/usr/include/CGAL/Cartesian/ is in libcgal-dev 4.2-5ubuntu1.
This file is owned by root:root, with mode 0o755.
..
/usr/include/CGAL/Cartesian/Aff_transformation_2.h
/usr/include/CGAL/Cartesian/Aff_transformation_3.h
/usr/include/CGAL/Cartesian/Aff_transformation_rep_2.h
/usr/include/CGAL/Cartesian/Aff_transformation_rep_3.h
/usr/include/CGAL/Cartesian/Cartesian_base.h
/usr/include/CGAL/Cartesian/Circle_2.h
/usr/include/CGAL/Cartesian/Circle_3.h
/usr/include/CGAL/Cartesian/Data_accessor_2.h
/usr/include/CGAL/Cartesian/Direction_2.h
/usr/include/CGAL/Cartesian/Direction_3.h
/usr/include/CGAL/Cartesian/Iso_cuboid_3.h
/usr/include/CGAL/Cartesian/Iso_rectangle_2.h
/usr/include/CGAL/Cartesian/Line_2.h
/usr/include/CGAL/Cartesian/Line_3.h
/usr/include/CGAL/Cartesian/MatrixC33.h
/usr/include/CGAL/Cartesian/Plane_3.h
/usr/include/CGAL/Cartesian/Point_2.h
/usr/include/CGAL/Cartesian/Point_3.h
/usr/include/CGAL/Cartesian/Ray_2.h
/usr/include/CGAL/Cartesian/Ray_3.h
/usr/include/CGAL/Cartesian/Rotation_rep_2.h
/usr/include/CGAL/Cartesian/Scaling_rep_2.h
/usr/include/CGAL/Cartesian/Scaling_rep_3.h
/usr/include/CGAL/Cartesian/Segment_2.h
/usr/include/CGAL/Cartesian/Segment_3.h
/usr/include/CGAL/Cartesian/Sphere_3.h
/usr/include/CGAL/Cartesian/Tetrahedron_3.h
/usr/include/CGAL/Cartesian/Translation_rep_2.h
/usr/include/CGAL/Cartesian/Translation_rep_3.h
/usr/include/CGAL/Cartesian/Triangle_2.h
/usr/include/CGAL/Cartesian/Triangle_3.h
/usr/include/CGAL/Cartesian/Vector_2.h
/usr/include/CGAL/Cartesian/Vector_3.h
/usr/include/CGAL/Cartesian/basic_constructions_2.h
/usr/include/CGAL/Cartesian/basic_constructions_3.h
/usr/include/CGAL/Cartesian/ft_constructions_2.h
/usr/include/CGAL/Cartesian/ft_constructions_3.h
/usr/include/CGAL/Cartesian/function_objects.h
/usr/include/CGAL/Cartesian/line_constructions_2.h
/usr/include/CGAL/Cartesian/plane_constructions_3.h
/usr/include/CGAL/Cartesian/point_constructions_2.h
/usr/include/CGAL/Cartesian/point_constructions_3.h
/usr/include/CGAL/Cartesian/predicates_on_directions_2.h
/usr/include/CGAL/Cartesian/predicates_on_planes_3.h
/usr/include/CGAL/Cartesian/predicates_on_points_2.h
/usr/include/CGAL/Cartesian/predicates_on_points_3.h
/usr/include/CGAL/Cartesian/solve_3.h