**
Our Ancient Friend and Brother,
the Great Pythagoras**
by **
Fra. Thomas D. Worrel, VII°**
**
Presented to the**
*
Societas
Rosicruciana In Civitatibus Foederatis*
California College, February 3, 1996
Later published in the SRICF -- *Ad
Lucem IV* 1996
*
"Let no one ignorant of Geometry
enter here"*
In our Masonic adventure we encounter
this great historical figure or his work more than once. The first meeting
occurs in the Third Degree in the company of the Hieroglyphical Emblems. We are
not told much, being only presented with one paragraph of information which, you
might say, contains a few odd statements. We hear that Pythagoras invented the
formula that is known as the Forty-Seventh Proposition of Euclid (better known
to us as the Pythagorean Theorem). That he traveled all over the known world:
Africa, Asia and Europe (it is more likely that he kept to the Mediterranean
rim). That he was initiated into several orders of priesthood. From this point
the paragraph begins to take on a strange twist. We are next told that he was
raised to the sublime degree of Master Mason (since Pythagoras lived in the 6th
century B.C. we can really count ourselves as being the world's oldest
Fraternity). And finally we are informed that when he first realized the
relationship that the Theorem defines he exclaimed EUREKA! I guess that is just
a piece of wisdom trivia that has been handed down for 25 centuries. And because
of his great excitement he sacrificed a hecatomb - which is a great public
sacrifice of probably 100 oxen. This is even stranger knowing that Pythagoras
was a vegetarian and is one of the earliest Western philosophers to teach the
doctrine of the transmigration of souls - that souls are immortal and are
continually reborn into new bodily forms.
We may be inclined to take lightly
this part of the Lecture due to its quasi-historical nature and oddities but
garner some feeling of respect and acknowledgement for an ancient philosopher
and mathematician. But upon closer examination of this paragraph we find that
such a casual attitude might be a mistake. I think we can be generous and give
the author some credit and assume that there is something more within what he
said (I think the paragraph was taken wholly from Thomas Smith Webb). One of the
first things that come to our attention is the fact that Pythagoras is one of
the only if not the only "outsider" mentioned in all the Blue Lodge Degrees.
This fact alone gives us pause to wonder why he has been spotlighted by our
Masonic ancestors. So who was this man given such high esteem in our Fraternity?
**
Pythagoras**
Pythagoras was probably born about
570 B.C. on the island of Samos. He was an Ionian Greek. He later immigrated to
Crotona in southern Italy where he founded a philosophical and religious
society. At one point it was persecuted and many of its leaders were killed.
Pythagoras resettled but eventually it happened again and the fraternity was
scattered.
It seemingly died out in the fourth
century B.C. Pythagoras himself died around 500 B.C. We do know a little about
Pythagoras and the Pythagoreans but the earliest is from Plato. His school grew
into a sort of brotherhood and fraternity with vows of secrecy. Therefore,
little was written down. The emblem of the society was a pentagram. At each
point of the star was a Greek letter which all together spelled "health" ( -
Upsilon, gamma, iota, theta, alpha). And we know that Apollo was of major
importance to their society. We know that:
*
"In earlier Greek theology, the Logos
was personified in the shining figure of Apollo, the god of light, musk,
geometry, and harmony, whose nature most closely reflects the highest
realizations of the Greek Spirit. As the god of harmony, he is said to have
invented all music. Apollo was the god of reason (logos), yet he was also a god
of prophecy. He is a personification of the celestial harmony, ...He was the
leader of the nine Muses, the goddesses of inspiration and the arts,..."*
(David Fideler, Jesus Christ. Sun of God, page 63)
Although Pythagoreanism is of vast
extent and far beyond the scope of this paper, so for brevity we can list its
main doctrines as: "the immortality of the soul, philosophy as an assimilation
to the divine, and the mathematical basis of the cosmos." (Encyclopedia of
Philosophy. Vol. 7, page 39) The particular interest of this paper is the
Hieroglyphical Emblem: the Forty- Seventh Problem of Euclid.**
The Forty-Seventh
Proposition of Euclid**
The Pythagorean theorem states that
for any right triangle the sum of the squares of its two legs equals the square
of its hypotenuse (a2 + b2 = c2). Or we could frame it as the sum of the square
of the horizontal and the square of the perpendicular equals the square of the
hypotenuse. We know this formulation was known before Pythagoras - there is
evidence in ancient Egyptian work, ancient China (the Chou Pei manuscript), and
the megalith builders. Regardless, it is attributed to Pythagoras and two
hundred years later Euclid compiled his "Elements of Mathematics" where this
particular proposition is found in Book One.
(47th) In every right angle triangle
the square on the hypotenuse is equal to the sum of the squares on the other two
sides.
(48th) If the square described on one
of the sides of a triangle is equal to the square described on the other sides,
then the angle contained by these two sides is a right angle.
This theorem has been called the root
of all geometry and the cornerstone of mathematics. The practical applications
alone are worthy of the high esteem that Masonry affords it. And this is the
interpretation of the lecture that is most considered when masons speak of it
But the meaning of this hieroglyphical emblem does not stop there.
The emblem we are usually presented
is the 3,4,5 right triangle in this fashion: The vertical line is of 3 units,
the horizontal is of 4 units, and the hypotenuse is of 5 units. Not only is our
attention called to this geometrical figure in the Master Mason degree, it is
also prominent in the Scottish Rite in the 20th Degree - Master of the Symbolic
Lodge and in the 25th Degree - Knight of the Brazen Serpent.
Rex Hutchens, commenting upon the
20th Degree in his book on the Scottish Rite explains that:
Nine is a perfect number, being the
triple of three. There are nine candles in three groups of three each on the
East, West, and South of the Altar. They form a graphic representation of the
47th Problem it makes no difference in the equation if the other two angles are
45 degrees each or 30 degrees and 60 degrees or 5 degrees and 85 degrees.
Because of the mystic meaning associated with numbers by the ancients, they
considered the most beautiful triangle of all, the right-angled triangle with
sides of 3,4 and 5 units of measure. (Rex Hutchens, *The Bridge to Light*,
p.171)
In the 25th Degree commentary
Hutchens describes the setting of this degree:
The ceremony takes place in four
apartments. They are all remarkable in their simplicity. The first is called the
House of the Earth. ...The second apartment is called the House of the Planets.
The third apartment is ... styled the House of the Sun and Moon.... The
principal chamber is called the House of the Light. Nine lights (candles) are
arranged on the altar in groups of three, forming a representation of the
Pythagorean Theorem, ... (Hutchens, *The Bridge to Light*, p.215)
The evidence that the particular
triangle alluded to in the Monitor is the 3,4,5 right triangle can be derived
from the odd comments about Pythagoras' exclamation "Eureka" in the Grecian
language. Here is where we can begin to apply the investigative tools of what is
called gematria. As you know the ancient letters were also numbers. The
correlation of numbers with letters gave ample opportunity to nest hidden
meaning within words, phrases, and names. For example, if we take the word
"Eureka" in Greek and consider the letters as numbers instead of letters, add
them up to get a total value we get 534 - the units of this special triangle.
Maybe we can even find hints of this
geometry in earlier degrees. A very interesting technique of symbolism can be
seen when two different types of symbolism are fused together or alluded to by
one another such as a legend that contains mathematical symbolism. For example,
many of the blacksmiths of the gods were crippled or lame. In many cases the
Sacred King was lame. The destiny of the Sacred King was to lose his life as a
sacrifice; an act which will regenerate the world. Usually the lameness and
sacrifice was deliberately caused. Vergil wrote a poem wherein the Queen who is
resolved to die offering herself as a victim in the fire, he writes: "beside the
altars, with one foot unshod, she calls as one about to die upon the gods and
upon the doom-witnessing stars." There is an association between lameness and
having one foot unshod. And in the idea of sacrifice and redemption. There is a
Byzantine painting known as "Our Lady of Perpetual Help". This painting is of
the Madonna holding her divine child. On each side of them there is an angel who
holds some of the images associated with the Crucifixion. The divine child is
looking at one angel and one of his shoes is falling off. We can even find this
idea in the slanting foot-rest of the Russian Cross in the Eastern Churches.
We can develop this further. In
geometry, there are three types of triangles: equilateral, isosceles and
scalene. The equilateral triangle has 3 equal sides; the isosceles has 2 equal
sides, and the scalene triangle has no equal sides. Scalene means "uneven", it
also means, "limping". Of all the infinite scalene triangles, the one thought of
by the ancients, as special - the king of them all, was the 3,4,5-unit triangle.
This one had the special properties
and it grew to have mystical properties as well. In so considering the symbolism
of the Egyptian structure one author states:
And so beneath the ideal pyramid,
with its four great equilaterals pointing heavenward as they converge above the
center of the basal square... there would be sacrificed, hidden in the
foundations so to speak, a limping but necessary scalene, supplying the
all-important right angle for the base and for the central elevation. (Denning &
Philips, The Magical Philosophy, Vol. 2 p.58)
As we consider geometry as symbolism
as well as Truth, we have to think of it as the ancients did. Pythagoras said
"All is Number" and in The Republic, Plato wrote: "The knowledge at which
geometry alms is the knowledge of the Eternal." The Eternal was to Plato the
archetypal Forms, or the timeless truths of existence. In other words, the
foundation of the universe. That aspect of the universe which always was and
ever will be.**
The Mystical Symbolism
of the Pythagorean Triangle**
According to Plutarch (46 - 120
C.E.),the Egyptians attributed the sides of the triangle in this fashion. The
vertical line was of 3 units and attributed to Osiris. The horizontal line was
of 4 units and attributed to Isis. And the hypotenuse was, of course, 5 units
and attributed to Horus, the son of Osiris and Isis. It is noteworthy that
Plutarch studied in the Academy at Athens and was a priest at Apollo's temple at
Delphi for 20 years. In the myth of Osiris and Isis, Osiris is killed which
makes Horus the Son of a Widow and links him with Hiram.
The units of the triangle's side are
significant. The three units of the Osiris vertical has been attributed to the
three Alchemical principles of Salt, Sulphur and Mercury (direct correspondence
with the Hindu concept of the Gunas: Tamas, Rajas and Sattva.). All things are
manifestations of these three principles according to Alchemical doctrine. The
four units of the horizontal line of Isis relate to the so-called four elements:
earth, air, water, and fire.
These are of course the four
Ancients. (Hindu classification: prithivi, vayu, apas, tejas). The ascending
Horus line with its five units represents the five kingdoms: mineral, plant,
animal, human, and the Fifth Kingdom. This is the Path of Return. The ascending
line finally connects back up with the Osirian line. The Fifth Kingdom
symbolizes the Adept as one who has consciously reunited with the Source of all
Being.
The angles that this special triangle
expresses are significant as well. Here we must dive deeper into the realm of
gematria. Remember that the assumption is that words with the same numerical
value are in some meaningful way connected. The set angles of the 3,4,5 triangle
(in whole numbers) are 90 degrees, 37 degrees, and 53 degrees. If we can
understand tat this geometrical figure is not only of the greatest practical
value but also of the greatest mystical significance we must assume that every
aspect of it sheds further Light upon our Quest. We can look upon this emblem as
representing the ongoing incarnation of Spirit and the ensuing ascent of
consciousness by building higher and more complex forms in which to express
Itself.
Looking at where the vertical meets
the horizontal (the conjunction of the Osiris and Isis) we have the 90-degree
angle - the angle of a square. By Hebrew gematria we know right away that 90 is
the value of the Hebrew word for Water - Mem (mem-yod-mem). of course this
reference is to Water as symbolical as in the alchemical statement: "Our Sun and
our Moon are conjoined in our Water." The union of the Father and Mother
produces the child Horus.
The angle at the conjunction of Isis
and Horus, the beginning of the ascension of the hypotenuse, is 37 degrees. We
know from our Qabala that 37 is the number of Adam's second son - Abel (Hebrew
spelling: heh-beth- lamed). Abel is considered a prototype of Christ. The number
37 is also associated with Yechidah - the Inmost Self (yod-cheth-yod-daleth-heh),
and the word for Ark used in the Greek translation of the Old Testament in
reference to both Moses and Noah - *he thibe*. (eta theta, iota, beta, eta).
The ark was the instrument used to ensure the continuing life.
The angle at the conjunction of Horus
and Osiris at the head of the comer is 53 degrees. This is the symbolical union
of the Father with the Son. The Hebrew words whose value is 53 includes Garden -
as in the Garden of Eden (gan: gimel-nun) and Stone (ehben: aleph-beth-nun). In
the Greek we find the word Acacia, the sprig of immortality (alpha-kappa-
alpha-kappa-iota-alpha). A further look at Ehben - stone- reveals another hidden
point of light. If we look at the letters or letter it, Ab or father (aleph-beth
or 3) and Ben or son (beth-nun or 52) can be joined in the letters aleph-ben-nun
(53) or ehben which is stone. In other words, the father and son are conjoined
in the Stone.
One further elaboration of these
ideas - and we could continue this for some time - is the connection of Horns
with Hiram Abiff (and Christ, Krishna, and Brother C.R. for that matter). The
numeral value in Hebrew for Hiram Abiff if 273. The same value is found in the
Hebrew words Aur Genoz meaning: the Hidden Light. We also find the familiar
phrase in Psalm 118:22 "the stone which the builders refused". In Hebrew it is
pronounced ehben masu ha-bonim and the value of this phrase - "the stone which
the builders refused" is 273 just like Hiram Abiff and the Hidden Light. And if
we listen to the syllables of this phrase out of Psalms we can find further
light on the significance of the substitute for the Lost Word. If we just take
the phrase "refused by the builders" (masu-ha- bonim) it equals the value 220.
This is another very important number for the gematria is related to the Hebrew
word for "lamb" (kaph-resh), the Latin Christus Deus et Homo or Christ, God and
Man; and *Novus Ordo Seclorum* - A New World Order.
With all this behind us I think that
we can conclude that the value of the Pythagorean triangle to Masonry is beyond
compare. It leads us into the inner recesses by its very nature. It links us
with the inner teachings of the Ancient Mystery Schools even taking us back to
the construction of the Pyramids with their triangular faces, four-fold base,
and five corners and faces; back to the megalithic builders, also shedding light
upon the cryptic words of the alchemists, aligns us with our Hindu brethren,
binds us with the three pillars of the Qabalistic Tree of Life - Mercy,
Severity, and Mildness and relating to our own pillars of Wisdom, Strength, and
Beauty and the Three Grand Masters of the Temple.
### bibliography
*
I am indebted to the following works
for their ideas on this subject*:
1.
__The True and Invisible
Rosicrucian Order__ by Paul
Poster Case
2.
__A Bridge to Light__
by Rex Hutchens
3.
__Jesus Christ: Sun of God__
by David Pideler
4.
__Hermetic Masonry__
by Frank C. Higgins
5.
__Geometry for the Practical
Man__ by J.E. Thompson
6.
__The Magic of Mathematics__
by Theoni Pappas
7.
__Stellar Theology and
Masonic Astronomy__ by
Robert Hewitt Brown
8.
__Restorations of Masonic
Geometry and Symbolry__ by
H.P.H. Bromwell
9.
__The Magical Philosophy Vol.
I - V__ by Melita Denning &
Osborne Phillips
**
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