'[ 210 3 
join A I, turn the lever about till A I is perpendicular 
to the horizon, and in that pofition it will be at reft. 
For if HB be drawn parallel to I A, and FCH 
perpendicular to HB and I A, then CF : CH : Cl; 
C B, or as the fcale to the counterpoife ^ that is, per- 
pendiculars from the center oftmotion to the lines of 
direction are reciprocally as the forces applied, there- 
fore in that cafe the forces balance each other. 
Cor. Join AB and draw CG parallel to A I, and 
A G : GB : : Cl : C B, or as the fcale to the coonter- 
poife, therefore G is their center of gravity, which 
lying in a perpendicular to the horizon palling thro’ 
the center of motion, again Ihews the lever to be at 
reft. 
SCH.OLI u M. 
There are indeed two pofitions in which the lever 
will be at reft, one when the center of gravity is 
above, and another whqn it is belovv the center of 
motion ,j the latter only is conlider’d in what fol- 
lows. 
'Let the arms C A and CB be equal, let the 
3- -weight of the counterpoife be fixt, but that 
of the fcale variable j then if the fixt line CA 
(=:CB) reprefent the former, the variable lined 
will reprefent the latter. In the line C I, take C D 
=C A and join AD ; thro’ the center C, draw ECK 
parallel to AD, which therefore bifedts the angle of 
the lever ACB, and the part EC may ftand for the 
index or cock of the lever. Let CP be perpendicu- 
lar to the horizon, and ECP the angle of the index 
with that perpendicular is equal to D AI ; but AC K 
is the femi-fum, and DAI the femi-difference of the 
angles 
