\begin{definition}[Definition:Cross-Ratio/Lines through Origin]
Let $\LL_1$, $\LL_2$, $\LL_3$ and $\LL_4$ be lines through the origin $O$ whose equations embedded in the Cartesian plane are as follows:
{{begin-eqn}}
{{eqn | ll= \LL_1:
      | l = y
      | r = \lambda x
}}
{{eqn | ll= \LL_2:
      | l = y
      | r = \mu x
}}
{{eqn | ll= \LL_3:
      | l = y
      | r = \lambda' x
}}
{{eqn | ll= \LL_4:
      | l = y
      | r = \mu' x
}}
{{end-eqn}}
The '''cross-ratio''' of $\LL_1$, $\LL_2$, $\LL_3$ and $\LL_4$, in that specific order, is defined and denoted:
:$\tuple {\lambda \mu, \lambda', \mu'} := \dfrac {\paren {\lambda - \lambda'} \paren {\mu - \mu'} } {\paren {\lambda - \mu'} \paren {\mu - \lambda'} }$
\end{definition}