Masonic Mathematics: The 47th Problem of Euclid

Past Master's Jewel, 1823. Thomas Harper (ca. 1735-1832). London. 2017.018.2. Photograph by David Bohl.

Do you remember the Pythagorean Theorem? This geometric figure, also known as the 47^th Problem of Euclid, represents the idea that the area of the two smaller squares created by using the lines of a right-angle triangle as bases is equal to the area of the largest square created in the same way. It is stated mathematically as c² = a² + b² in which “c” is the hypotenuse (longest side) and “a” and “b” are the other two sides. Like many geometric expressions, it’s difficult to describe with words, but its meaning is fairly comprehensible visually.

Luckily, then, this symbol appears on Masonic aprons, jewels, pitchers, quilts, lantern slides, mark medals, tracing boards, and other decorative and ritual material in the collection of the Scottish Rite Masonic Museum & Library. Freemasonry draws symbols from a variety of sources, including geometry, to teach instructive lessons to its members.

This geometric figure has two names associated with some of mathematics’ historic giants: Pythagoras (ca. 570 B.C.E. – ca. 495 B.C.E.) and Euclid (ca. 300 B.C.E.). However, its roots reach back further. Babylonians (ca. 1900 - 1600 B.C.E) used it to solve geometric problems that involved right triangles. In Freemasonry, it is often called the 47^th Problem of Euclid. This symbol is introduced in the 3^rd or Master Mason degree.

The object shown here, an engraved Past Master’s jewel, bears a particularly compelling visual representation of this noteworthy geometric figure. English silversmith Thomas Harper (ca. 1735-1832) crafted this jewel, marking it with his initials and British silver hallmarks. The “leopard’s head” mark indicates that the silver was hallmarked in London after 1822. The lowercase “h” indicates Harper made the item in 1823, according to the “date letters” that were used in British silver.

Past Master's Jewel, 1823. Thomas Harper (ca. 1735-1832). London. 2017.018.2. Photograph by David Bohl.

This form of a Past Master’s jewel featuring a right-angle square with a rectangle engraved with a depiction of the 47^th Problem of Euclid, was popular in English lodges in the early decades of the 1800s. This style of jewel inspired Past Master’s jewels in Pennsylvania, which often have a right-angle square bearing a suspended rectangle with the geometric figure engraved on it.

This fascinating Past Master’s jewel is currently on view at the museum in "What's in a Portrait?" and in our online exhibition. You can see other items in the museum’s collection that bear the 47^th Problem of Euclid on our searchable online collections database.