A Demonstration of the Theorom of Pascal.
The five points - A, B, C, B', C' - move freely on the screen plane.
Point A' is constructed as a point on the conic determined by A, B, C, B' and C'.
A' moves on the conic as Point T moves along the line B'C'.
Points t1, t2, and t3 are determined as the intersection of lines connecting opposite sides of the Mystic Hexagon determined by A, B, C, A', B', C'.
The points t1, t2, t3 are colinear, says Pascal.
The screen plane is projected from:
- any point ( "E*" ) on the plane determined by the points t1, t3 and any third point ("pl1") not on the screen plane
- onto any plane parallel to the plane on which E* moves.
The images of the lines connecting the opposite side of the Mystic Hexagon are, as constructed, always parallel; the image of t1 or of t2 or of t3 cannot be made to appear, as the image points are colinear on the vanishing line of the construction.
Pascal, it appears, is correct.