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Longitude : $ \lambda $. Latitude : $ \phi $.

\begin{equation*}
\mu = sin \left(\phi\right)
\end{equation*}

\begin{align*}
\mu &= \frac{m + \mu' \times p}{p + \mu' \times m} \\
m &= 1 - \frac{1}{C^2} \\
p &= 1 + \frac{1}{C^2}
\end{align*}

\begin{align*}
d\mu &= \frac{p^2 - m^2}{\left(p + \mu' \times m\right)^2} \times d\mu' \\
dX' &= cos \left(\phi'\right) \times d\lambda' \\
dY' &= d\phi'
\end{align*}

\begin{align*}
dX' &= \sqrt{\frac{\left(p + \mu' \times m\right)^2}{p^2 - m^2}} \times dX \\
dY' &= \sqrt{\frac{\left(p + \mu' \times m\right)^2}{p^2 - m^2}} \times dY
\end{align*}




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