diff --git a/00.brainstorming-pedagogical-teams/40.collection-existing-pedagogical-content/04.reference-frames-coordinate-systems/textbook.fr.md b/00.brainstorming-pedagogical-teams/40.collection-existing-pedagogical-content/04.reference-frames-coordinate-systems/textbook.fr.md
index 84e08203e..682a4174f 100644
--- a/00.brainstorming-pedagogical-teams/40.collection-existing-pedagogical-content/04.reference-frames-coordinate-systems/textbook.fr.md
+++ b/00.brainstorming-pedagogical-teams/40.collection-existing-pedagogical-content/04.reference-frames-coordinate-systems/textbook.fr.md
@@ -155,7 +155,7 @@ of the point M when only the coordinate x increases in an infinitesimal way) wri
 $`\partial\overrightarrow{OM}_y=\dfrac{\partial \overrightarrow{OM}}{\partial y}\cdot dy`$,
 $`\quad\overrightarrow{e_y}=\dfrac{\partial\overrightarrow{OM}_y}{||\partial\overrightarrow{OM}_y||}`$<br>
 $`\partial\overrightarrow{OM}_z=\dfrac{\partial \overrightarrow{OM}}{\partial z}\cdot dz`$,
-$`\overrightarrow{e_z}=\dfrac{\partial\overrightarrow{OM}_z}{||\partial\overrightarrow{OM}_z||}`$
+$`\quad\overrightarrow{e_z}=\dfrac{\partial\overrightarrow{OM}_z}{||\partial\overrightarrow{OM}_z||}`$
 
 * **N3 ($`\rightarrow`$ N4)**<br> 
 [ES] Los vectores $`\overrightarrow{e_x}`$, $`\overrightarrow{e_y}`$ y $`\overrightarrow{e_z}`$ 
@@ -170,7 +170,10 @@ En coordonnées cartésiennes, les vecteurs de base gardent la
 [EN] The vectors $`\overrightarrow{e_x}`$, $`\overrightarrow{e_y}`$ y $`\overrightarrow{e_z}`$ 
 form an **orthonormal basis** of space. It is the **base associated with Cartesian coordinates**.
 In Cartesian coordinates, the base vectors keep the 
-**same direction whatever the position of the point $`M`$**.
+**same direction whatever the position of the point $`M`$**.<br>
+<br>$`(\overrightarrow{e_x},\overrightarrow{e_x},\overrightarrow{e_x})`$ 
+base ortogonal independiente de la posición de $`M`$ / base orthogonale indépendante
+de la position de $`M`$ / orthogonal basis independent of the position of $`M`$.
 
 * **N3 ($`\rightarrow`$ N4)**<br>
 [ES] La norma del vector $`\partial\overrightarrow{OM}_x=\overrightarrow{dl_x}`$