47th Proposition of Euclid in Freemasonry: Meaning of the Masonic Symbol

Quick answer: The 47th Proposition of Euclid is the geometric theorem better known as the Pythagorean theorem: in a right-angled triangle, the square on the longest side equals the sum of the squares on the other two. In Freemasonry, its diagram became an emblem of geometry, accurate squaring and, in some jurisdictions, the office of Past Master.

The theorem

The proposition is number 47 in the first book of Euclid's Elements, the Greek geometry textbook written around 300 BC. Its simplest practical case is the 3-4-5 triangle: a triangle whose sides measure three, four and five units always contains a perfect right angle. Builders have long used that fact to set out and test square corners.

Why it matters in Freemasonry

Freemasonry uses the working tools of the stonemason as moral emblems, and the square is among the most important of them. The 47th Proposition is the geometric means of proving that a square is true. Masonic writers have used it as a symbol of geometry itself since at least the 1730s, and James Anderson's Constitutions of 1723 already gave the proposition pride of place in the history of the craft.

The Past Master's jewel

In 1815 the first Book of Constitutions of the United Grand Lodge of England prescribed the jewel of a Past Master as the square with the diagram of the 47th Proposition engraved on a silver plate hanging within it, a design still used in English Freemasonry. Other jurisdictions differ: the Past Master's jewel in Scotland and Ireland traditionally uses other emblems, though the proposition appears in Masonic lectures widely.

Legends and history

Masonic lore sometimes embellishes Pythagoras's discovery with colourful stories; these are best treated as legend. Historians also note that the relationship itself was understood and used in Babylonia and elsewhere long before the Greek proof.

The 47th Proposition in jewellery

A design based on the 47th Proposition references geometry, the craft of building and a distinctively Masonic emblem. See the AURYN 47th Proposition charm, or read our guide to Freemasonry symbols.

Frequently asked questions

Is Euclid’s 47th Proposition the Pythagorean theorem?

Yes. Proposition 47 of Book I of Euclid’s Elements proves the relationship now usually called the Pythagorean theorem for right-angled triangles.

Why is the 47th Proposition used in Freemasonry?

It connects geometry with the practical and symbolic importance of the square. In Masonic interpretation it can represent accurate building, geometric knowledge and the broader ideal of ordering work by measure and reason.

Is the 47th Proposition the Past Master’s symbol everywhere?

No. Masonic practice varies by jurisdiction. The proposition has a particularly strong connection with the Past Master’s jewel in English Freemasonry, while other Masonic jurisdictions use different emblems or arrangements.