On Menelaus and Ceva 6-figures in Moufang projective planes
Let \(A_ 1,A_ 2,A_ 3\) be non-collinear points of a projective plane, furthermore let \(A''_ i\) be the fourth harmonic point of \(A_ j,A_ k\), and \(A'_ i\) with \(\{i,j,k\}=\{1,2,3\}\), i.e. \(H(A_ jA_ k,A'_ iA''_ i)\). If the plane is desarguesian, then it is known that \(A'_ 1,A'_ 2,A'_ 3\) are collinear iff \(A_ 1A''_ 1,A_ 2A''_ 2,A_ 3A''_ 3\) are concurrent. The authors extend this result to Moufang planes. It is a pity that the authors did not illustrate their proof by figures.
scientific article; zbMATH DE number 3917105