Index
Pappus was a Greek geometer who lived around 300 AD. Pappus' Theorem is one of the most important in Projective Geometry (and is an important precursor to the Theorem of Desargues). For now, however, we will look at its existence in the euclidean plane.
Pappus' Theorem. If lines l and m meet at a point O, with P, Q and R in l and S, T and U in m, and if l(P,T) || l(Q,U), while l(Q,S) || l(R,T) then l(P,S) || l(Q,U).
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PROBLEM 23: Give a proof of this theorem in the euclidean plane. You'll need to remember some elementary facts from high school geometry about similar triangles.
Solution
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References: Batten, Bennett, Beutelspacher & Rosenbaum, Polster.
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