Update textbook.fr.md

12.temporary_ins/02.arithmetic-number-theory/10.n1/10.integers-and-their-representation/10.main/textbook.fr.md

@@ -72,47 +72,27 @@ Il sait que si il ne comprends pas un mots, il y a des explications de vocabulai
 
 ------------------->
 
-! *vocabulaire :* un *axe*
-!
-! Un axe est une *droite orientée par une flèche*.   
-!
-! La flèche indique le *sens* de lecture, qui va *du plus petit ($`-`$) au plus grand ($`+`$)*
-!
-! Traditionnellement, la flèche pointe *de la gauche vers la droite* ou *du bas vers le haut*.
-!
-! <details markdown=1>
-! <summary>
-! What is the apparent magnification of the cathedral ?
-! </summary>
-! * Apparent magnification = angular magnification = magnifying power.
-!
-! * As calculated previously, standing 400 metres from the cathedral, the 90 m heigh
-! cathedral sustends the apparent angles of $`\alpha=arctan\left(\dfrac{90}{400}\right)=0.221\;rad=12.7°`$ 
-! at your eye.<br>
-! <br>
-! * The image of the cathedral is 1.7 cm heigth and is located between the lens 
-! (from its vertex $`S2`$) and your eyes and at 2.5cm from the lens. If your eye is
-! 20cm away from the lens, so the distance eye-image is 17.5 cm (we use no algebraic values).
-! Thus the image of the catedral subtends the apparent angle 
-! $`\alpha'=arctan\left(\dfrac{1.7}{17.5}\right)=0.097\;rad=5.6°`$ at your eye.<br>
-! <br>
-! * The apparent magnification $`M_A`$ of the cathedral throught the lensball for my 
-! eye in that position is<br>
-!  $`M_A=\dfrac{\alpha'}{\alpha}=\dfrac{0.097}{0.221}=0.44`$.<br><br>
-!  Taking into account that the image is reversed, the algebraic value of the apparent
-! magnification is $`\overline{M_A}=-0.44`$.<br>
-! <br>
-! * You could obtained directly this algebraic value of $`M_A`$ by considering algebraic
-! lengthes and angles values in the calculations :<br><br> 
-! $`\overline{M_A}=\dfrac{\overline{\alpha'}}{\overline{\alpha}}`$
-! $`=\dfrac  {arctan\left(\frac{-0.017}{-0.175}\right)} {arctan\left(\frac{90}{-400}\right)}`$ $`=\dfrac{0.097}{-0.221}=-0.44`$
-!
-! ![](graduated-axis_L800.png)<br>
-! _Cathedral of Orleans (France)_
-! </details>
-! </details>
-! </details>
-! </details>
+!!!!! *vocabulaire :* un *axe*
+!!!!!
+!!!!! Un axe est une *droite orientée par une flèche*.   
+!!!!!
+!!!!! La flèche indique le *sens* de lecture, qui va *du plus petit ($`-`$) au plus grand ($`+`$)*
+!!!!!
+!!!!! Traditionnellement, la flèche pointe *de la gauche vers la droite* ou *du bas vers le haut*.
+!!!!!
+!!!!! <details markdown=1>
+!!!!! <summary>
+!!!!!! What is the apparent magnification of the cathedral ?
+!!!!! </summary>
+!!!!! * Apparent magnification = angular magnification = magnifying power.
+!!!!!
+!!!!! * As calculated previously, standing 400 metres from the cathedral, the 90 m heigh
+!!!!! cathedral sustends the apparent angles of $`\alpha=arctan\left(\dfrac{90}{400}\right)=0.221\;rad=12.7°`$ 
+!!!!! at your eye.<br>
+!!!!!
+!!!!! ![](graduated-axis_L800.png)<br>
+!!!!! _Cathedral of Orleans (France)_
+!!!!! </details>