Although the Magic Squares are a prolific branch of recreational mathematics it is the seven Kameas, or Planetary Magick Squares that are of interest to students of Ceremonial Magick. Since first being published by Agrippa in De Occulta Philosophia in 1510, these squares have been employed in making talismans with an almost unchanged method of use ever since. The Kameas formed a large part of the Golden Dawn teaching on Talismanic Magick and figures prominently in Franz Hartmann’s classic Magick White & Black.
The calculation of the Magick Squares of the Planets is a simple matter involving a few simple mechanical operations and only the most rudimentary mathematical ability.
The calculation of the Squares of the odd numbers is a simple process. Write down the numbers of the square in their regular succession from left to right and top to bottom. Next, separate the central numbers by enclosing them in a square grid turned at a 45 angle to the series of numerals. Finally, insert the segregated numbers into their opposite places in the turned grid.
The construction of the Magick Squares of the even numbers is slightly more complicated, and will require a little more experimentation. Taking the Square of Four, for instance: write the numerical sequence from right to left, and top to bottom. Next, as the diagonals are already in their correct positions, the others need simply to be rotated in a regular fashion. The top two middle squares drop straight down into their opposite squares, whilst the bottom two number exchange places to make the top line to be the sequence : 4, 14, 15, 1; and the bottom line : 16, 3, 2, 13. Lastly, the remaining numbers exchange places by the same method, the two on the right moving straight across and the two on the left trading places as before.
For the square of six, the process is slightly more complex again, but still only a matter of mechanical manipulation. Once again, write the numerals of the sequence into their squares in order, from right to left and from top to bottom. Again, the diagonals are already correctly placed. Again, the four innermost exchangeable numerals are moved as above. Finally, the outer ring of numerals then trade places by the same principal, with the middle two pairs rotating diagonally and anticlockwise, so that all four numerals change places and partners.
All of this sound much more complicated than it really is, and an half an hour of effort will clear the matter up for all but the least mathematically endowed among us. By simple experimentation, the correct solutions can easily be found for all of the Kameas, and their veracity checked by the simple process of addition.