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:


 * $\tuple {1, 5, 9}$: common difference $4$
 * $\tuple {2, 5, 8}$: common difference $3$
 * $\tuple {3, 5, 7}$: common difference $2$
 * $\tuple {4, 5, 6}$: common difference $1$