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.

A Thomas Harper Jewel

Among the many treasures in the collection of the Grand Lodge of Masons in Massachusetts on extended loan to the Scottish Rite Masonic Museum & Library is this jewel manufactured by London silversmith Thomas Harper (ca. 1744-1832). Harper, a prolific and skilled smith, produced a variety of Masonic jewels in the late 1790s and first decades of the 1800s, including officers’ jewels, mark jewels and presentation jewels.  An active Freemason and an officer for the Antient Grand Lodge, he played a role in bringing together the Antients and the Moderns to form the United Grand Lodge of England in 1813.  Today collectors prize his work.  In honor of Harper’s many accomplishments as a craftsman and as a Mason, in 1996 a group of British brethren founded a Lodge of Research named in his honor. 

How this jewel became part of the collection of the Grand Lodge of Massachusetts is not known.  Hallmarks date it to 1811.  Its design—an oval in which much of the silver has been cut away (a technique called piercing) to form the shapes of several Masonic symbols—is one Harper produced many times.  An engraver outlined, detailed and embellished each of the emblems—a square, compasses, a level, plumb rule and a maul—on the jewel.  Cut glass stones set in silver ornament the hinge of the compasses, as well as form the bobs on plumb rule and level.  Pierced jewels, with only thin pieces of metal connecting different elements are fragile.  This one is missing a trowel that used to span the space between the right hand leg of the compasses and the rim.  You can view  jewels similar to this one as well as others Harper made in the collections database of the Library and Museum of Freemasonry, at the United Grand Lodge of England.

Intriguingly, long before Harper made this jewel or founded his London business as a Masonic jeweler, he lived in the American colonies.  In the 1700s he made his home in Charleston, South Carolina, the biggest and most prosperous city in the South at the time. There he advertised as a jeweler, goldsmith and seller of imported jewelry and silversmith’s tools. Researchers have noted that he was involved in Freemasonry in Charleston; he served as Junior Warden for Lodge No. 190 in 1774.  The likely-London born Harper (the place and date of Harper’s birth are not clear) chose not to join the colonists in their fight against the British government and, as a consequence, left South Carolina for the Dutch West Indies with his family (which eventually grew to include over ten children) in 1778.  The richest and most interesting information about Harper’s career in Carolina comes from the 1780s petition he made for lost property to the British government.  Among the losses he claimed were a small house and 465 acres outside of Charleston, an enslaved man who worked in his business, uncollected debts and four years of unrealized work as a silversmith.  Harper valued his losses at over four thousand pounds.  In spite of having a taken a sizeable financial hit early in his career, Harper rallied.  He established himself as a silversmith in London in the 1790s and worked in that trade until his death in 1832.   

Photo:

Jewel, 1811, Thomas Harper (ca. 1744-1832), London, England.  Collection of the Grand Lodge of Masons in Massachusetts, GL2004.3158.

References: 

E. Milby Burton, South Carolina Silversmiths 1690-1860, Rutland, Vermont: The Charles E. Tuttle Company, 1968.

Canada, Loyalist Claims, 1766-1835, ancestry.com.

Timothy Kent, “Thomas Harper (1736-1832), Masonic Jeweller and the Jewels of His Period,” Ars Quatuor Coronatorum (2004), 103-115.

Timothy Kent, “Thomas Harper, Masonic Jeweller and the Jewels of His Period,” Silver Studies (2005), 13-17.