Lines through Center Square of Order 3 Magic Square are in Arithmetic Sequence

Theorem
Consider the order 3 magic square:

Each of the lines through the center cell contain $3$ integers in arithmetic progression.

Proof
By observation:


 * $\left({1, 5, 9}\right)$: common difference $4$
 * $\left({2, 5, 8}\right)$: common difference $3$
 * $\left({3, 5, 7}\right)$: common difference $2$
 * $\left({4, 5, 6}\right)$: common difference $1$