diff --git a/Triangulation/doc/Triangulation/CGAL/Triangulation.h b/Triangulation/doc/Triangulation/CGAL/Triangulation.h
index 9f198797dd9..bf01cfdce74 100644
--- a/Triangulation/doc/Triangulation/CGAL/Triangulation.h
+++ b/Triangulation/doc/Triangulation/CGAL/Triangulation.h
@@ -214,7 +214,8 @@ type (a signed integral type)
 typedef TriangulationDataStructure_::difference_type difference_type;
 
 /*!
-\enum used by `Triangulation` to specify which case occurs when locating a point in the triangulation
+\enum Locate_type 
+\brief Used by `Triangulation` to specify which case occurs when locating a point in the triangulation.
 */
 enum Locate_type { ON_VERTEX=0, /*!< when the located point coincides with a vertex of the triangulation */
                    IN_FACE, /*!< when the point is in the interior of a face of dimension equal or less than `maximal_dimension()` - 2 */
diff --git a/Triangulation/doc/Triangulation/Triangulation.txt b/Triangulation/doc/Triangulation/Triangulation.txt
index 12c63333fd2..962ec2bfe97 100644
--- a/Triangulation/doc/Triangulation/Triangulation.txt
+++ b/Triangulation/doc/Triangulation/Triangulation.txt
@@ -117,7 +117,7 @@ triangulation data structure and can then be obtained using the method `tds.maxi
 A triangulation data structure also knows the <I>current dimension</I> of its full cells,
 which can be obtained using `tds.current_dimension()`. In the sequel, let
 us denote the maximal dimension with \f$ D \f$ and the current dimension with \f$ d \f$.
-The inequalities \f$ -2 \leq d \leq D\f$ and \f$ 0 \le D\f$ always hold.
+The inequalities \f$ -2 \leq d \leq D\f$ and \f$ 0 < D\f$ always hold.
 The special meaning of negative values for \f$d\f$ is explained below.
 
 ## The Set of Faces ##
@@ -453,22 +453,21 @@ Let \f$ {S}^{(w)}\f$ be a set of weighted points in \f$ \mathbb{R}^D\f$. Let
 \f$ {p}^{(w)}=(p,w_p), p\in\mathbb{R}^D, w_p\in\mathbb{R}\f$ and
 \f$ {z}^{(w)}=(z,w_z), z\in\mathbb{R}^D, w_z\in\mathbb{R}\f$ 
 be two weighted points.
-If all weights are positive, a weighted point
-\f$ {p}^{(w)}=(p,w_p)\f$ can also be seen as a sphere of center \f$ p\f$ and
-radius \f$ \sqrt{w_p}\f$.
+A weighted point \f$ {p}^{(w)}=(p,w_p)\f$ can also be seen as a sphere of 
+center \f$ p\f$ and radius \f$ \sqrt{w_p}\f$.
 The <I>power product</I> (or <I>power distance</I> )
 between \f$ {p}^{(w)}\f$ and \f$ {z}^{(w)}\f$ is
 defined as
 \f[ \Pi({p}^{(w)},{z}^{(w)}) = {\|{p-z}\|^2-w_p-w_z} \f]
 where \f$ \|{p-z}\|\f$ is the Euclidean distance between \f$ p\f$ and \f$ z\f$.
 \f$ {p}^{(w)}\f$ and \f$ {z}^{(w)}\f$
-are said to be <I>orthogonal</I> if \f$ \Pi{({p}^{(w)}-{z}^{(w)})}
+are said to be <I>orthogonal</I> if \f$ \Pi({p}^{(w)},{z}^{(w)})
 = 0\f$.
 
 \f$D + 1\f$ weighted points have a unique common orthogonal weighted point 
 called the <I>power sphere</I>. A sphere \f$ {z}^{(w)}\f$ is said to be
 <I>regular</I> if \f$ \forall {p}^{(w)}\in{S}^{(w)},
-\Pi{({p}^{(w)}-{z}^{(w)})}\geq 0\f$.
+\Pi({p}^{(w)},{z}^{(w)})\geq 0\f$.
 
 A triangulation of \f$ {S}^{(w)}\f$ is <I>regular</I> if the power spheres
 of all simplices are regular.