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We determine barycentric coordinates of triangle centers in the ellipticplane. The main focus is put on centers that lie on lines whose euclidean limit(triangle excess --> 0) is the Euler line or the Brocard line. We alsoinvestigate curves which can serve in elliptic geometry as substitutes for theeuclidean nine-point-circle, the first Lemoine circle or the apolloniancircles.

On Centers and Central Lines of Triangles in the Elliptic Plane