EXPLORING DESARGUES' THEOREM
Desargues Theorem (p. 29, Tondeur): Let line(AA'), line(BB'), and line(CC') be three distinct and concurrent lines with D as the common intersection point. Let points A" = the intersection of line(BC) and line(B'C'), the intersection B"=line(AC) and the intersection of line(A'C'), and C"=line(AB) and line(A'B') be the intersection points of pairs of corresponding lines as indicated (assuming none of these lines are parallel). Then A", B", and C" are collinear.
From another perspective:
Desargues Theorem states the following:
Two projective triangles are perspective with respect to a point (P) if and only if they are perspective with respect to a line. (XYZ) (Wallace & West p. 360). This is illustrated in the following java applet.
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