deletions | additions       diff --git a/section_Equations_E_x_frac__.tex b/section_Equations_E_x_frac__.tex  index 618d7e3..3c2089c 100644  --- a/section_Equations_E_x_frac__.tex  +++ b/section_Equations_E_x_frac__.tex 
...
$$E(x) := \frac{x_1^2}{e_1^2} + \frac{x_2^2}{e_2^2} + \frac{x_3^2}{e_3^2} - 1 = 0$$  Let $y$ be a point outside the ellipsoid:  $$y = \begin{bmatrix} y_1 \\ y_2 \\ y_3 \end{bmatrix}$$  For any point $x = \begin{bmatrix} x_1 & x_2 & x_3 \end{bmatrix}^{T}$ on the ellipsoid we have: have\footnote{http://www.geometrictools.com/Documentation/DistancePointEllipseEllipsoid.pdf}:  $$y - x = \frac{1}{2} t \nabla E(x)   = t \begin{bmatrix}   \frac{1}{e_1^2} && \\  
...