Resources / Language and number

Planetary Kamea and Sigil Workbench

Seven magic squares, Saturn's three-by-three to the Moon's nine-by-nine, as Agrippa printed them. Run along any row, column or diagonal and the square adds itself up in front of you. Then spell a name in Hebrew letters and watch its sigil drawn across the cells, one letter at a time.

The sums and the gematria are arithmetic. The sigil depends on how large values are reduced to fit the square, and practice varied. The rule in use is named beside every result, and the line drawn is a reconstruction, not Agrippa's printed sigil.

Choose a planet

Agrippa's table of Saturn

The square of Saturn

Order: 3
Constant: 15
Total: 45

✓ Holds each of 1–9 exactly once. ✓ 8 of 8 lines sum to 15 = 3 × (3² + 1) ÷ 2. ✓ Cells total 45.

Hover, tap or focus a handle beside the square to sum that row, column or diagonal. Every one should come to 15.

Sigil trace

Step 5 of 5

Letter: ל Lamed
Value: 30
Reduction: 30 → 3Rule: Drop zeros as needed (Aiq Bekar)
Target: Cell 3, row 2, column 1

Stroke from cell 1 to cell 3. This is the last letter: the short bar closes the sigil.

All 8 lines, summed

Row 1: 4 + 9 + 2 = 15
Row 2: 3 + 5 + 7 = 15
Row 3: 8 + 1 + 6 = 15
Column 1: 4 + 3 + 8 = 15
Column 2: 9 + 5 + 1 = 15
Column 3: 2 + 7 + 6 = 15
Diagonal, top left to bottom right: 4 + 5 + 6 = 15
Diagonal, bottom left to top right: 8 + 5 + 2 = 15

This is the same arrangement of nine numbers as the Chinese Luo Shu as it is usually drawn. There is only one three-by-three magic square up to rotation and reflection, so the match by itself says nothing about transmission.

Names on Saturn's square

Intelligence and Spirit

From Agrippa's table, with the Hebrew spellings and numbers it gives. The value beside each is recomputed by gematria.

Spell a name

Letters or numbers

Hebrew letter palette

Final forms

Ordinary value in the gematria total, but placed on the square from their Nine Chambers values (500–900) under this rule.

Or type numbers (Hebrew also accepted)

Separate numbers with spaces or commas, for example 1 3 10 1 30. Each number is placed as if it were a letter of that value. Up to 40 letters or numbers.

Values above n² must be reduced

Reduction rule

Rule

While the value is larger than n², strike one zero: 200 → 20 → 2. A value that fits is left alone. Final forms enter at their Nine Chambers places, 500 to 900: final Kaph 500 → 50 → 5 on Saturn.

Where it comes from

The method later writers associate with the Golden Dawn's kamea sigils, and the usual one in modern manuals. It leans on the Aiq Bekar or Qabalah of Nine Chambers, which groups letters whose values differ only by zeros: Aleph, Yod, Qoph; Beth, Kaph, Resh; and so on. That table sets the five final forms after Tav, at 500 to 900, so they are placed from there. Agrippa printed sigils but did not say how they were drawn.

Practice varied. No printed source settles one rule for every sigil, so the rule in use is named wherever a result is shown.

On Saturn, by Drop zeros as needed (Aiq Bekar)

Letter by letter

Each letter or number, its value, its reduction under Drop zeros as needed (Aiq Bekar), and the cell it lands on
#	Letter	Value	Reduced	Cell
1	אAleph	1	fits	1r3 c2
2	גGimel	3	fits	3r2 c1
3	יYod	10	10 → 1	1r3 c2
4	אAleph	1	fits	1r3 c2 · repeat ×2
5	לLamed	30	30 → 3	3r2 c1

Gematria total 45 — equals the total of Saturn's square.

The tradition

A planetary magic square sets the numbers 1 to n² in a grid so that every row, every column and both diagonals add to the same sum. Seven such squares, of orders three to nine, were given to the seven planets in their Chaldean order: Saturn's three-by-three, Jupiter's four-by-four, down to the Moon's nine-by-nine. Kamea, from a Hebrew word for an amulet, is the name the later English tradition uses for them; Agrippa calls them the tables of the planets.

Magic squares were long worked in the Islamic world, and the planetary set circulated in Latin manuscripts before Agrippa printed it in 1533. His tables give each square with numbers drawn from it, and the names of Intelligences and Spirits whose Hebrew letters mostly sum to those numbers; Venus is the clearest exception. The Hermetic Order of the Golden Dawn inherited the squares and names, and the practice of drawing a sigil by tracing a name letter by letter from cell to cell is associated with that inheritance.

Reading the instrument

The square is checked, not asserted. Hover or focus any row, column or diagonal handle and its cells are summed live against the constant n(n² + 1) ÷ 2; the list beneath the square gives every line at once.
Enter a name from the palette, from the planet's listed names, or by typing Hebrew or raw numbers. Letters are counted by standard gematria, with final forms at their ordinary value. None of the names traced here contains one, and the tables themselves are not consistent: Bne Seraphim's 1252 counts final Mem as 600, while Elim's 81, a divine name in the Moon's table, counts it as 40. The two Nine Chambers rules place final forms from 500 to 900 when reducing, as the Aiq Bekar table does, without changing the total.
A value larger than the square has to be reduced before it can land on a cell. The rule in force is printed beside every result. Switch rules to watch the same name take a different shape.
The sigil runs from a small circle on the first letter to a short bar on the last. When two letters in a row land on the same cell, the instrument draws a small loop there and says so, rather than hiding a stroke of zero length.
The received numbers are not uniform. Most names equal their square's constant or total, but Hagiel's 49 is the count of Venus's cells, Venus's plural Intelligences, Bne Seraphim, are given 1252, which is none of the square's numbers and needs final Mem at 600, and the Moon's Intelligence is a compound title whose spelling varies.

Where it descends from

Three Books of Occult Philosophy: Agrippa's compendium, printed in full in 1533. Book II, chapter 22 gives the seven tables with their seals, the numbers taken from each, and the names of the Intelligences and Spirits with their Hebrew spellings. It does not explain how the sigils were drawn.
The Magus: Francis Barrett's 1801 compilation, which reprinted Agrippa's tables and seals for English readers.
The Golden Dawn: Israel Regardie's publication of the Order's papers, the route by which Agrippa's squares and names, and sigil-drawing on them, reached most modern practice.

What this does not claim

The squares, line sums and gematria are arithmetic and are checked live. The sigil is a reconstruction by a named rule. It is not a copy of the sigil Agrippa printed for that name: reconstructions match some printed sigils closely and others poorly, and the woodcuts vary between editions. Practice varied, and the different reduction rules put the same letter on different cells. Nothing here claims that a square or a sigil has any effect.