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 c644efe9a..65dcbe2fd 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
@@ -46,7 +46,7 @@ $`dl=\sqrt{dx^2+dy^2+dz^2}`$
 
 $`M=M(\rho, \phi, z)`$
 
-$`dl=\sqrt{d\rho^2+ (\rho d\phi)^2+dz^2}`$
+$`dl=\sqrt{d\rho^2+ (\rho\,d\phi)^2+dz^2}`$
 
 
 
@@ -57,6 +57,6 @@ $`dl=\sqrt{d\rho^2+ (\rho d\phi)^2+dz^2}`$
 
 $`M=M(\rho, \theta, \phi)`$
 
-$`dl=\sqrt{d\rho^2+\rho d\phi^2+dz^2}`$
+$`dl=\sqrt{dr^2+(r\,d\theta)^2+(r\,sin\,\theta\,d\phi)^2}`$