Geometry in Freemasonry

"No one enters here who is not a Geometer !" This was the sentence Plato had inscribed on the pediment of his school, the Academy. And Freemasonry could put the same sentence at the entrance to its Lodges, so important a role does Geometry play in it. Doesn't Freemasonry state in many of its rituals that Geometry is the most useful science for a Mason ? Aren’t the two most emblematic tools of Freemasonry the Compass and the Square, which, before being tools for builders and craftsmen, are instruments of Geometry ? As we shall see, Geometry has been honoured by Builders since time immemorial, and Freemasonry, which claims to have inherited from them, has followed in their footsteps.

Geometry in ancient times

We started with Plato, but basically all the Greek philosophers were concerned with Geometry, starting with Pythagoras and Euclid, who are so often referred to in the Old Charges of English Masons, which date back to the end of the 14th century. Pythagoras, Euclid, Thales - these are names you all heard at school, and you may have thought they were just mathematicians. However, they were not: they were Philosophers in the highest sense of the word, in other words, lovers of Knowledge.

From a Platonic point of view, for example, Geometry is much more than just a technical or academic discipline. It is a means of applying thought to reality, which resides in the Ideas (i.e. in the purest abstraction), and of which the manifested phenomena are only pale images. For example, the Triangle exists in itself, as an Idea, i.e. as a category of thought. You can mentally contemplate a Triangle, you can draw it, you can specify whether it is an equilateral, isosceles, right-angled or scalene Triangle, you know the sum of its angles, you can calculate its area... But have you ever seen a perfect Triangle in Nature? You've only seen approximations, but that in no way prevents you from being able to think about all the characteristics of the triangle, without having to observe a concrete, material phenomenon.

This is why Geometry, far from being confined to the technical trades that needed it (the so-called Servile Arts), was integrated into the intellectual training curriculum of Latin Antiquity, which was generalised under Charlemagne and lasted throughout the Middle Ages : the Liberal Arts, which are seven in number and can be divided into two parts, the Trivium and the Quadrivium.

The Trivium (the threefold path) was the first part taught and included the Arts relating to the "power of the word". These were Grammar, Dialectics and Rhetoric, arts that enabled students to express themselves clearly and structure their thoughts through the logic of reasoning.

The Quadrivium (the fourfold path) was taught to those who had mastered the Trivium. The four Arts of the Quadrivium concerned the "power of numbers". They were Arithmetic, Music, Geometry and Astronomy. On completion of the Quadrivium, students were awarded the title of Master of Arts and, from the 12th century onwards, could enter university. The knowledge transmitted by the Liberal Arts was considered to be the noblest and most elevated, as it led to philosophy and theology.

Geometry for the Ancient Builders 

It was undoubtedly to assert the nobility of their profession that medieval English Masons, from the 14th century onwards, equated Masonry with Geometry. The oldest version of the Old Charges, the Regius manuscript (generally dated 1390) begins with the words : "Here begin the constitutions of the art of geometry according to Euclid". Later Old Charges would also describe Masonry as Geometry, adding in praise of the Seven Liberal Arts, which is still absent from the Regius.

By doing so, the Old Charges placed Masonry among the noblest and most complete branches of knowledge, clearly refusing to consider it as a Servile Art. The way was paved for the development of speculative Freemasonry.

Geometry in speculative Freemasonry 

Inheriting this tradition, Freemasonry speaks a lot about Geometry. It is omnipresent in its symbolism, first and foremost through its many working tools : the square, the compass, the ruler, the level and the perpendicular are construction tools, but they are also instruments of Geometry, which for the speculative Freemason become keys to understanding the world and himself. The Old Charges' intuition that Masonry was founded on the Liberal Arts, in the same way as philosophy and theology, is therefore verified. It is not technical knowledge that Freemasons seek, but complete philosophical and spiritual knowledge of the world and of themselves.

But it is in the Fellowcraft degree that, in most Masonic Rites, Geometry is most explicitly presented. The climax of the reception of the second degree is the finding of the Blazing Star, with the letter G at its centre. The Blazing Star is a pentagram, which was already the emblem of the Pythagorean school. It is constructed according to the Golden Proportion and is reproduced ad infinitum, in both the infinitely large and the infinitely small. In fact, in the central pentagon of the Blazing Star, you can draw a new inverted star, at the heart of which you can draw a new star, and so on. In the same way, the five points of the Blazing Star form a pentagon which becomes the centre of a larger Star, itself the centre of an even larger Star. Along with the Triangle, which is the first, simplest and purest geometric form, the Blazing Star is probably the best symbol of Geometry. And it is good to see that some Lodges continue to teach their Fellowcrafts the Art of tracing the Blazing Star in the traditional way, i.e. with the Compass and Ruler. Having had the privilege of receiving such instruction, we can testify that it is an extraordinary experience and an incomparable medium for reflection and meditation.

The letter G placed at the heart of the Star reinforces its geometric dimension. It can be interpreted in different ways (God, Gravitation, Generation, Gnosis, etc.), but the most obvious meaning is Geometry. And it's no coincidence that some Fellowcraft rituals no longer speak of the Great Architect of the Universe, but of the Great Geometer of the Universe.

But the Fellowcraft degree is not the only one to be concerned with Geometry. This is also the case for the Grand Architect, the 12th degree of the Ancient Accepted Scottish Rite. In this degree, the recipient is presented with a geometry case containing seven tools, the list of which may vary from square, simple compass, four-pointed compass, ruler, line-drawer, proportional compass, folding ruler, protractor, plumb bob and drawing pin.

In the instruction for this grade, the following question is asked "What is the first of all the arts ?", to which the answer is "Architecture, of which Geometry is the key, as well as the rule of all the sciences". The intuition of the medieval builders who wanted to make Masonry an Art, a noble Knowledge, is fully achieved in this degree.