Connection of two imaginary points

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