Generally speaking, some of these angles were taken from Pythagoras, who talked in terms of the significance of 'numbers" rather than "angles. From my readings on the subject, I am convinced that Plato's discourses upon geometry and the significance of the various "Platonic solids" are essentially taken from Pythagoras' work, just as Pythagoras came up with these notions following his lengthy stay in Egypt as a priesthood initiate.
Fascinating how these "trails" just keep going backward until they vanish into the mists of pre-recorded history.
Bear in mind that the Ceremony of the Nine Angles was composed within the conceptual and iconographic limits of the Age of Satan. Nor was it intended to be an extensive, exhaustive "last word" on the angles or other included concepts; it was conceived as a noetic vision and GBM expression. The following comments pertain to my ideas at that time and deliberately avoid embellishing the CNA with the more sophisticated concepts to which I have since been sensitized through my own work and the many brilliant examinations by other Setians.
FIRST ANGLE: Unity. The concept of the Universe as the totality of existence.
Note that this does not admit to monotheism (except in the sense of Deism), because there is no room for conceptual distance between a God and a worshipper. The "laughing one" is Azathoth, who is "blind" and an "idiot" because in a condition of perfect unity there is naught else to see, not any knowledge of anything else possible. [Understand, of course, that I was taking H.P. Lovecraft's gods rather beyond his story-telling version of them. I don't in the least represent these as Lovecraft's own ideas, although I rather think that he would not have found fault with such elaborations.] In geometry a singularity identifies a locus only; there is no extension in any direction. Even the locus is "both there and not", since it has no dimensions at all. Hence there are an infinite number of loci, for example on a one-inch- long line: an interesting mathemagical paradox.
SECOND ANGLE: Duality. The profound and necessarily total change of unity into symmetry and polarity (and its symbolic representations: Horus and Set, Yang and Yin, etc.) The "orderer of the planes and angles' is Yog- Sothoth, who is, as the shaper of energy and matter, described as the author of Earth in its matter/energy/evolutionary configuration. Note that in pure duality there is no room for judgment between the two; there is only one or the other. In duality geometry creates a single extension (a line).
THIRD ANGLE: This is a very critical stage, because the existence of a third element introduces the notion of choice between the two opposites, either absolutely or relatively (Aristotelian system) or of choice to aspire or not to aspire to universal perfections (= Platonic/Pythagorean system). This is Nyarlathotep, otherwise Set, otherwise Lucifer/Satan, otherwise Prometheus, otherwise Thoth, who has created the power of perspective and the independent psyche of judgment. Here "knowledge"
becomes possible. In geometry we now have the triangle, which is the most rigid of figures and also creates a two-dimensional plane. Note that, per the Book of Coming
Forth by Night, the Horus/Set relationship actually fits into a threefold matrix rather than a twofold one. Set is an independent Intelligence with perspective upon the nonconscious objective universe on one hand and the chaos of the anti-objective universe
(HarWer) on the other. The simple Horus/Set duality results from primitive Aristotelian thinking (so kick me, Tharrud Terclis!).
FOURTH ANGLE: The Ram of the Sun (Shub-Niggurath/Amon) is a manifestation of the "awakened" human psyche as energized by the Messenger. It is thus that "Satan" is known to humanity: a personalized reflection, as it were, of the results of the Messenger's…