Archimedes Texts

327
their parts do draw by Lines of Direction, which all concur in one
and the same Point; and Forces and their parts may be understood
to draw in such sort that all the Lines of Direction are parallel to
each other.

In the second place, we suppose that a Force and its Line of Di
rection abiding alwaies in the same position, as also the Center
of the Ballance or Leaver, be the Arm what it will that is drawn
from the Center of the Ballance to the Line of Direction, the
Force drawing alwaies in the same fashion, will alwaies produce
the same Effect.

As, in this second Figure, the Center of the Ballance being A,
the Force B, and the Line of Direction

B F prolonged, as occasion shall re
quire, in which the Arms A G, A C, and
A F do determine, in this position let
the Line B F be fastned to the Arm
A F, or A C, or to another Arm drawn
from the Center A to the Line of Di
rection ^{*} B F: we suppose that this

Force B shall alwaies work the same
Effect upon the Ballance. And if
drawing by the Arm A C it make an
Equilibrium with the Force D drawing by the Arm A E, when
ever it shall draw by the Arms A F or A G, it shall likewise make
an Equilibrium with the Force D drawing by the Arm A E. This
Principle although it be not expresly found in Authors, yet it is
tacitly supposed by all those that have writ on this Argument, and
Experience constantly confirmeth it.

* In the Original
it is writ, but by
the mistake of
the Transcriber,
a la ligue de di
rection A F.

If the Arms of a Ballance or Leaver are directly placed the one to
the other, and that being equal they sustain equal Forces, of which
the Angles of Direction are Right An

gles, these Forces do alwaies weigh
equally upon the Center of the Bal
lance, whether that they be near to the
same Center, or far distant, or both
conjoyned in the Center it self; as in
this Figure the Ballance being E D,
the Center A, the equal Arms A D
and A E, let us sustain equal Forces H and I, of which the Angles