## The cross ratio
is first of all a relation between a pair of points
P and a pair of lines _{1}, P_{2}g. In homogeneous coordinates, it has the value_{3}, g_{4}D[P_{1},P_{2};g_{3}, g_{4}] =
(<g _{3}P_{1}>/<g_{3}P_{2}>)/(<g_{4}P_{1}>/<g_{4}P_{2}>) and is projectively invariant. When one understands the lines as connection of points P with some point _{3}, P_{4}S, we obtain a value for two pairs of points, which does not depend on the choice of S, when P are collinear with _{3}, P_{4}P. When one understands the points _{1}, P_{2}P
as intersection of lines _{1}, P_{2}g with some line _{1}, g_{2}s, we obtain a value for two pairs of lines, which does not depend on the choice of s, when g are concurrent with _{1}, g_{2}g.
_{3}, g_{4}
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