Current Theme:  Meta-Geometry

The One Circle                The Secret Doctrine book i p.1-7

Triad and Tetraktis          SD i 59-60

Nature Geometrizes         SD i 97

Numbers and Transformation  SD ii 33-34

The Cross and the Decade      SD ii 573--576, 580-589

The Hebdomad           SD ii 590-593, 600-605

The Tetragram             Isis Unveiled i 505-508

Indian and  Chaldean Cosmogony      Isis Unveiled ii 266-271

The Cube Unfolded     Transactions   i 88-91

Numbers and Polarity         Transactions 140-143

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From the Section: The One Circle                The Secret Doctrine book i p.1-7

AN Archaic Manuscript — a collection of palm leaves made impermeable to water, fire, and air, by some specific unknown process — is before the writer's eye. On the first page is an immaculate white disk within a dull black ground. On the following page, the same disk, but with a central point. The first, the student knows to represent Kosmos in Eternity, before the re-awakening of still slumbering Energy, the emanation of the Word in later systems. The point in the hitherto immaculate Disk, Space and Eternity in Pralaya, denotes the dawn of differentiation. It is the Point in the Mundane Egg (see Part II., "The Mundane Egg"), the germ within the latter which will become the Universe, the ALL, the boundless, periodical Kosmos, this germ being latent and active, periodically and by turns. The one circle is divine Unity, from which all proceeds, whither all returns. Its circumference — a forcibly limited symbol, in view of the limitation of the human mind — indicates the abstract, ever incognisable PRESENCE, and its plane, the Universal Soul, although the two are one. Only the face of the Disk being white and the ground all around black, shows clearly that its plane is the only knowledge, dim and hazy though it still is, that is attainable by man. It is on this plane that the Manvantaric manifestations begin; for it is in this SOUL that slumbers, during the Pralaya, the Divine Thought,* wherein lies concealed the plan of every future Cosmogony and Theogony.

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SD i page 272

The Secret Doctrine is the accumulated Wisdom of the Ages, and its cosmogony alone is the most stupendous and elaborate system: e.g., even in the exotericism of the Purânas. But such is the mysterious power of Occult symbolism, that the facts which have actually occupied countless generations of initiated seers and prophets to marshal, to set down and explain, in the bewildering series of evolutionary progress, are all recorded on a few pages of geometrical signs and glyphs.

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Triad and Tetraktis          SD i 59-60

Say the Kabalists: "The Deity is one, because It is infinite. It is triple, because it is ever manifesting." This manifestation is triple in its aspects, for it requires, as Aristotle has it, three principles for every natural body to become objective: privation, form, and matter.* Privation meant in the mind of the great philosopher that which the Occultists call the prototypes impressed in the Astral Light — the lowest plane and world of Anima Mundi. The union of these three principles depends upon a fourth — the LIFE which radiates from the summits of the Unreachable, to become an universally diffused Essence on the manifested planes of Existence. And this QUATERNARY (Father, Mother, Son, as a UNITY, and a quaternary, as a living manifestation) has been the means of leading to the very archaic Idea of Immaculate Conception, now finally crystallized into a dogma of the Christian Church, which carnalized this metaphysical idea beyond any common sense. For one has but to read the Kabala and study its numerical methods of interpretation to find the origin of that dogma. It is purely astronomical, mathematical, and pre-eminently metaphysical: the Male element in Nature (personified by the male deities and Logoi — Viraj, or Brahmâ; Horus, or Osiris, etc., etc.) is born through, not from, an immaculate source, personified by the "Mother"; because that Male having a Mother cannot have a "Father" — the abstract Deity being sexless, and not even a Being but Be-ness, or Life itself. Let us render this in the mathematical language of the author of "The Source of Measures." Speaking of the "Measure of a Man" and his numerical (Kabalistic) value, he writes that in Genesis, ch. iv., v. 1, "It is called the 'Man even Jehovah' 

Measure, and this is obtained in this way, viz.: 113 x 5 = 565, and the value 565 can be placed under the form of expression 56.5 x 10 = 565. Here the Man-number 113 becomes a factor of 56.5 x 10, and the (Kabalistic) reading of this last numbered expression is Jod, He, Vau, He, or Jehovah. . . . The expansion of 565 into 56.5 x 10 is purposed to show the emanation of the male (Jod) from the female (Eva) principle; or, so to speak, the birth of a male element from an immaculate source, in other words, an immaculate conception."

Thus is repeated on Earth the mystery enacted, according to the Seers, on the divine plane. The "Son" of the immaculate Celestial Virgin (or the undifferentiated cosmic protyle, Matter in its infinitude) is born again on Earth as the Son of the terrestrial Eve — our mother Earth, and becomes Humanity as a total — past, present, and future — for Jehovah or Jod-he-vau-he is androgyne, or both male and female. Above, the Son is the whole KOSMOS; below, he is MANKIND. The triad or triangle becomes Tetraktis, the Sacred Pythagorean number, the perfect Square, and a 6-faced cube on Earth. The Macroprosopus (the Great Face) is now Microprosopus (the lesser face); or, as the Kabalists have it, the "Ancient of Days," descending on Adam Kadmon whom he uses as his vehicle to manifest through, gets transformed into Tetragrammaton. It is now in the "Lap of Maya," the Great Illusion, and between itself and the Reality has the Astral Light, the great Deceiver of man's limited senses, unless Knowledge through Paramarthasatya comes to the rescue.

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OM Symbol

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Yin Yang Symbol

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We could connect this symbol with the involution,evolution concept in the Theosophical Tenets group.  It is interesting that the seed of the opposite is at the heart of both sides.

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Nature Geometrizes         SD i 97

We see Cosmic matter scattering and forming itself into elements; grouped into the mystic four within the fifth element — Ether, the lining of Akasa, the Anima Mundi or Mother of Kosmos. "Dots, Lines, Triangles, Cubes, Circles" and finally "Spheres" — why or how? Because, says the Commentary, such is the first law of Nature, and because Nature geometrizes universally in all her manifestations. There is an inherent law — not only in the primordial, but also in the manifested matter of our phenomenal plane — by which Nature correlates her geometrical forms, and later, also, her compound elements; and in which there is no place for accident or chance. It is a fundamental law in Occultism, that there is no rest or cessation of motion in Nature.* That which seems rest is only the change of one form into another; the change of substance going hand in hand with that of form — as we are taught in Occult physics, which thus seem to have anticipated the discovery of the "Conservation of matter" by a considerable time. Says the ancient Commentary † to Stanza IV.: —

"The Mother is the fiery Fish of Life. She scatters her spawn and the Breath (Motion) heats and quickens it. The grains (of spawn) are soon attracted to each other and form the curds in the Ocean (of Space). The larger lumps coalesce and receive new spawn —in fiery dots, triangles and cubes, which ripen, and at the appointed time some of the lumps detach themselves and assume spheroidal form, a process which they effect only when not interfered with by the others. After which, law No. * * * comes into operation. Motion (the Breath) becomes the whirlwind and sets them into rotation."

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Numbers and Transformation  SD ii 33-34

Symbols: all these are based upon and start from the figures given from the Archaic Manuscript in the proem of Book I. , the symbol of evolution and fall into generation or matter, is reflected in the old Mexican sculptures or paintings, as it is in the Kabalistic Sephiroth, and the Egyptian Tau. Examine the Mexican MSS (Add. MSS. Brit. Mus. 9789)*; you will find in it a tree whose trunk is covered with ten fruits ready to be plucked by a male and female, one on each side of it, while from the top of the trunk two branches shoot horizontally to the right and left, thus forming a perfect  (tau), the ends of the two branches, moreover, each bearing a triple bunch, with a bird  the bird of immortality, Atman or the divine Spirit  sitting between the two, and thus making the seventh. This represents the same idea as the Sephirothal Tree, ten in all, yet, when separated from its upper triad, leaving Seven. These are the celestial fruits, the ten or  10, born out of the two invisible male and female seeds, making up the 12, or the Dodecahedron of the Universe. The mystic system contains the , the central point; the 3 or ; the five, , and the seven or , or again ; the triangle in the square and the synthesizing point in the interlaced double triangles. This for the world of the archetypes. The phenomenal world receives its culmination and the reflex of all in MAN. Therefore he is the mystic square  in his metaphysical aspect  the Tetraktis; and becomes the Cube on the creative plain. His symbol is the cube unfolded  and 6 becoming 7, or the  three crossways (the female) and four vertically; and this is man, the culmination of the deity on Earth, whose body is the cross of flesh, on, through, and in which he is ever crucifying and putting to death the divine Logos or his HIGHER SELF.

    "The universe," says every Philosophy and Cosmogony, "hath a Ruler (Rulers collectively) set over it, which is called the WORD (Logos); the fabricating Spirit is its Queen: which two are the First Power after the ONE."

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Good basic metaphysic stuff - fortunately the first 35 pages of volume 2 give a pretty nice, accessible summary of the whole metaphysical system (with a few difficulties here and there, of course), so one of the fundamental sections, IMO.

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Could you add a few  more thoughts to why this is one of the "fundamental sections" from your point of view?

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Permalink Reply by Casady on January 23, 2015 at 12:50pm
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at your service... More precisely, the first two stanzas give a decent recap of all of Vol. one. So that's pp. 13-44 - you have a very good recap of the triple logos in stanza I and stanza 2 has a good metaphysical outline of the septenary system and the 7 sacred planet especially - moreover, you also get some good basics on Pythagorean and kabbalistic metaphysics, which are part of the fundamental notions, I would say.

So any if one wishes to avoid reading the very difficult vol. One, I would suggest a few basic, relatively simple, and quite comprehensive sections: the proem, I, 3.11 (On the elements and the atoms), I, 3.15 (Gods, Monads, Atoms) (and maybe 16. Cyclic Evolution and Karma) and Stanzas I & II of vol. 2 . If someone is able to understand those 60 or so pages, then I would say they have a solid grasp of the fundamentals of the esoteric worldview, common to all the major esoteric cosmologies (although even those 60 pages probably require quite a bit of work, initially). (PS - I would also throw in I, 2. 3 & 4 - Primordial Substance & Divine Thought, Chaos, Theos, Kosmos, for good measure, so some 75 pages, more or less, not too bad).

Permalink Reply by Grace Cunningham on January 27, 2015 at 11:09am
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Thank  you  kindly Casady.  I might add the Six Items found in Summing up: SD i 272-276  This touches on the key principles of the Esoterica Philosophy quite well including a reference in the first item concerning glyphs and sympbols which our Meta-Geometry discussion is mainly about I believe.

Permalink Reply by Casady on January 27, 2015 at 1:55pm
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good point Grace, one of the better known sections, that would surely need to be in the primer...

Permalink Reply by ModeratorTN on January 21, 2015 at 8:34pm
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The Cross and the Decade      SD ii 573--576, 580-589

This Decade representing the Universe and its evolution out of Silence and the unknown Depths of the Spiritual Soul, or anima mundi, presented two sides or aspects to the student. It could be, and was at first so used and applied to the Macrocosm, after which it descended to the Microcosm, or Man. There was, then, the purely intellectual and metaphysical, or the "inner Science," and the as purely materialistic or "surface science," both of which could be expounded by and contained in the Decade. It could be studied, in short, from the Universals of Plato, and the inductive method of Aristotle. The former started from a divine comprehension, when the plurality proceeded from unity, or the digits of the decade appeared, but to be finally re-absorbed, lost in the infinite Circle. The latter depended on sensuous perception alone, when the Decade could be regarded either as the unity that multiplies, or matter which differentiates, its study being limited to the plane surface; to the Cross, or the Seven which proceeds from the ten — or the perfect number, on Earth as in heaven.

Permalink Reply by ModeratorTN on January 25, 2015 at 11:49pm
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The Hebdomad           SD ii 590-593, 600-605

THE MYSTERIES OF THE HEBDOMAD.

WE must not close this Part on the Symbolism of Archaic History, without an attempt to explain the perpetual recurrence of this truly mystic number in every scripture known to the Orientalists. As every religion, from the oldest to the latest, claims its presence, and explains it on its own grounds agreeably with its own special dogmas, this is no easy task. We can, therefore, do no better or more explanatory work than to give a bird's-eye view of all. These sacred numbers (3, 4, 7) are the sacred numbers of Light, Life, and Union — especially in this present manvantara, our Life-cycle; of which number seven is the special representative, or the Factor number. This has now to be demonstrated.

If one happened to ask a Brahmin learned in the Upanishads — so full of the secret wisdom of old, why "he, of whom seven forefathers have drunk the juice of the moon-plant, is trisuparna," as Bopaveda is credited with saying; and why the Somapa Pitris should be worshipped by the Brahmin trisuparna — very few could answer the question; or, if they knew, they would still less satisfy one's curiosity. Let us, then, hold to what the old Esoteric doctrine teaches.

Permalink Reply by Grace Cunningham on January 27, 2015 at 11:12am
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What are some of the geometrical forms or shapes that represents the 7 best?

Permalink Reply by Casady on February 1, 2015 at 1:37pm
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Here's some real basic Pythagorean stuff (quite close to what Blavatsky generally discusses):

http://www.american-buddha.com/cult.pythagsourcebook.intro.htm

and a little more developped:

http://www.american-buddha.com/cult.pythagsourcebook.2.32.htm

the Platonic solids:

http://www.technologyuk.net/mathematics/geometry/platonic_solids.shtml

Permalink Reply by Gerry Kiffe on February 3, 2015 at 10:11am
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Thank you for these Casady.

Permalink Reply by Casady on February 1, 2015 at 12:03pm
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Here's a few basic passages from Proclus commentary on Euclid, a classic for the history of mathematics, also loaded with esoteric mathematical concepts:

For this reason both in Nous and in the intermediate orders of souls-that is, those natures that directly breathe life into bodies- the limiting factors have an essential priority over the things that are limited, as being less divisible, more uniform, and more sovereign; for among immaterial forms unity is more perfect than plurality, the partless more perfect than what proceeds in and away from it, and what bounds more perfect that what gets its limit from something other than itself. (In Euclid 86)

  ‘’To this difficulty we reply that the imagination in its activity is not divisible only, neither is it indivisible. Rather it moves from the undivided to the divided, from the unformed, to what is formed’’ (95)

 Hence the unit is without position, since it is immaterial and outside all extension and place; but the point has position because it occurs in the bosom of imagination and is therefore enmattered. Owing to its affinity with the principles, the unit is simpler than the point, for the point, by having position, goes beyond the unit. And additional determinants in the bodiless concepts effect a lessening of being in the things that accept them. (96)

 But let us recall the more Pythagorean doctrine that posits the point as analogous to the monad, the line to the dyad, the surface to the triad, and the solid to the tetrad. On the other hand, considering them as extended, we shall find that the line is one-dimensional, the surface two-dimensional, and the solid three-dimensional; hence Aristotle says that body comes to completion with the number three. (98)

‘’Hence the Limit, the Unlimited, and the Mixed are present in all of them. Aristotle’s opinion is the same as Plato’s; for every line, he says, either straight, or circular, or a mixture of the two. For this reason there are three species of motion-motion in a straight line, motion in a circle, and mixed motion’’ (105).

 (Proclus A Commentary on the First Book of Euclid's Elements, G. Morrow, transl. Princeton)

Permalink Reply by Casady on March 16, 2015 at 1:53pm
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...says an Occult axiom: "Circle is the Thought, diameter is Word, and their union is Life." SD2, 106

Explain, oh Lanoo (disciple).” — “The One is an unbroken Circle (ring) with no circumference, for it is nowhere and everywhere; the One is the boundless plane of the Circle, manifesting a diameter only during the manvantaric periods; the One is the indivisible point found nowhere, perceived everywhere during those periods; it is the Vertical and the Horizontal, the Father and the Mother, the summit and base of the Father,the two extremities of the Mother, reaching in reality nowhere, for the One is the Ring as also the rings that are within that Ring. Light in darkness and darkness in light: the Breath which is eternal. It proceeds from without inwardly, when it is everywhere, and from within outwardly, when it is nowhere — (i.e., maya,† one of the centres‡)." SD I, 11

Permalink Reply by Gerry Kiffe on March 18, 2015 at 1:30pm
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Casady please give us your translation of what is being said here, draw us to the most important strains of thoughts you see here.

Permalink Reply by Casady on April 10, 2015 at 2:16pm
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I just wanted to draw attention to some of the important number of Dzyan occult commentaries scattered throughout the SD - the ones above being comments on the Pythagorean metaphysical geometry found in the Proem and slokas 1 &2 of Vol. 2 - the first one being a neat, succinct formulation and the second having echoes of the hermetic 'God is a circle' phrase. Here's a third one:

These numbers are explained in the “Commentaries” in these words.

The Circle is not the “One” but the ALL. In the higher [heaven] the impenetrable Rajah [“ad bhutam,”see “Atharva-Veda” X., 105], it [the Circle] becomes One, because [it is]the indivisible, and there can be no Tau in it.

In the second [of the three Rajamsi” (triteye),or the three Worlds”] the one becomes two [male and female]; and three [add the Son or logos];and the Sacred Four [“tetractis,” or the Tetragrammaton.”]

In the third [the lower world or our earth]the number becomes four, and three, and two. Take the first two, and thou wilt

obtain Seven, the sacred number of life; blend [the latter] with the middle Rajah, and thou wilt have Nine, the sacred number of BEING and BECOMING.”*sd2 621-22