Nipher — Graphical Algebra. 



197 



Figure 4 shows clearly the nature of the changes from 

 the conditions in Fig. 1. When the sides of the two 

 squares lying along the horizontal axis were increased to 

 y X y and # X # as in Fig. 2, the rectangle a of Fig. 1 was 



nL.o 



Fig. 4. 



made longer and became y X y in length, but its width 

 remained unchanged. It was still y — x. The rectangle b 

 of Fig. 1 was replaced by two rectangles whose lengths 

 were still x but in one of these rectangles, the width had 

 increased from y — x to y 2 — yx = y (y — x) and in the 

 other rectangle the width had increased from y — # to 

 x (y — x) =xy — x 2 . 



When the next change was made, from Fig. 2 to Fig. 4 

 the two rectangles to the right of x X x 2 in Fig. 2 did 

 not change in width but their length increased from x to 



