On Machines in General. 137 



applied^ while others form obtuse angles with their points. 

 This being granted, J shall call the former rnoi ing or soliciting 

 forces; and the olhers resisting forces : for instance, it a 

 person raises a weight by means of a lever, a pulley, a screw, 

 &c., it is clear that the weight and the velocity of the weight 

 necessarily form by their concurrence an obtuse angle; 

 otherwise it is evident that the weight would descend m 

 place of ascending ; but the vis matrix and its velocity torm 

 an acute angle : thus, according to our definition, the weight 

 will be the resisting force, and the eflbrt of the person wilj 

 be the soliciting force : it is evident, in short, that the latter 

 tends to favour the actual movement of the machine, while 

 the other opposes it. 



We shall observe that the soliciting forces may be di- 

 rected in the same ratio with their velocities, since then the 

 angle formed by their concurrence is null, and consequently 

 acute, and the resisting forces may act in the direction pre- 

 cisely opposite to that of their velocities, since then the 

 angle formed by their concurrence is 180% and consequently 

 obtuse. 



It is also to be remarked, that any force which is soli- 

 citing might become resisting if the movement should 

 change; that any force which is resisting at a certain in- 

 stant, may become soliciting at another instant ; and last- 

 ly, in order to judge ot it at each instant, we must consider 

 the angle which it makes with the velocity of the point 

 where we suppose it applied : if this angle be acute, the 

 force will be solicilinii; and if it be obtuse, it will be resist- 

 ing, until the angle in question changes. We see from this, 

 that if we make any system of power assume a geometrical 

 movement, each of them will be soliciting or resisting in 

 re-pect of this geometrical movement, accordingly as the 

 angle formed by this force and by u& geometrical velocity 

 shall be acute or obtuse. 



XXXII. If a force P be moved with the velocitv ?/, and 

 the angle formed by the concurrence ot n and F be 2, the 

 quantity P cosine zud t, in 'v Inch d t expresMS the clement 

 of time, will be named momentum 0} activiti/, consumed 

 by the force P during (i /; i.e. the momentum ot activity 



consumed 



