Not the most gentle exercise for someone who just learned how to add.
If you divide all the entries by 36, you'll see that this is a magic square of order 11 (magic constant 671).
The Wolfram Mathworld article on magic squares explains various ways of generating magic squares. It looks like De Morgan used what came to be known as the "Siamese method" starting in the cell (6,7) with an order vector of (1,1) (shown in blue below) and a break vector of (0,2) (shown in red below).
