diff --git a/00.brainstorming-pedagogical-teams/40.collection-existing-pedagogical-content/40.classical-mechanics/10.main/textbook.fr.md b/00.brainstorming-pedagogical-teams/40.collection-existing-pedagogical-content/40.classical-mechanics/10.main/textbook.fr.md
index 280e0f604..b0dc4015b 100644
--- a/00.brainstorming-pedagogical-teams/40.collection-existing-pedagogical-content/40.classical-mechanics/10.main/textbook.fr.md
+++ b/00.brainstorming-pedagogical-teams/40.collection-existing-pedagogical-content/40.classical-mechanics/10.main/textbook.fr.md
@@ -254,7 +254,7 @@ remember to replace (auto-tra) with your initials (YYY).
 [EN] Galileo's transformations
 
 $`\mathbf{
-\left\{\begin{array}{r}
+\left\{\begin{array}{l}
 t'=t \\
 x'=x-V_x\,t \\
 y'=y-V_y\,t \\   
@@ -270,6 +270,27 @@ z'=z-V_z\,t
 [EN] theorem of addition of velocities
 
 
+$`\mathbf{
+\left\{\begin{array}{l}
+t'=dt \\
+\dfrac{dx'}{dt'}=\dfrac{dx}{dt}-V_x \\
+\dfrac{dy'}{dt'}=\dfrac{dy}{dt}-V_y \\ 
+\dfrac{dz'}{dt'}=\dfrac{dz}{dt}-V_z 
+\end{array}
+\right.
+}`$
+$`\quad\Longrightarrow`$
+$`\mathbf{
+\left\{\begin{array}{l}
+v_x'=v_x-V_x \\
+v_y'=v_y-V_y \\
+v_z'=v_z-V_z \\
+\end{array}
+\right.
+}`$
+
+
+
 *CLAPTMEC-FU-050* : 
 [ES] teorema de la invariancia de aceleraciones
 [FR] théorème de l'invariance des accélérations