The Scrolls of Ptah No. 3 The Geometry of the Pillars and Throne of the Hegemon

by Fra. A:.O:.C:., Artisan of the Het Nuit Lodge, OSOGD
Beltane, 2002 ev.

Sacred geometrical mysteries of the Pillars.

In designing the throne and pillars for our Temple, I was drawn to the sacred geometry of the Egyptians on whose symbolism our temple godforms are based.

It is a fascinating subject, and far more complex than can be dealt with in this short monograph. Consult the reference list at the end for more study. I will only try to briefly describe the basic elements and how they apply to the matter at hand.

[Click here to see mechanical drawing.]

The geometry developed by Imhotep and used for all the sacred construction of the late dynasty Egyptians is based on logarithmic progressions. The ancient geometers called them Spira Mirabilis, the “Miraculous Spirals.” Forms of “magical” proportion can be generated by application of geometric and algebraic harmony. These were the original “masonic” secrets, for when applied not only do physical structures have pleasing aesthetic proportion, but they are also the most sturdy way to build something. Knowing how to build a structure that wouldn’t fall over was powerful knowledge in the ancient world, for every king wanted a palace and a kingdom that wouldn’t fall apart at the first storm or earthquake.

Certain geometric forms emerge when applying such formulae as pi, “squaring the circle” and the Golden Section; they grow “organically” by applying them to various proportions of a structure. This technique is known as geomonic expansion. I’ve applied all these formulae to the design of the Throne and Pillars. These are the central elements of the temple, and occupy an important place in our temple philosophy. I believe that constructing them to sacred geometric proportions will magnify their magical influence powerfully. And all of the temple furniture can be further generated from the same basic structures.

The primary unit of measurement used is four inches. This corresponds to “one hand” in ancient measurement, and serves as the integer of 1. Everything else relates to this basic whole number unit.

We begin with the throne of the Hegemon itself. It is a cube measuring 5 hands on each side, making it 20 inches square on each surface. (5 corresponding to the five Elements.) A back rest of equal height rises from one edge. This is the basic form of the classic Egyptian throne. [fig.1] (This will also serve as the basis of all the thrones in the hall, and doubling it will be the height of the Cubical Altar. Essentially, all the Thrones are “double cubes” with only one side of the upper cube, which forms the backrest.)


From this measurement, the size of the platform under the throne is generated by means of the Golden Section [fig.2], referred to by the Greek letter phi. Like pi, phi is an irrational number, expressed as 1.6180339… in arithmetic. Algebraically it is a three-term subset where a:b::b:(a+b), or a is to b in the same way as b is to a plus b. Proportions of sacred buildings, from the Egyptian temples to Solomon’s temple to later gothic cathedrals were formed in this way. The length of each side of the Great Pyramid from the center point of the bottom edge to the top is phi to the length of each half of the egde. [Fig.3] Imhotep was the first architect to realize that this proportion yielded a stable structure that would neither collapse inward on itself, nor fall apart due to “landslides” outward. Therefore the blocks of the Great Pyramid have needed no mortar between them to remain standing for over 4000 years.

Fig. 2 Fig.3

Again, I wont go into the deeper occult meanings of the Golden Section; please refer to the reference list. But it is a transcendental relationship that illuminates the generation of a 3rd unique entity from 2 entities, of triplicity from duality, and so expresses the Mystery of Ra-Hoor-Khuit.


The drawing in Figure 4 shows the generation of the Golden Section. Inside the double square in the center, a line is drawn from point A to point B, which bisects the line between the squares at the exact center, X. The compass is placed at X, and an arc is drawn that meets the base line CD. The relationship of the length of side a of the square to the length of a plus the length of side b of the small rectangle is 1:1.6180339…

The next step is to create a square from the resulting length of phi baseline, which in turn generates a smaller square with sides equal to the proportion 1/pi^2 which gives us the size of the cubical base under each Pillar. The diameter of the Pillar is the size of a circle within the square of a side of the cubical base.

The side platforms on which the Pillars rest are rectangles formed form the length of phi minus the length of the side of the main platforms square, by the length of platform square. When a Vescia Piscis is drawn using the center mark of the central square on each side, the Pillars will sit in the apexes of the Vescia. This is also the exact center of each rectangle, further expressing the sacredness of the design. [fig 5]


The complete formula of the Throne and Pillars. The square AMKJ is the primary form, from which all others are generated. An arc drawn from M to N with the center point P on line JK with a radius of PA generates, from the Golden Section, a baseline of JN. This in turn generates the square ABCD which defines the central platform, and square KNDL, which gives the size of the circular Pillars, by squaring the circle. Square CDRQ is implied to generate the centerlines P and S, used to derive the Golden Section.

Square AMJK determines the size of the Throne, which is placed in the dead center of ABCD.

The side platforms are defined by ACEG and BFHD. The size of the side platforms are generated, the baseline of which is determined by the arc GH drawn with the center point at S, with a radius defined by SA. The opposing arc running from E to F defines a vescia picis with arc GH and the circles of the Pillars are placed at the apexes of the vescia.

The calculations of the Vescia Picis are shown in Figure 6. The Vescia, like the Golden Section, appears in Sacred Geometry of almost every tradition, from the Egyptians to the Shelia Na Gig of the Celts to the doorways to the Catacombs of the Gnostic Christians. The Egyptians looked on it as the shape of the Eyes of Ra and Horus. Using the Vescia — a Feminine geometric form — to invoke the placement of the Columns (the Masculine forms) and the Throne (of Ma’at, who is the balance between all forces) further reinforces the symbolism of the Columns marking the Doorway between the Realms.


The Vescia is a function of the square root of 3, while the Golden Section is a function of the square root of 5. Thus the entire construct partakes in the symbolism of both 3 (the Triune of Isis-Osiris-Horus, or Nuit-Hadit-RaHoorKhuit) and the Five Elements.

The Vescia is also 1 / 6th of the area of the circles that generated it, and so the placement of the Throne (measuring 5 units on a side) within the Vescia (as defined by the Pillars) fulfills the magickal expression of 5=6, the Portal of the Adept. The 6 value is “occult”, hidden, expressed only in the relationship of the proportions, but still something another Adept could “decode” and understand. And the Deep Mind of any sentient being does understand.

The capstones of the pillars are identical stained-glass tetrahydrons (a pyramid with a base and three sides), colored red, that will be lit from within by miraculous (battery powered) means. (Maybe they should pulsate with specific “geometrially” correct patterns.) The ratio of the base to the height will be phi, as with the Great Pyramid.

This design yields an overall dimension of six feet across and 2 feet, 8 inches deep. If the pillars are also six feet in overall height, then the three-dimensional expression of the Golden Section is complete. The basic design calls for the throne, the pillars, and the platform they occupy, to form one interlocking structure, but one that can be taken apart for storage and transportation. The Throne is free-standing and can be moved by means of handles on the back, making it less awkward in ritual. One of the design specs I’m going to use for our temple furniture is that it all be portable, so we can literally “construct” our Hall anywhere we wish


The operative idea here is to construct a receiver/transmitter “device” that links the Temple to the Astral. I can see uses for this beyond it’s place in the Hall of the Neophytes and in other Invocations. Rituals could be developed around it where any “portal” is required, or it could be cast in the role of a psychic “receiver” for purposes of divination readings (especially using trance-based oraclular systems). It could be a transmitter (current flows both ways!) for spellcastings and enchantments, or even a “launching pad” for sevitors!

Geomonic expansion, based on the transcendental numbers, is how you tune it to the forces with which you wish to interact. (The Circle is the most basic expansion of a transcendental number and every traditon of magic or myticism includes a Circle symbol.) With sacred geometry we link our work to the very fabric of reality itself.

The “higher” mathematics were once only understood by Initiates of the Mysteries. In fact, that hasn’t changed, even though most things can be found in print or on networks now. Some secrets are self-selecting and have no need to be “guarded”.


Sacred Geometry, Geoffry Pennick

Sacred Geometry, Philosphy and Practice, Robert Lawlor

Time Stands Still, Keith Critchlow

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