It sounds like hermeticism
I'm interested in geometry and pythagoreanism too, and how it can be found in plato as idea of good, and forms in the realm of idea.
Hindu also had this idea of deva, and fundemental forces, like the svatika , and other 'pattern', either it's with sound, or geometric pattern, hindu had a mathematics tradition early, and also all creation of music scale comes from this knowledge of mathematics to begin with, hindu had their own music scale, even if it's different from the one pythagora made, they are both based on some application of mathematics principle to bind 'music' to 'soul'.
Like this :
[ul]THE FOUR STAGES OF SOUND[/ul]
[ul]The Vedas form the sound-manifestation of Ishvara. That sound has four divisions,—Para which finds manifestation only in Prana, Pasyanti which finds manifestation in the mind, Madhyama which finds manifestation in the Indriyas, and Vaikhari which finds manifestation in articulate expression.[/ul]
[ul]Articulation is the last and grossest expression of divine sound-energy. The highest manifestation of sound-energy, the primal voice, the divine voice is Para. The Para voice becomes the root-ideas or germ-thoughts. It is the first manifestation of voice. In Para the sound remains in an undifferentiated form. Para, Pasyanti, Madhyama and Vaikhari are the various gradations of sound. Madhyama is the intermediate unexpressed state of sound. Its seat is the heart.[/ul]
[ul]The seat of Pasyanti is the navel or the Manipura Chakra. Yogins who have subtle inner vision can experience the Pasyanti state of a word which has colour and form, which is common for all languages and which has the vibrating homogeneity of sound. Indians, Europeans, Americans, Africans, Japanese, birds, beasts—all experience the same Bhavana of a thing in the Pasyanti state of voice or sound. Gesture is a sort of mute subtle language. It is one and the same for all persons. Any individual of any country will make the same gesture by holding his hand to his mouth in a particular manner, when he is thirsty. As one and the same power or Shakti working through the ears becomes hearing, through the eyes becomes seeing and so forth, the same Pasyanti assumes different forms of sound when materialised. The Lord manifests Himself through his Mayaic power first as Para Vani in the Muladhara Chakra at the navel, then as Madhyama in the heart and then eventually as Vaikhari in the throat and mouth. This is the divine descent of His voice. All the Vaikhari is His voice only. It is the voice of the Virat Purusha.[/ul]
This whole book is very interesting in this hinduist view of man as a microcosm, and how geometry as cosmic principle, can also be found in the human soul, and related to 'spirituality'. Sometime i don't see much discinction in hinduism either if they study consciousness, astronomy, 'science', mathematics, they use the same set of core principle in all disciplines.
In the west pythagora is the one who coined the whole idea of frequencies, sinus, trigonometry, the idea of square & circle found in masonry for me it's really directly pythagorean.
Crowley studied this also, he speaks about different music scales or music pattern that can be used to attain certain state of mind.
Binaureal beats, conqurete music, and synthetic 'digital' sound are also a direct application of geometry and 'digits' to art.
About the "lost world" , socrates had the idea that truth is more 'remembered' from our soul rather than learned from exterior sources. Because we are never taught really what the concept of truth is about and how to recognize it, so the soul must know from birth what truth is, and he has to remember it. Or maybe it's reference to ancient civilisation, or 'lost eden' myth, or 'genetic memory' , or past live memory too.
Liebniz is more complex to study, but he is said to have been a rosicrucians, and he is also great mathematician , he studied this whole relation between god, optimal world, mathematics, 'identities', numbers, reason. Not that much geometry, but frequencies and sound it was already studied in antiquity.