Pappus's hexagon theorem

Attributed to the Ancient Greek mathematician Pappus of Alexandria (c. 290–c. 350 AD).

Pappus's hexagon theorem

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

• Pappian
• Pappus line