Nipher—Graphical Algebra. 195 
purely geometrical methods, without assuming any 
known values for 2 and y. If a straight line is drawn 
upon a sheet of paper, the square of which that line is a 
side, and the cube of which that square is to be a face, can 
be drawn, without any measurement of the length of the 
original line in terms of the centimeter or the inch. 
Similarly if vertical and horizontal lines are drawn in- 
tersecting at a point which is to be common to the corners 
of two squares, having areas y2 and a we may mark 
upon these two axes points distant 1, 2 and y from the 
origin. These distances may have any length. The unit 
of length chosen may be any arbitrary and unknown 
length. 
Fig. 3. 
In Fig. 3 the unit when finally measured is found to 
be 0.5 em. and « and y to be 1.5 and 2.5 em. 
Draw a line through the point marked 1 on the ver- 
tical axis, to the point marked y on the horizontal axis. 
Lines drawn parallel to this line throngh points marked 
* and y on the vertical axis, will pass through points 
distant ay and y* from the origin on the horizontal axis. 
These distances may then be laid off upon the vertical 
axis and the operation may be continued. All of the 
lengths in the preceding diagram can be thus laid off. 
