SOLUTION OF A DYNAMICAL PROBLEM. 325 



of motion of the plane ; and so on ; whether the motion of the 

 plane varies continuously or discontinuously, in direction, in 

 velocity, or in both. In the case proposed the motion of the 

 plane (by which throughout I mean the element thereof in con- 

 tact with the sphere) is always normal to a line drawn to a 

 fixed point. Therefore the motion of the centre is so too, 

 therefore the centre describes a circle whose centre is perpen- 

 dicularly over the said fixed point. Q.E.D. 



