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Connection of two imaginary points

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