For example. Given that all edges of a parallelepiped are equal, and its four diagonals are $a$, $b$, $c$, and $d$, find the edge length of this parallelepiped.
Let the edge length of the parallelepiped be \( x \). According to the above theorem, we have:
\[
\begin{aligned}
& 4 \cdot 3 x^{2}=a^{2}+b^{2}+c^{2}+d^{2} \\
\therefore x & =\sqrt{\frac{a^{2}+b^{2}+c^{2}+d^{2}}{12}} \\
& =\frac{\sqrt{3\left(a^{2}+b^{2}+c^{2}+d^{2}\right)},}{6}
\end{aligned}
\]

Thus, the edge length of the parallelepiped is
\[
\sqrt{3\left(a^{2}+b^{2}+c^{2}+d^{2}\right)} \text {. }
\]
6
The theorem from the 6-year key high school textbook "Solid Geometry" on page 58, "The square of a diagonal of a rectangular prism is equal to the sum of the squares of the three edges meeting at a vertex," can be proven succinctly using this theorem. Let the length, width, and height be \( a \), \( b \), and \( c \) respectively, and the diagonal length be \( l \). By the Apollo theorem, we have:
\[
\begin{array}{l}
4 l^{2}=4\left(a^{2}+b^{2}+c^{2}\right) \\
\therefore l^{2}=a^{2}+b^{2}+c^{2} . \text { Proven. }
\end{array}
\]
(Author's affiliation: No. 2 High School, Wuxi City, Jiangsu Province)