THEOSOPHY, Vol. 64, No. 7, May, 1976
(Pages 203-211; Size: 27K)




NOTE.--This is the second installment of a three-part collation of statements taken from H. P. Blavatsky's Secret Doctrine.

THE transcendental application of geometry to Cosmic and divine theogony -- the Alpha and the Omega of mystical conception -- became dwarfed after Pythagoras by Aristotle. By omitting the Point and the Circle, and taking no account of the apex, he reduced the metaphysical value of the idea, and thus limited the doctrine of magnitude to a simple TRIAD -- the line, the surface, and the body. ... "Space is a substantial though (apparently) an absolutely unknowable living Entity." (New Aspects, p. 9.) Such is, nevertheless, the Kabalistic teaching, and it is that of Archaic philosophy. Space is the real world, while our world is an artificial one. It is the One Unity throughout its infinitude: in its bottomless depths as on its illusive surface; a surface studded with countless phenomenal Universes, systems and mirage-like worlds. Nevertheless, to the Eastern Occultist, who is an objective Idealist at the bottom, in the real world, which is a Unity of Forces, there is "a connection of all matter in the plenum," as Leibnitz would say. This is symbolized in the Pythagorean Triangle.

It consists of ten points inscribed pyramid-like (from one to the last four) within its three lines, and it symbolizes the Universe in the famous Pythagorean Decade. The upper single dot is a Monad, and represents a Unit-Point, which is the Unity from whence all proceeds, and all is of the same essence with it. While the ten dots within the triangle represent the phenomenal world, the three sides of the equilateral triangle which enclose the pyramid of dots are the barriers of noumenal Matter, or Substance, that separate it from the world of Thought. "Pythagoras considered a point to correspond in proportion to unity; a line to 2; a superficies to 3; a solid to 4; and he defined a point as a Monad having position, and the beginning of all things; a line was thought to correspond with duality, because it was produced by the first motion from indivisible nature, and formed the junction of two points. A superficies was compared to the number three because it is the first of all causes that are found in figures; for a circle, which is the principal of all round figures, comprises a triad, in centre -- space -- circumference. But a triangle, which is the first of all rectilineal figures, is included in a ternary, and receives its form according to that number; and was considered by the Pythagoreans to be the creator of all sublunary things. The four points at the base of the Pythagorean triangle correspond with a solid or cube, which combines the principles of length, breadth, and thickness, for no solid can have less than four extreme boundary points." (Pythag. Triangle, p. 19).

It is argued that "the human mind cannot conceive an indivisible unit short of the annihilation of the idea with its subject." This is an error, as the Pythagoreans have proved, and a number of Seers before them, although there is a special training for it, and although the profane mind can hardly grasp it. But there are such things as metamathematics and metageometry. Even mathematics pure and simple proceed from the Universal to the particular, from the mathematical, hence indivisible Point, to solid figures. The teaching originated in India, and was taught in Europe by Pythagoras, who, throwing a veil over the Circle and the Point -- which no living man can define except as incomprehensible abstractions -- laid the origin of the differentiated Cosmic matter in the basic or horizontal line of the Triangle. Thus the latter became the earliest of geometrical figures. As an emblem applicable to the objective idea, the simple triangle became a solid. When repeated in stone on the four cardinal points, it assumed the shape of the Pyramid -- the symbol of the phenomenal merging into the noumenal Universe of thought -- at the apex of the four triangles; and, as an "imaginary figure constructed of three mathematical lines," it symbolized the subjective spheres -- those lines "enclosing a mathematical space -- which is equal to nothing enclosing nothing." ... It is the AIN-SOPH -- the NO-THING.

Our most eminent chemists and physicists are earnestly pursuing the not hopeless attempt of finally tracing to its hiding-place the protyle, or the basic line of the Pythagorean triangle. The latter is, as said, the grandest conception imaginable, as it symbolizes both the ideal and the visible universes. In the realm of the Esoteric sciences the unit divided ad infinitum, instead of losing its unity, approaches with every division the planes of the only eternal REALITY. The eye of the SEER can follow and behold it in all its pregenetic glory. This same idea of the reality of the subjective, and the unreality of the objective universes, is found at the bottom of the Pythagorean and Platonic teachings -- limited to the Elect alone.

But the Duad, although the origin of Evil, or Matter -- thence unreal in philosophy -- is still Substance during Manvantara, and is often called the third monad, in Occultism, and the connecting line as between two Points, ... or Numbers which proceeded from THAT, "which was before all Numbers," as expressed by Rabbi Barahiel. And from this Duad proceeded all the Scintillas of the three upper and the four lower worlds or planes -- which are in constant interaction and correspondence. This is a teaching which the Kabala has in common with Eastern Occultism. It is only in the anthromorphised systems (such as the Kabala has now greatly become) that Shekinah-Sakti is feminine. As such she becomes the Duad of Pythagoras, the two straight lines of the symbol that can never meet, which therefore form no geometrical figure and are the symbol of matter. Out of this Duad, when united in one basic line of the triangle on the lower plane (the upper Triangle of the Sephirothal Tree), emerge the Elohim, or Deity in Cosmic Nature, with the true Kabalists the lowest designation, translated in the Bible "God." ... Out of these issue the Scintillas.

The Spirit of Life and Immortality was everywhere symbolized by a circle: hence the serpent biting his tail, represents the circle of Wisdom in infinity; as does the astronomical cross -- the cross within a circle. The incorporeal intelligences (the Planetary Spirits, or Creative Powers) were always represented under the form of circles. In the primitive philosophy of the Hierophants these invisible circles were the prototypic causes and builders of all the heavenly orbs, which were their visible bodies or coverings, and of which they were the souls. It was certainly a universal teaching in antiquity. (See Ezekiel, ch. I.)

"Before the mathematical numbers," says Proclus (in Quinto Libro, EUCLID), "there are the Self-moving numbers; before the figures apparent -- the vital figures, and before producing the material worlds which move in a Circle, the Creative Power produced the invisible Circles."

Deus enim et circulus est, says Pherecydes, in his hymn to Jupiter. It was a Hermetic axiom, and Pythagoras prescribed such a circular prostration and posture during the hours of contemplation....

The Brahminical "Golden Egg," from within which emerges Brahmâ, the creative deity, is the "circle with the Central Point" of Pythagoras, and its fitting symbol. In the Secret Doctrine the concealed UNITY -- whether representing PARABRAHMAM, or the "GREAT EXTREME of Confucius, or the Deity concealed by PHTA, the Eternal Light, or again the Jewish EN-SOPH, is always found to be symbolized by a circle or the "nought" (absolute No-Thing and Nothing, because it is infinite and the ALL); while the god-manifested (by its works) is referred to as the diameter of that circle. The symbolism of the underlying idea is thus made evident: the right line passing through the centre of a circle has, in the geometrical sense, length, but neither breadth or thickness: it is an imaginary and feminine symbol, crossing eternity and made to rest on the plane of existence of the phenomenal world. It is dimensional, whereas its circle is dimensionless, or, to use an algebraical term, it is the dimension of an equation. Another way of symbolizing the idea is found in the Pythagorean sacred Decade which synthesizes, in the dual numeral Ten (the 1 and a circle or cipher), the absolute ALL, manifesting itself in the WORD or generative Power of Creation.


Those who would feel inclined to argue upon this Pythagorean symbol by objecting that it is not yet ascertained, so far, at what period of antiquity the nought or cipher occurs for the first time --  especially in India -- are referred to Vol. II of "Isis Unveiled," pp. 299, 300, et seq.

Admitting for argument's sake that the ancient world was not acquainted with our modes of calculation or Arabic figures -- though we know it was -- yet the circle and diameter idea is there to show that it was the first symbol in cosmogony. Plato and his school never understood the Deity otherwise, many epithets of his applied to the "God over all" ... notwithstanding. Plato having been initiated, could not believe in a personal God -- a gigantic Shadow of Man. His epithets of "monarch" and "Law-giver of the Universe" bear an abstract meaning well understood by every Occultist, who, no less than any Christian, believes in the One Law that governs the Universe, recognizing it at the same time as immutable. "Beyond all finite existences," he says, "and secondary causes, all laws, ideas and principles, there is an INTELLIGENCE or MIND (noûs), the first principle of all principles, the Supreme Idea on which all other ideas are grounded ... the ultimate substance from which all things derive their being and essence, the first and efficient cause of all the order, and harmony, and beauty and excellency, and goodness, which pervades the Universe" -- who is called, by way of preëminence and excellence, the Supreme(1) good "the god," and "the god over all." These words apply, as Plato himself shows, neither to the "Creator" nor to the "Father" of our modern Monotheist, but to the ideal and abstract cause. For, as he says, "the god over all, is not the truth or the intelligence, but the FATHER of it," and its Primal cause. Is it Plato, the greatest pupil of the archaic Sages, a sage himself, for whom there was but a single object of attainment in this life -- REAL KNOWLEDGE -- who would have ever believed in a deity that curses and damns men for ever, on the slightest provocation? Not he, who considered only those to be genuine philosophers and students of truth who possessed the knowledge of the really existing in opposition to mere seeming; of the always existing in opposition to the transitory; and of that which exists permanently in opposition to that which waxes, wanes, and is developed and destroyed alternately.(2) Speusippus and Xenocrates followed in his footsteps. The ONE, the original, had no existence, in the sense applied to it by mortal men. "The honoured one dwells in the centre as in the circumference, but it is only the reflection of the Deity -- the world Soul"(3) -- the plane of the surface of the circle. The Cross and Circle are a universal conception -- as old as human mind itself. They stand foremost on the list of the long series of, so to say, international symbols, which expressed very often great scientific truths, besides their direct bearing upon psychological, and even physiological mysteries; and this symbol is precisely one of this kind, and is based upon the oldest esoteric cosmogony.

The shadowy, but firmly rooted image of God, as the noumenon of all, was called more philosophically by the ancient (and modern) philosophers and Occultists -- "Gods," or the creative fashioning Powers. The modes of expression may have been different, and the ideas more or less philosophically enunciated by all sacred and profane Antiquity; but the fundamental thought was the same. For Pythagoras the Forces were Spiritual Entities, Gods independent of planets and Matter as we see and know them on Earth, who are the rulers of the Sidereal Heaven. Plato represented the planets as moved by an intrinsic Rector, one with his dwelling, like "A boatman in his boat." As for Aristotle, he called those rulers "immaterial substances"; though as one who had never been initiated, he rejected the gods as Entities. But this did not prevent him from recognizing the fact that the stars and planets "were not inanimate masses but acting and living bodies indeed...."

"Plato [writes Boulanger] in his fourth book of Laws, says that, long before the construction of the first cities, Saturn had established on earth a certain form of government under which man was very happy. As it is the golden age he refers to, or to that reign of gods so celebrated in ancient fables ... let us see the ideas he had of that happy age, and what was the occasion he had to introduce this fable into a treatise on politics. According to Plato, in order to obtain clear and precise ideas on royalty, its origin and power, one has to turn back to the first principles of history and tradition. Great changes, he says, have occurred in days of old, in heaven and on earth, and the present state of things is one of the results (Karma). Our traditions tell us of many marvels, of changes that have taken place in the course of the Sun, of Saturn's reign, and of a thousand other matters that remained scattered about in human memory; but one never hears anything of the EVILwhich has produced those revolutions, nor of the evil which directly followed them. Yet ... that Evil is the principle one has to talk about, to be able to treat of royalty and the origin of power."

That evil, Plato seems to see in the sameness or consubstantiality of the natures of the rulers and the ruled, for he says that long before man built his cities, in the golden age, there was naught but happiness on earth, for there were no needs. Why? Because Saturn, knowing that man could not rule man, without injustice filling forthwith the universe through his whims and vanity, would not allow any mortal to obtain power over his fellow creatures. To do this the god used the same means we use ourselves with regard to our flocks. We do not place a bullock or a ram over our bullocks and rams, but give them a leader, a shepherd, i.e., a being of a species quite different from their own and of a superior nature. It is just what Saturn did. He loved mankind and placed to rule over it no mortal King or prince but -- "Spirits and genii ... of a divine nature more excellent than that of man."

It was god, the Logos (the synthesis of the Host) who thus presiding over the genii, became the first shepherd and leader of men.(4) When the world had ceased to be so governed and the gods retired, "ferocious beasts devoured a portion of mankind." "Left to their own resources and industry, inventors then appeared among them successively and discovered fire, wheat, wine; and public gratitude deified them ..." ("De Legibus" I, iv.; in Crit. and in Politic).

How precise and true is Plato's expression, how profound and philosophical his remark on the (human) soul or EGO, when he defined it as "a compound of the same and the other." And yet how little this hint has been understood, since the world took it to mean that the soul was the breath of God, of Jehovah. It is "the same and the other," as the great Initiate-Philosopher said; for the EGO (the "Higher Self" when merged with and in the Divine Monad) is Man, and yet the same as the "OTHER," the Angel in him incarnated, as the same with the universal MAHAT. The great classics and philosophers felt this truth, when saying that "there must be something within us which produces our thoughts. Something very subtle; it is a breath; it is fire; it is ether; it is quintessence; it is a slender likeness; it is an intellection; it is a number; it is harmony ..." (Voltaire).

The Great Gods create men with the bodies of birds of the desert, human beings, "seven kings, brothers of the same family," etc., which is a reference to the locomotive qualities of the primary ethereal bodies of men, which could fly as well as they could walk,(5) but who "were destroyed" because they were not "perfect," i.e., they were sexless, like the Kings of Edom."

Plato speaks, in the Phaedrus, of a winged race of men. Aristophanes (in Plato's Banquet), speaks of a race androgynous and with round bodies. In Pymander, all the animal kingdom even is double-sexed. Thus it is said: "The circuit having been accomplished, the knot was loosened ... and all the animals, which were equally androgynous, were untied, (separated) together with man...." for.... "the causes had to produce effects on earth." Again, in the ancient Quiché Manuscript, the Popol Vuh -- published by the late Abbé Brasseur de Bourbourg -- the first men are described as a race "whose sight was unlimited, and who knew all things at once": thus showing the divine knowledge of Gods, not mortals. The Secret Doctrine, correcting the unavoidable exaggerations of popular fancy, gives the facts as they are recorded in the Archaic symbols.

What say the old sages, the philosopher-teachers of antiquity? Aristophanes speaks thus on the subject in Plato's "Banquet": "Our nature of old was not the same as it is now. It was androgynous, the form and name partaking of, and being common to both the male and female. ... Their bodies were round, and the manner of their running circular.(6) They were terrible in force and strength and had prodigious ambition. Hence Zeus divided each of them into two, making them weaker; Apollo, under his direction, closed up the skin."

The separation of the sexes was in the programme of nature and of natural evolution; and the creative faculty in male and female was a gift of Divine wisdom. In the truth of such traditions the whole of antiquity, from the patrician philosopher to the humblest spiritually inclined plebian, has believed. And as we proceed, we may successfully show that the relative truth of such legends, if not their absolute exactness -- vouched for by such giants of intellect as were Solon, Pythagoras, Plato and others -- begins to dawn upon more than one modern scientist.

In view of this circular form, the "I" issuing from the "O," or the egg, or the male from the female in the androgyne, it is strange to find a scholar saying -- on the ground that the most ancient Indian MSS. show no trace of it -- that the ancient Aryans were ignorant of the decimal notation. The 10, being the sacred number of the universe, was secret and esoteric, both as the unit and cipher, or zero, the circle. As to the Pythagoreans, we need but turn to the ancient manuscripts of Boethius's Geometry, composed in the sixth century, to find among the Pythagorean numerals the 1 and the nought, as the first and final ciphers. And Porphyry, who quotes from the Pythagorean Moderatus, says that the numerals of Pythagoras were "hieroglyphical symbols, by means whereof he explained ideas concerning the nature of things," or the origin of the universe. Pythagoras derived his knowledge from India; and we find Professor Max Müller corroborating this statement, at least so far as to allow the Neo-Pythagoreans to have been the first teachers of "ciphering," among the Greeks and Romans; that "they at Alexandria, or in Syria, became acquainted with the Indian figures, and adapted them to the Pythagorean abacus" (our figures). This cautious admission implies that Pythagoras himself was acquainted with but nine figures. Thus we might reasonably answer that, although we possess no certain proof (exoterically) that the decimal notation was known by Pythagoras, who lived on the very close of the archaic ages, we have yet sufficient evidence to show that the full numbers, as given by Boethius, were known to the Pythagoreans, even before Alexandria was built. This evidence we find in Aristotle, who says that "some philosophers hold that ideas and numbers are of the same nature, and amount to TEN in all." This, we believe, will be sufficient to show that the decimal notation was known among them at least as early as four centuries B.C., for Aristotle does not seem to treat the question as an innovation of the "Neo-Pythagoreans."

NOTE.--The volume and page references to the Secret Doctrine for the material in this installment are as follows: i, 615-19; ii, 552-5; ii, 554-5; i, 492-3; ii, 372-3; ii, 88, 89; ii, 55; ii, 96; ii, 133-34; ii, 217; i, 360, 361.

COMPILER'S NOTE: The following is a separate item which followed the above article but was on the same page. I felt it was useful to include it here:

We need not mind what we have not done nor yet what we have done. Have care only for what we are doing; so shall we best work and serve. Like St. Paul, we find the spirit willing but the flesh weak, yet the latter gets stronger all the time. It looks weaker than it is because of the higher standard of judgment we apply to it. Always the inner is the more perfect, and it is that which does the work of perfecting. "He who seeth that all his actions are performed by nature only and that the Self within is not the actor sees indeed." 


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(1) Cocker's "Christianity and Greek Philosophy," xi, p. 377.
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(2) See "Isis Unveiled," Before the Veil, xii, (Vol. I.).
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(3) Plato; "Parmenides," 141, E.
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(4) The Secret Doctrine explains and expounds that which Plato says, for it teaches that those "inventors" were gods and demi-gods (Devas and Rishis) who had become -- some deliberately, some forced to by Karma -- incarnated in man.
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(5) Remember the "winged Races" of Plato; and the Popol Vuh accounts of the first human race, which could walk, fly and see objects, however distant.
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(6) Compare Ezekiel's vision (chap. I) of the four divine beings who "had the likeness of a man" and yet had the appearance of a wheel, "when they went they went upon their four sides ... for tho spirit of the living creature was in the wheel."
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