## 6. Sacred Geometry: the Square, Part 2

This is the sixth in a series of articles discussing Sacred Geometry. We left off last week’s discussion of the Square noting that it was the best symbol to represent the manifest or 3-D realm of creation. To understand, in terms of Sacred Geometry, this is true we need to follow a process known as

For this process we will be relying heavily on Pythagoras, the famous Greek mathematician, who taught that the experience of life in the 3-D manifest realm of the finite was expressly for the purpose of discovering and manifesting the supernatural existence even as we are yet in our physical finite bodies. Pythagoras urged his students to view the finite for clues on how intrinsically it contains a power to express the infinite. He urged us to ponder the abstract principles operating behind the scenes. With this urging in mind, we see that Pythagorean mathematics dealt strictly in whole numbers--i.e. definable, manifested states that could be verified in everyday life.

How Pythagoras determined that the geometric frame of the Square is the best symbol of finite perfection came as a result of a process known as

Our first task is to derive a perfect square from a circle and line--the first two shapes in Sacred Geometry’s symbols for bringing forth the seen (manifest) realm from the unseen. This process is to be achieved with the simple instruments of a compass and a strait edge or measuring stick, much like the Messianic emblem.

*Squaring the Circle*.For this process we will be relying heavily on Pythagoras, the famous Greek mathematician, who taught that the experience of life in the 3-D manifest realm of the finite was expressly for the purpose of discovering and manifesting the supernatural existence even as we are yet in our physical finite bodies. Pythagoras urged his students to view the finite for clues on how intrinsically it contains a power to express the infinite. He urged us to ponder the abstract principles operating behind the scenes. With this urging in mind, we see that Pythagorean mathematics dealt strictly in whole numbers--i.e. definable, manifested states that could be verified in everyday life.

How Pythagoras determined that the geometric frame of the Square is the best symbol of finite perfection came as a result of a process known as

*Squaring of the Circle*.Our first task is to derive a perfect square from a circle and line--the first two shapes in Sacred Geometry’s symbols for bringing forth the seen (manifest) realm from the unseen. This process is to be achieved with the simple instruments of a compass and a strait edge or measuring stick, much like the Messianic emblem.

**Step 1:**For this process we will start with a line (AB) and locate any point C below line AB and somewhere near its midpoint. Using C as the center and CB as the radius, swing an arc making a circle: cutting AB at point D. Draw a line from C to D and continue that line until it intersects the circle at E. Draw the line EB. Notice that it is perpendicular to AB.

**Step 2:**With B as the center and a radius of AB swing a second arch cutting the extension of BE at G. Using the same radius (AB) swing two more arches first with G as the center and then with A as the center. Where these arches cross will be at B and the new point F which completes the Square.

In the following diagram, you can begin to see that by using the diagonal of the smallest square as the radius the next larger circle, you can create the squares that graduated in size. In this way, one squares the circle and then in turn circles the square. What is important to note is that in this growth process, you go from circle to line to triangle to square. Square two is exactly double in area to square 1; square 3 is double in area to square 2, etc.

The diagonal of the second square (tipped on its side) becomes the side of the third square, whose diagonal is 2 times the diagonal of the original square or 2¸. The largest square in the diagram to the right has a diagonal that is 4 times the diagonal of the original square (4¸). In short the square divided by its diagonal provides an archetypal model for geometric proportions and progressions where each term is multiplied by a constant value (in this case the diagonal of the first square which is also the root of the second square (¸) in order to achieve the next term in the progression. In the relationship between proportion and progression, we are reminded of an alchemical axiom:Everything in Creation is formed from a fixed, immutable component (proportion) as well as a volatile, mutable component (progression). |

The relationship between the

The term “root” is an ancient designation which associated the mathematical root to the root of a plant. Both are

Natural forms understood as symbols help reveal metaphysical archetypal principles that can guide us on our quest for truth. The square root of two is the geometric function which represents the universal metaphor of the root, and the root represents the

More will be said about the

____________________________________________

[1] Robert Lawlor’s

*fixed*and the*volatile*(between proportion and progression) is central to understanding the crux of Sacred Geometry.*Everything which is in the manifest realms belongs to the ever-flowing*

progressions of constant change.progressions of constant change.

*The fix or immutable laws belong to*

the metaphysical realms. Chathe metaphysical realms. Cha

*nge is the only guaranteed constant in the*

physical realm.physical realm.

*The unchanging generative principles reside in the*

metaphysical realmmetaphysical realm

The term “root” is an ancient designation which associated the mathematical root to the root of a plant. Both are

*causative*--were it not for the roots, the plant would not exist. In the case a mathematical root, the root is embedded not in the ground but in the square. Further, the root cells of a plant are a powerful metaphor for the principles of integration and transformation. The root is a symbol for the law of sacrifice in nature; its efforts are not for its own benefit but to uplift the plant in its movement toward the light.Natural forms understood as symbols help reveal metaphysical archetypal principles that can guide us on our quest for truth. The square root of two is the geometric function which represents the universal metaphor of the root, and the root represents the

*Principle of Transformation*.*To seek the root is to return to the source and to return to the source is*

to pursue one’s destiny.to pursue one’s destiny.

**[1]**More will be said about the

*Principle of Transformation*in next week’s article, when we continue our discussion of the Square.____________________________________________

[1] Robert Lawlor’s

__Sacred Geometry: Philosophy and Practice__.