Roberval, Gilles Personne de Letter to Fermat 1665, tr. Thomas Salusbury

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326
without impediment by this Line, the Force and the Line shall
take some certain position in which they shall rest, and the Line
shall of necessity be streight, let that Line be termed the Pendant,
or Line of Direction of the Force. And let the Point by which it is
fastned to the Fulciment be called the Point of Suspension: which
may sometimes be the Arm of a Leaver or Ballance; and then let
the Line drawn from the Center of the Fulciment of the Leaver
or Ballance to the Point of Suspension be named the Distance or
the Arm of the Force: which we suppose to be a Line fixed, and
considered without Gravity. Moreover, let the Angle comprehen­
ded betwixt the Arm of the Force and the Line of Direction be
termed the Angle of the Direction of the Force.

AXIOM I.

After these Definitions we lay down for a Principle, that in the
Leaver, and in the Ballance, Equal Forces drawing by Arms
that are equal, and at equall Angles of Direction, do draw equal­
ly. And if in this Position they draw one against the other they
shall make an Equilibrium: but if they draw together, or towards
the same part, the Effect shall be double.

If the Forces being equal, and the Augles of Direction also
equal, the Arms be unequal, the Force that shall be suspended at
the greater Arm shall work the greater Effect.

As in this Figure, the Center of the Ballance or Leaver being A,

if the Arms A B and A C are equal,
as also the Angles A B D, and A C E,
the equal Forces D and E shall
draw equally, and make an Equili­
brium. So likewise the Arm A F be­
ing equal to A B, the Angle A F G
to the Angle A B D, and the Force
G to D, these two Forces ^{*} G and D

draw equally; and in regard that
they draw both one way, the Effect
shall be double.

* In the M. S.
Copy it is C and
D.

In the same manner the Forces G and E shall make an Equilibri­
um; as also I and L shall counterpoise, if (being equal) the Arms
A K and A H, and the Angles A H T, and A K L be equal.

The same shall befall in the Forces P and R, if all things be
disposed as before. And in this case we make no other distinction
betwixt Weights and other Forces save only this, that Weights all
tend towards the Center of Grave Bodies, and Forces may be un­
derstood to tend all towards all parts of the Universe, with so
much greater or lesser Impetus than Weights. So that Weights and