BERKELEY'S ANALYST (i734) 79 



I answer, I can conceive Velocity and Motion in a 

 Point of Space ; that is, without any assignable 

 Length or Extension described by it . . . for . . . 

 if a cause acts continually upon a given Thing . . . 

 there must be a continuai Increase of its Velocity : 

 the Velocity cannot be the same in any two 

 difìferent Points," as in the case of falling bodies, 

 Referring to A^ + B^, Walton continues : ''I agree 

 with him that nothing is the Product of nothing 

 multipl'd by something ; but must know what he 

 means by the vanishing of the Gnomon ^ and Sum 

 of the two Rectangles . . . before I give him a 

 direct Answer. If by vanishing he means that 

 they vanish and become nothmg as Areas, I grant 

 they do ; but absolutely deny, upon such an Evan- 

 escence of the Gnomon and Sum of the two 

 Rectangles by the moving back of the Sides of the 

 Gnomon till they come to coincìde with those of 

 the Rectangle, that nothing remains. For there 

 stili remain the moving Sides, which are now 

 become the Sides of the Rectangle, . . . the 

 Motion of the Gnomon is the same with the Sum of 

 the Motions of the Two Rectangles, when they 

 evanesce, and are converted into the two Sides of 

 the Rectangle AB. If a point moves forward to 

 generate a Line, and afterwards the same Point 

 moves back again to destroy the Line with the very 

 same Degrees of Velocity, in ali Parts of the Line 



^ If a parallelogram is extended in length and breadth and if the 

 originai parallelogram be removed, the remaining figure is called the 

 gnomon. 



