= Pascal's theorem
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For six distinct points on an irreducible <conic> in the complex <projective plane>, the three intersections of opposite sides of the resulting hexagon are collinear. Form the two cubics given by the products of alternate side equations. They meet at the six <conic> points and the three opposite-side intersections. Applying <residual intersection through a curve pencil> with degrees three and two places the last three points on a line. This is the <conic> counterpart of <Pappus's hexagon theorem> for two lines.
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