[alogo] A theorem of Steiner-4

Steiner Lehrsatz 4, bd I, p. 177
Apply three times the theorem of Pappus and get three lines (GHI), (KLM) and (NOP). They pass all through the same point.

[0_0] [0_1] [0_2]
[1_0] [1_1] [1_2]

(GHI) is invariant under the homography, constructible through the tool [ Transforms \ Homography 1 conic _ ], which maps A, B, C to F, E, D correspondingly. Analogous statements hold for the other lines (KLM) and (NOP) too.

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