Washington DC Monumental Core Shown to Be
Analogous to the Milan Cathedral

The Canon

A book entitled The Canon (400 pages, available on line) published in 1897, promises to give us a clue about the method practiced by the old architects in building the temples and cathedrals, as well as the principles which were the common groundwork of all the arts and sciences; that is, an established canonical law underlying the practice of building, and the other arts.

Principles = theory, and method = praxis, technique. The book aims, then, to show us a method of construction, actually a design technique called consrtuction geometry, and then the philosophical notions that underlie that.

The author suggests that, since everything in the "old world" centered in religion and the priests were practically the masters of that world, the secrets for building temples or cathedrals under ecclesiastical authority were the secrets of religion; that is the esoteric doctrine of religion.

Simply stated, this means that religous structures were intended to encoded the local Canon, like the Pyramids in Egypt. You may recall the story of Enoch who, after having been warned of the Flood, had built two pillars engraved with the sum totality of human knowledge. (Note: Enoch stories are about the transmission and preservation of knowledge).

Temples and catherdrals were encyclopedic; archives of symbol sets, the meaning of which were held secret by a relative few.

Peter Tompkins writes:

"In Egypt the temple was the expression of a self-perpetuating group of initiates responsible for keeping intact a wisdom, based on a precise knowledge of universal laws; a sacred science passed on through myth, ritual and music, based on number and measure, incorporated into structures and built into tombs and temples. It is the same knowledge passed on to the builders of the great medieval cathedrals- a profound understanding of universal harmonic, rythmic and proportional laws and a precise knowledge of the manner in which to employ these laws to create a desired effect." (pp452-3 "The Magic of Obelisks")

Construction Geometry

Geometric design, depends on what are called "regulating lines" to aid in the placement of features in a designed work. The regulating lines are usually derived from digonals of squares and rectangles, the favorite ratios being 1:1 and 1:2. The 1:1 ratio features circles and squares, and 45 degree triangles that are half a square; all of which symbolize equality.

The 1:2 is produce by two different triangles. Using an example of a window, we can say that the 60 degree angle diagonal (below) makes the width half the diagonal, while a 63+ degree angle produces a window whose width is half it's height. 1:2 symbolizes unity in duality.

All three of these depend on easy to remember and use geometric figures that produces whole number ratios. [Beware of people pushing the square root of three, you can't find that on a measuring tape, and multiplying by it is a nightmare.] The method itself was designed to be simple enough that even an apprentice could pick it up. What was kept secret among the building masters and the clergy was the mystical meanings behind the use of the different ratios.

Polygonal Mesh Projection

Moderns who have discovered the method, have dubbed it "polygonal propogation", because it depends on a mesh or grid that is developed by projecting the lines of regular geometric figures (polygons- triangle, square, pentagon, hexagon) inscribed in a circle. See the image below, taken from the crypt of a cathedral architect, which features a grid pattern on the roof of the model that he is holding.

The most popular forms of this are:

  • Ad Triangulum, based on a hexagon in a circle, and which produces figures with 3, 6, 9, 12, 15 and 18 points on a circle.

  • Ad quadratum, based on a cross or a square in a circle, and which produces figures with 4, 8, 12 and 16 points on a circle, like a compass.

  • Quintile, based on a pentagon in a circle, and which produces figures with 5, 10, 15 and 20 points on the circle.

    You will note that each of these represents one term of the famous 3-4-5 right triangle. As the numbers show, you can also use 6-8-10 or 9-12-15, etc. Whole number ratios.


    Mandala- A Circle and Square

    While it is true that all regular polygons represent the notion of equality, in that they are composed of equal sides and equal angles, only the square has the same number of degrees as the cirlcle (360), making them a matched pair (the 1 to 1 ratio), like the compass and square chosen to symbolically represent the two. Note that the (carpenter's) square is associated with the square (polygon) as the symbol for the element of earth, and with the cube as a symbol for materiality and 3D time-space, while the compass is naturally associated with the circle as the symbol for spirit and the sphere as a symbol for the vault of the sky and heavens.

    The conjunction of the circle and square came to represent the meeting of heaven and earth, and the madala based on this form represents the cosmos in relationship to divine forces, as well as a union of opposites, a crossing if you will. Architecturally this connection between heaven and earth is represented by the pillar, column, or obelisk. A column connects the roof to the floor, and is round with a square base. The archetype of this is the Djed Pillar.

    Tons Brunes, in his"Secrets of Ancient Geometry", suggests that the cross is the "first geometric addition to the circle and square", and is the key to the developement of numerals and the alphabet. He demonstrates in the book, how the circle inscribed in a square and quartered by the cross enabled Egyptians to inscribe other basic figures such as the pentagon, hexagon and octagon, etc.

    The Principle of Crossing

    Schwaller de Lubicz, in his book "The Temple of Man", introduces what he calls "the principle of crossing" as a symbol for the process by which things come into being. All acts of creeation, whether physical, intellectual or spiritual, require a crossing of opposites, whether it be time and space, spirit and matter, light and dark or male and female. The circle in a square produces a "plus" sign and a "times" sign, both signs of increase.

    The simplest geometric expression of this notion is the crossing of vertical and horizontal lines which produces the warp and weft of weaving. Note that there are many legends which feature baskets, webs, nets and weavers as symbols of the creating and creation.

    The Royal Wedding

    The alchemists uses the term "royal wedding" to refer to this principle of unity in duality, and symbolized it by the Star of David composed of two intertwining equilateral triangles. The yin/yang symbol represents the interpenetration, strife and unity of opposites. Interpenetration because, the white has black at the center, and visa versa- symbolizing that their respective meanings are complementary. Strife because they are mutually exclusive, and unity, because it takes both to complete the notion.

    The temple or cathedral was seen as an instrument of the fusion of heaven and earth, just as the Djed pillar, and the old standing stones were.

    This use of sexual metaphor, is right in line with the ancient tendency to illustrate philosophical principles using naturalistic images, and has been greatly misunderstood.

    The Establishment of Rome

    The mandala forms the ground plans of both sacred and secular buildings, but often goes unnoticed. A number of cities have been founded on the mandala ground plan as well. Plutarch tells us that the Etruscans taught the foundation of a city as a secret rite. The purpose of the mandala ground plan was to symbolically transform the city into an ordered cosmos, a sacred place; to establish the cities relationship with the other realm.

    Plutarch's account of the foundation of Rome tells how Romulus first dug a round pit (called "mundus", literally the world)), and threw offerings of the fruits of the earth into it (compare to Masonic cornerstone ceremonies). Around the pit, Romulus drew a boundary for the city in a circle with a plow drawn by a bull and a cow. The city was then divided into four parts by two main arteries running N-S and E-W, the point of intersection being the pit at the center. In later times the church or cathedral was positioned at the intersection.

    You will please note three examples of "crossing" in this story; the cross itself, the circle and the cross, and the bull and cow. Note as well, that plowing, like warfare, is an old sexual meatphor.

    Urbs Quadrata

    A city fashioned in this manner has a circular shape, and many medieval cities founded on the mandal plan were surrounded by circular walls, but in old descriptions, Rome is called urbs quadrata, the square city. Attempts to reconcile this apparent contradiction have suggested that "square" means 90 degrees and not a polygon, meaning that the city was square to the meridian, or that the streets formed a regular grid.

    Then again, it could be interpreted as a square set within a circle, as we see in this image of the District of Columbia, which encompasses a 10 x 10 mile area.

    Vesica Piscis

    The term vesica piscis refers to a figure formed by the overlapping (crossing) of two equal circles, such that the center of each lies on the circumference of the other; another symbol of unity in duality. Speaking of the vesica, Jonathan Hale (in his book "The Old Way of Seeing Things") says, "In every gothic church, the shape is repeated like an incantation wherever one looks, and it may persist in the building's cross section (elevation), where it becomes an enclosing geometry of regulating lines".

    Continuing he suggests that the shape represents the materialization of spirit, the joining of the temporal and the spiritual, and a place where body and spirit come together. The gothic cathedral builders, he says, were not attempting to produce beauty alone; their purpose was to embody aspects of the universal spirit.

    The vesica is essentially a dual symbol which expresses the principle of crossing thru the twin circles, the twin equilateral triangles forming the rhombus, and by the pairs of right triangles that form the equilateral ones; essentially by mirror symmetry. This notion is reflected in the fact that the square (right) triangles have a short leg that is half the hypotenuse. The ratio being expressed here is 1:2.


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