400 DEMO NSTRJ T ION of the 



E, and fufpend the weight G from B ; then, fince the equili- 

 brium is flill 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 i \ 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 F ' f 

 fucceifively double, triple, &c. of FB, it may in like manner be 

 fhewn, that, in thefe cafes, the proportion holds true. 



Lemma. 



If any weight BCcb, (fig. 2. No. J.J, of uniform shape and density, 

 is placed on a lever A <p, whose fulcrum is <p, it has the same ten- 

 dency to turn the lever round <p, as if it were suspended from a 

 point G, so taken that b G — G c. 



If 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 <p. But the weight W, acting upwards at the 

 point G, has the fame power to turn the lever round <p, as an 

 equal weight w, acting downwards at G. Confequently the 

 tendency of the weight BC to turn the lever round <p, is the 

 feme as the tendency of an equal weight w, acting downwards 

 atG. 



Prop. II. 



If two forces applied to a lever, and acling 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. 



Let A<pd, (fig. 2. No. 2.) be a lever whofe fulcrum is <p, and 

 let it be loaded with a weight BD d b of uniform fhape and den- 



fity. 



