Masonic Geometry

Frank C. Higgins

The figure, which we are now about to examine, is one of the most striking of the entire series to come under observation and, at the same time, one of the most instructive, as demonstrating that all given figures in cosmic geometry are, in effect, metamorphoses of preceding figures and capable, in turn, of conversion into still other divine thought forms. The characteristic triangle of the Squared Circle of equal perimeters, which constitutes the vertical section of the Great Pyramid of Cheops at Gizeh, is here defined, by the relation of the center of the circle to the base of the square, but, as has already been pointed out, the proportion of the Square contained within the Circle, constitutes an oblong of three by four, dimensions which we have, already, and must again, frequently bring under discussion.

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When we turn the side lines of this figure, inwardly, until their upper extremeties meet in the center, we find that we have produced the triangle of next greatest importance, that of which the base and vertical axis are respectively the side of a square and the radius of a Circle of equal Area thereto. Constructing a third triangle, from the meeting point of these two side lines, to the base of the Square, we find ourselves, also, in possession of a side plane of the same Great Pyramid, another link in the chain connecting that stupendous monument with the cosmic science of Antiquity.

The mutual relations of Pyramid triangles, are that the axis of the side plane is equal to one side of the vertical section. Therefore in the triangle of the Squared Circle of equal perimeters, will be found the common factor between the Pyramids of Egypt and those of America, as the vertical section of the former and side plane of the latter.

The practical evolution of these pyramids from the proportions in question is wonderfully illustrated by a figure which at first glance appears to be the conventiona1 Fortyseventh problem of Euclid, but which is really based on a right angle of four by five instead of one of 3×4.

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A curious application of the Euclidean principle


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The square of four defines the length of the common base line, which triangulated to the centers of the remaining squares supply us with correct pat­ terns of the antipodean Pyramids. The fact that the smaller of the two i s unknown to Egypt, while the Egyptian form is equally present in Central America, is seeming proof of an intelligence between the ancient priesthoods on both sides of the Atlantic Ocean.

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This assumption seems to be corroborated by a curious figure surviving among the Hopi Indians of Arizona and New Mexico which has been classed by the savants of ‘the Smithsonian Institute of Washington as a “Bird figure.”
Closer examination will show that this is really a Circle de­ scribed upon an oblong, the long sides one of which serves as a diameter, being fourteen and the short ones eight parts in length. Such an oblong is equal to a Square, 11 x 11, while the diameter multiplied by 3 1/7, is as Pi to the circumference of the Circle and the Circle equal in circumference to the Square. The presence in this figure of a characteristic Egyptian Pyramid, placed base to base with a Teocalli or Mexican Pyramid both of which are founded upon the Pi proportion, speaks for itself. This same problem is profusely repeated as a symbolic figure, all over the facade of the great Temple of Hathor at Dendereh, Egypt.

Furthermore this oblong of 8 x 14, or in simple terms 4 x 7 (which so closely approximates 9 x 16 as to be confounded with it in ancient superficial measurements) produces our “Equal Area” triangles, as the oblong of 10 x 6 does that of “Equal Perimeters.”

The same peculiar property of reproducing itself four times when embodied in a Keystone is shown by the Area triangle as we have observed in its fellow and innumerable specimens of both dimensions have been discovered by the writer, as found in Chaldean and Phoenician tombs. In fact the dissimulation of these two basic geometrical theorems in the guise of religious symbols, architectural motifs and amulets of one kind and another, is the most interesting and convincing evidence of the one time universal community of thought, on this subject, to be found in the world. They are found in the most unusual and unexpected places but wherever they are encountered one may be sure that the Square and Compasses, in the hands of our ancient brethren, have been applied to the mysteries, of cosmic law.

The casual reader may be frankly advised that the subject matter of these papers will not be understood at its full value unless studied for the express purpose of mastering its intrica­ cies. It is because Freemasonry is really based upon this ancient learning that so many Masonic charlatans have found it easier to deny the lofty inspiration of the craft, than to attempt to cope with its intellectual exigencies.

The writer and some of his fellow students of these cosmic marvels have found one of the easiest ways of becoming familiar with their various elements, to be to cut from stiff cardboard, sheet celluloid or metal, a series of templates or angle measures, involving the principal dimensions. These can readily be applied to photographs and drawings of ancient architectural de­ tails, symbols, religious and mystical objects and natural forms and so employed will reveal a world of meaning little dreamed of by the narrow minded.

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The intelligent Freemason will, by this means suddenly find the apparently boastful and pedantic language of our ancient ritual, which many of his would-be leaders prefer to insist upon as having little or no meaning at all, full of splendid significance and an importance transcending his most sanguine expectations.

No simpler or better examples of genuine Masonic Geometry could be presented than the development, here exhibited, of the two Circle Squaring triangles (Base and Radius) from their respective oblongs; 9×16, approximating 4×7 and 10x 16, approximating 5x 8. The further development of these figures into the two Keystones of Ancient Craft Masonry1is also exhibited. Only the second survives, today, in the Mark Master degree of the Royal Arch Chapter but examples of the former are found, not only in ancient architecture but as Amulets, a favorite manner of displaying the two keystone proportions being to combine them in a single figure.

The great Gopurams or Temple gateways of Dravidian architecture in Southern India, are gigantic figures of this sort, buried under masses of sculptured embellishment.

Their specific angles of 77, 86, 96 and 103 degrees will be found to be those of the sloping Pylons of Egyptian temples and to, at once, account for the curious individuality of this particular school of construction.

The famous entablature on the grand temple of Abydos representing the Pharaoh Seti I offering to the gods Amun and Ra, shows that monarch be­ tween the seated figures of the two gods, each of whom bears a Nile-measuring staff in his hand. Drawings usually treat this detail carelessly but photographs show that the staff of Amun, the Ram­ headed god inclines to the perpendicular at an angle of twenty-three and onehalf degrees, while that of Ra inclines at an angle of fourteen degrees. The crown of the latter god is also a symbol of the 4 x 7

Bildschirmfoto 2015-08-31 um 00.31.01The Zeus Otriculi of the proportion. The inference to be drawn Vatican Museum Rome from this, that one of these gods symbolizes “Time” and the other “Space” is too pointed for controversy and that the ancient Keystone, embodying both proportions symbolized the divine union of both is equally presumable.

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We find this same geometrical occultism carried along from Amun to
Jove, whom the later Ro­
mans identified with him.
The angle of 23 ½ degrees
is expressed on the countenance of the latter by parting the hair on the face to express it.

Throughout the entire body of symbolism great and small of the ancient civilization of the New World, we shall find these basic forms repeated.

In the American Museum of Natural History, New York, are to be found fabrics which once formed the robes of the Sun priests of the Peruvian Incas. On a number of these, one remarks peculiar bird figures which seem altogether freakish until one grasps the idea that they are really intended to display by their fan like tails the specific dimensions of the “Perimeter” and “Circumference” triangles, the dimensions of their bases being given in tales on the tails and of their vertical axis, in points on the birds’ crests. The same manner of displaying geometrical dimensions have also been observed in the figures of fishes and human beings. The subject is almost inexhaustable but enough has been said and exhibited to carry conviction that no mere coincidences can be claimed to account for so many examples in complete accord.
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Having arrived, at last, through slow stages of evolution, at the development of what, for want of a better name, I am constrained to term the “Jehovah” trapezoid, we are compelled, by many important considerations to confine ourselves for a space to the study of this particular figure and its many historical, scientific and theological bearings.
I am satisfied, that after ages of dissimulation and mystification, we are upon the direct track of the precise considerations which crystallized themselves into the marvellous conception of Israel’s unique and unapproachable Creator.

Let it not, for one moment, be imagined that this subject is approached thoughtlessly or irreverently. We continue to work out our finite existences, in the presence of the same omnipotent, omniscient and omnipresent Power, which men have termed by a thousand names, without adding to or subtracting from its infinite substance.
Our analysis, in the present instance, is entirely in the interest of eternal Truth.
Upon no subject, has been written so much of the wild and helplessly speculative or of the inexplicably mystical, as concerning this wonderful four-letter name of God, the ineffable Tetragrammaton.

It may simplify our conceptions, in advance, and supply a substantial groundwork for future discussion, to briefly out line the popular credences which have hitherto gathered around this sacred theological riddle of the ages.
The unquestioning pious belief of centuries has clung to a literal interpretation of the Biblical narrative contained in the book of Exodus, where Moses is said to have received it as a supernatural communication from the midst of a “burning bush.” To the unimaginative literalist, fortified with his supreme confidence that the Almighty did not disdain to stoop to feats of legerdemain, ventriloquism and necromancy, in order to vindicate the popular aphorism to the effect that “Nothing is impossible to God,” this is a picturesque and con vincing tale. To the student of Oriental trends of thought and modes of expression, however, the possibility arises of there having been both symbolism and metaphor, involved in the attribution of a miraculous participation of the sacred Word.

If we are to harbor this hypothesis, even for a moment, we are irresistibly driven to take refuge in the known factors to cur rent Jewish mysticism, their tremendous energy in devising ways and means of mystery concealment and their intellectual passion for all manner of sacred anagrams, acrostics, jeux dc mots and double meanings, a tendency which finds its supreme expression in the mysteries of their holy Kabbalah.

If the writer of these lines may lay any claim whatsoever to inspiration, it will be to have conceived, many years ago, that rational and comprehensible reasons existed, somewhere, for those otherwise extravagant incoherencies which have been transmitted to us, from the remote past, as “Divine Mysteries.”
The preference of the vulgar mind for the tricks of the conjurer and the dark utterances of the charlatan, need not here be dilated upon.

In the days preceding the separation of secular science from mystic marvel, the outcroppings of the former were indescribable, except in the language of the latter.

A man’s having a happy thought, while in bed, at night, resulting in some material benefit to himself or a neighbor, would be described—“And behold the Lord threw a deep sleep upon his servant—. And the spirit of the Lord appeared unto him, saying, “Arise and do thus and so.” When subsequent generations came to make a picture of the event, the artist’s personal conception of what the “Spirit of the Lord” must have looked like, became the crowning effort of the design.
So it must have been with the story of Moses’ reception of the “Ineffable Name.” The tale is of a mystical, figurative nature describing the spiritual aspects of purely physical observations. The “burning bush” is a conical universe filled with solar and stellar radiance and the “Name of God” is made manifest to the inner perceptions of Moses from the very premises which we are now about to describe for he—“learned in all the “Nyisdom of the Egyptians,” was Priest, Philosopher, Astronomer, Geometer, Arithmetician, Physicist and Philologist. But we are by no means dependent upon either surmises or assumptions concerning this important archeological as well as theological problem. There are inner evidences which we will find and which we will examine.

The labors of European savants, in recent years, have gone far to convince us, upon historical grounds, alone, that the assumption of a Mosaic origin, for the “Great and Sacred Name,” is incorrect. Prof. Delitsch has deciphered the form inscription of a Babylonian tablet antedating the days of Moses, at thousand years, to the effect that “Jehovahis Ilu” The same ancient sources supply us with long lists of theophoros or “god-bearing” names of which the Divine Name constitutes one of the syllables. We have a dozen distinct, so-called “pagan” names for a Supreme Being, which are even more palpably imitative of the Tetragrammaton than Olympian “Jove,” and, at least, one “pagan” deity, who will be adequately described, possessing all the symbolic attributes.

The fallacies concerning this remarkable word or name have been as notable as its more reasonable attributes. Well might it be considered a “lost word” in that its true significances have been forgotten, save to a mystic few, for ages.
The most commonly received hypothesis on the part of those who have sought an extra-Biblical interpretation of the name “Jehovah,” is that it was the name of a mere tribal god, “jealous of,” because in competition with, the gods of other races.

Scholars have found a derivation from the verb hayah “to be,” because every tense of “being,” in the abstract, is con jugated with words composed only of the letters J, V and H, as found in the Tetragrammaton. This latter fact is correct, only the grammatical expressions have been arbitrarily created to correspond with the theological sense of “Being.” The word itself came first.

It is the contention of the writer, upon numerous grounds, that this sacred name is of completely scientific derivation and descends to us from a time unimaginably remote, with all its wealth of expression.

From the custom of the ancient Semitic peoples to employ letters as numerals, it was possible to present, in the shape of a Word, a mathematical formula, which could be shewn as the “least common factor” of a mathematical Universe and, hence its seed or nucleus. Evidences remain which show that there once existed a transcendent science, woven about the ineffable Name, demonstrating its bearing upon every phase of manifested existence. But the surviving records and’ demonstrations of this science have failed to transmit other than the bare externals, to our own age. We arrive at the truth by a curious fitting together of facts, figures and tradition, very much as in trigonometry, by knowing two angles we can easily find the third. We are surrounded by the dismembered vestiges of this ancient Jehovistic science cult, as by the fragments of some great picture puzzle. We have as a basis, the known facts of universal astronomy, which are the same today as yesterday and tomorrow. We know that the structure of our universe and the time periods of its various evolutions conform to a single mathematical law, not by aberrations or eccentricities, but regularly and rythmically, as the swinging of the pendulum, in a well regulated clock, no matter how stupendous the quantities involved in measuring time, space or proportion may be. Having these circumstances in mind, when we are confronted with cabalistic words, phrases or symbols, which conform to the ascertainable scientific truths of our cosmic environment, we are forced to recognize that those who put them into circulation, knew what they were about and that we have correctly interpreted their purposes. The fact that all of these propositions continually return, one upon the other, in vicious circles, only serves to accentuate the fact that the bond of unity, demonstrating the infinite One-ness, is not hard to find or understand. It is only the obtuseness of human conceit which bars the way to understanding, through its perpetual clamoring for “divine mysteries,” which shall be senseless to human comprehension. We will examine the simple aspects of this “Jehovah” trapezoid before we attempt to fathom its more complicated relations.

In order to make this possible, I have reduced them to a plate of ten diagrams, the first of which (1) shows the geometrical relation existing between the figure and the oblong of 3 x 4, which was the principal glyph of the Egyptian mysteries. This oblong is divided into two “Pythagorean” triangles of 3—4—5 dimensions each. The result of the combination precisely agrees with the three Names of God communicated to Moses in Exodus VI, 3:
“I appeared unto Abraham, unto Isaac and unto Jacob by the name of AL SHDI, but by my name JHVH was I not made known to them.”

The value of the first Name, according to Hebrew gemairia is 345, while that of the Name given at the “burning bush” AHIH ASHR AHIH (“I Am that I Am”), is 543. Even the Hebrew name of Moses, MSHE, is 345, so that the play on these quantities is unmistakable, the spiritual significance of the numbers in question being the Atma-Buddhi principle of the Vedas, (Sun, 5; Moon, 4; Mercury, 3) which is the union of the Divine Spirit and Divine Wisdom. The addition of 345+543 being 888, the value of both the Greek names Jesous and Christos, giving an additional clue to the occult development of the doc trine of the LOGOS (20+6+3+6+300=345). Furthermore the three “eights” of 888, equal 24, which is 3+4+5 twice repeated, or a return of the problem into itself. The boundary of the central figure, by the geometrical outline of 10—5—6—5 (JHVH), is a strikingly graphic illustration of the doctrinal relations of “Father and Son,” which have for sole present foundation, the Theological dictum, which disdains to explain— even if able to do so.


Before proceeding with the interesting demonstrations which we shall be enabled to make, of the universality of the ancient secret science, based upon the cosmic formula implied by the ineffable Name of JHVH, it will be useful for us to review some of the ground over which we have already passed, with reference to fresh angles of observation.

Readers of Mr. Howard Underhill’s remarkable article in September Azoth on “Set and Seb” will recollect his statement, founded on tradition rather than such research as we are now pursuing, that “Saturn (Seb) is Jehovah, God of the Jews.”

To begin with, the mere reversal of the orthography of “SEB” into “BES,” tells the story at once.

Certainly Saturn was the slowest moving planet known to the ancients and thus became the symbol of Kromos or “Time” but then, what is JHVH but Past, Present and Future, together with all they embody?

There is no such thing as “Time,” however, without a Chronometer, or Time measuring method. Time is only per- ceptable through variation. If all things moved in infinite unison there would be no “Time,” but the moment that one object moves faster or slower than another, a ratio is established, which if the phenomena be periodic, impresses our senses with the notion of what we term “Time.”

All manifested nature being in incessant movement, a sense of “Time,” is one of our strongest impressions, so strong that we can only conceive of a possible state in which there would be no “Time,” by formulating an hypothesis of no motion in space.

Now the JHVH trapezoid, which we have so carefully examined, relates to “Time,” because it constitutes the cosmic mechanism, by which the periodic evolutions of Earth are made apparent to its dwellers.

The Zodiacal and other symbolisms of the ancient world which remain to us are only intelligible, when we admit that the ancients possessed a knowledge which, up to comparatively recently, we have complacently assumed was not theirs.

“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 goodness of the Great Artificer of the Universe (Artifex Universus Mundi, A. U. M.) and view with delight the proportions which connect this Vast machine. By it we discover how the planets move in their respective orbits and demonstrate their various revolutions. By it we account for the return of the seasons and the variety of scenes which each season displays to the discerning eye. Numberless worlds are around us, all framed by the same Divine Artist which roll through the vast expanse and are conducted by the same unerring law of Nature.” This statement, the origin of which, every Mason will recognize, is

the crux of the whole Mystery. JHVH is the self-existing, self exerting “Law of Nature” and this law was discovered so long ago as what we call the “Bronze Age” of humanity, as shown by the now decipherable symbolisms of that distant era.

When we apprehend this natural law, and recognize the stupendous fact that notwithstanding its extreme simplicity it is what it is, we quickly find that the mystery symbols of all times and places whether graphic or oral, cryptic, arithmetical or geometric, are covert allusions to one and the same thing. Like the great Natural world, of which it is the foundation stone, this law is single in its essence and protean in its manifestations.

Throughout both the sacred scriptures of all peoples and the ritual of Freemasonry, we encounter a mass of otherwise meaningless numerical formulas and cryptic words, which have no apparent sense to their present custodians. Were we enabled to interpret but a few of the myriad expressions met with, we might suspect the “long arm of mere coincidence” but when we find all to be equally embraced and discover the method of their contrivance we are bound to submit to the evidence.

Masonry, in her higher degrees, gives us some hint of the lines, along which to work by allusions to “Angles of Oblongs” and her mystic numbers 3, 5, 7 and 9, but she nowhere tells us that the chief cosmic angles are those of Oblongs.



Or that the sum of these numbers is 40, represented by the letter “M,” the mystic symbol of the Logos.

Observed as either geometrical figures or arithmetical quantities, they constitute the base of all Natural forms and the root of all cosmic quantities.

Their angles are employed, above all other, in the Divine elaboration of our physical environment. Observing our Earth on a Mercator, or flat projection, we note, on each hemisphere, two girdles or belts, crossing each other at an angle of twenty-three and one-half degrees. These are the Equator and the Plane of the Ecliptic. Their existence presupposes two vertical lines crossing them at right angles, which indeed exist and are, respectively, the Earth’s Axis and a line parallel with the pole of the Ecliptic.

These, also, necessarily traverse each other, at the same angles.

The Pole of the Ecliptic, which is an imaginary line drawn vertically through the centre of the Sun, remains fixed, while the Earth’s axis, circling ever around the latter’s orbit, executes a gyroscopic movement, which in the course of 12,960 years causes it to incline at the same angle, in the same season in the precisely opposite direction, after which it consumes the same period of time in returning to its original position. This is called the Precession of the Equinoxes by reason of which the Equinoctial and Solstitial points of each year are retarded just fifty seconds of arc, amounting to 72 years per degree and 2,160 years per sign of thirty degrees. The mythological aspects of this circumstance will be found fully set forth in our series of papers on “The Zodiac in Religion and Freemasonry,” in previous issues of AZOTH. What may be termed the cosmic cone, is the volume of space swept by the Earth’s axis in executing the Precessional revolution, which will have, as its vertical section, a triangle with an apex of twice 23 1/2° or Forty-seven degrees. Here we have, at once, as will be seen by the illustrations, the basis of our “Jehovah” trapezoid as a measurer of cosmic Time. We prove that the ancient world had complete cognizance of these facts, studied them and caused them to be made the foundation of their religious mysteries, by innumerable circumstances which we are now enabled to intelligently follow.

As we have been able to demonstrate, the JHVH trapezoid, not only displays the mechanism of our revolving Universe, but embodies also the arithmetical quantities associated with it in hours, days, months and years.

The evidences that this extraordinary proposition is not a myth, but a body of truth which has been hidden under a veil of symbolism for ages, are not few or scattered, but litter the Earth profusely, for those who know how to read them.

In bringing to a close this particular series of demonstrative articles, although not, I trust, my labors in behalf of a clearer future understanding of such things, I desire to again assert, this time from the standpoint of one who has submitted reasonable proofs of his premises, the fact that the main physical facts of our Universe, particularly those which most intimately concern the Earth upon which we live and its true relations to our own Solar system, are not discoveries of any recent period. When obstinate pedagogues and “moon stricken” Theologians shall have succeeded, as they inevitably will, though how wearisome the wait, in disgusting mankind with the hollowness and insin cerity of their libels upon what we still term the ancient “pagan” world, it will be realized that the stigmatized pagans of old had a clearer vision of ultimate truth than has been achieved by two thousand years of so called Christian civilization.
The effort of an outnumbering swarm of intellectual pygmies to burden the world with the fetters of an unreasonable, not to say impossible theology, has compelled the reprobation en passant of every avenue of enquiry through which “Truth” might have been arrived at. It has compelled the repeated assassina tion of Truth, every time it has been seen that Truth must die in order that a lie or a false assumption might live. Our studies, in the realm of “Masonic Geometry,” have taught us that, granted the existence of an omnipresent, omnipotent “Cause of causes,” that this Divine Arbiter does not elect to create in freak ish and inexplicable abandon but that His entire work is a mas terpiece of mechanism so synchronized and synergetic, as to con stitute precisely that unity in multiplicity and multiplicity in unhy for which theology proffers explanations which are incomprehensible, where they are not merely .idiotic.

The Laws of Nature, emanating from the Divine Source are all characterized by the manifestation of ratios and relativi ties of Time, Space, Number and Proportion which permit of the dissimulation of facts relating to one proposition under the terms of all the others. The cubical contents of a stone of given proportion may be made to yield a cycle of planetary evolution or by the substitution of letters for numbers, a deep and basic scientific truth may be concealed in a mere word.

Ancient Craft Masonry was, therefore, first the scientific knowledge of Universal conditions, necessary to fathom and formulate their apparent law and secondly the ability to translate this law into terms of symbolism and architecture, so as to record it for the benefit of future generations.

When once the system is rightly understood, as it is begin ning to be by students of broad view and open mind, they are enabled to read the Mound Builder’s tumulus, the Druidic circle, the Pagan Temple, or the Christian Cathedral like an open book.

The seemingly diverse mythologies and theologies of both ancient and modern worlds give up their simple hidden secret, in that one and all are allegories of the Divine paternity evinced in the all-pervading Law and the closer to us mediation of the Sun god or Solar Logos, to which we turn for life, light and sustenance.

We have not yet had time or opportunity to dwell upon the more abstruse mysteries of this wonderful system, but it will interest the student that his ancient brethren, the Pythagorean Philosophers, were deeply interested in the Fourth dimension and had already associated it with what Theosophists term the “Astral plane” and discovered its materialization under the aspect of “Time” as completely as our Einstein of the present day.

There remains also another aspect of this remarkable sub ject to be developed and that is the working out of this cosmic law of form in the botanical and mineral worlds. Long ere philosophers in pillared halls and shady groves were solemnly working out their problems of correspondence between, Pyra mids, Cubes, Squares, Circles, Triangles and other planes and solids and the mighty laws of Nature and synthesising them in Mason’ry, God, Himself, was laboring in the depths of Earth, in the trackless domain of Air, in Ocean depths and Fiery vor tices, constructing the characteristic crystals of inorganic mat ter, the various proportions of which, still unstudied, from a Masonic standpoint, precisely respond to the great cosmic form ulae which man has mastered and made his own. God made Pyramids and Cubes in Chalcopyrites and Fluorite, ten million years before Cheops erected the same forms on the banks of the Nile or Solomon his “Holy of Holies,” on Mount Moriah.

Knowing as we now do the meaning of the cosmic angles (“Angles of Oblongs”) scattered so freely throughout the do main of ancient symbolism it is interesting to turn to a diagram which illustrates the simple method undoubtedly employed by the ancients to secure their undoubted.

We have the evidence of History that Eratosthenes, Libra rian of Alexandria (B.C. 270-196) in the reign of the great Ptolemy, calculated the distance from Alexandria to Syene up the almost vertical Nile as one-fiftieth of the Circumference of the Earth and we also know that the moment we know either the the diameter or the circumference of a circle that we are able to readily geometrize all of its other dimensions.
The position of the great Pyramid of Gizeh, however on the thirtieth parallel of North latitude, precisely the same distance from Philce, where the Tropic of Cancer crosses, is, however, complete evidence that Eratosthenes merely shifted a calculation filched from the ancient Priesthood of Egypt to a more flattering relation to himself and his royal master as another scientific rogue, Sosigenes, sold the 3 6 3 d 6 h formula of the Solar Year to Julius Cassar as his own calculation whereas it was a Magian secret.


The intention of our diagram, is to show the Thirtieth paral lel of East Longitude facing the Sun, at the Left, and the Mid night meridian at the Right. Common to both of these positions, the Pole Star, Alpha Draconis at the era B.C. 2170, when the Great Pyramid of Gizeh was built, equidistant from North Pole and the Center of the Earth, was approximately thirty degrees above the Gizeh horizon. The long tube or gallery directed to this star, in the body of the Pyramid enabled it to be seen by both day and night as Herodotus reports the stars could be seen at mid-day from the bottom of the Well of Syene.

The difference in elevation of the Pole Star above the hori zon five thousand stadia further South, together with the knowl edge that it stood directly over the North Pole as well as accurate knowledge of the location of the Tropics and the Plane of Eclip tic, was sufficient to permit of the working out of all the neces sary data by the simplest rules of trigonometry. It will also be observed that the parallels of latitude 30°, N. and 30°, S. describe an Oblong of 4×7 while the Tropical parallels describe one of 4 x9 . The almost imperceptible difference existing between the halves of these two proportions (7×8 and 8×9) gave rise to an Amulet of these dimensions among the Adept in the Ancient Wisdom, which is one of the most widely distributed of pre historic times, being found among the Babylonians, Egyptians,
Persians, Chinese and Mound Builders of the U. S. A. Further more, the angles formed between the Meridian of Gizeh and the line of vision to the Pole Star (Parallax) and between the latter and a straight line drawn between Gizeh and the North Pole are respectively 63° and 5 8 the characteristic angles of the side planes of the Great Pyramid. The value of a Hexagram anyone of the dimensions of which was known, in estimating the dis tances on any circle or globe surrounding it can also, easily be seen.
In conclusion, it can be laid down as an axiom that wherever the accentuation of certain angles is observed to be a salient fea ture of ancient Architecture that such angles will be found to belong to the physical Geography of our Earth or the Structure of the Solar system.

The writer is conscious of the fact that this has been but a crude and rudimentary presentation of a subject worthy of un limited extension in more competent hands, but to have once more introduced the subject of Cosmo-Gcometry to the attention of the learned after its oblivion of ages is a satisfaction he would not readily forego.
Editor’s Note. Our Masonic editorial collaborator, Bro. Higgins feels that he has imparted enough of his great subject to the Neophyte to enable the latter and future students, with the aid of back volumes of AZOTH, to devote their attention to various remarkable applications of the system in question, which will be made the subject of future papers describing such in detail.


(AZOTH 1920)