The 47th Proposition of Euclid is a geometric symbol which when combined with a square becomes the Past Master's jewel in the jurisdiction of the Grand Lodge of England, Pennsylvania and a few other jurisdictions.
Masonic literature that is dedicated to the symbolism and rituals of the Three degrees do not refer to the Past Master's symbol of England. Therefore, the only way to research the true meaning of the jewel is to divide it into a square and the 47th proposition of Euclid.
The research information on the 47th proposition of Euclid is quite limited and rare. This famous geometrical symbol is full of symbolism and value but it is overlooked because of its lack of use. This leaves room for Masonic Scholars to examine the symbol and theorize its meaning. The intent of this paper to examine the jewel and theorize its true Masonic meaning.
In order to fully understand the 47th proposition, the origin of the idea of the sacred numbers must be examined. The ancient Hebrews believed and it is written in the Kabalah that numbers and numeration of numbers explained God's universe. Indeed, if the properties of nature are examined, said properties can be explained in numbers. The science of Geometry is based on the theory of numbers and their relationship and the science of Geometry is the basis of Freemasonry.
The Kabalah refers to a symbol called the Tetractys. The tetractys has many mystic meanings. It was used in the Kabalah to represent the name of God.
As shown in the diagram there are numerations of the Tetractys that form the sacred numbers. Ancient Hebrew did consist of numbers. Letters were used as numbers. One letter by itself was the number 1, two letters was two, and so on. From the diagram above each line represents the numbers 1, 2, 3, and 4. Now for the numerations; add the first line to the second line - 3; add the second line to the third line - 5; add the third line to the fourth line - 7; add the second, third and forth line together - 9; add all four lines together - 10.
Therefore, the number 1, 2, 3, 4, 5, 7, 9, and 10 were considered sacred numbers. The properties of nature can be expressed terms of the sacred numbers. Masonry has its basisis in nature, Geometry, the Kabalah and the Holy Bible.
The number one tells us about there being only 1 true and living God.
The number two is referred to as the Duad, the symbol of Antagonism. The concepts of good and evil, light and darkness, Cain and Abel, and so on.
Three is referred to as the Triad and expressed as a right-angled triangle. The Deity is symbolized as the Trinity, he creates, preserves and destroys. There are three principal colors or rays in the rainbow which can be intermixed to get seven; the three are blue, yellow, and red. The chemicals salt, sulphur and mercury are the great symbol of the alchemist.
The number four is express by the square, or four right-angled triangles. Pison which is described in the Bible as the river which flowed in the Garden of Eden, was divided into four streams. Nature is described as coming from the four corners of the Earth.
The addition of the Duad and the Triad is the number five. This number is expressed by the Pentalpha (Blazing Star) of Pythagoras. It is was believed that there were 5 smaller planets orbiting Earth; Mercury, Venus, Mars, Jupiter and Saturn. There were two greater bodies orbiting Earth being the Sun and the Moon constituting the seven celestial spheres. Five is generally combined with two to give seven. Christ fed His disciples and the multitude with five loaves of bread and two fish.
Seven is a sacred number with many natural occurrences. There were seven planets and spheres presided over by seven archangels. There are seven colors in the rainbow. The week is divided into seven days. God created the universe in six day and rested on the seventh. Israel was in the hand of Midian seven years before Gideon delivered them. The number seven consists of many more occurrences.
Nine is square of the three and therefore nine is the square of the Diety. Nine in itself is sacred for this reason.
Ten is inclusive of the other numbers. Most especially because it is the cumulation of the Tetractys.
At this point it should be clear how the sacred numbers arose. The principles of Geometry and the other sciences are based on numbers. Now that the reasoning behind the sacred numbers is known let's examine the 47th proposition.
The 47th proposition of Euclid is a geometric symbol whose properties were known even before Pythagoras. Pythagoras in the year 525 BC develop the principles of Geometry. The most famous theory of Pythagoras is the Pythagorean Theory. This theorem deals with right triangles. The theory is "In every right-angled triangle. the sum of the squares of the base and perpendicular is equal to the square of the hypothenuse. Between Pythagoras and Euclla (Euclia livea around 300 BC) was the development of the concept of the irrational number. Euclid felt that Pythagorean Geometry was incomplete because it did not take into account the concept of the irrational number. Euclid, therefore, expanded on all of Pythagoras' theorems. The Pythagorean Theorem of right triangles was expanded to the 47th proposition of Euclid.
The 47th proposition is based on the right triangle and its properties. The addition is that if you draw a right triangle, then create a square from each line of the right triangle, you then have the drawing shown above. The area of the square drawn from the base added to the area of the square drawn from the perpendicular is equal to the area of the square draw from the hypotenuse. This is an expansion of the Pythagorean theorem and is an essential component of geometry.
If we examine the symbol and look at its mathematics we find that if we take the first 10 numbers;
1,2,3,4,5,6,7,8,9,10
Take the squares of the numbers:
1,4,9,16,25,36,49,81,100
Using the theory of Pythagoras (the basis of the 47th proposition), subtract the first number in the sequence from the second, and so on
3, 5, 7, 9, 11, 13, 15, 17, 19
We arrive at the sacred number sequence of 3, 5, 7, 9 What have we proven thus far? It is that the 47th proposition is composed of four sacred numbers In Masonry we find the repetition of the sacred numbers 3, 5, 7, 9 in its symbolism
The number three is seen constantly in Masonry The symbol of the Diety is the right-angled triangle, three sided There are three Great Light- and three Lesser Lights We give three raps at a door to gain entrance into a Lodge The Lodge is governed by three officers, a Worshipful Master, Senior and Junior Warden This list could continue on for some time Therefore, when the number three ls examined as a Masonic symbol it can represent every symbol that is made of three parts.
The number five is also seen in Masonry The fifth degree is the Past Master's degree, the highest honor of the Blue Lodge There are five elected officers in a Lodge There are the five principle orders of achitecture and the five senses
Seven is also seen in Masonic symbolism The Blue Lodge must have seven Master Masons in order to open a Master Masons' Lodge There are the seven liberal arts and seven degrees up to the Holy Royal Arch Degree.
The number nine is represented as the ninth arch of the temple
Therefore, if the sacred numbers 3, 5, 7, 9 can each represent a variety of symbols then when each number is examined as a Masonlc symbol, the symbol is a composition of all symbols that contain the numeration. If this is true then the 47th proposition which is the cumulation of the sacred numbers 3, 5, 7, and 9 can represent all Masonic symbols
The 47th proposition, therefore, becomes the one symbol in ancient craft Masonry which describes all the symbols of Masonry. Indeed, if the Worshipful Master is supposed to be the keeper of Blue Lodge Masonry, he too represents all the symbolism of Masonry Then what better symbol to use for the Past Master's jewel than the 47th proposition and the square? This jewel best describes Masonry and the knowledge that the Worshipful Master must obtain to perform this highest duty
The symbol which is a composite and cumulation of all Masonic symbols and ideals is expressed in the 47th proposition This symbol (along with the square), is indeed the proper jewel for the Past Master The man who becomes Worshipful Master of his Lodge will retire, in time, and become a Past Master, but his obligation to his Lodge and his lov of Freemasonry cannot die, not just because he wears the absolute symbol of all Freemasonry but also has the ideals of Freemasonry engraved on his heart.
When the 47th proposition is applied to man; the horizontal line of the triangle represents the physical body, the perpendicular line represents the mind and the hypotenuse represents the spirit. The body and mind are joined at a right angle to form the perfect square. Man's spiritual evolution is affected by, and dependent upon his physical and mental development but the spirit is always dominant in the complete man.
In Masonry we teach that all men are on the level (the horizonal line); and that every man should always stand upright (the perpendicular) and that you must believe in God (the hypotenuse). Thus every man forms a right triangle in Masonry and since the right triangle is also the symbol of God, every man who lives on the "triangle" is truely an image of God. Is this not what Masonry is all about?
Bibliography
The Morals and Dogma of the First Three Degree, Ancient and Accepted Rite, Supreme Council of the 33rd Degree, Southern Jurisdiction, USA
Collection of the Prestonian Lectures, Vol I, "Medieval Master Masons and Their Secrets", Covey-Crump, Quatuor Coronati Lodge Publisher, London, England
Tied to the Masonic Apron Strings, Pollard, Macoy Publishing, Richmond Virginia
Encyclopedia of Freemasonry, Mackey, McClure Publishing
Freemasonry: The Craft and its Symbols, Roberts, Macoy Publishing
Freemasonry: Its Hidden Meaning, Steinmetz, Macoy Publishing
Encyclopedia Britannica, Volumes on Euclid and Pythagoras (dates)