The Saturn table is a three by three square holding the numbers one to nine, arranged so that every row, column and diagonal adds to fifteen, and so that the whole square totals forty five. It is the smallest magic square that exists, and it is very much older than the magic that uses it: the same arrangement is the Chinese Lo Shu, attested long before it reached Latin Europe, and the atlas records it under that name as well.
What Renaissance planetary magic added was a way of reading numbers out of the square and back into names. In the scheme set out in Agrippa's Three Books of Occult Philosophy, printed in 1533, each planet is given four spirit names whose Hebrew letters, added by their numerical values, reproduce the square's own numbers. For Saturn the intelligence Agiel and the spirit Zazel both come to forty five, the total of the square. The names are not arbitrary labels attached to the table; they are derived from it, and a reader who knows the gematria can check the arithmetic.
The seal of the planet is produced the same way, by drawing a line from cell to cell in numerical order across the grid, so that the figure is a trace of the square rather than an invented sigil. The atlas does not reproduce the seals, because a seal copied inexactly is worse than no seal at all.
The pattern is uniform across the seven. Each planet has its square, the square has its sums, and the sums generate the names.