Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. ThÃ©bault''s theorem is the name given variously to one of the geometry problems proposed by the French mathematician Victor ThÃ©bault, individually known as ThÃ©bault''s problem I, II, and III. Given any parallelogram, construct on its sides four squares external to the parallelogram. The quadrilateral formed by joining the centers of those four squares is a square. It is a special case of van Aubel''s theorem.Given a square, construct equilateral triangles on two adjacent edges, either both inside or both outside the square. Then the triangle formed by joining the vertex of the square distant from both triangles and the vertices of the triangles distant from the square is equilateral.