Verging (or insertion) is a characteristic use of a moving marked ruler. Given a point and two straight lines and , verging through with respect to and determines two points and that are one unit apart and such that is on a straight line through and , with on and on . By use of verging, geometric constructions beyond those allowed by the Euclidean straightedge and compass can be carried out. For example, trisection of an angle.

Verging through the point with respect to the lines with equations and gives coordinates of in terms of , and as the roots of a fourth-degree polynomial.

This Demonstration is based on [1, pp. 124, 125].

Reference

[1] G. E. Martin, Geometric Constructions, NewYork: Springer, 1998.