Lines [math]a,b,c[/math] are the sides of the triangle [math]ABC[/math] and [math]P[/math] is a point not on any of them. Then [math]p[/math] is a line not though any of [math]A,B,C[/math]. The point [math]P[/math] and line [math]p[/math] determine 6 points on the sides of the triangle: [math]P_a=a\cdot AP, P_b = b\cdot BP, P_c = c\cdot CP, A_p= a\cdot p, B_p = b\cdot p, C_p = c\cdot p[/math].