diff --git a/Triangulation_on_sphere_2/doc/Triangulation_on_sphere_2/CGAL/Delaunay_triangulation_on_sphere_2.h b/Triangulation_on_sphere_2/doc/Triangulation_on_sphere_2/CGAL/Delaunay_triangulation_on_sphere_2.h
index ce00270f578..3486cec300e 100644
--- a/Triangulation_on_sphere_2/doc/Triangulation_on_sphere_2/CGAL/Delaunay_triangulation_on_sphere_2.h
+++ b/Triangulation_on_sphere_2/doc/Triangulation_on_sphere_2/CGAL/Delaunay_triangulation_on_sphere_2.h
@@ -81,7 +81,7 @@ public:
   /*!
   Inserts the point `p`.
   If the point `p` coincides with an already existing vertex, this vertex is returned
-  and the triangulation is not updated.
+  and the triangulation remains unchanged.
   The optional parameter `f` is used to give a hint about the location of `p`.
   */
   Vertex_handle insert(const Point& p, Face_handle f = Face_handle());
diff --git a/Triangulation_on_sphere_2/doc/Triangulation_on_sphere_2/CGAL/Delaunay_triangulation_sphere_traits_2.h b/Triangulation_on_sphere_2/doc/Triangulation_on_sphere_2/CGAL/Delaunay_triangulation_sphere_traits_2.h
index 4d969d77b66..5a93dd25842 100644
--- a/Triangulation_on_sphere_2/doc/Triangulation_on_sphere_2/CGAL/Delaunay_triangulation_sphere_traits_2.h
+++ b/Triangulation_on_sphere_2/doc/Triangulation_on_sphere_2/CGAL/Delaunay_triangulation_sphere_traits_2.h
@@ -62,7 +62,7 @@ public:
   ///
   typedef typename K::Compare_xyz_3                 Compare_on_sphere_2;
 
-  /// If the kernel cannot represent algeabric coordinates exactly, there is a tolerance
+  /// If the kernel cannot represent algebraic coordinates exactly, there is a tolerance
   /// around the sphere, and thus different points can actually be the same point.
   /// This particular equality functor checks if both query points are on the sphere and
   /// are aligned (and on the same side) with the center of the sphere.
@@ -109,7 +109,7 @@ public:
   /// or whether `p` is within an automatically computed small distance otherwise.
   bool is_on_sphere(const Point_on_sphere_2& p) const;
 
-  /// Returns `false` if `K` can represent algeabric coordinates, or whether the distance
+  /// Returns `false` if `K` can represent algebraic coordinates, or whether the distance
   /// between `p` and `q` is lower than \f$ 2 \sqrt{R\delta} \f$ otherwise.
   bool are_points_too_close(const Point_on_sphere_2& p, const Point_on_sphere_2& q) const;
 
diff --git a/Triangulation_on_sphere_2/doc/Triangulation_on_sphere_2/CGAL/Geographical_coordinates_traits_2.h b/Triangulation_on_sphere_2/doc/Triangulation_on_sphere_2/CGAL/Geographical_coordinates_traits_2.h
index cd4a9aae882..82668f7bb5e 100644
--- a/Triangulation_on_sphere_2/doc/Triangulation_on_sphere_2/CGAL/Geographical_coordinates_traits_2.h
+++ b/Triangulation_on_sphere_2/doc/Triangulation_on_sphere_2/CGAL/Geographical_coordinates_traits_2.h
@@ -102,7 +102,7 @@ public:
 \ingroup PkgTriangulationOnSphere2TriangulationClasses
 
 This class represents coordinates of the Geographical Coordinates System,
-that is a pair of two values representing a longitude and a latitude.
+that is a pair of two values representing a latitude and a longitude.
 
 \tparam K a kernel type; must be a model of `Kernel`
 
@@ -115,7 +115,7 @@ public:
   typedef typename K::FT                            FT;
 
   ///
-  typedef FT                                        latitude;
+  typedef FT                                        Latitude;
 
   ///
   typedef FT                                        Longitude;
@@ -126,7 +126,7 @@ public:
   /// Construct a point on the sphere at coordinates `(la, lo)`.
   ///
   /// \pre `la` is within `[-90; 90[` and `lo` is within `[-180; 180[`.
-  Geographical_coordinates(const latitude la, const Longitude lo);
+  Geographical_coordinates(const Latitude la, const Longitude lo);
 };
 
 } // namespace CGAL
diff --git a/Triangulation_on_sphere_2/doc/Triangulation_on_sphere_2/CGAL/Triangulation_on_sphere_2.h b/Triangulation_on_sphere_2/doc/Triangulation_on_sphere_2/CGAL/Triangulation_on_sphere_2.h
index 2b93415318c..3f4b76dd994 100644
--- a/Triangulation_on_sphere_2/doc/Triangulation_on_sphere_2/CGAL/Triangulation_on_sphere_2.h
+++ b/Triangulation_on_sphere_2/doc/Triangulation_on_sphere_2/CGAL/Triangulation_on_sphere_2.h
@@ -14,14 +14,14 @@ This triangulation class is very similar to `CGAL::Triangulation_2` as both clas
 triangulations of 2-manifold domain without boundary. A significant difference is that
 in the case of Euclidean 2D triangulation, it is necessary to introduce so-called <i>infinite
 faces</i> to complete the convex hull into an actual 2-manifold without boundary that the triangulation
-data structure can represent. This is not necessary for triangulations of the sphere,
-that is already perfectly adapted to the triangulation data structure.
+data structure can represent. This is not necessary for triangulations on the sphere,
+which are already perfectly adapted to the triangulation data structure.
 
 There is an exception to the previous statement: in the degenerate configuration
 where all points of \f$ \mathcal{S}\f$ lie on the same hemisphere, the triangulation has a border.
 Internally, the triangulation data structure must however remain a 2-manifold at all time,
-and to ensure this fictitious faces called <i>ghost faces</i> are added. In contrast, faces that
-not ghost-faces are called <i>solid</i> faces.
+and to ensure this fictitious faces called <i>ghost faces</i> are added. We call faces that
+are not ghost faces <em>solid faces</em>.
 
 \tparam Traits is the geometric traits, which must be a model of the concept `TriangulationOnSphereTraits_2`.
 
@@ -241,7 +241,7 @@ public:
   size_type number_of_faces() const;
 
   /*!
-  Returns the number of ghost_faces.
+  Returns the number of ghost faces.
   */
   size_type number_of_ghost_faces() const;
 
@@ -251,12 +251,12 @@ public:
   /// @{
 
   /*!
-  Returns the geometric position of the vertex `*v`.
+  Returns the geometric position of the vertex `v`.
   */
   const Point& point(const Vertex_handle v);
 
   /*!
-  Returns the geometric position of the `i`-th vertex of the face `*f`.
+  Returns the geometric position of the `i`-th vertex of the face `f`.
   */
   const Point& point(const Face_handle f, const int i);
 
@@ -443,7 +443,7 @@ public:
   /*!
   Specifies which case occurs when locating a point in the triangulation.
   */
-  enum Locate_type { VERTEX=0, /*!< when the located point coincides with a vertex of the triangulation */
+  enum Locate_type { VERTEX=0, /*!< when the point coincides with a vertex of the triangulation */
                      EDGE, /*!< when the point is in the relative interior of an edge */
                      FACE, /*!< when the point is in the interior of a face */
                      OUTSIDE_CONVEX_HULL, /*!< when the point is outside the convex hull but in the affine hull of the current triangulation */
diff --git a/Triangulation_on_sphere_2/doc/Triangulation_on_sphere_2/Concepts/DelaunayTriangulationOnSphereTraits_2.h b/Triangulation_on_sphere_2/doc/Triangulation_on_sphere_2/Concepts/DelaunayTriangulationOnSphereTraits_2.h
index bc74a153364..1421779d76f 100644
--- a/Triangulation_on_sphere_2/doc/Triangulation_on_sphere_2/Concepts/DelaunayTriangulationOnSphereTraits_2.h
+++ b/Triangulation_on_sphere_2/doc/Triangulation_on_sphere_2/Concepts/DelaunayTriangulationOnSphereTraits_2.h
@@ -30,7 +30,7 @@ public:
   ///
   /// `Point_3 operator()(Point_3 p, Point_3 q, Point_3 r)`
   ///
-  /// which returns the center of the circle circumscribed to face with vertices `p`, `q`, and `r`.
+  /// which returns the center of the circle circumscribed to the face with vertices `p`, `q`, and `r`.
   ///
   /// \note This type is only required for the computation of dual objects (Voronoi vertex)
   /// and a dummy type can be used otherwise.
diff --git a/Triangulation_on_sphere_2/doc/Triangulation_on_sphere_2/Concepts/TriangulationOnSphereFaceBase_2.h b/Triangulation_on_sphere_2/doc/Triangulation_on_sphere_2/Concepts/TriangulationOnSphereFaceBase_2.h
index b89ed9a68b2..9203b5df644 100644
--- a/Triangulation_on_sphere_2/doc/Triangulation_on_sphere_2/Concepts/TriangulationOnSphereFaceBase_2.h
+++ b/Triangulation_on_sphere_2/doc/Triangulation_on_sphere_2/Concepts/TriangulationOnSphereFaceBase_2.h
@@ -11,7 +11,7 @@ on the sphere.
 The data structure concept `TriangulationDataStructure_2` was primarily designed
 to serve as a data structure for the 2D triangulation classes of \cgal, which are triangulations
 embedded in the 2D Euclidean plane.
-However its genericy makes it usable for any orientable triangulated surface without boundary,
+However its genericity makes it usable for any orientable triangulated surface without boundary,
 regardless of the dimensionality of the space the triangulation is embedded in, and thus
 it is a valid data structure for the triangulations on the sphere of this package.