theorem :: MENELAUS:18

for A, B, C, A1, B1, C1 being Point of (TOP-REAL 2)
for lambda, mu, nu being Real st A,B,C is_a_triangle & A1 = ((1 - lambda) * B) + (lambda * C) & B1 = ((1 - mu) * C) + (mu * A) & C1 = ((1 - nu) * A) + (nu * B) & lambda <> 1 & mu <> 1 & nu <> 1 holds
( A1,B1,C1 are_collinear iff ((lambda / (1 - lambda)) * (mu / (1 - mu))) * (nu / (1 - nu)) = - 1 )