210 Trans. Acad. Sct. 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® — a", between the limits n= 2 and n= 20. 
Symbolic Triangle. 
y” eos Ee veel 
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? and 2. The sum of 
these terms is the combined length of the two strips. The 
product (y— 2) (y+) gives the value y?—2*. These 
symbols may represent any value greater than zer0- 
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 Vx. These symbols probably be- 
long to the left of y and x in Fig. 2, approaching nearer 
to the apex of the triangle. 
