# Planetary magic squares

Magick squares are used to draw in the influences of their corresponding planet. Be mindful that with any work of magick, where you include the universal forces, they must be in harmony with your intent. A magick square kamea in Hebrew is an array of numbers arranged in a square so that the sum of any row is equal to the sum of any column.

For most magick squares, the sum of either of the diagonal also equals the sum of either a row or column. Magick squares have been esteemed for their magickal and mathematical properties for thousands of years in China, India, and the Middle East. In a magical context, the term magic square is also applied to a variety of word squares or number squares found in magical grimoiresincluding some that do not follow any obvious pattern, and even those with differing numbers of rows and columns.

They are generally intended for use as talismans. The derivation of the sigil of Hagiel, the planetary intelligence of Venus, drawn on the magic square of Venus. Each Hebrew letter provides a numerical value, giving the vertices of the sigil. However, we are only concerned here with the seven kamea, which have been traditionally associated with the seven planets in practical qabalah.

Each of these kamea is associated with a planetary Sephirah on the Tree of Life. The seal is used in talismanic magic to represent the entire pattern square and to act as a witness or governor for them. The seal is the epitome or synthesis of the square. The Intelligence of a planet is viewed as an evolutionary, guiding, inspiring, or informing entity. However, the Spirit of a planet is traditionally considered more of a blind or neutral force. A letter should never be reduced further than necessary.

The resulting numerical sequence is then traces on the appropriate kamea to produce the sigil of that name. The traditional seals and sigils do not in all cases follow the entire numerical sequence of each name. Some of the longer sigils seem to have been shortened or compressed for easier use.

In any case, I am reproducing them in essentially the same forms given by both Wm. Barrett and Israel Regardie, as these are the traditional forms of the sigils. Here is detailed in an abridged form an ancient form of magick that has been presented traditionally and updated for modern practitioners. They illustrate the incorporation of magick squares and sigils for greater success in your workings.

Each Magick Square represents a matrix of planetary energy. Magick squares are based on the original work done by ancient mathematicians in their description of numbers. Magickal practitioners expanded on this to carry over the correlation between a number and its corresponding planet, therefore representing planetary energy in a mathematical format.

A magick square is made up using three key numbers. The first one is the planetary number. The second is the square of the planetary number or the planetary number multiplied by itself. The third is the sum of the square or all the incremental numbers starting at 1 that it takes to fill the boxes in the square added together and then divided by the planetary number. Saturn is represented by the number 3. Start by drawing the magick square with 3 boxes horizontally and vertically for a total of 9 squares the square of 3 being 9.

Each row of numbers in the magick square, horizontally and vertically, must equal 15 the sum of the square of the planetary number of 3. When drawing the Magick Square, all numbers should be placed in the square, in sequence beginning with number 1. This is the magick square representing Saturn. Notice that the square is 3 by 3 and that all the rows equal In magickal terms a sigil is a unitary glyph derived from a name, word, or magickal formula by means of a direct analogical process such as numerical conversion and tracing upon magick squares [kamea].

If the appropriate process is reversed, then the name or word may be retrieved from the pattern of the sigil.A square grid with n cells on each side is said to have order n. The mathematical study of magic squares typically deals with its construction, classification, and enumeration. Although completely general methods for producing all the magic squares of all orders do not exist, historically three general techniques have been discovered: by bordering method, by making composite magic squares, and by adding two preliminary squares.

There are also more specific strategies like the continuous enumeration method that reproduces specific patterns. This classification is based on different techniques required to construct odd, evenly even, and oddly even squares. Beside this, depending on further properties, magic squares are also classified as associative magic squarespandiagonal magic squaresmost-perfect magic squaresand so on. More challengingly, attempts have also been made to classify all the magic squares of a given order as transformations of a smaller set of squares.

The enumeration of most-perfect magic squares of any order was only accomplished in the late 20th century. In regard to magic sum, the problem of magic squares only requires the sum of each row, column and diagonal to be equal, it does not require the sum to be a particular value. Thus, although magic squares may contain negative integers, they are just variations by adding or multiplying a negative number to every positive integer in the original square. However, in some places, " magic squares " is used as a general term to cover both the normal and non-normal ones, especially when non-normal ones are under discussion.

Moreover, the term " magic squares " is sometimes also used to refer to various types of word squares. Magic squares have a long history, dating back to at least BCE in China.

At various times they have acquired magical or mythical significance, and have appeared as symbols in works of art. In modern times they have been generalized a number of ways, including using extra or different constraints, multiplying instead of adding cells, using alternate shapes or more than two dimensions, and replacing numbers with shapes and addition with geometric operations.

The third order magic square was known to Chinese mathematicians as early as BCE, and explicitly given by the first century of the common era. The first datable instance of the fourth-order magic square occur in CE in India. Specimens of magic squares of order 3 to 9 appear in an encyclopedia from Baghdad c. By the end of 12th century, the general methods for constructing magic squares were well established. Around this time, some of these squares were increasingly used in conjunction with magic letters, as in Shams Al-ma'ariffor occult purposes.

Magic squares were made known to Europe through translation of Arabic sources as occult objects during the Renaissance, and the general theory had to be re-discovered independent of prior developments in China, India, and Middle East. Also notable are the ancient cultures with a tradition of mathematics and numerology that did not discover the magic squares: Greeks, Babylonians, Egyptians, and Pre-Columbian Americans. This is the earliest appearance of a magic square on record; and it was mainly used for divination and astrology.

He also gives six magic circles of varying complexity. The above magic squares of orders 3 to 9 are taken from Yang Hui's treatise, in which the Luo Shu principle is clearly evident. The high point of Chinese mathematics that deals with the magic squares seems to be contained in the work of Yang Hui; but even as a collection of older methods, this work is much more primitive, lacking general methods for constructing magic squares of any order, compared to a similar collection written around the same time by the Byzantine scholar Manuel Moschopoulos.

The Japanese interest in magic square began after the dissemination of Yang Hui's Suanfa and Cheng Dawei's Suanfa tongzong in the 17th century, and almost all the wasans devoted their time to its study. In the edition of Ketsugi-shoIsomura Kittoku gave both odd and even ordered bordered magic squares as well as magic circles; while the edition of the same book contained a large section on magic squares, demonstrating that he had a general method for constructing bordered magic squares.

The largest square Mosei constructs is of 19th order. This is the first Japanese book to give a general treatment of magic squares in which the algorithms for constructing odd, singly even and doubly even bordered magic squares are clearly described.

A fourth-order magic cube was constructed by Yoshizane Tanaka — in Rakusho-kikan The study of magic squares was continued by Seki's pupils, notably by Katahiro Takebe, whose squares were displayed in the fourth volume of Ichigen Kappo by Shukei Irie, Yoshisuke Matsunaga in Hojin-Shin-jutsuYoshihiro Kurushima in Kyushi Iko who rediscovered a method to produce the odd squares given by Agrippa [15]and Naonobu Ajima.

After this, attempts at enumerating the magic squares was initiated by Yamaji.

For instance, the Kubera-Kolama magic square of order three, is commonly painted on floors in India.Get Instant Access. Magical squares, or cameas, are often used as a basis for the construction of individual sigils.

In fact, the traditional sigils for planetary spirits and demons have been cabbalistically construed with the help of these cameas. Since this technique belongs to yet another important branch of sigil magic and is relatively unknown, it shall be covered here.

The following explanations are based on Israel Regardie's excellent bookHow to Make and Use Talismans, which contains a very clear summary, though the author refers to the older material of the Golden Dawn and other writers have explained the system elsewhere. Unfortunately, these cannot be taught here and would lead away from our main topic. Readers who are quite unfamiliar with these disciplines should refer to the relevant literature listed in the bibliography.

The alphabet with its assigned numerical values is as follows:. Depending on the appropriate magical camea, sometimes it is necessary to reduce a numerical value so that the pertinent number in the camea can be touched when drawing the sigil.

For example, look at the demon Bartzabel of the Mars sphere, following Regardie p. In Hebrew this name is written from right to left :. You will note that the numbers ,90 and 30 do not appear in the magical square; deleting the zeros in our demon's name gives us 2,9 and 3.

Usually the sigil begins with a curlicue and ends with a stroke. If any one number is covered twice, two arcs are drawn. Let's have a look at this sigil in its camea in Figure To complete the picture, the following pages consist of the magical cameas of the planets together with the sigils of their intelligences and demons, as well as the planetary seals, which have been developed with a very similar but slightly different method.

Beside each numbered camea you will find a square containing the Hebrew letters according to their numerical values, which may save you a lot of trouble constructing your sigils in the Hermetic tradition. The illustrations are taken from Agrippa's classic work De Occulta Philosophia 2nd vol.

The rule of marking the beginning and the end of a planetary sigil, namely to start with a curlicue and to end with a stroke, has not been followed throughout. This may be due to Agrippa's intention of preventing any possible abuse.

By marking the beginning and the end of such a sigil we have all the directional information necessary to draw it in evocation with the exception of the composed sigils.

I have deliberately not "corrected" the sigils because I wanted to present the traditional form without any changes of my own. Furthermore, these corrections might confuse those readers unfamiliar with the subject if they suddenly come across different versions of one and the same sigil in other traditional books. For practice, however, I advise you to redraw the sigils and correct them where necessary.

Prolonged He, letter of the holy name Eloh Nakhiel, Intelligence of the Sun How-ToOccult Writing. Way back in February,I posted my first how-to on constructing and launching sigils. That one used the freestyle method.

Here is another technique for creating sigils using a magick square or kamea. A magickal square is a grid of numbers where the sum of every row and column is the same. The simplest magickal square that you will find is one containing the numbers 1 through 9. Making a sigil on a magickal square relies on numerology. There are many types of numerology, but I will stick to the western or Pythagorean type because it is the easiest to understand.

In western numerology, all of the letters in the alphabet have a value of 1 to 9. Here is an example. From there, you can figure out what letter would go on each square and start to spell words with them by connecting the letters. Method one: Draw a circle on the letter W where you start, then draw a line to each of the other letters.

That leaves you with WLLM. Now remove out any repeating letters, which leaves you with WLM. Draw the sigil on the square using the same method as above. As you will see, this results in a much more simplistic shape.

I would have to decide between the two which is right for the work I was doing.

However, the second method can prove useful when you are turning a long phrase into a sigil. From here, you can spell out any word or phrase you like. Another wrinkle of numerology is that your word or phrase will reduce down to a single number. That equals That means that William has been reduced to a 3. But you want to know a secret? Many magicians do not worry about sigils at this level. That said, you can take your magickal squares to the next level by including planetary correspondences in your work.

The most simple of magickal squares, the three by three grid shown here, is also known as the magickal square or kamea of Saturn. There are magickal squares which correspond to all of the seven classical planets, the Sun, the Moon, Mercury, Venus, Mars, Jupiter, and Saturn. After researching these planets and how they influence us energetically, you may decide that it would be best to draw your sigil on another of the more complex squares.

This can require a different type of numerology. I have frequently used the kamea of Jupiter while creating sigils this June Domagick because it served my purposes best — but the numerology I used drew on the numbering the sixteen letters of the Younger Futhark!These pages detail an ancient form of magick that have been updated for modern practitioners.

It incorporates the use of magick squares and sigils for a more focused intent in spell work. Magick squares are used to draw in the influences of their corresponding planet. Bear in mind that with any work of magick the inclusion of universal forces should be in harmony with your intent.

Each Magick Square represents a matrix of planetary energy. Magick squares are based on the original work done by ancient mathematicians in their description of numbers. Magical practitioners expanded on this to carry over the correlation between a number and its corresponding planet, therefore representing planetary energy in a mathematical format.

Each magick square is made up using three key numbers. The first is the planetary number itself.

## Encyclopedia of Magick Squares Planetary Angels And Spirits of Ceremonial Magic

The second is the square of the planetary number or the planetary number multiplied by itself. The third is the sum of the square or all the incremental numbers starting at 1 that it takes to fill the boxes in the square added together and then divided by the planetary number. When drawing the magick square all of the numbers should be placed in the square in sequence beginning with then number 1. Below is the magick square representing Saturn.

Notice, as mentioned above, that our square is 3 by 3 and that all the rows equal A sigil is a signature, if you will. It can be seen a symbol of our intent. Sigils incorporated with other influences can add great direction and focus to spell work. Sigils can be traced in air, carved on candles, drawn on paper and burned etc. Sigils can be drawn and formed using the magick squares that have been described above. Saturn is the planet that rules institutions such as banks, real estate transactions, investments, educational institutions etc.

Lets say our intent was for successful investing. We want a sigil to represent ourselves at being successful in our investment endeavours.

So we pick the word investor which will be our sigil, the visualization of self as a smart investor, surrounded by favourable aspects and clear choices to make our money grow. Now…how do you determine how to draw your sigil. Using the Western system of numerology, each letter has a numerical equivalent that is detailed in the chart below.

Referring back to our work with Saturn for a favourable investment strategy, select a word of phrase that you want drawn into a sigil. We take our key word of investor and map it to the chart shown above.

Then by starting with our first corresponding number and continuing through each in order, we draw out our sigil. Using some of the other correspondences for Saturn, we could carve this sigil into a black candle anointed with bergamot or cypress.

We can also surround the candle with onyx and place it on top of the world card from a tarot deck. Imagine the magick square as the accelerator and the planetary seal as the brakes.Also known as magic squares, the kamea are mathematical structures that have been associated with both planetary magic and the modern Hermetic Kabbalah.

Each planet has its corresponding kamea, but it is more correct to say that each positive whole number has its corresponding kamea and that each number is used to represent specific planetary spheres. Let's take a look at this without relying upon overly analytical mathematical formalisms. Let's use the kamea of Jupiter to illustrate all of the concepts associated with these mathematical constructs.

Jupiter is the fourth sphere in Hermetic cosmology because it comes after the first and second spheres of primordial archetypes and after the third sphere of Saturn. Hermetic cosmology, as well as the Kabbalah, start at the Divine and work their way down.

Jupiter's Magic Square

Hence Jupiter is the fourth sphere down and its principal number is four in terms of its kamea. This means that the kamea for Jupiter is a 4x4 matrix as illustrated below. That's how we start constructing the Jupiterian kamea. The next step, mathematically, is to determine which positive whole numbers fit into each cell so that the arithmetic sum of every column, row, and the diagonal equal the same number.

Luckily, this has been solved for the modern day occultist thanks to Hermes Trismegistus' initial foray into this field and we get the following structure.

That is how the kamea for Jupiter is constructed and the same process occurs for the kamea of the other planetary spheres.

### Planetary Magical Squares

Each of the seven classical planetary spheres has a sigil associated with it that is constructed from its kamea. There are, of course, the traditional symbols of the planets that we think of zodiacally, but these are distinct from the sigils we refer to here. Let's illustrate by seeing how we construct the planetary sigil for Jupiter. Sigil construction is more of an art than a science, to be honest, but the idea is to create a symbol that touches upon all the numbers of the kamea and expresses the archetypes of that particular planetary sphere.

So for Jupiter, we begin by making an 'X'-like structure of perpendicular lines that touch upon the diagonals of the kamea. In sigil crafting, it's traditional whatever that means to end open line segments with a small circle.

So that presents to us the following sigil. To finish this sigil, we need to touch upon the remainder of the numbers in the cells while still maintaing aesthetic pleasure and the characteristics of the sphere. To do this we encompass the untouched numbers with a circle. What precisely this means in the context of Jupiter has to with its qualities of expansion within the partitions of form and is elucidated upon in the section on Jupiter.

But we end up with a sigil suitable for the planetary sphere. The final result is depicted below, removing the kamea from the picture and leaving only the symbols that we used to construct the sigil for the planet: simple shapes like lines and a circle. This is the meditative sigil for the visually-inclined magician while the analytically-inclined might prefer the kamea itself. Toggle navigation. Home Planetary Magic Kamea Kamea Also known as magic squares, the kamea are mathematical structures that have been associated with both planetary magic and the modern Hermetic Kabbalah.In the Western Occult Tradition, each planet has traditionally been associated with a series of numbers and particular organizations of those numbers.

One such method of numerological arrangement is the magic square. The divine names associated with Saturn all have numerological values of 3, 9, or These values are calculated by writing out the names in Hebrew and then adding up the value of each included letter, as each Hebrew letter can represent both a sound and a numerical value.

The seal of Saturn is constructed by drawing lines that intersect every number within the magic square. The divine names associated with Jupiter all have numerological values of 4 or The names of the intelligence of Jupiter and the spirit of Jupiter are The square is constructed by first filling in each square with numbers 1 to 16 consecutively, starting at the bottom left with 1 and working upward toward the upper right with Then specific pairs of numbers are inverted, i.

Opposite ends of the diagonals are inverted, as are the inner numbers on the diagonals, so that the following pairs are inverted: 1 and 16, 4 and 13, 7 and 10, and 11 and 6. The remaining numbers are not moved.

The seal of Jupiter is constructed by drawing lines that intersect every number within the magic square. The divine names associated with Mars all have numerological values of 5 or The names of the intelligence of Mars and the spirit of Mars have a value of The square is constructed by arranging the numbers consecutively in a pre-arranged pattern. In general, numbering moves down and to the right. Hence, 2 is down and to the right of 1. When the down and right motion would take you off the edge of the square, it wraps around.

Thus, since 2 is on the bottom edge, 3 is still to the right of 2, but it's at the top of the square instead of the bottom. When this pattern runs up against numbers already placed, the pattern shifts two rows down. Thus, 4 is on the left, 5 is one down and one to the right of 4, and if that motion were to be repeated, it would collide with the already placed 1. Instead, 6 appears two rows down from 5, and the pattern continues.

The seal of Mars is constructed by drawing lines that intersect every number within the magic square. The divine names associated with The Sun all have numerological values of 6 or The name of the intelligence of the Sun has a value of and the spirit of the Sun has a value of The creation of the square of the Sun is messy. It is constructed by first filling in each square with numbers 1 to 36 consecutively, starting at the bottom left with 1 and working upward toward the upper right with Numbers inside the boxes along the main diagonals of the square are then inverted, i.

For example, 1 and 36 change places, as does 31 and 6. Once this is done, more pairs of numbers still need to be inverted to make all of the rows and columns to add up to There is no clean rule to follow to do such: it appears to have been done through trial and error.

The seal of the Sun is constructed by drawing lines that intersect every number within the magic square. The name of the intelligence of Venus has a value if The name of the spirit of Venus has a value ofand the name of the intelligence of Venus has a value of The seal of Venus is constructed by drawing lines that intersect every number within the magic square.