MECHANICS. 71 



sion of the equilibrium, were to happen, are pro- 

 perly denominated virtual. 



c. The different cases of the lever, whether it be 

 straight or crooked, and the forces perpendicular or 

 oblique, are all comprehended in the preceding pro- 

 positions. The case of oblique forces admits of a 

 very concise expression, in terms of the angles. 



1 28. If two oblique forces be applied to the ex- 

 tremities of a straight lever, there will be an equi- 

 librium between them, if they be inversely as the 

 lengths of the arms by which they act, multiplied 

 into the sines of the angles which their directions 

 make with the lever. 



It is evident that this proposition is general, and com- 

 prehends the case of perpendicular forces. 



129. If a beam of any kind be kept in equilibrium 

 by three forces applied to different points in it, these 

 forces must either be parallel, or must converge to 

 the same point. 



a. If at the point to which the three lines converge, we 

 take parts in those lines proportional to the forces, 

 they will form the sides and the diagonal of a pa- 

 rallelogram ; and if at the point in which this dia- 

 gonal intersects the beam, we suppose a fulcrum to 

 i>e placed ; the beam will be converted into an ordi- 



narv 



