Salusbury, Thomas, Mathematical collections and translations (Tome I), 1667

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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.
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

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.
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.
OF THE
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.