47th problem of Euclid
A right triangle with a square on each side, the theorem that is the 47th proposition in the first book of Euclid's Elements. In Freemasonry it appears on the Past Master's jewel.
Meaning
In George Thornburgh's 1903 monitor the 47th problem is an emblem of the third degree that 'teaches Masons to be general lovers of the arts and sciences'. The Grand Lodge of California lists it among the less familiar Masonic symbols. It is also part of the jewel worn by a Past Master of a lodge in English Freemasonry, the form it took by 1798 or 1799.
Origin and history
James Anderson put a drawing of the 47th proposition on the frontispiece of the first Book of Constitutions in 1723, and again in 1738.
Pythagoras and 'Eureka'
The monitors tell how Pythagoras discovered the theorem, cried 'Eureka', 'I have found it', and sacrificed a hecatomb. A 1943 study in Miscellanea Latomorum disagreed on each point: the theorem is not necessarily Pythagoras's, the story of the word and the sacrifice is an error of Plutarch's, and the proposition builders actually use to prove a square, by the 3, 4 and 5 method, is the 48th, its converse.
Write in the Freemasons’ cipher
stringmash.comPigpen cipherThe grid cipher once used for lodge records, drawn from any text you type.Read next
- Next in Masonic symbolsApronThe white apron every Freemason wears in the lodge, known as the badge of a Mason.
- The same shape in Hanukkah symbolsDreidelA four-sided spinning top played with at Hanukkah. Its Hebrew letters, nun, gimel, hei and shin, stand for “a great miracle happened there”; in Israel a pei replaces the shin, for “a great miracle happened here”.
See also
Square and compasses, The letter G, All-seeing eye, Double-headed eagle, Boaz and Jachin, Checkered pavement.
Sources
- Masonic Monitor of the Degrees of Entered Apprentice, Fellow Craft and Master Mason, George Thornburgh, 1903, approved by the Grand Lodge of Arkansas, Project Gutenberg, Master Mason degree, emblems
- Euclid's 47th proposition, Miscellanea Latomorum, new series vol. 27, no. 8 (May 1943), pp. 123–125, Grand Lodge of British Columbia and Yukon
- Freemasonry Symbols, Masons of California (Grand Lodge of California)
The same shape elsewhere
Browse symbols formed from squares and rectangles or triangles.
Researched, edited and approved by Rory Hansen before publishing. Last reviewed September 25, 2026. How we research
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