QUESTIONS AND PROBLEMS^311
FIGURE 23. The four-line locus. If a point moves so that the
product of its distances to two lines bears a constant ratio to the
product of its distances to two other lines, it must move in a conic.
In this illustration, two conies satisfy the condition: one an ellipse,
the other a hyperbola.
10.9. In the Pythagorean tradition there were two kinds of mathematical activity.
One kind, represented by the attempt to extend the theory of the transformation of
polygons to circles and solid figures, is an attempt to discover new facts and enlarge
the sphere of mathematics—to generalize. The other, represented by the discovery
