Nipher—Graphical Algebra. 203 
significance as when the 3d power is so represented. 
Also any numerical value raised to any power, may be 
represented in space of two dimensions or as a straight 
line. 
Kq. (6) may also be represented by a diagram analo-. 
gous to that in Fig. 4. There will be three strip areas 
across the top of the square x°, instead of the two areas 
aand 6. Their common length is y*. There will be three 
rectangles replacing c and d of Fig. 4, the height of each 
being «#*. The width of these strips can be found by 
dividing these factors into the terms of Eq. 6. 
All of the terms of the developed function y® — a® can 
be identified in a diagram, in which y and @ are laid off 
on the vertical axis, and y®* and 2? are laid off along 
the horizontal axis. The strip a of Fig. 1 will increase in 
length as n increases, but its width y—a will remain 
constant. It will be represented by the first term. Below 
this strip, will be a series of rectangles having a common 
height x. They will represent the second and succeeding 
terms of the developed function. 
The value of (y-+2)* may be represented by an area. 
Assume for example y=5 and «=3. Construct a 
Square whose sides are (y+)? =64. Divide the sides 
into segments whose lengths are y? = 25, 27y—30 and 
«*=9. Draw lines across the square through the points 
Separating these segments. The square (y+ )* will 
then be divided into nine rectangles, representing the 
six terms of the expanded binominal (y-+2)*. If x be 
considered negative, some of these rectangles must be 
considered negative in value. Their location in the 
Square will be a matter of interest to the young experl- 
menter. If in addition y=a, the sum of the positive 
and negative areas will be equal. 
Issued May 9, 1918 
