1drawing upon the Arm A F, and the other, to wit H, upon the Arm

A C: now, by the firſt Propoſition, G and H ſhall make an Equili

brium upon the Balance C A F: But, by the firſt Principle, the Force

D upon the Arm A B worketh the ſame effect as the Force G on

the Arm A F: Therefore the Force D upon the Arm A B maketh

an Equilibrium with the Force H upon A C: And the Force H

drawing in the ſame manner upon the Arm A C as the Force E, by

the ſame firſt Axiom, the Force D upon the Arm A B ſhall make an

Equilibrium with the Force E upon the Arm A C.

A C: now, by the firſt Propoſition, G and H ſhall make an Equili

brium upon the Balance C A F: But, by the firſt Principle, the Force

D upon the Arm A B worketh the ſame effect as the Force G on

the Arm A F: Therefore the Force D upon the Arm A B maketh

an Equilibrium with the Force H upon A C: And the Force H

drawing in the ſame manner upon the Arm A C as the Force E, by

the ſame firſt Axiom, the Force D upon the Arm A B ſhall make an

Equilibrium with the Force E upon the Arm A C.

Now, in the following Figure, let the Center of the Balance be

A, the Arms A B and A C, the Lines of Direction B D and C E

which are not Perpendicular to the Arms, and the Forces D and E

drawing likewiſe by the Lines of Direction, upon which Perpen

diculars are erected unto the Center A, that is A F upon B D, and

A G upon E C, and that as A F is to A G, ſo is the Force E to the

Force D: which Forces draw one

226[Figure 226]

againſt the other: I ſay, that they will

make an Equilibrium upon the Balance

C A B: For let the Lines A F and A G

be underſtood to be the two Arms of

a Balance G A F, upon which the For

ces D and E do draw by the Lines of

Direction F D and G E: Theſe Forces

ſhall make an Equilibrium, by the firſt

part of this ſecond Propoſition; but, by the ſecond Axiom, the Force

D upon the Arm A F hath the ſame Effect as upon the Arm A B:

Therefore the Force D upon the Arm A B maketh an Equilibrium

with the Force E upon the Arm A C.

A, the Arms A B and A C, the Lines of Direction B D and C E

which are not Perpendicular to the Arms, and the Forces D and E

drawing likewiſe by the Lines of Direction, upon which Perpen

diculars are erected unto the Center A, that is A F upon B D, and

A G upon E C, and that as A F is to A G, ſo is the Force E to the

Force D: which Forces draw one

226[Figure 226]

againſt the other: I ſay, that they will

make an Equilibrium upon the Balance

C A B: For let the Lines A F and A G

be underſtood to be the two Arms of

a Balance G A F, upon which the For

ces D and E do draw by the Lines of

Direction F D and G E: Theſe Forces

ſhall make an Equilibrium, by the firſt

part of this ſecond Propoſition; but, by the ſecond Axiom, the Force

D upon the Arm A F hath the ſame Effect as upon the Arm A B:

Therefore the Force D upon the Arm A B maketh an Equilibrium

with the Force E upon the Arm A C.

There are many Caſes, according to the Series of Perpendicu

lars, but it will be eaſie for you to ſee that they have all but one

and the ſame Demonſtration.

lars, but it will be eaſie for you to ſee that they have all but one

and the ſame Demonſtration.

It is alſo eaſie to demonſtrate, that if the Forces draw both on

one ſide they ſhall make the ſame Effect one as another, and that

the Effect of two together ſhall be double to that of one alone.

one ſide they ſhall make the ſame Effect one as another, and that

the Effect of two together ſhall be double to that of one alone.

OF THE

GEOSTATICKS.

GEOSTATICKS.

The Principle which you demand for the Geoſtaticks is,

That if two equal Weights are conjoyned by a right

Line fixed and void of Gravity, and that being ſo di

ſpoſed they may deſcend freely, they will never reſt till

that the middle of the Line, that is the Center of Gravitation of

the Ancients, unites it ſelf to the common Center of Grave Bodies.

That if two equal Weights are conjoyned by a right

Line fixed and void of Gravity, and that being ſo di

ſpoſed they may deſcend freely, they will never reſt till

that the middle of the Line, that is the Center of Gravitation of

the Ancients, unites it ſelf to the common Center of Grave Bodies.