( 1 1 6 ) 
by moving the Balance into the Pofition a b ; which 
fhews the Velocity of P to be the perpendicular Line 
e a, and the Velocity of B will be the perpendicular 
Line bg: For if the Weights P and W are equal, 
and alfo the Lines e a and b g, their Momenta made 
up of e a multiplied into W, and multiplied into 
P, will be equal, as will appear by their deftroying 
one another in making an jEquilibrium. But if the 
Body W was removed to M, and fufpended at the 
Point D, then its Velocity being only/ d, it would 
be over-balanc’d by the Body P j becaufe/i multi- 
plied into M, would produce a lefs Momentum than 
P multiplied into b g. 
As the Arcs A a,B b, and D d defcribed by the Ends 
ofthe Balance orPointsof Sufpenfion are proportionable 
to their Sines e a % g b, and d f y as alfo the Radii or 
Diftances C A, C B, and C D ; in the Cafe of this 
common fort of Balance, the Arcs defcribed by the 
Weights, or their Points of Sufpenlion, or the Di- 
ftances from the Center may be taken for the Veloci- 
ties of the Weights hanging at A, B, or D ; and there- 
fore the afting Force of the Weights will be recipro- 
cally as their Diftances from the Center. 
Scholium. 
The Diftances from the Center are taken here 
for theVelocities of the Bodies, only becaufe they are 
proportional to the Lines e a, b g,. and/ d, which are 
the true Velocities. For there are a great many Cafes 
wherein the Velocities are neither proportionable to 
the Diftances from the Center of Motion of a Machine, 
nor- 
