Let a1, a2, a3 denote the sides α1, α2, α3 the angles and A1, A2, A3 the vertices of a triangle in the Euclidean plane. A point P, whose distances from the sides α1, α2, α3 are in the ratio p1: p2: p3 will be denoted by P[p1]. p1, p2, p3 are called the normal coordinates of P. Thus the unit point E[l] is the incentro of the triangle, S[cosec α1] is the centroid, M[cos α1] is the circumcentre, and H[sec α1] is the orthocentre. Similarly, using normal line coordinates, we have l0 [l] is the unit line, l∞[sin α1] is the line at infinity and lH[cos α1] is the axis of the altitudes.