Pappus's hexagon theorem

Etymology
Attributed to the Ancient Greek mathematician (c. 290–c. 350 AD).

Proper noun

 * 1)  A theorem valid for projective planes over any field, stating that, given one set of collinear points $$A, B, C,$$ and another set of collinear points $$a,b,c,$$, the intersection points $$X,Y,Z$$ of line pairs $$Ab$$ and $$aB, Ac$$ and $$aC, Bc$$ and $$bC$$ are collinear, lying on the "Pappus line". These three points are the points of intersection of the "opposite" sides of the hexagon $$AbCaBc$$.