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Some translations into non-euclidean geometry of classical theorems of planarprojective geometry are explored. The existence of some common triangle centersis dedeuced from theorems of Pascal and Chasles. Desargues' Theorem allows toconstruct a non-euclidean version of the Euler line and the nine-point circleof a triangle. The whole non-euclidean trigonometry (for triangles andgeneralizaed triangles) can be deduced from Menelaus' Theorem. A theorem ofCarnot about affine triangles implies the non-euclidean versions of anothertheorem of Carnot about euclidean triangles. Finally, it is given theprojective theorem which is hidden behind all the laws of cosines ofnon-euclidean triangles and generalized triangles.

Non-euclidean shadows of classical projective theorems