Masonic Geometry

[Tamrin]

Masonic Geometry

Short Talk Bulletin - Vol. 12, May 1934, No.5
<www.phoenixmasonry.org>

(Excerpt)

Geometry, the first and noblest of sciences, is the basis on which the superstructure of Masonry is erected. By geometry we may curiously trace nature, through her various windings, to her most concealed recesses. By it, we discover the power, the wisdom, and the goodness of the Grand Artificer of the Universe, and view with delight the proportions which connect this vast machine. By it, we discover how the planets move in their different orbits, and demonstrate their various revolutions. By it, we account for the return of seasons and the variety of scenes which each season displays to the discerning eye.

Woman Teaching Geometry
using the square and compasses

[Tamrin]

The 47th Problem of Euclid - The Veil Lifted

by William Steve Burkle, Pietre-Stones Review of Freemasonry

(Excerpt)

To progress beyond the fundamental concepts and arrive at the door of understanding, preparatory study of the history and mathematics of the 47th Problem is indeed essential; but ultimately one must discern that the true Masonic importance of the 47th Problem lies not in its mathematical utility (which is considerable), but in the fact that the 47th Problem as put forth by Euclid is intended to apply to a very specific case of a right triangle having sides with lengths in the specific proportions of 3, 4, and 5.

M.P. Hall

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THE CUBIT

By Wor. Bro. Gordon J. Row

It is said that King Solomon recruited over 150,000 stonemasons, hewers of timber, artificers of precious metals, labourers and overseers from all over the land, many speaking strange tongues, making communication difficult. This was not his only problem, a greater one was the lack of a uniform measure of length by which the stones, timbers, and all other materials could be joined with accuracy.

The CUBIT was a measure of length used by the Hebrews, Egyptians and Babylonians, being the distance from the elbow to the tip of the middle finger. So the CUBIT would vary by the physical size of the workman or overseer. This needed to be “standardised” if a project like the construction of the Temple was to proceed to a satisfactory conclusion.

Archaeological research has revealed that in Solomon’s day there were at least three different cubits in use:-

• a LAND CUBIT which was used for plotting the layout of the Temple’s courts and the surrounding terraces, it had a length of about 17.6 inches (447 mm)
  
• a BUILDING CUBIT used in the construction of buildings was about 14.4 inches (366 mm) long
  
• a GOLD CUBIT used in the making of the gold and silver vessels and the decorative work was about 10.8 inches (274 mm).

All these are multiples of the basic palm breadth of 3.6 inches (91.44 mm) which was used by the Babylonians and Hebrews. It is claimed the workmen at the Temple fashioned a rope of human hair which was knotted at three, four and five cubits. Human hair was selected because it is unaffected by heat or cold and maintains a constant length.

The Egyptian Cubit was devised about 3000BC and was standardised by a Royal Master Cubit of black granite, against which all the Cubic Sticks were checked at regular intervals.

The Royal Cubit (20.62 inches, 524 mm) was (20.62 inches, 524 mm) was subdivided in a rather complicated way. The basic unit was the DIGIT, a fingers breadth, of which there are 28 in the Royal Cubit. The digit in turn was subdivided. The 14th digit on the Cubit stick was divided into 16 equal parts. The next digit was divided into 15 equal parts, and so on, to the 28th digit which was divided into two equal parts. Thus the smallest division, 1/16th of a digit, was equal to 1/148th part of a Royal Cubit, (0.046 inches or 1.17 mm).

The accuracy of the Cubit Stick is evidenced by the Great Pyramid of Giza; thousands were employed on its construction, yet its sides vary no more than 0.05% from the mean length of 755.8 feet (230.37 m)—about 4.5 inches in 755 feet or 11.5 cm in 230 m!!! This is a great testimonial to those builders who worked with nothing more accurate than a Cubit Stick. HOW WOULD YOU GO WITH A 24” GAUGE?

[Tamrin]

EYE OF HORUS FRACTIONS

(Excerpt)

The Eye of Horus fraction system was based on the Eye of Horus symbol. This system was used to record prescriptions, land and grain.

Fractions are created by combining sections of the Eye of Horus symbol. Each section has a different value. The complete Eye of Horus with all parts in place has a value of 1. In reality the complete Eye of Horus represents 63/64, which is rounded off to 1.

The system is based on halves. Half of 1 equals 1/2, half of 1/2 equals 1/4 and so on until the smallest value of 1/64. By adding together the values of different sections fractions are created.

[Tamrin]

Pythagoras & Music of the Spheres

There is geometry in the humming of the strings
... there is music in the spacing of the spheres.

Dartmouth College, Mathematics Dept. (Geometry)

(Excerpt)

We'll look at the Pythagoreans' ideas about numbers, as a prelude to our next unit on number symbolism. Finally, we'll introduce a new idea that will be recurring theme throughout this course, the musical ratios, which will reappear in discussions of the architecture of the Renaissance.

[Tamrin]

[Tamrin]

The 47th proposition

THE 47th PROPOSITION OF THE IST BOOK OF EUCLID AS PART OF THE JEWEL OF A PAST MASTER.
By Bro. Thomas Greene, AQC, vol. xiv, for the year 1901. pp. 27-30.

(Excerpt - Linked above)

THE Jewel of the Past Master in Scotland consists of the Square, the Compasses, and an Arc of a Circle:—In Ireland of the Square and Compasses with the capital "G" in the centre:—In England for 85 years, at least, it has been the Square with the 47th Proposition of Euclid pendent within it. An Irish poet wrote.—

"Trath is one, and so is light,
Yet how many shades of it."

Freemasonry itself might be looked on as exemplifying unity without monotony; so let it not be supposed that because they are different there is anything exclusively English, or Irish, or Scotch, about the Past Master’s Jewel in each case; all are beautiful links in the chainwork of continuation from Operative to Speculative Masonry; all remind us that the master of an Operative Lodge worked out his plans by that branch of science to which we give the general name of "Geometry," and which is represented in the Irish Jewel by the Capital "G," which along with the 47th Proposition were in use both in England and in Ireland probably before 1723; and if we make a comparison at all, to my mind it should be in favour of the "G" as, primarily at least, standing for Geometry," the basis of all Operative Masonic Work, and including that 47th Proposition with which I am about to deal.