Iophiel

The planetary magic of Jupiter gathers the names, seals and number-square attached to that planet in the Western magical tradition. Its magic square, or kamea, is of order 4, a grid of 4 by 4 cells holding the numbers 1 to 16 so that every row, column and diagonal sums to 34.

Square, intelligence and spirit

From that square are derived, by gematria, the names of the planet's two governing powers: the Intelligence Iophiel, the ordering and benevolent aspect, and the Spirit Hismael, the raw and unmediated force. This apparatus was set out by Heinrich Cornelius Agrippa in the Three Books of Occult Philosophy (1533), drawing on earlier Hebrew and Arabic number-magic. To the same planet is also joined an Olympic Spirit, here Bethor, one of the seven planetary governors named in the Arbatel of Magic (1575).

These names, squares and hierarchies are described here as an element of the documented tradition of Renaissance ceremonial magic, studied historically; the spirits are not reified.

The Jupiter table is a four by four square of the numbers one to sixteen, with every row, column and diagonal adding to thirty four and the whole square totalling one hundred and thirty six. The same square, in one of its many equivalent arrangements, is the one Durer engraved into Melencolia I in 1514, with the year worked into the two centre cells of the bottom row, and that engraving is the reason this particular square is the most reproduced object in the whole tradition.

Agrippa's Three Books of Occult Philosophy distributes four names to each planet: an intelligence, a spirit, and two further names of the planet and its order of spirits. For Jupiter the intelligence is Iophiel and the spirit Hismael, and both are constructed so that their Hebrew letter values return numbers taken from the table. The method is the same for all seven planets and it is the whole point of the system: the names are consequences of the arithmetic rather than revelations attached to it.

The tradition treats the even ordered squares as harder cases, and they are. A three by three square has one solution up to rotation; a four by four has eight hundred and eighty. Which arrangement a manuscript uses therefore varies, and comparing two copies of a Jupiter table will often show different cells holding different numbers while the sums stay fixed. That variability is a useful reminder that these are constructed objects with a documented printing history, not fixed revelations.