OF THE LAWS OF MOTION. 153 



5. I now proceed to shew in what manner the Laws of Motion 

 depend upon these three axioms. 



Bodies move in lines straight or curved, they move more or less 

 rapidly, and their motions are variously affected by other bodies. This 

 succession of occurrences suggests the conceptions of certain properties 

 or attributes of the motions of bodies, as their direction and velocity, 

 by means of which the laws of such occurrences may be exprest. 

 And these properties or attributes are conceived as belonging to the 

 body at each j)^^^^ of its motion, and as changing from one point to 

 another. Thus the body, at each point of its path, moves in a 

 certain direction, and with a certain velocity. 



These properties, direction and velocity for instance, are subject 

 to the rule stated in the first axiom : they cannot change without 

 some cause ; and when any changes in the motions of a body are 

 seen to depend on its position relative to another body or to any part 

 of space, such other body, or such other part of space, is said to 

 exert a Jbrce upon the moving body. Also the force exerted upon 

 the moving body is considered to be of a certain value at each 

 point of the body's motion ; and though it may change from one point 

 to another, its changes must depend upon the position of the points 

 only, and not upon the velocity and direction of the moving body. 

 For the force which acts upon the body is conceived as a property of 

 the bodies, or points, or lines, or surfaces among which the moving body 

 is placed; the force at all points therefore depends upon the position 

 with regard to the bodies and spaces of which the force is a property ; 

 but remains the same, whatever be the circumstances of the body 

 moved. The circumstances of the body moved cannot be a cause 

 which shall change the force acting at any point of space, although 

 they may alter the effect which that force produces upon the body. 

 Thus, gravity is the same force at the same point of space, whether it 

 have to act upon a body at rest or in motion ; although it still remains 

 to be seen whether it will produce the same effect in the two cases. 



6. This being established, we can now see of what nature the 

 laws of motion must be, and can state in a few words the proofs 



