(Pappus's Theorem) Assume that T0, U0, and V0 are collinear and that T1, U1, and V1 are collinear. Consider these three points: (i) the intersection V2 of the lines T0U1 and T1U0, (ii) the intersection U2 of the lines T0V1 and T1V0, and (iii) the intersection T2 of U0V1 and U1V0.
(a) Draw a (Euclidean) picture.
(b) Apply the lemma used in Desargue's Theorem to get simple homogeneous coordinate vectors for the T's and V0.
(c) Find the resulting homogeneous coordinate vectors for U's (these must each involve a parameter as, e.g., U0 could be anywhere on the T0V0 line).
(d) Find the resulting homogeneous coordinate vectors for V1.
(e) Find the resulting homogeneous coordinate vectors for V2. (It also involves two parameters.)
(f) Show that the product of the three parameters is 1.
(g) Verify that V2 is on the T2U2 line.