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GEOMETRY: ANCIENT FREEMASONRY - April 06, 1961
PRESENTED TO: THUNDER BAY LODGE A.F. & A.M. No. 618 BY FORT WILLIAM LODGE A.F. & A.M. No. 415
THUNDER BAY, ONTARIO
FREEMASONRY as we know it today may be likened to a mighty river whose waters come from many streams. No one as far as I have been able to learn, has shown definitely how Operative Masonry, in organized form, came into being, despite the many speculations on the subject. It is true that the builders of King Solomon’s Temple were workers in stone, timber and metal, but there is nothing to show that they were an independent organization. They were in fact, the servants of King Solomon and Hiram, King of Tyre.
The first known standards of measurement were established in the advanced civilizations along the Nile and on the plains of Chaldea. The cubit became known as the standard unit of measure. This was the distance from the point of the bent elbow to the tip of the middle finger, roughly eighteen inches or six palms, and was referred to as the cubit of man. The digit was the width of the middle finger at the middle finger joint, or ¾ of an inch, and is contained in eighteen inches 24 times. The Palm was the width of the four fingers at the middle joint, or about three inches; the Hand still used to measure the height of horses includes the thumb of about one inch added to the palm is approximately four inches. The Span is the length between the tip of the thumb and the tip of the little finger of the outstretched hand, a half of a cubit or 9 inches. The Fathom, an ancient Egyptian measure is equal to the length of the outstretched arms or approximately 6 feet; one half-fathom is three feet from the tip of the nose to the tip of the outstretched arm.
The Royal Cubit used by the Egyptians in the construction of the pyramids consisted of seven palms making the length 21 inches, but the cubit rods found in the tombs was a small fraction short of this measurement. Moses who was a member of the household of Pharaoh must have been acquainted with the Royal Cubit, as he had the highest educational privileges and opportunities. In Acts 7-22 we find the following: “AND MOSES WAS LEARNED IN ALL THE WISDOM OF THE EGYPTIANS AND WAS MIGHTY IN WORDS AND DEEDS”.
Albert Pike claims that Moses for many years was priest in the Temple of the Sun at Heliopolis which was near the Pyramid of Osarsiph. He was undoubtedly an initiate of the Temples of Egypt and learned in their highest rites and ceremonies. It is quite likely that the same cubit of measurement of the Egyptians was used in the building of the tabernacle which bears his name. In the Biblical terms it is known as the Sacred Cubit. Undoubtedly Solomon used the Sacred Cubit when the Temple was constructed on Mount Moriah. Ezekiel one of the four prophets carried prisoner to Babylon had a vision which he relates in Ezekiel 40 1-5, quoted in part “AND IN THE MAN’ S HAND A MEASURING REED OF SIX CUBITS AND A HAND BREADTH”.
Therefore it seems that the cubit has a spiritual as well as a material significance. The measure being originally derived from the human body as well as its component parts was symbolically termed the “measure of Man”. It was symbolically a measure of his faithfulness in the performance of his duties to God and his fellow man.
In the year 1799 A.D. Emperor Napoleon appointed a committee of scientists to undertake the tasks of deciphering the hieroglyphics found on the monuments in Egypt. In the meantime one of these men found a scroll at the museum in Turin, Italy which contained the ground plans and dimensions of the chambers passage ways and vaults at the Catacombs of Osimandya, which was located near the City of Alexandria. The measurements were in cubits. Great care was taken in measuring these catacombs in French metres. The result when these measurements were compared with those of the scroll was to find that that the cubit measured .523524 metres plus. Transposed to our standard was found to be 2O.6111l3988 inches plus. A cubit rod which was found to be in the possession of the French Government practically verified this measurement.
On October 7th 1948, Jewel P. Lightfoot of the Grand Lodge of Texas was appointed by the Grand Lodge of Texas to make a detailed study of the Pillars of Jachin and Boaz. Among some of his findings was the method by which the length of the Egyptian Royal Cubit was probably determined. Without going into a series of Mathematical calculations the answer resolves itself into the perfect relationship of the circumference to its diametre. These numbers arrived at were 20612 for the circumference and 6561 for the diametre and dividing the result is 3.14159426 plus, or what is known a PI.
When we point off three places from right to left it will give us 20.612 and 6.561 and if we adopt the inch as a unit of measurement 20.612 it surprisingly turns out to be the number of inches in the Royal Cubit. The important thing to remember about this relation of the circumference to the diametre is that it checks almost to perfection with the rod found by the French scientists. It is evident that the number 20612 does not originate from human sources but is based on some universal law of mathematics in relation of numbers - a law not created by man.
THE TEMPLE OF GIZEH
About 10 miles from the City of Cairo is located the Great Pyramid of Gizeh. It occupies a ground area of about 13 acres and is 485 feet in height. This Pyramid was built about 3600 B.C. or some twenty centuries before the time of Moses. Most of the pyramids of Egypt were constructed principal1y to serve as tombs for the higher classes of Egyptian dead. However it has been established that the great pyramid of Gizeh which the Greeks called Cheops and the first one constructed in the earliest days of the world was not designed primarily for this purpose. The northern edge of its square base bordered exactly on the 30th parallel north of the equator. This was the dividing line between what was then known as Upper and Lower Egypt. Although it is the burying place of Khufu and his Queen, it was constructed for making astronomical calculations and observations. This pyramid displays a high degree of knowledge in the science of astronomy and their work in this field is a marvel of accuracy even present-day standards. The reason for its construction, primarily, was undoubtedly to preserve for all ages, a knowledge of the source of the unit of measure employed in nature and by mankind to perpetuate a knowledge of time measure, linear measures distance from earth to sun, length of the solar year etc. No other subject relating to antiquity has been the cause of a more intensive investigation and study by scientists. The method of construction of this monumental pile of huge stones is still a mystery today, and is considered on the seven wonder of the world and is a wonder of architecture. The finely polished rose-pink granite stones were fitted together with seams of a thickness of l/l0,000th part of an inch. It does not prove the existence of organized Masonry at that time despite the fact they were workers in stone, for judging from the conditions as they were in the far distant past it is reasonable to conclude the workers were simply slaves of the rulers who built them.
The measurements of the pyramid both inside and outside bear a curious relationship to each other. It presents a riddle to the scientific mind with various references to cycles and events in history which foretold events that transpired many centuries after the pyramid was built. It also implies many laws in the science of numbers which seem to repeat for emphasis, to reveal a mathematical truth as illustrated in the following;
The bases of the four sides were fixed at the length of 365.242 pyramid inches -- the length 365.242 to an absolute fraction of the days in a mean solar year.
The area of each of the triangular aides is five acres or exactly 365 and a quarter cubits which correspond to the number of days in the year.
The four sides together have the same number of cubits exactly as there are days in four years including leap year.
If a rod were placed with one end in the centre of the original apex of the building and another swung around on a horizontal plane the circle would include within it the same number of inches as there are days in a century (36524.2)
The Kings Chamber, inside the pyramid, if the length is made the diameter of a circle, then a square of the same area has the 365.242 inches on each of its sides which is again the number of days in a solar year. Add the length and height together and divide by the breadth and the result is 3.14159 the number that squares the circle. From the top of the heavily built layer to the vertical centre line of the pyramid divided by 10 is the exact length in inches as the base line is in cubits (365) and a quarter or the equivalent to the number of days in one year. When the same course is divided by its height from the ground, the number is 3.14159 by which the circle is squared. Again if the height of the building is divided into twice the base the same number 3.14159 is the result.
In the Kings Chamber is a large stone coffin, of such size it could not be taken out or in since the pyramid was first built. All the proportions are geometrical, and its sides and bottom are cubically identical with its internal space. The length of its two sides to its height is a circle to its diameter, while its volume is just twice the dimensions if its bottom and its whole measure is just the 50th part the size of the King’s Chamber. It has exactly the same cubic capacity as the Ark of the Covenant that many generations later was given by God to Moses in the wi1derness Exodus 37 – 1. The Jewish “Lava of Washing” also is of the same dimensions while the Brazen Sea or “Lava of the Molten Sea in King Solomon’ a Temple at Jerusalem, was just 50 times the capacity of the coffin. The length and breadth divided by its height again give the number that squares the circle (3.14159).
The Great Pyramid was not built in imitation of others, it was the first. Nothing of its kind had ever been undertaken before. Looking back to the time it was constructed, it is more than reasonable to assume that it could not have been accomplished by the mind of man alone. This pile of huge stones and the method of construction have scientists and engineers puzzled even today. This belief in the Master Architect is the only plausible answer to this enigma. It is supported in Jeremiah 32.18-20 as follows: the mighty God -- which has set sings and wonders in the land of Egypt even to this day. Also in Isaiah 19.19 we find the following in that day shall there be an altar to the Lord in the midst of the land of Egypt, and a pillar at the border thereof to the Lord. In furtherance to this belief, we are told of the plans for the Temple of Solomon in 1 Chronicles 28.19. “All this, said David, the Lord made me understand in writing by His Hand upon me, even all the works of this pattern.” It is will to realize that many of the tools of the Craft appear to have originated in Egypt. The Obelisk known as Cleopatra‘s Needle dating back to 1500 B.C. was presented to America in 1878 by the Khedive of Egypt. When it was disassembled for shipment, the foundations revealed symbols of Masonry, Trestle-board, Master’s mark, trowel, square, rough and polished cubes. Many such working tools have been found in excavations of pyramids as well as Egyptian mummy’s aprons and regalia similar to our Masonic ones.
Egypt had from the earliest times used symbolism as a method of instruction. Egyptian civilization at the time of Moses was very old. The Pyramid of Gizeh was, with all its mysteries built many generations before the time of Moses. With this understanding, the expression “from time immemorial” takes on a new meaning while it leaves to the scientists, secrets yet to be discovered by the fifth science the most revered.
About 500 B.C. Pythagoras founded a brotherhood of young men to whom he imparted his mathematical knowledge after swearing them to secrecy. A century later there were schools in Athens where philosophers such as Plato who taught men law Politics, public speaking, and mathematics. This might be considered as the beginning of public education, at least for the advanced sciences which formerly were carefully guarded secrets of the few. About 300 B.C. Euclid gathered all available material and wrote a series of books including the discovery of Pythagoras, which we now know as the 47th problem of Euclid. He compiled thirteen books in all, six of which are still in use. Even to-day our geometry is mostly a streamlined version of Euclid. This should eliminate any confusion among Craftsmen as to whom credit is due for the discovery of this theorem. In 332 B.C. when Alexander conquered Egypt, the city of Alexandria was founded by his orders and named after him. It became the chief seat of learning in the Mediterranean area continuing until many years after his death. Then we come to the year 762 A.D. when Mohammed united the whole of Arabia and founded Baghdad as the chief seat of learning. They invented the Arabic system of numerals which we use to-day. Thus the science of Egypt and Greece then became known and available to the Moslem world. Never before in history had the knowledge of mathematics progressed in a single century as it did between 800 A.D. AND 900 A.D. where East met West in Baghdad.
The growth of plant life even has mathematical implications. Take time to examine leaf clusters of foliage and petals of flowers. The number 3 singly or in multiples, is most commonly found. In our esoteric work this number exceeds all other odd numbers. It is also found or implied in Great Light to exceed by far any other. Professor John Crawford Pierce of Goddard University in a Masonic Publication states:
“The spiral, which originates in what is known as the Golden Section, is one of the most basic things in the architecture of nature. These spirals go in both directions increasing in a uniform manner which corresponds to the numbers on a mathematical scale used in higher mathematics. This is also true of the daisies, asters, and their relatives with compound head flowers. It is further illustrated by the orderly arrangements in the growth of leaves on the stalks of various plants.”
But let us take the larger plants as trees, the maple, the beech, the ash, the oak and the holly. In the maple and ash we will make one complete turn and touch at two points which we will represent by the fraction ½; the beech we will make one complete turn and touch at three points which we will represent by the fraction 1/3; the oak two circles and touch on five points i.e. 2/5 and the holly three circles and touch on eight points. Thus if we add the numerators and denominators of the maple and beech, the result is 2/5 which is the spiral of the oak. Add the spiral of the beech and oak the result is 3/8, which is the spiral of the holly. It is said that there is no spiral existing that does not fit into this geometrical pattern. Thus as the scientist with the aid of mathematics probes deeper into the secrets of nature the closer he comes to an understanding of the Divine Plan. By astronomical observations he views with awe and reverence the immensity of the creation and the littleness of man in the physical scheme of nature. We, who have been created in His Image have been endowed with the ability to understand this science which brings order out of chaos, have unlocked the secret of the atom, created new substances and discovered new forces in nature, are still only beginning to understand the wonder of His works. While, aided by mathematics, we may read in the books of nature evidence of His Power at work we must not rely on this alone. The Mason who is in search of Light must seek the Master’s Word for final instructions in the building of his spiritual edifice, that his building not made with hands may find favour in the sight of the Supreme Architect. We have advanced much further in the material things of Life than we have in our ethics and our social behaviour. We need further moral and spiritual adjustment in our relation of man to man and mankind and mankind to solve the problems of to-day. This is truly the time that we are very much in need of Applied Masonry.
W. M. John Davies
Lecturer: W. Bro. W.T. Biggar
WORSHIPFUL BROTHER J.H. MCMULLIN:-
In presenting THUNDER BAY LODGE A.F. & A.M. NO. 618 G.R.C., with the TRAVELLING SQUARE the words of Lord Alfred Tennyson written in 1850 seem very appropriate for this occasion,
Our little systems have their day;
They have their day and cease to be;
They are broken lights of thee,
And thou, 0 Lord, art more than they.
We have but faith; we cannot know;
For knowledge is of things we see;
And yet we trust it comes from thee,
A beam in darkness let it grow.
Let knowledge grow from more to more,
But more of reverence in us dwell;
That mind and soul, according well,
May make one music as before.
WALTER T. BIGGAR, W.M, — 1936.
APRIL 6, 1961
We speed you on your journey, SYMBOLIZING our pursuit of the WISDOM OF THE AGES, and as you pause here and you pause there may the lessons you may impart to all MASONS may reveal to us the splendour of its beauty, and with reverential awe bow before HIM who is the GRAND GEOMATRICIAN OF THE UNIVERSE.
W.T. BIGCAR, W.M. - 1936.