The Law of Tangents

by Steven M. Adkins

In a series of posts over the last year we have examined several images of objects, logos and street patterns which involve triangles. This, in certain contexts, may be linked to Masonic symbolism. We're not entirely sure this is the case, but we've set off down a path and intend to follow it until it either leads to an end....or we turn back from exhaustion, boredom or disillusionment.

Some time ago, a friend told us that Freemasons in France were heavily involved in the business of real estate and property development, in addition to building. They are Masons, after all!

We have no idea whether or not this is true. We did begin to find, however, in a recent bout of pyramid obsession, several companies which in fact use pyramids as their logo. Soon after, the triangle began popping up everywhere. One goes to withdraw money from the cash machine and just next door is a real estate agency with a pyramid logo. One visits a client in a neighboring town and across the street there's a builder with a triangle logo. What gives? Coincidence? Was our friend right about Freemasons and the real estate business?

Would a triangle logo indicate this is so, in any event? Maybe a triangle is simply like the three balls of the pawnshop or the striped pole of the barber, a symbol of the trade. It's a logical choice. The figure appears solid, stable, yet dynamic. It evokes the roof of a house; it's a visibly striking and fundamental form. Not to mention the architect uses triangles as part of the trade; it's one of the essential tools.....the square, the compass, the triangle, the ruler. Seeing any of them in the context of the industry is unsurprising.

Ultimately, for us this all hinges on one unverifiable statement made by a friend. Which is exactly the point. We become the focal point for objectively verifiable facts which come to assume meaningful patterns when filtered through the subjective lens of our brain. "Now we see but a poor reflection as in a mirror; then we shall see face to face. Now I know in part; then I shall know fully, even as I am fully known." (1 Cor. 13)

Before we begin posting the pictures we've been taking of said triangles--which are becoming copious--we thought we'd quote liberally from Mackey's Encyclopedia of Freemasonry and its Kindred Sciences.

We posses a copy of this Encyclopedia, but found it already transcribed on the web by the Phoenixmasonry Museum and Library. Curator Dave Lettelier has kindly given us permission to copy and paste the entries they've transcribed, thus saving us a bit of work. Thanks! Please give the site a visit and peruse their excellent collection of articles.

We have reformatted the text to try and mimic the original a little more closely, and we have made a few slight alterations to correspond more exactly to our copy of the original, but otherwise have not altered the text.

We have also added the images. Don't be surprised to see them cropping up everywhere cheap conspiracy theories are sold!


There is no symbol more important in its significance, more various in its application, or more generally diffused throughout the whole system of Freemasonry, than the triangle. An examination of it, therefore, cannot fail to be interesting to the Masonic student.

The equilateral triangle appears to have been adopted by nearly all the nations of antiquity as a symbol of the Deity,
in some of his forms or emanations, and hence, probably, the prevailing influence of this symbol was carried into the Jewish system, where the yod within the triangle was made to represent the Tetragrammaton, or sacred name of God.

The equilateral triangle, says Brother D. W. Nash (Freem. Mag. iv., 294), "viewed in the light of the doctrines of those who gave it currency as a divine symbol, represents the Great First Cause, the Creator and Container of all things, as one and indivisible, manifesting Himself in an infinity of forms and attributes in this visible universe." Among the Egyptians, the darkness through which the candidate for initiation was made to pass was symbolized by the trowel, an important Masonic implement, which, in their system of hieroglyphics, has the form of a triangle. The equilateral triangle they considered as the most perfect of figures, and a representative of the great principle of animated existence, each of its sides referring to one of the three departments of creation, the animal, vegetable, and mineral.

The equilateral triangle is to be found scattered throughout the Masonic system. It forms in the Royal Arch the figure within which the jewels of the officers are suspended. It is in the Ineffable Degrees the sacred Delta, everywhere presenting itself as the symbol of the Grand Architect of the Universe. In Ancient Craft Masonry, it is constantly exhibited as the element of important ceremonies. The seats of the principal officers are arranged in a triangular form, the three Lesser Lights have the same situation, and the Square and Compasses form, by their union on the greater light, two triangles meeting at their bases. In short, the equilateral triangle may be considered as one of the most constant forms of Masonic symbolism.

The right-angled triangle is another form of this figure which is deserving of attention. Among the Egyptians, it was the symbol of universal nature; the base representing Osiris, or the male principle; the perpendicular, Isis, or the female principle; and the hypotenuse, Horus, their son, or the product of the male and female principle.

This symbol was received by Pythagoras from the Egyptians during his long sojourn in that country, and with it he also learned the peculiar property it possessed, namely, that the sum of the squares of the two shorter sides is equal to the square of the longest side symbolically expressed by the formula, that the product of Osiris and Isis is Horus. This figure has been adopted in the Third Degree of Freemasonry, and will be there recognized as the Forty-seventh Problem of Euclid (see Geometry, Circle, Square, and Forty-seventh Problem).

Triangle and Square.
As the Delta was the initial letter of Deity with the ancients, so its synonym is among modern nations, It is a type of the Eternal, the All-Powerful, the Self Existent.

The material world is typified by the Square as passive matter, in opposition to force symbolized by the Triangle.

The Square is also an emblem of humanity, as the Delta or Triangle typifies Deity.

The delta, Triangle, and Compasses are essentially the same. The raising one point, and then another, signifies that the divine or higher portion of our nature should increase in power, and control the baser tendencies. This is the real, the practical "journey toward the Last."

The interlacing Triangles or Deltas symbolize the union of the two principles or forces, the active and passive, male and female, pervading the universe. (1.)

The two Triangles, one white and the other black, interlacing, typify the mingling of the two apparent powers in nature, darkness and light, error and truth, ignorance and wisdom, evil and good, throughout human life. (2.)

The Triangle and Square together form the Pyramid (3.), as seen l in the Entered Apprentice's Apron. In this combination the Pyramid is the metaphor for units of matter and force, as well as the oneness of man and God. The numbers 3, 5, 7, 9, have their places in the parts and points of the Square and Triangle when in pyramidal form, and imply Perfection (see Pointed Cubical Stone.)

Triangle, Radiated.
A Triangle placed within and surrounded by a circle of rays. This circle is called in Christian art, a Glory. When this Glory is distinct from the Triangle, and surrounds it in the form of a circle, it is then an emblem of God's Eternal glory. This is the usual form in religious uses. But when, as is most usual in the Masonic symbol, the rays emanate from the center of the Triangle, and, as it were, enshroud it in their brilliancy, it is symbolic of the Divine Light. The perverted ideas of the Pagans referred these rays of light to their sun-god and their Sabian worship.

But the true Masonic idea of this Glory is, that it symbolizes that Eternal Light of Wisdom which surrounds the Supreme Architect as a Sea of Glory, and from Him as a common center emanates to the universe of His creation.





Museum Home Page     Phoenixmasonry Home Page

Copyrighted 1999 - 2019   Phoenixmasonry, Inc.      The Fine Print