Freemasonry’s concern with geometry goes back to its beginnings, setting a precedent to that academic research which in the last 100 years or so has flourished in the west as the history of Mathematics. Few who have devoted themselves to research in this field have underestimated the knowledge of previous generations - and just as each mathematician should know the history, so too should Freemasons understand something of the geometry which informs their rituals and their social existence.
    In times gone by, masons in search of the history could turn to the Old Charges, where the history of geometry is traced from the time of the Great Flood to the time of the great architects. The Old Charges are wonderful documents which give us an understanding of the knowledge and beliefs of the medieval master masons. Some of them treat the story of Euclid as the fount of all Freemasonry 1, while some editions of Euclid (fl. Alexandria c.330-260 BC) were accompanied by prefaces which bear stylistic comparison with the Old Charges, for example John Dee’s Mathematical Praeface to the 1570 English translation of Euclid’s The Elements. Dee’s work refers to “our heavenly Archemaster”, and sees in the exposition of geometry a path to the knowledge of God :

Many other artes also there are which beautifie the minde of man: but of all other none do more garnishe & beautifie it, then those artes which are called Mathematicall. Unto the knowledge of which no man can attaine, without the perfecte knowledge and instruction of the principles, groundes, and Elementes of Geometrie.
    ... from henceforth, in this my Praeface, will I frame my talke, to Plato his fugitiue Scholers: or rather to such who well can, (and also will), vse their utward senses, to the glory of God, the benefit of their Countrey, and their owne secret contentation, or honest preferment, on this earthly Scaffold.

Much of the history contained in the Old Charges is actually a story, repeating the names of the most prominent men in the history of geometry and architecture. The name of Euclid unites both operative and speculative interest or rather, theory and practice. This has long been observed by masonic scholars, such as Bro Rev. F. de P. Castells when he observed that “the language of our Masonic Ritual is very frequently the language of Euclid; and if we compare the two works, we find many points of contact and many coincidences.” (The Geometry of Freemasonry. Taunton. 1915).
    The story, parable and drama of Freemasonry are all put within the space of geometry, and that space was encompassed by one book, a book believed in by western civilisation for longer than it has the Bible itself. From the third century BC to the 19th, that volume of near-sacred law was Euclid’s The Elements.
    Speculation abounds as to the identity of the author. Lack of evidence concerning his life has led some to see it as the work of a number of geometricians, while masonic lore informs us that.

...after this proclamation was made came this worthy Clarke Euclid and said unto the Kinge and his Nobles if you will betake your children unto my government I will teach them the seven Liberal Sciences whereby they may live honestly and like gentlemen upon this condition that you will grant me a Commission to have rule and power over them according as science ought to be ruled and upon this Covenant I shall take care and charge of them: the Kinge and his counsel granted the same and sealled the Commission and then this worthy Docter tooke to him those Lordes sonnes and taught them the science of Geometrie in practise for to worke all manner of worthy that should bellong to building of Temples Churches Castles mannors Towers houses and all manner of buildings And he gave them a charge. 2

Professional mathematicians, on the other hand, tend to agree that the thirteen books of The Elements were more likely to have been assembled rather than written by Euclid : “The individual books are of quite different merit and certainly do not all originate from the same author.” (Evolution of Mathematical Thought. Herbert Meschkowski. 1965.p.5). An interesting parallel regarding something of what might have occurred can be found in events which took place during the 1930s.
    In that decade there was a group of mainly French mathematicians who initiated a syllabus for undergraduates. They considered that the task would be facilitated by each writing of what he knew best and then combining their work. However, the difficult economic and political climate (some of the authors were Germans) made finding a publisher difficult. Their solution was to invent a fictitious mathematician, a shy man of exotic origin named Nicholas Bourbaki. Under this name they produced many books, some of which are still standard texts for mathematicians. In order to co-ordinate their writings, the authors - among whom was André Weil to whom we owe the story - would convene their meetings under the name Bourbaki conferences. After some years, one of the Parisian contributors received a letter from the Greek Consul in Paris. The man insisted on meeting Mr Bourbaki for very personal reasons. Overwhelmed by curiosity, the next Bourbaki conference sent an envoy to the Consul, only to be told that the Consul sought to meet an unknown relative whose name was that of the fictitious mathematician! Perhaps it would have been to our avail if another man called Euclid had gone to Alexandria around the year 300 BC to find his namessake, then we might know more about Euclid, possible author of the first known geometrical compendium in the world. For our purposes, the name Euclid and the book are one.
    But how did Euclid become part of medieval (and Renaissance) masonic lore? In the ninth century, Baghdad was home to a community of ‘Sabian’ polymaths who had originally flourished in Harran, and who took as their prophet Hermes Trismegistos (renamed Enoch or Idris to bring them in line with approved Koranic sources) whose writings were regarded by them as their sacred law. Hermes was of course central to ancient masonic lore as the medieval Old Charges testify. The most important of these Baghdad polymaths was Thabit ibn Qurra (835-901), described in von Eschenbach’s Parzifal (c.1200. ch.13) as a philosopher “who fathomed abstruse arts” and an apologist for the scientific knowledge of the old pagan world. Among the many late pagan (and frequently Neoplatonist) works translated into Arabic by Thabit was an improved translation of Ishak b.Hunain’s version of Euclid’s The Elements. It was Thabit’s version of Euclid which brought Gérard of Cremona (1114-1187) to Toledo in search of the magico-scientific work the Almagest over 200 years later. Indeed, many of the Sabian works finally reached the minor renaissance of the West in the 12th and 13th centuries in Latin translations, made at the Toledo school founded by Archbishop Raymond under Archdeacon Dominico Gundisalvi.
    Gérard of Cremona also translated other works by Thabit, including the Liber Carastonis sive de Statera, on the physics of balance, and it is by virtue of these transmissions that Gérard of Cremona became known as the “father of Arabism in Europe” : an influence which would later fortify the scientific aspect of the Renaissance. As late as the mid-sixteenth century, the great Elizabethan mathematician and magus, John Dee, when compiling his Monas Hieroglyphica (1564), used Thabit’s De imaginibus: a treatise on planetary images, reflecting the talismanic type of Neoplatonic celestial magic. According to the late Professor Max Meyerhof : “Belonging to the pagan sect of the Sabians and at heart deeply attached to paganism, Thabit is one of the most eminent representatives in the Middle Ages of the tradition of classical culture.” The late, great medievalist Jean Gimpel gave to the Arabs - especially with reference to their geometrical knowledge - the greatest possible credit in making the medieval architectural explosion possible.
    It should come as no surprise therefore to find the name of Euclid high up in the pantheon of masonic heroes and little wonder that both medieval masons and Renaissance-influenced 17th century scholars and gentlemen interested in Freemasonry should have regarded Euclid as one of their own.

Notes
1. See the compendium of early masonic mss. by Knoop, Hamer and Jones which shows the contents of the two mss. the Regius MS (c.1390) and the Cooke MS (c.1400-1410). Through the comparison, it can be seen how much of the story is dedicated to geometry within these old documents.
2. From the Buchanan MS in The History of Freemasonry. Gould.p.94ff.

Snezana Lawrence is finishing her Phd at the History of Mathematics Dept. (Open University) on the Geometry of Architecture and Freemasonry in 19th century England. She is also a contributor to the Transactions of the Quatuor Coronati Lodge of Research No. 2076 and the journal Historia Mathematica.