# LaTeX2HTML 99.1 release (March 30, 1999)
# Associate images original text with physical files.


$key = q/;a_{11}x'^2+a_{22}y'^2+2a_{03}z'+d_{00};=;0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="288" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="img10.gif"
 ALT="$ \;a_{11}x'^2+a_{22}y'^2+2a_{03}z'+d_{00}\;= \; 0$">|; 

$key = q/displaystylea_{11}x'^2+a_{22}y'^2+d_{00};=;0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="218" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="img12.gif"
 ALT="$\displaystyle a_{11}x'^2+a_{22}y'^2+d_{00}\;= \; 0.$">|; 

$key = q/,a_{02}=0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="70" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="img28.gif"
 ALT="$ \,a_{02} = 0 \,$">|; 

$key = q/{displaymath}left{array{{l}x'=x''<row_mark>y'=y''-displaystylefrac{d_{00}}{2a_{02}}<row_mark>z'=z''<row_mark>array{right.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="138" HEIGHT="104" BORDER="0"
 SRC="img31.gif"
 ALT="\begin{displaymath}
\left\{
\begin{array}{l}
x' = x'' \\\\
y' = y'' - \displ...
...ac{d_{00}}{2a_{02}} \\\\
z' = z'' \\\\
\end{array}
\right.
\end{displaymath}">|; 

$key = q/displaystylea_{11}x''^2+2a_{02}y'';=;0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="180" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="img32.gif"
 ALT="$\displaystyle a_{11}x''^2+2a_{02}y''\;= \; 0.$">|; 

$key = q/,a_{02}neq0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="70" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="img30.gif"
 ALT="$ \,a_{02} \neq 0 \,$">|; 

$key = q/displaystylea_{11}x'^2+d_{00};=;0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="149" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="img29.gif"
 ALT="$\displaystyle a_{11}x'^2+d_{00}\;= \; 0.$">|; 

$key = q/displaystylea_{11}x'^2+a_{22}y'^2+a_{33}z'^2+c_{00};=;0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="280" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="img4.gif"
 ALT="$\displaystyle a_{11}x'^2+a_{22}y'^2+a_{33}z'^2+c_{00}\;= \; 0$">|; 

$key = q/:a_{22}=a_{33}=0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="120" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="img17.gif"
 ALT="$ \: a_{22} = a_{33} = 0 \,$">|; 

$key = q/,a_{02}=0:;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="71" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="img23.gif"
 ALT="$ \,a_{02} = 0
\:$">|; 

$key = q/,a_{11}neq0,a_{22}neq0:;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="138" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="img6.gif"
 ALT="$ \,a_{11} \neq 0,
a_{22} \neq 0 \:$">|; 

$key = q/displaystylea_{11}x''^2+a_{11}(y'')^2+a_{11}(z'')^2+b_{00}=0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="314" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="img35.gif"
 ALT="$\displaystyle a_{11}x''^2+a_{11}(y'')^2+a_{11}(z'')^2+b_{00} = 0.
$">|; 

$key = q/;a_{11}x'^2+2a_{02}y'+d_{00};=;0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="225" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="img27.gif"
 ALT="$ \;a_{11}x'^2+2a_{02}y'+d_{00}\;= \; 0. $">|; 

$key = q/:textbf{z}:;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="img26.gif"
 ALT="$ \:\textbf{z}\:$">|; 

$key = q/,a_{02}neq0:;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="71" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="img21.gif"
 ALT="$ \,a_{02} \neq 0 \:$">|; 

$key = q/displaystylea_{11}left(x+displaystylefrac{a_{01}}{a_{11}}right)^2+a_{22}left(x+d_{02}^2}{a_{22}}-displaystylefrac{a_{03}^2}{a_{33}}+b_{00}=0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="661" HEIGHT="70" ALIGN="MIDDLE" BORDER="0"
 SRC="img2.gif"
 ALT="$\displaystyle a_{11} \left( x + \displaystyle\frac{a_{01}}{a_{11}} \right)^2 +
...
...rac{a_{02}
^2}{a_{22}} - \displaystyle\frac{a_{03} ^2}{a_{33}} + b_{00} = 0.
$">|; 

$key = q/,mathcal{Q},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="img1.gif"
 ALT="$ \,\mathcal{Q} \,$">|; 

$key = q/displaystylea_{11}x''^2+a_{11}y''^2+a_{11}z''^2+2a_{11}x''y''+2a_{11}x''z''+2a_{11}y''z''+2a_{02}y''+2a_{03}z''+d_{00}=0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="711" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="img34.gif"
 ALT="$\displaystyle a_{11}x''^2+a_{11}y''^2+a_{11}z''^2+ 2a_{11}x'' y''+2a_{11}x''
z''+2a_{11}y'' z''+ 2a_{02}y''+2a_{03}z''+d_{00} = 0.
$">|; 

$key = q/,a_{11}neq0,:;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="76" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="img16.gif"
 ALT="$ \,a_{11}
\neq 0, \:$">|; 

$key = q/,a_{03}=0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="70" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="img11.gif"
 ALT="$ \,a_{03} = 0 \,$">|; 

$key = q/displaystylea_{11}x''^2+a_{22}y''^2+2a_{03}z'';=;0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="252" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="img15.gif"
 ALT="$\displaystyle a_{11}x''^2+a_{22}y''^2+2a_{03}z''\;= \; 0.$">|; 

$key = q/{displaymath}left{array{{l}x=x'-displaystylefrac{a_{01}}{a_{11}}<row_mark>,<row_ystylefrac{a_{03}}{a_{33}}<row_mark>array{right.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="122" HEIGHT="174" BORDER="0"
 SRC="img3.gif"
 ALT="\begin{displaymath}
\left\{
\begin{array}{l}
x = x' - \displaystyle\frac{a_{0...
...\displaystyle\frac{a_{03}}{a_{33}} \\\\
\end{array}
\right.
\end{displaymath}">|; 

$key = q/,a_{03}neq0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="70" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="img13.gif"
 ALT="$ \,a_{03} \neq 0 \,$">|; 

$key = q/a_{11}x^2+a_{22}y^2+2a_{01}x+2a_{02}y+2a_{03}z+a_{00};=;0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="403" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="img8.gif"
 ALT="$ a_{11}x^2+a_{22}y^2+2a_{01}x+2a_{02}y+2a_{03}z+a_{00}\;= \; 0$">|; 

$key = q/{displaymath}left{array{{l}x'=x''+y''+z''displaystylefrac{}{}<row_mark>y'=y''disz'=z''displaystylefrac{}{}<row_mark>array{right.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="163" HEIGHT="104" BORDER="0"
 SRC="img33.gif"
 ALT="\begin{displaymath}
\left\{
\begin{array}{l}
x' = x'' + y'' + z''\displaystyl...
...
z' = z'' \displaystyle\frac{}{} \\\\
\end{array}
\right.
\end{displaymath}">|; 

$key = q/:a_{03}=0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="71" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="img22.gif"
 ALT="$ \:a_{03}
= 0 \,$">|; 

$key = q/{displaymath}left{array{{l}x=x'-displaystylefrac{a_{01}}{a_{11}}<row_mark>y=y'dik>z=z'displaystylefrac{}{}<row_mark>array{right.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="122" HEIGHT="110" BORDER="0"
 SRC="img19.gif"
 ALT="\begin{displaymath}
\left\{
\begin{array}{l}
x = x' - \displaystyle\frac{a_{0...
...\
z = z' \displaystyle\frac{}{} \\\\
\end{array}
\right.
\end{displaymath}">|; 

$key = q/{displaymath}left{array{{l}x=x'-displaystylefrac{a_{01}}{a_{11}}<row_mark>,<row_}<row_mark>,<row_mark>z=z'<row_mark>array{right.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="122" HEIGHT="167" BORDER="0"
 SRC="img9.gif"
 ALT="\begin{displaymath}
\left\{
\begin{array}{l}
x = x' - \displaystyle\frac{a_{0...
...02}}{a_{22}} \\\\
\, \\\\
z = z' \\\\
\end{array}
\right.
\end{displaymath}">|; 

$key = q/:a_{33}=0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="71" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="img7.gif"
 ALT="$ \: a_{33} = 0 \,$">|; 

$key = q/:textbf{y}:;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="img25.gif"
 ALT="$ \:\textbf{y} \:$">|; 

$key = q/,c_{00}inmathbb{C},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="71" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="img5.gif"
 ALT="$ \,c_{00} \in \mathbb {C} \,$">|; 

$key = q/{displaymath}left{array{{l}x'=x''displaystylefrac{}{}<row_mark>y'=y''displaystylstylefrac{d_{00}}{2a_{03}}<row_mark>array{right.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="138" HEIGHT="114" BORDER="0"
 SRC="img14.gif"
 ALT="\begin{displaymath}
\left\{
\begin{array}{l}
x' = x'' \displaystyle\frac{}{} ...
...displaystyle\frac{d_{00}}{2a_{03}} \\\\
\end{array}
\right.
\end{displaymath}">|; 

$key = q/:a_{03}neq0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="71" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="img24.gif"
 ALT="$ \:a_{03} \neq 0 \,$">|; 

$key = q/displaystylea_{11}x'^2+2a_{02}y'+2a_{03}z'+d_{00};=;0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="290" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="img20.gif"
 ALT="$\displaystyle a_{11}x'^2+2a_{02}y'+2a_{03}z'+d_{00}\;= \; 0. $">|; 

$key = q/a_{11}x^2+2a_{01}x+2a_{02}y+2a_{03}z+a_{00};=;0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="339" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="img18.gif"
 ALT="$ a_{11}x^2+2a_{01}x+2a_{02}y+2a_{03}z+a_{00}\;= \; 0$">|; 

1;

