Why the 47th Problem of Euclid?

This might, at first blush, seem to be obvious. After all, masons are taught in the lecture of the Second Degree that Geometry is the first and noblest of sciences, the foundation upon which the superstructure of Freemasonry is erected. In the third degree, we are also taught that the 47th Problem of Euclid, also known as the Pythagorean Theorem, teaches us to be great lovers of the arts and sciences.

So it makes sense, on the surface, we would look to Euclidian mathematics as operative Masons. So, lets first take a look at what the 47^th Proposition states mathematically:

In right angled triangles the square on the side subtending the right angle is equal to the squares on the sides containing the right angle. Using this formula, we can prove a circle and a right angle, a square and much more, all of which are essential for the operative mason. This formula is essential in any construction effort, hence is obvious importance to operative masons.

But, we are not operative masons, we are speculative only. That being the case, why is the 47^th Problem of Euclid important to us? Or is it?

Anderson's “Constitutions” published in 1723, mentions

“The Greater Pythagoras, provided the Author of the 47th Proposition of Euclid's first Book, which, if duly observed, is the Foundation of all Masonry, sacred, civil, and military…” and in the Third Degree lecture: “This wise philosopher (Pythagoras) 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.”

Masonry, as a speculative science concerns itself with morality, upright behavior and the brotherhood of man. Since we are speculative masons, there must be a more significant reason for the 47^th Problem of Euclid, a meaning within a meaning. The thinking man must ask himself, what relationship does geometry (the square is an emblem of truth and morality) have to morality that it would be an emblem of morality?

The answer is right before us, but as with all things Masonic, one must go back to the foundation. At the time the first grand lodge was founded, the 47^th problem of Euclid was more commonly known as the Pythagorean Theorem. So why did those early ritualists chose to use the 47^th Problem of Euclid?

First, it was not Pythagoras who discovered the rule that is referenced by his name. The Egyptians used this principle long before Pythagoras set it down to measure their fields after the annual Nile floods washed away the boundary markers. Pythagoras is the man who proved that the process works.

History records that Pythagoras established a society with philosophical, religious and political aims. Shrouded in secrecy, they believed that only by truly understanding the universe could one achieve salvation of the soul, and as Divinity created all things, studying it over a period of several lifetimes, could bring one closer to Divinity itself. As such, it was believed that through study and reason could one start to understand Divinity. Clearly, reason is based on measurable things (such as through numbers and objects), and is easier to understand if expressed in that matter by a larger number of people.

Hence the society devoted much of its time to the mathematics, including Geometry to try to explain and express matters using numbers. Being able to explain many unknowns using reason (and numbers) was incorporated in Freemasonry, which sets it opposite to the Church, which emphasizes faith over reason. Indeed, Pope Pius IX, in his encyclical, Qui Pluribus, dated 9 November 1846, attacked those who “put human reason above faith, and who believe in human progress.” Many people consider this to be a reference to Freemasonry.

This is interesting, because in the Book of Wisdom 11:20 we read:

Even apart from these, men could fall at a single breath when pursued by justice and scattered by the breath of thy power. But thou hast arranged all things by measure and number and weight.

So the very “measurement of things” the Church objects to is mentioned in Scripture as being a universal "standard" that allows men to understand their world and their surroundings.

Geometry is about measuring and creating standards, understanding and reasoning. These things were opposed by the early church leaders, so it is understandable that Freemasonry, as a bastion of reasoning and moral philosophy would conceal its secrets within geometry.

This still leaves us with the question, “Why the 47^th Problem of Euclid and not the 1^st or the second? The reason it was chosen was to conceal the greater truth!

In the 18^th century, there was another philosopher, a moral philosopher, who presented his moral philosophy in the same format that Euclid used to present his geometrical problems. More than that, he titled his book: “Ethics,” and based his ethics upon the format used by “Euclid” to present his mathematical formulas. This philosopher was Benedict Spinoza (1632-1677), and strangely enough, the 47^th Problem:

PROP. XLVII. The human mind has an adequate knowledge of the eternal and infinite essence of God.

Jeff Peace once wrote me:

When you consider that the early speculative Freemasons considered Freemasonry to be "a peculiar system of morality veiled in allegory and illustrated by symbols," it seems logical to conclude that hidden somewhere within the Masonic system lay hidden a system of morality that was peculiar (unique).

Slightly before speculative Freemasonry appeared on the scene a famous philosopher wrote a book of ethics (morality) that was truly peculiar (unique), it was so unique that he was labeled a heretic and copies of his book were burned. His book was peculiar in more ways than just his ideas, it was written in the same format as Euclid’s "Book of Elements," it was a moral philosophy based on the logical format of Geometry.

Freemasonry is about morality, and the 47^th problem of Freemasonry is about morality… Masonic symbolism is the building of a moral edifice… perhaps the two Euclidian problems, having the same name, influenced the use of the symbol of geometry to represent both… mathematics and morality.

Just something else to think about.

May the blessings of heaven rest upon us and all regular masons, may brotherly love prevail, and every moral and social virtue, cement us.