The notion of identifying all [[Point|Ponits]] in [[Homogeneous Coordinates]] on the [[Lines|Line]] from $\tilde{0}$ to point $\tilde P$ to be referring to the same point $P$.
$\huge
\mat{x\\y\\z} \equiv \mat{\frac{x}{z} \\ \frac{y}{z} \\1}
$
>[!info]
>$ \huge \begin{align}
>
\let \tilde P &= \mat{x\\y\\z} \\
P &= \mat{\frac{x}{z} \\ \frac{y}{z}\\1}
\end{align}$