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 8b75c1c8d..c644efe9a 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
@@ -42,18 +42,11 @@ $`dl=\sqrt{dx^2+dy^2+dz^2}`$
 
 
 
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 ### Coordonnées cylindriques (N3-N4)
 
+$`M=M(\rho, \phi, z)`$
 
+$`dl=\sqrt{d\rho^2+ (\rho d\phi)^2+dz^2}`$
 
 
 
@@ -62,4 +55,8 @@ $`dl=\sqrt{dx^2+dy^2+dz^2}`$
 
 ### Coordonnées sphériques (N3-N4)
 
+$`M=M(\rho, \theta, \phi)`$
+
+$`dl=\sqrt{d\rho^2+\rho d\phi^2+dz^2}`$
+