# Connection of two imaginary points

Author:
Ben Geels
Given two imaginary points. Construct the line connecting the points. The two points are each one of the double points of an elliptic involution on a line. These evolutions are respresented by an arrow on the carrier of these points. Vector A and vector B (in red) A semi circle is constructed on the amplitude of the involutions. On lina a: Take the intersection of a and b as . Draw and perpendicular. and are inner and outer bisectrixes of triangle The four points are two pairs of points in the given involution. Likewise for point B and the four points and The two ranges of four points X an Y are perspective both from M and from N
In N four lines determine an elliptic involution, of wich the two imaginary double lines are the lines that connect the imaginary points A and B. Because The elliptic involution on line a has two double points and , (Likewise B on b.) we have four connecting imaginary lines. Two in N: and and two in M: and