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 70645a097..78dfb8b85 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
@@ -254,15 +254,16 @@ $`=dx\;\overrightarrow{e_x}+dy\;\overrightarrow{e_y}+dz\;\overrightarrow{e_z}`$<
 [EN] y its norm (or length) is thescalar line element :<br>
 <br>$`||\overrightarrow{dl}||=\sqrt{dl_x^2+dl_y^2+dl_z^2}=\sqrt{dx^2+dy^2+dz^2}`$<br>
 <br>$`||\overrightarrow{dl}||=\sqrt{\overrightarrow{dl}\cdot\overrightarrow{dl}}`$
-$`=\sqrt{(dx\;\overrightarrow{e_x}+dy\;\overrightarrow{e_y}+dz\;\overrightarrow{e_z})\cdot
-(dx\;\overrightarrow{e_x}+dy\;\overrightarrow{e_y}+dz\;\overrightarrow{e_z})}`$
-$`=\sqrt{dx^2\;(\overrightarrow{e_x}\cdot\overrightarrow{e_x})
-+dy^2\;(\overrightarrow{e_y}\cdot\overrightarrow{e_y})   
-+dz^2\;(\overrightarrow{e_z}\cdot\overrightarrow{e_z})`$
-$`+2\,dx\,dy\,x(\overrightarrow{e_x}\cdot\overrightarrow{e_y})`$
-$`+2\,dx\,dz\,x(\overrightarrow{e_x}\cdot\overrightarrow{e_z})`$
-$`+2\,dy\,dz\,x(\overrightarrow{e_y}\cdot\overrightarrow{e_z})}`$
+$`=\sqrt{(dl_x\;\overrightarrow{e_x}+dl_y\;\overrightarrow{e_y}+dl_z\;\overrightarrow{e_z})\cdot
+(dl_x\;\overrightarrow{e_x}+dl_y\;\overrightarrow{e_y}+dl_z\;\overrightarrow{e_z})}`$
+$`=\sqrt{dl_x^2\;(\overrightarrow{e_x}\cdot\overrightarrow{e_x})
++dl_y^2\;(\overrightarrow{e_y}\cdot\overrightarrow{e_y})   
++dl_z^2\;(\overrightarrow{e_z}\cdot\overrightarrow{e_z})`$
+$`+2\,dl_x\,dl_y\,x(\overrightarrow{e_x}\cdot\overrightarrow{e_y})`$
+$`+2\,dl_x\,dl_z\,x(\overrightarrow{e_x}\cdot\overrightarrow{e_z})`$
+$`+2\,dl_y\,dl_z\,x(\overrightarrow{e_y}\cdot\overrightarrow{e_z})}`$
 $`=\sqrt{dl_x^2+dl_y^2+dl_z^2}`$
+$`=\sqrt{dx^2+dy^2+dz^2}`$
 
 
 * **N3 ($`\rightarrow`$ N4)**<br>