400 DEMONSTRATION of the 
E, and fufpend the weight G from B; then, fince the equili- 
brium is ftill preferved after thefe two fubftitutions, we have a 
weight C, of one pound, acting at the extremity of the arm AF, 
in equilibrio with the weights D and G, which together make 
two pounds, acting at the extremity of the arm FB. But FA is 
to FB as 2 is to 1; therefore an equilibrium takes place, when 
the weights are reciprocally proportional to the arms, in the 
particular cafe when the arms are as 2 to 1. By making Ff 
fucceflively double, triple, &c. of FB, it may in like manner be 
fhewn, that, in thefe cafes, the propofition holds true. 
LEMMA. 
If any weight BC cb, (fig. a. No. 1.), of uniform shape and density, 
is placed on a lever A 0, whose fulcrum is 9, it has the same ten- 
dency to turn the lever round 9, as if it were suspended from a 
point G, so taken that bG =Ge. 
Ir a weight W, of the fame magnitude with BC, acts upwards 
at the point G, it will be in equilibrium with the weight BC, 
and will therefore deftroy the tendency of that weight to turn 
the lever round g. But the weight W, acting upwards at the 
point G, has the fame power to turn the lever round 9, as an 
equal weight w, acting downwards at G. Confequently the 
tendency of the weight BC to turn the lever round 9, is the 
fame as the tendency of an equal weight w, acting downwards 
at G, 
Prop. II. 
If two forces applied to a lever, and acting at right angles to it, 
have the same tendency to turn the lever round its centre of mo- 
tion, they are reciprocally proportional to the distances of the points 
at which they are applied from the centre of motion. 
Ler A od, (fig. 2. No. 2.) be a lever whofe fulcrum is 9, and 
let it be loaded with a weight BD dé of uniform fhape and den- 
fity. 
