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Looking once again at figure 2, the similarities between points and lines are striking. Their representations, for example, are identical, and the formula for the intersection of two lines is the same as the formula for the connecting line between two points. These observations are not the result of coincidence but are rather a result of the duality that exists between points and lines in the projective plane. In other words, any theorem or statement that is true for the projective plane can be reworded by substituting points for lines and lines for points, and the resulting statement will be true as well.

Stanley Birchfield