I want to prove Pappus' Theorem using affine combinations. The theorem states that given two lines $l_1$ and $l_2$ in the plane and six points $A_i,B_i,C_i \in l_i (i=1,2)$ show that the points $A_3= B_1 C_2 \cap B_2 C_1$, $B_3 = A_1 C_2 \cap A_2 C_1$ and $C_3= A_1B_2 \cap A_2B_1$ are collinear.
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