of the Fulciment unto the Lines of Direction

of the Forces, drawing the one againſt the other, they ſhall make

an Equilibrium, and drawing on one and the ſame ſide, they ſhall

have a like Effect, that is to ſay, that they ſhall have as much Force

the one as the other, to move the Balance.

In this Figure let the Center of the Balance be A, the Arm A B,

bigger than A C, and firſt let the Lines of Direction B D, and E C

be perpendicular to the Arms A B and A C, by which Lines the

Forces D and E (which may be made of Weights if one will) do

draw; and that there is the ſame rate

225[Figure 225]

of the Force D to the Force E as there

is betwixt the Arm A C to the Arm

A B: the Forces drawing one againſt

the other, I ſay, that they will make an

Equilibrium upon the Balance C A B.

For let the Arm C A be prolonged

unto F, ſo as that AF may be equal to

A B: and let C A F be conſidered as a

ſtreight Balance, of which let the Center be A: and let there be

ſuppoſed two Forces G and H, of which and of all their parts the

Lines of Direction are parallel to the Line C E, and that the

Force G be equal to the Force D, and H to E, the one, to wit G,

bigger than A C, and firſt let the Lines of Direction B D, and E C

be perpendicular to the Arms A B and A C, by which Lines the

Forces D and E (which may be made of Weights if one will) do

draw; and that there is the ſame rate

225[Figure 225]

of the Force D to the Force E as there

is betwixt the Arm A C to the Arm

A B: the Forces drawing one againſt

the other, I ſay, that they will make an

Equilibrium upon the Balance C A B.

For let the Arm C A be prolonged

unto F, ſo as that AF may be equal to

A B: and let C A F be conſidered as a

ſtreight Balance, of which let the Center be A: and let there be

ſuppoſed two Forces G and H, of which and of all their parts the

Lines of Direction are parallel to the Line C E, and that the

Force G be equal to the Force D, and H to E, the one, to wit G,