SO OUTLINES Of NATURAL PHILOSOPHY. 



66. If three forces which impel a body at the 

 same time, be proportional and parallel to the three 

 sides of a triangle, so that the angle contained by 

 any two of them is the supplement of the angle 

 contained by the corresponding sides of the triangle, 

 these forces will be in equilibrium. 



a. The converse of this is also true, viz. that if the 

 three forces are in equilibrium, they are propor- 

 tional to the sides of a triangle, &c. 



b. When three forces are in equilibrium, any two of 

 them is greater than the third. 



p. If three forces are in equilibrium, they are all in 

 the same plane. 



67. If there be an equilibrium between three 

 forces, AB, AC, AE, (fig. 3.) and if from any point 

 F, in the direction of one of them, perpendiculars, 

 FG, FH, be drawn to the other two, these perpen- 

 diculars will be inversely as the forces AC, AB, on 

 the directions of which they fall. 



For if FC, FB are drawn, the triangles FAC, FAB 

 are equal, as they are on the same base AF, and 

 have equal altitudes, the perpendiculars from B and 

 on the diagonal AE. Therefore FG x AC - 

 FH x AB, or FG : FH : : AB ; AC. 



68. If three forces are in equilibrium, and if 

 perpendiculars be drawn to their directions, inter- 

 secting one another in three points, the sides of the 

 triangle so formed will be proportional to the 



forces. 



