210 



Trans. Acad. Sci. of St. Louis. 



Fig. 2 is a triangle of terms needed in the construction 

 of any diagram similar to that forming Fig. 1, for the 

 function y n — x n , between the limits n = 2 and n = 20. 



Fig. 2. 



Symbolic Triangle. 



y n — x n . 



In the left vertical column are the lengths y and x. The 

 difference between these two lengths, is the width of the 

 strips between the two squares y 2 and x 2 . The sum of 

 these terms is the combined length of the two strips. The 

 product (y — x) (y -\- x) gives the value y 2 — x 2 . These 

 symbols may represent any value greater than zero. 

 The distance between any two points in space cannot be 

 less than zero. In the equation last above written they 

 are replaced by Vy and V#. These symbols probably be- 

 long to the left of y and x in Fig. 2, approaching nearer 

 to the apex of the triangle. 



