The Problem of Euclid

What is it about about Euclid's 47th Problem that has made it such a venerated symbol in Freemasonry?

This is a question that many masons have asked over the years. There are many answers to this question, all of them with some sort of merit (even if it just shows us the folly of looking too closely in the wrong direction). Let's start with the enigmas.

Euclid's 47th problem (or more properly, proposition) is merely a proof for the theorem first put forth by Pythagoras. Most of us learned about it in school by the name of the Pythagorean Theorem. There are actually more proofs for the Pythagorean Theorem than any other geometrical problem! Euclid was not the first to discover a proof for the theory, and so has no special claim to the theorem than many other mathematicians (including President Garfield). Why this specific answer to the theorem was chosen, is perhaps a clue to its inclusion in the degree.

Pythagoras is reported (by masons) to have exclaimed 'Eureka!' when he discovered the answer to the problem, and then to have sacrificed a hecatomb (or a 100 oxen) in gratitude. This is certainly excessive! The phrase Eureka is most famously attributed to Archimedes, exclaimed when he was bathing and 'discovered' the correspondence between volume and weight, i.e. mass. But, as Pythagoras was also a Grecian, this is permissible, although slightly confusing.

The most simple and straightforward solution is that the 47th problem was widely used by masons to figure perfect squares. Without this utilitarian theorem, their buildings would have ended up in a more trapezoidal form rather than having squared corners. This is certainly a reasonable meaning: a way to test your Square (one of the prime symbols of masonry for other reasons) would be crucial to success as an operative mason.

Allegorically, the 47th problem could be compared to any number of different symbolic triads in and out of the lodge. I personally find it interesting to compare the problem to the three pillars, Wisdom, Strength and Beauty as represented in the Kabbalistic tree of life. I was going to draw you all a cool little picture showing how the typical triangle of 3x5x7 fits over the tree and shows it pointing to Hokhmah (wisdom), Gevurah (severity, judgment or strength) and Tiferet (beauty or harmony... but it looks out of proportion when actually held up the the square. This phenomena ends up being true of most of the allegories applied to the problem, they don't hold up under investigation. When looking for an allegorical solution to Euclid's Proposition, make sure there is something more to it than that they both happen to have three sides or attributes.

A very popular idea that has been running around for about 2000 years (since Plutarch wrote about it) is that, to the Egyptians, the sides of the right triangle represented the Gods Osiris, Horus and Isis. Albert Pike refuted it by scoffing, and we are left wondering about the likelihood of both of them.

Another fascinating explanation, is put forth in this blog post. It gives a whole new slant to the question.

If we are looking for a mystical meaning behind the 47th proposition of Euclid, there are many avenues that we can explore. Albert Pike will take you to visit the Hindus, and expound upon the numbers 3, 5 and 7. Others will tell you how they relate to the Hermetic traditions, or Alchemy or a hundred other traditions. But, behind each of these complexities lies a more simple style of truth, teaching us how to apply their teachings and ideas to the way we live our lives. The 47th problem of Euclid won't actually turn lead into gold, or give you the ability to fly, but it just might give you the secret to living a fuller life if you look at it just the right way. If you happen to find one of its secrets, make sure to yell Eureka! when you do.