The construction of Freudenthal's Magic Square, which contains the
exceptional simple Lie algebras of types $F_4,E_6,E_7$ and $E_8$, in
terms of symmetric composition algebras is further developed here.
The para-Hurwitz algebras, which form a subclass of the symmetric
composition algebras, will be defined, in the split case, in terms
of the natural two dimensional module for the simple Lie algebra
$\mathfrak{sl}_2$. As a consequence, it will be shown how all the Lie
algebras in Freudenthal's Magic Square can be constructed, in a
unified way, using copies of $\mathfrak{sl}_2$ and of its natural module.