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[103] | 1 | ;; Prove Desargues Theorem.
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| 2 | ;;
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| 3 | ;; Desargues Theorem (Wikipedia): In a projective space, two triangles
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| 4 | ;; are in perspective axially if and only if they are in perspective
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| 5 | ;; centrally.
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| 6 |
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| 7 | (translate-theorem
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| 8 | (
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| 9 | ;; If
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| 10 |
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| 11 | ;; Triangles are in perspective centrally
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| 12 | ;; O is the center of projectivity
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| 13 | (collinear A0 A1 O)
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| 14 | (collinear B0 B1 O)
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| 15 | (collinear C0 C1 O)
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| 16 |
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| 17 | ;; and X, Y, Z are points on the axis of projectivity
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| 18 | (collinear A0 C0 Y)
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| 19 | (collinear B0 C0 X)
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| 20 | (collinear A0 B0 Z)
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| 21 |
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| 22 | (collinear A1 C1 Y)
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| 23 | (collinear B1 C1 X)
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| 24 | (collinear A1 B1 Z)
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| 25 | )
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| 26 | ;; Then
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| 27 | ((collinear X Y Z)
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| 28 |
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| 29 | ;; What if X Y X are at infinity?
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| 30 | ;; Or one of the triangles is degenerate?
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| 31 |
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| 32 | ;;(identical-points A0 C0)
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| 33 | ;;(identical-points A0 B0)
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| 34 | ;;(identical-points B0 C0)
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| 35 |
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| 36 | ;;(identical-points A1 C1)
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| 37 | ;;(identical-points A1 B1)
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| 38 | ;;(identical-points B1 C1)
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| 39 |
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| 40 | )
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| 41 | ;; :order #'grlex>
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| 42 | )
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| 43 |
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