Euclid, Freemasonry, and Philosophical Geometry

In the last section of the Master Mason degree lecture recited in Preston-Webb Masonic ritual, Euclid's 47th Proposition from his collected Elements of Geometry is only briefly referenced:

“The Forty-seventh Problem of Euclid was an invention of our ancient friend and brother, the great Pythagoras...This wise philosopher enriched his mind abundantly in a general knowledge of things, and more especially in Geometry, or Masonry. On this subject he drew out many problems and theorems, and, among the most distinguished, he erected this, when, in the joy of his heart, he exclaimed Eureka, in the Greek language signifying, "I have found it," and upon the discovery of which he is said to have sacrificed a hecatomb. It teaches Masons to be general lovers of the arts and sciences.”

Anderson's Constitutions of 1723 follows the trail from Pythagoras to Euclid, who was credited with assembling the various theories of geometry into a cohesive science, or as Anderson calls it, the Royal Art: 

"[T]he Greater PYTHAGORAS, prov’d the Author of the 47th Proposition of Euclid’s first Book, which, if duly observ’d, is the Foundation of all Masonry, sacred, civil, and Military...

"But after PYTHAGORAS, Geometry became the darling Study of Greece, where many learned Philosophers arose, some of whom invented sundry Propositions, or Elements of Geometry, and reduc’d them to the use of the mechanical Arts. Nor need we doubt that Masonry kept pace with Geometry; or rather, always follow’d it in proportion’d gradual Improvements, until the wonderful EUCLID of Tyre flourish’d at Alexandria; who gathering up the scatter’d Elements of Geometry, digested them into a Method that was never yet mended, (and for which his Name will be ever celebrated) under the Patronage of PTOLOMEUS, the Son of Lagus King of Egypt, one of the immediate Successors of Alexander the Great."

Apart from Freemasonry's obvious operative-era connection to the science of geometry, how did Euclid's 4th century BC writings wind up being referenced in an 18th century fraternal organization in Britain? 

It turns out that Euclid's theories were actually common currency among Enlightenment era political philosophers, and were not necessarily being used for mathematics. They were being applied to demonstrate the scientific "proof" of concepts like equality among men, even as late as Abraham Lincoln's arguments against slavery in the 1850s and 60s. It's not an enormous leap of imagination to suspect that Founders like Jefferson, Franklin, Madison, Hamilton, John Jay, and many others probably had a volume of Euclid's Elements lurking on their bookshelves at home.

Nautilus is an online magazine dedicated, in part, to applying science to everyday life. An article recently appeared that explores this Euclidean application to philosophical thought. 

From Euclid As Founding Father, by Adam Kucharsky:

“In the course of my law-reading I constantly came upon the word demonstrate,” Lincoln said. “I thought, at first, that I understood its meaning, but soon became satisfied that I did not.” Resolving to understand it better, he went to his father’s house and “staid there till I could give any propositions in the six books of Euclid at sight.”

He was referring to the first six of books of Euclid’s Elements, an Ancient Greek mathematical text. On the face of it, Euclid’s Elements was nothing but a dry textbook: There were no illustrative examples, no mention of people, and no motivation for the analyses it presented. But it was also a landmark, a way of constructing universal truths, a wonder that would outlast even the great lighthouse in Euclid’s home city of Alexandria.

Elements proposed that definitions were at the foundation of knowledge, and led to self-evident axioms that needed no proof. From these definitions and axioms, Euclid showed how to prove dozens of mathematical propositions, producing knowledge that was objective and undeniable. A person of reason would have to accept a proven fact, no matter what their personal beliefs or convictions were. Elements would become a best-selling work, second only to the bible in printed editions, and used until recently as the standard text for mathematics classes. It profoundly influenced Western thought, and shaped Western science and art. What’s less recognized is its role in the creation of modern politics: The distance from proofs about equilateral triangles to the foundations of democracy in Europe and the United States turned out to be just about two millennia.

John Locke was an early pioneer of Euclidean thinking in politics. Born in 1632, the Englishman grew up in a time of turbulence, with a nine-year civil war beginning in 1642. Locke, whose father had fought against the Royalists in the war, would go on to develop a great interest in the concept of morality. In forming his ideology, Locke took guidance from the logical structure of Elements. He believed that by following the logical consequences of self-evident statements “as incontestable as those in mathematics,” it would be possible to demonstrate what was right and wrong.

Historically, absolute monarchs and the church had dictated laws and justice. Enlightenment thinkers such as Locke sought to challenge this tradition. Rather than defining equality from above, he wanted to root it in natural, objective laws. Locke believed that the “natural rights” of a society could be established in a similar manner to geometric theorems, and would therefore be “as certain as any demonstration of Euclid.”

Like Euclid, Locke defined terms, then used these definitions to prove moral claims. For example, Locke defined property as “a right to any thing,” and injustice as “the invasion or violation of that right.” The statement “where there is no property there is no injustice” resulted naturally from these definitions. In his Two Treatises of Government, published in 1689, Locke noted that “creatures of the same species and rank, promiscuously born to all the same advantages of nature, and the use of the same faculties, should also be equal one amongst another.” It was therefore self-evident that, in the absence of rules or laws, humanity’s natural state was “free, equal, and independent.” He concluded that the aim of a government should be to preserve the natural rights of life, liberty, and property.

(Read the whole article HERE.)

Several 17th and 18th century philosophers like Benedict Spinoza and Thomas Hobbes used Euclid's Elements as a basis for demonstrating the truth of their philosophical theories. So it's not surprising that the Royal Society members and other Enlightenment thinkers who helped transform Freemasonry from an "operative" skill to a "speculative" philosophy for tolerance and equality among diverse members would sneak Euclid under the door.

H/T to Redditer "poor_yoricks_skull" today.