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.

Andrew P. Gilkey: Treasurer of his Lodge

Andrew P. Gilkey, 1860-1870. Probably Maine. Gift in Memory of Jacques Noel Jacobsen, 2008.038.16.

Sometimes even a small clue can lead to information about an object or image in the collection of the Scottish Rite Masonic Museum & Library. This photographic portrait shows a man wearing Masonic regalia, standing on a patterned floor in front of a plain background, with one hand resting on a stylish side chair. Along with an apron, he wears an interestingly shaped sash (which may have actually been a separate collar and sash that appear as one piece in this image), and an officer’s jewel suspended from a ribbon around his neck. His jewel is in the shape of two crossed keys. In Freemasonry, this symbol indicates the lodge office of Treasurer. To add pizazz to the image, an artist painted the sash blue and gold and added gold to the apron and jewel. This special treatment enhances the simple portrait and draws attention to the sitter’s regalia. An inscription on the back of this photograph, produced in the pocket-sized carte-de-visite format popular in the 1860s, records the name of the sitter, Andrew P. Gilkey, along with the information that he was the “Treasurer Royal Arch Masons.” This inscription offers valuable clues about the subject of the portrait.

Census takers recorded a man named Andrew P. Gilkey (1809-1890). This man was a resident of Islesborough, Maine, from 1840 through 1880. An 1876 business directory listed Gilkey as a carpenter and builder in the same community—an island town in Penobscot Bay. Membership records at the Grand Lodge of Maine show that Andrew P. Gilkey received his degrees at Island Lodge No. 89 in Islesborough in 1857. From 1860 through 1870, the Grand Lodge noted that Gilkey served as Treasurer of his lodge. A notice in the Portland newspaper confirms that he held this office in 1870.

Although the inscription on the back of the photograph suggests Gilkey was a Royal Arch Freemason, his name does not appear in the Proceedings of the Grand Chapter of Maine as the treasurer of a chapter during the 1860s. As well, the apron he wears in this portrait features symbols related to Craft, rather than Royal Arch, Freemasonry. It is possible that the inscription on the back of the photograph noted the name and office of the sitter but misstated his connection with Royal Arch Masonry.

Married twice, Gilkey outlived both of his wives and four of his children. His grave marker, near those of family, bears his name, his age at his death, and a symbol of Freemasonry, a square and compasses with the letter G, emphasizing his long-time association with the fraternity.  

References: 

“Masonic,” Daily Eastern Argus (Portland, ME), March 15, 1870, [3].

Maine Business Directory(Boston, MA: Briggs & Co., 1876), 63.

John Pendleton Farrow, History of Islesborough, Maine (Bangor, ME: Thomas W. Burr, 1893), 212-213.

Jewels in Blue

Cyanotype of a Past Master's Jewel made for Otis E. Weld, 33°. Probably Boston, Massachusetts. Loaned by The Grand Lodge of Masons in Massachusetts, GL2004.10643g.

In 1842, British scientist and astronomer Sir John Herschel (1792-1871) invented the cyanotype process—a photographic printing method that produces a cyan-blue print, commonly known as a blueprint. Engineers, scientists and photographers used the process as a simple and low-cost way to produce copies of drawings, photographs, and technical and architectural plans, from the 1870s through the 1950s.

Some cyanotype examples are in the Grand Lodge of Masons in Massachusetts collection at the Scottish Rite Masonic Museum & Library. These particular cyanotypes are photographs of Masonic jewels and likely belonged to Otis Everett Weld, 33°(1840-1897). They are part of a larger group that appear to be documenting jewels owned by Weld. Weld, born in Boston, was head of the Otis E. Weld & Co, wine merchants and director of the Third National Bank and Bolyston Insurance Company.

Initiated in 1866 in the Lodge of Eleusis, he served as Junior Grand Warden and Grand Master of the Grand Lodge of Massachusetts in 1880 and 1894, respectively. Weld was also a member of St. Bernard Commandery and St. Andrew’s Chapter, both in Boston, and a trustee and financial benefactor for Masonic organizations.

In the June 1897 Grand Lodge of Massachusetts proceedings Thomas W. Davis (1844-1914) offered these kind words in his memorial, "His advancement in our Order was due not alone to his gifts of popularity, boundless though they seemed; not because he was an appreciative student of the ritual, but because the teachings of the Institution permeated his very being...".

These photographs show the varied ways the cyanotype process could be utilized beyond architectural plans. Have you encountered images using this photographic process? Have you seen jewels similar to Otis E. Welds's? Let us know in the comments section below.

References:

Proceedings of the Grand Lodge of Massachusetts, (Boston, Massachusetts: Rockwell & Churchill, 1897) 101.

Cyanotypes, The Atlas of Analytical Signatures of Photographic Processes The Getty Conservation Institute,https://www.getty.edu/conservation/publications_resources/pdf_publications/pdf/atlas_cyanotype.pdf, accessed June 2019.

Cyanotype of Grand Master's Jewel made for Otis E. Weld, 33°. Probably Boston, Massachusetts. Loaned by The Grand Lodge of Masons in Massachusetts, GL2004.10643e