Golden Fleece > Geometry
craftsman's art and music's measure
The measurement of land
The domestication of cereals about 10,000 years ago eventually gave rise to the need to measure land. The domesitication of animals (goats, sheep, pigs and cattle) about a thousand years later, became the basis for the conflict between the tillers of soil and the herders of animals. During this time circular houses evolved into structures with rectangular rooms.
The earlier cultivation of wild cereals may have been facilitated by global warming between 14,000 and 10,000 years ago, when average temperatures increased and climate stabilised with less variation of temperature. The climate became more arid with more clearly defined seasons. These changes encouraged the spread of wild cereal grasses, that grew in abundance until the spread of forests diminished the amount of open land. Sea levels rose about 30 meters and the ancient wolves of Alaska became extinct as well as the saber-toothed cat and other large mammals.
There was a sudden drop in temperature around the world about 5,000 years ago, which created cooler and dryer conditions. The cities of Sumer developed as irrigation was invented. Gilgamesh ruled the city of Uruk. The scribal schools (Sumerian edubba) were run by professional teachers (called "fathers"), who with their own teaching assistants ("elder brothers") taught the "sons of the tablet house" in their particular fields. There were three specialist areas of training; language, counting and surveying (scribe of the field). Scribes were responsible not only for writing, but for calculating quantities and surveying fields. The scribes were an almost completely lay group; priests and royal officials were usually illiterate.
The knowledge of how to form a perfect square was important in the art of building from the time of the ancient Egyptians. The Harpedonaptae (literally translated, means "rope stretchers") of ancient Egypt were highly skilled specialists, who were called in to lay out the foundation lines of buildings.
The cornerstone was laid at the northeast corner of the building because the Harpedonaptae first laid out the north and south lines by observation of the stars and the sun. A rope with evenly spaced knots was then used to form perfect corners of buildings and pyramids. The ancient Egyptians knew that a triangle with sides 3, 4, and 5 makes a right angle.
The ancient Egyptians knew about the relationship of squares on the sides of a 3, 4, 5 triangle; 9+16=25. It was a the ancient Greeks, who recognised the general theorum that applies to all right angle triangles, known as the 47th Proposition of Euclid. The square drawn on the side opposite the right angle (of any right angle triangle) is equal to the squares drawn on the sides that make the right angle. The proof of the 47th Proposition of Euclid depends on the knowledge that the area of any triangle is half the base by the perpendicular height. Geometry is a Greek word, which means the measurement of land.
Free and accepted masons of the eighteenth century adopted the carpenter's square as a symbol to illustrate a code of conduct. The shorter arm represented integrity, derived from the three moral virtues; faith, hope and charity. The longer arm represented sincerity, expressed as the four social virtues; prudence, fortitude, temperance and justice.
The education of free men used allegory to present knowledge. In the medieval university, study of the seven liberal arts began with the Trivium; grammar, rhetoric, logic and then progressed to the Quadrivium; geometry, arithmetic, music and astronomy.
Freemasons have created many illustrations of their symbols. In this design a carpenter's square and compasses rest on a closed Bible, with a trowel in the foreground. The seven stars around the moon allude to the seven liberal arts and sciences or to seven Masons, who must be present to initiate a candidate. The United Grand Lodge of England decribes seven progressive offices in a booklet that you can view online or download as a pdf file: Steward, Inner Guard, Junior and Senior Deacons, Junior and Senior Wardens and Master of the lodge.
At the time of Sir Christopher Wren, a lodge was formed by five masons: Tyler, Junior and Senior Wardens, Master of the lodge and the newest freemason. Tyler was an ancient office, responsible for delivering summons to lodge meetings and acting as doorkeeper, which was particularly important for any Lodges meeting in a tavern. The Tyler also had a traditional role of representing poor and distressed freemasons.
The newest freemason had an important role in the admisison of the next apprentice. First he would admit the candidate on the point of the trowel. In the north east part of the lodge, he would present the flat surface of the trowel to the candidate to receive any contributions for poor and distressed freemasons. Finally he would pass the trowel to the new apprentice. This is the origin of the expression, "that Monarchs themselves have not thought it derogatory to their dignity to exchange the sceptre for the trowel."
This Compass Table represents the intertwined compass and square in three dimensions. A carpenter's square is paired with a wooden compass and the curved edge of the glass table top matches the radius of the compass arms.
In medieval paintings, God was depicted as the Grand Geometrician, measuring the earth with a drafting compass, the tool used in architecture to make a perfect circle.
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