From 7ca69c714dfbeafdbc07a5c0346f34ca4f4e3498 Mon Sep 17 00:00:00 2001
From: Claude Meny <claude.meny@irap.omp.eu>
Date: Fri, 29 Jan 2021 12:18:31 +0100
Subject: [PATCH] Update textbook.en.md

---
 .../30.cylindrical-coordinates/10.main/textbook.en.md     | 8 ++++----
 1 file changed, 4 insertions(+), 4 deletions(-)

diff --git a/12.temporary_ins/05.coordinates-systems/30.cylindrical-coordinates/10.main/textbook.en.md b/12.temporary_ins/05.coordinates-systems/30.cylindrical-coordinates/10.main/textbook.en.md
index faa60a7ed..39686e2e5 100644
--- a/12.temporary_ins/05.coordinates-systems/30.cylindrical-coordinates/10.main/textbook.en.md
+++ b/12.temporary_ins/05.coordinates-systems/30.cylindrical-coordinates/10.main/textbook.en.md
@@ -47,7 +47,7 @@ $`\def\PSclosed{\mathscr{S}_{\displaystyle\tiny\bigcirc}}`$
 
 * * CS300 *:
 
-Reference frame: Cartesian coordinate system $ `(O, x, y, z)` $
+Reference frame: Cartesian coordinate system $`(O, x, y, z)`$
 \ - **1 point $`O`$ origin** of the space. <br>
 \ - **3 axes** named **$`Ox,Oy,Oz`$**, intersecting at $`O`$, **orthogonal 2 to 2**. <br>
 \ - **1 unit of length**. <br>
@@ -55,7 +55,7 @@ Reference frame: Cartesian coordinate system $ `(O, x, y, z)` $
 ! can give :
 
 The cylindrical coordinates are defined from a Cartesian coordinate system, i.e.
-\- 1 point $`O`  origin of space. <br>
+\- 1 point $`O`$ origin of space. <br>
 \- 3 axes named $`Ox, Oy, Oz`$, intersecting at $`O`$, orthogonal 2 to 2. <br>
 \- 1 unit of length. <br>
 
@@ -77,7 +77,7 @@ a *direct trihedron*.<br>
 \- The **coordinate $`z_M`$** of the point $`M`$ is the *algebraic distance $`\overline {Om_z}`$*
 between the point $`O`$ and the point $`m_z`$.
 
-**$`\rho_M=\overline{Om_ {xy}}`$, $`\varphi_M = \widehat{xOm_y}`, $`z_M =Om_z`$**
+**$`\rho_M=\overline{Om_ {xy}}`$, $`\varphi_M = \widehat{xOm_y}`$, $`z_M =Om_z`$**
 
 ! can give :
 
@@ -85,7 +85,7 @@ The cylindrical coordinates are ordered and noted $`(\rho,\varphi,z)`$.
 
 For any point $`M`$ in space:
 
-\- The $`\ rho_M`$ coordinate of the point $`M`$ is the nonalgebraic distance $`Om_{xy}`$
+\- The $`\rho_M`$ coordinate of the point $`M`$ is the nonalgebraic distance $`Om_{xy}`$
 between point $`O`$ and point $ m_{xy}`$. <br>
 \- The coordinate $`\varphi_M`$ of the point $`M`$ is the nonalgebraic angle
 $`\widehat{xOm_{xy}}`$ between the axis $`Ox`$ and the half-line $`Om_ {xy}`$,