The planetary squares from Mars to the Moon: numbers and symbols
The magic squares of Mars, the Sun, Venus, Mercury and the Moon: sums, totals, metals and the meanings attributed to them in Agrippa's Renaissance tradition.
The series of planetary squares is one of the most orderly constructions of Renaissance magic. Each planet of ancient cosmology corresponds to a square of increasing size: three cells per side for Saturn, four for Jupiter, and so on up to nine for the Moon. After the first two, which have a history of their own, five tables remain that complete the system and reveal its internal logic.
The order of planets and numbers
The order follows the traditional sequence of the celestial spheres, from the farthest to the nearest to the Earth: Saturn, Jupiter, Mars, the Sun, Venus, Mercury, the Moon. Mars receives the square of five, whose magic sum is sixty-five. The Sun has the square of six, summing to one hundred and eleven. Venus has seven, summing to one hundred and seventy-five, Mercury eight, with two hundred and sixty, and the Moon nine, with three hundred and sixty-nine.
Each square also has a total, the sum of all its cells. For Mars it is three hundred and twenty-five, for the Sun six hundred and sixty-six, for Venus one thousand two hundred and twenty-five, for Mercury two thousand and eighty and for the Moon three thousand three hundred and twenty-one. Renaissance authors gave these figures a symbolic value and connected them, through the numerical value of Hebrew letters, to the names of the planetary intelligences and spirits.
Names, metals and correspondences
Renaissance tables associate each square with the traditional metal of its planet, according to a correspondence that goes back to late antique alchemy: iron for Mars, gold for the Sun, copper for Venus, quicksilver for Mercury, silver for the Moon. The case of the Sun is the best known. The total of six hundred and sixty-six corresponds to the name of the solar spirit, which Agrippa calls Sorath, and the coincidence with the number in the Book of Revelation has fuelled much later speculation.
Each table was credited with qualities matching the character of its planet. The square of Mars was linked to courage and strength, that of the Sun to glory and the favour of the powerful, that of Venus to love and harmony. Mercury governed eloquence and trade, the Moon journeys and dreams. These are symbolic attributions, drawn from traditional astrology rather than from observation.
Before and after Agrippa
Agrippa did not invent these tables. Squares of various orders were already known to Arabic authors and appeared in late medieval Latin manuscripts, sometimes with different arrangements. His achievement was to present them systematically, together with the seals derived from them, in a printed book that enjoyed enormous circulation. From that moment, in 1533, his versions became the canonical ones for the Western tradition.
After him the tables were reprinted countless times, translated into English in 1651 and taken up by the occultists of the nineteenth century. Meanwhile mathematicians studied magic squares for their numerical properties: in the seventeenth century the Frenchman Bernard Frénicle de Bessy listed all eight hundred and eighty distinct squares of order four, a result published after his death.
The series of seven squares is an eloquent example of how the Renaissance tried to hold mathematics, astronomy and symbolism together. Today these patterns interest both historians of esotericism and lovers of arithmetic, who find in them construction problems that are still studied. They are two worlds that were united in the sixteenth century and that modern science later separated.