After a quick break Novus is back with their digital series! Hope all of you have taken care during this time and your family is well. While California Masonry is still under lockdown our digital efforts are still pushing forward. Please enjoy the next article in our series. – MM, WM N.V 864
“Be there or be square”, “He’s just a square”, “A square deal”, and “Square up” are all phrases you may be familiar with. Each of them has a slightly different meaning but each uses the common word ‘Square’. When the term ‘square’ is used in the company of a Freemason, his mind should turn to two thoughts, namely the phrase “Act upon the square” and the 47th Problem (Proposition) of Euclid.
Masonic ritual tells us that a ‘Square’ is an angle of ninety degrees or the one-fourth part of a circle. A square then is a perfect thing. If it is eighty-nine degrees or ninety-one degrees for example, it is not perfect and therefore not a true square. When Masons are taught to “Act upon the square”, they are being admonished to deal with every fellow creature with whom they come in contact, ‘on the level’ and in an ‘upright’ manner. They are taught to strive to be a ‘perfect’ human being just as a square is a perfect entity.
This brings us to the second meaning of the word ‘square’ as perceived by a Mason in regard to the 47th Problem of Euclid. The basis of the Problem is geometry as discovered by our Brother Pythagoras (not Euclid) and even earlier by the Egyptians. We all know from high school geometry that the Pythagorean Theorem states that a2 + b2 = c2 (or 3:4:5) as seen in the two illustrations below. The following, from Brother Thomas Greene of the Quatuor Coronati Lodge in London, will further explain.
‘By it (the 47th proposition) we can prove that in a triangle, one of the angles of which is a right angle, the square of the side opposite the right angle to both the squares on the sides containing the right angle: it follows then that if we make any triangle in which the square of one side is equal to both squares of the other two sides, then the angle opposite that side must be a true right angle – the angle of a correct square… In order to get a correct square angle, it is therefore only necessary to make a triangle the sides of which are in the proportion of 3-4-5. In connection with this, it is of much interest to know that as the standard and symbol of perfection with Speculative Masons now is the square, so this right-angled triangle, which is almost identical, was with the Egyptians several thousand years ago as their standard and symbol of perfection; and they make it also the basis of all their measurements; looking upon it is the symbol of Universal Nature, the side with length 4 being Osiris the male principle, side length 3 the female principle Isis, and side length 5 Horus the son, the product of these two principles. They further said that 3 was the perfect odd number, that 4 was the square of 2 the first even number, and 5 was the sum of 3 and 2.’
We need to transcend beyond the mathematics to a higher plane of Masonic understanding regarding this theory. Let us first digress for a moment.
Craft Masonry consists of three degrees, the Entered Apprentice, the Fellowcraft, and the Master Mason Degree. Each degree builds on the previous degree and each degree is dependent on the other two. Now, it takes seven (7) officers to open a Lodge of Entered Apprentices; five (5) to open a Lodge of Fellowcraft Masons, and three (3) to open a Lodge of Master Masons. The 3, 5, and 7 are important numbers to all Masons for many reasons, as we know.
Consider that the 3 officers it takes to open a Master Mason’s lodge represent the ‘a’ side of the right triangle, the vertical side, which is also the ‘upright’ side in our illustration above. In the illustration below it represents the leg with 3 units. The 5 that are required to open a Lodge of Fellowcraft Masons represent the base, or ‘b’ side of the triangle which is the horizontal or ‘level’ leg or the side with 4 units from below. And the 7 that it takes to open a lodge of Apprentices represents the ‘c’ leg or hypotenuse of the triangle which is the 5-unit leg. Therefore, the 3, 5, 7 equates to the 3, 4, 5 which is the 47th Problem! Also, consider that the Junior Warden’s jewel is a plumb representing acting ‘uprightly’ in our stations in life. The Senior Wardens jewel is the ‘level’ which represents dealing with our fellow human beings ‘on the level’, and the Master’s jewel is the ‘square’ which reminds us that we should always ‘act upon the square’ with everyone and in everything we do.
The 47th Problem of Euclid or 3:4:5
Anderson’s Constitutions of 1723 refers to the 47th Proposition of Euclid as an ‘amazing proposition’. It IS amazing in that it not only assisted men throughout history in building fine edifices to the highest degree of accuracy, but also continues, in the hearts and minds of modern Freemasons, to remind us how to deal with our fellow creatures. The Problem is not about the math but rather directs us down a path to define Divine truth with respect to moral and intellectual capacities that we possess. If we learn to deal with people in a just and upright manner, deal with everyone on the level and be square in all our doings, we will have fulfilled the true meaning of the 47th Problem of Euclid. We will have squared our square.
As a side comment, it is interesting to note that old and modern English Masons use the square and the 47th Problem as the jewel of their Past Masters.