The Monad -- only the emanation and reflection of the Point (Logos) in the phenomenal World -- becomes, as the apex of the manifested equilateral triangle, the "Father." The left side or line is the Duad , the "Mother," regarded as the evil, counteracting principle (Plutarch, De Placitis Placitorum ); the right side represents the Son ("his Mother's husband" in every Cosmogony, as one with the apex ); at the basic line is the Universal plane of productive Nature, unifying on the phenomenal plane Father-Mother-Son, as these were unified in the apex , in the supersensuous World.** By mystic transmutation they became the Quaternary -- the triangle became the T ETRAKTIS.
[[Footnote(s)]] ------------------------------------------------- * See Kant's Critique de la Raison pure (Barni's transl., Vol.
II., p.
54).
** In the Greek and Latin churches -- which regard marriage as one of the sacraments -- the officiating priest during the marriage ceremony represents the apex of the triangle; the bride its left feminine side and the bridegroom the right one, while the horizontal line is symbolised by the row of witness, the bridesmaids and best-men.
But behind [[Footnote continued on next page]] [[Vol.
1, Page]] 615 SPACE, FORCE AND MATTER.
This 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.
His modern heirs, who play at Idealism, have interpreted these three geometrical figures as Space, Force, and Matter -- "the potencies of an interacting Unity."* Materialistic Science, perceiving but the basic line of the manifested "triangle" -- the plane of matter -- translates it practically as (Father)- M ATTER, (Mother)- M ATTER, and (Son)- M ATTER, and theoretically as Matter, Force, and Correlation.
But to the average physicist, as remarked by a Kabalist, "Space, Force, Matter, are, what signs in algebra are to the mathematician, merely conventional symbols;" or "Force as force, and Matter as matter, are as absolutely unknowable as is the assumed empty space in which they are held to interact." As symbols representing abstractions, "the physicist bases reasoned hypotheses of the origin of things .
.
.
.
and sees three needs in what he terms creation: ( a ) a place wherein to create; ( b ) a medium by which to create; ( c ) a material from which to create.
And in giving a logical expression to this hypothesis through the terms space, force, matter, he believes he has proved the existence of that which each of these represents as he conceives it to be ."** The physicist who regards Space merely as a representation of our mind, or extension unrelated to things in it, which Locke defined as capable of neither resistance nor motion; the paradoxical materialist, who would have a void there, where he can see no matter, would reject with the utmost contempt the proposition that "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.
[[Footnote(s)]] ------------------------------------------------- [[Footnote continued from previous page]] the priest there is the altar with its mysterious containments and symbolic meaning, inside of which no one but the consecrated priests ought to enter.
In the early days of Christianity the marriage ceremony was a mystery and a true symbol.
Now, however, even the churches have lost the true meaning of this symbolism.
* See Von Hartmann's and Herbert Spencer's works.
** "New Aspects of Life," by Henry Pratt, M.D.
[[Vol.
1, Page]] 616 THE SECRET DOCTRINE.
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 Decad.
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.
The Hermetic axiom that the structure of the cosmos is reflected at every scale — 'as above, so below; as within, so without' — making each level a legible map of the others.
The entire passage maps geometric figures (point, line, triangle, Tetractis) onto cosmic and divine structure, asserting that the geometric form is a legible map of the theogonic hierarchy.
Narratives or doctrines of cosmic origin — how heaven, earth, and the primordial deities first came into being. The Kojiki's deities born alone on the Plain of High Heaven, Voluspo's Ginnungagap, Genesis's tohu wa-bohu, the Timaeus's Demiurge fashioning the Receptacle, the Hesiodic Theogony, the Kalevala's egg-cosmogony, Egyptian Nun-and-Atum. Distinct from emanation_hierarchy (structural-ontological cascade), letters_of_creation (mechanism of creation), and apocatastasis/frashokereti (end-state restoration); cosmogony is temporally-narrative beginning.
The passage narrates the origin of cosmic matter from the Point through the Monad and the triangle's basic line, explicitly stating that Pythagoras 'laid the origin of the differentiated Cosmic matter in the basic or horizontal line of the Triangle.'
A chain of divine beings or principles flowing downward from a single transcendent source (the One or the Father), each level less perfect than the one above.
The passage describes a clear cascade from the Point (Logos) through the Monad to the Father-Mother-Son triad and then to the phenomenal plane, with the triangle becoming the Tetractis through 'mystic transmutation.'
A historical or mythical chain of transmission for secret wisdom from master to disciple across time and cultures — the credential of the teaching, not merely its content. Distinct from oral_tradition (the spoken-not-written modality of transmission, which a lineage may or may not use) and hidden_sayings (the concealment-for-readiness of a teaching's meaning, independent of who transmitted it or in what unbroken chain).
The passage states 'The teaching originated in India, and was taught in Europe by Pythagoras,' establishing a chain of transmission for the geometric-cosmological doctrine across cultures and time.
The Hermetic doctrine that a masculine-feminine generative principle operates on every plane of being, not only the biological — present at all times as a structural feature of creation itself. Distinct from divine_marriage (a specific reunification event or symbol) and aeons (paired divine beings arranged in syzygies, not a universal structural claim).
The masculine-feminine generative principle is structurally embedded in the triangle: the left side is the 'Mother' (feminine, counteracting) and the right side is the 'Son' (masculine), with the apex as 'Father,' making gender a structural feature of creation itself.
The divine reason, word, or ordering principle through which the universe was created; mediates between the transcendent God and the material world.
The Logos is explicitly identified as the Point from which the Monad emanates and reflects into the phenomenal world, functioning as the mediating ordering principle between the transcendent and the manifested.
The absolutely simple, undivided first principle from which all multiplicity and existence flows.
The Monad is explicitly named as 'the emanation and reflection of the Point (Logos)' and as 'a Unit-Point, which is the Unity from whence all proceeds,' serving as the central figure around which the entire geometric-cosmological argument is built.
Numbers, proportions, and mathematical relationships as the underlying structure of divine reality.
The Pythagorean Tetractis and Decad are central to the passage, with the ten points symbolizing the Universe and the numbers one through four corresponding to point, line, surface, and solid as the basis of cosmic structure.
The doctrine that the one Godhead or first principle subsists as three co-equal aspects or persons rather than a bare unity — the Christian Father/Son/Holy Ghost invoked in the recurring liturgical formula 'In the Name of the Father, and of the Son, and of the Holy Ghost,' but structurally the same pattern as the Egyptian Amen/Ptah/Osiris, the Hindu Brahma/Vishnu/Siva, and the Kabbalistic Chochmah/Binah/Kether triads that esoteric writers explicitly map onto it as instances of one universal law. Distinct from unity_of_being (the general claim that all existence is one substance, agnostic about internal plurality) and divine_simplicity (God as having no parts or divisions at all) in asserting a definite three-aspected differentiation within a single divine essence.
The Father-Mother-Son structure is explicitly mapped onto the equilateral triangle's apex and two sides, with the passage noting this pattern appears 'in every Cosmogony' and is symbolized in the marriage ceremony.