Of right triangles and odd squares
If we look at the center of the odd sized squares in Agrippa’s magic squares (Saturn, Mars, Mercury, Moon), we can spot lengths of the sides of right triangles. By extension, this holds for all odd sized squares built in the same way.
3² + 4² = 5²
5² + 12² = 13²
7² + 24² = 25²
9² + 40² = 41²
…
27² + 364² = 365²
…
Of magic triangles
Now if we consider the associated right triangles sides length (Saturn, Mars, Mercury & Venus triangles).
3² = 4 + 5
5² = 12 + 13
7² = 24 + 25
9² = 40 + 41
…
27² = 364 + 365
…
Of squares summed
Then looking at the center square of each odd sized squares, we can see that they can be written as sum of two squares.
5 = 1 ² + 2 ²
13 = 2 ²+ 3 ²
25 = 3 ²+ 4 ²
41 = 4 ²+ 5 ²
…
365 = 13 ² + 14 ²
…