Nipher — Graphical Algebra. 



199 



The difference between these areas y 9 and x 9 or 

 y 9 — x 9 may be expressed by dividing by y — x, and 

 multiplying this factor into the terms of the quotient. 



y 9 — x 9 = y s (y — x)-\-y 7 x(y — x) 



+ y 6 oc 2 (y — x) -j- y 5 x s (y — x) 

 + y 4 x 4 (y — x)+ y 3 x 5 (y — x) 

 + y 2 x 6 (y — x) + y x 1 (y — x) 

 + x 8 (y — x) (4) 



Fig. 5. 



The first four terms may be written 

 y 5 Xy 3 (y — x) or y 5 (y* —y 3 x) 

 y 5 X y 2 x (y — x) or y 5 (y 3 x — y 2 x 2 ) 

 y 5 X y x 2 (y — x) or y 5 (y 2 x 2 — y x 3 ) 

 y 5 X x 3 (y — x) or y 5 (y x 3 — x*) 



These terms represent the areas of four rectangles, 

 marked a, b, c and d in Fig. 5. They have a common 

 length y s . 



