Numerology,was invented to quantify, tabulate and create concepts to be applied at useful purposes. The role of numbers in esoteric studies was largely originated from and developed by Pythagoras in the fifth century BC from maths developed first by the Babylonians.Pythagoras believed the secrets and real nature of the world could be arrived at by finding the real nature of numbers. Using fractions and ratios Pythagoras invented a system of musical notation from ratios of sounds represented by mathematical symbols. Pythagoras also studied geometry and originated a mystical philosophy that incorporated math that spread to areas as far and diverse as Western Europe and India.
In the fourth century BC Aristotle who had had instruction in Pythagorean concepts as well as from Plato and Socrates before him and pre Socratic cosmogony before them, taught that numbers were the only ideas that had no existence in the physical world but only in the universal mind. This teaching was contrasted from Plato’s teaching that everything has a higher existence as an eternal idea af of which the corporeal thing is a mere imitation. Aristotle believed numbers were derived from number one and that the numbers that followed after started with the dyad which allowed for expression of the plural from unified being after the first multiplicity. Like numbers planes and solids had no existence in the form of physical objects but could be used in ways of thinking about physical bodies. The infinite unity of the cosmos bestowed existence to unequal, finite numbers in the act of creation from an infinite being that could have no parts divisibility or differentiation since these could not have arisen from or predicated as distinct from an infinite unity. Homologies from Plotinus to Lao Tzu give account of plural modes of existence or a manifestation of being producing new realms in the manner of “the one becoming two, the two becoming three” and so on. The view of more modern philosophy that number is a primary as opposed to a secondary quality, since as Aristotle himself held that a thing could not both be and not be, is consistent with more modern views on how we perceive.
Geometric ratios which can be used to calculate cosmological, and religious meaning in the construction of ancient monuments like Soloman’s temple or the great Pyramids is also used in astrology to measure geometric relations between astral and celestial bodies from the location of these bodies relative to each other to a measure of so many degrees on an astrological chart, which allows the astrologer to read the positions from the information available to him or her. The constant ratio Phi or “Golden mean” is useful for studying the proportion of geometric shapes when in cosmic relation and for plotting terms in a geometric system which may involve aspects of a religious system like the tree of life better known as the Kabbala. The use of geometric symbols in representing the composition of matter involved cubes, pyramids, octahedron, icosahedron, and dodecahedron as symbols for earth, fire, air, water and cosmos or ether. The triangle was considered as the fundamental shape of all matter being the most basic stable shape. Familiar geometric shapes composed of triangles include the star of David, consisting of two triangles brought together symbolizing personal power. The cube is composed of six sides that can be broken into twelve equilateral triangles, unfolding int a cross shape and with similarities in dimensions to Soloman’s temple in Jerusalem.The pentacle is a configuration if pentagram and isosceles triangle that can be shown to be be extended infinitely inwardly and outwardly even simultaneously in macrocosm and microcosm. When circumscribed by a circle the pentacle takes up exactly half the area of the circle, to name a few of the many, some of the inverse relations to this shape which symbolizes a perfectly balanced person.
Geometric shapes of the symbols for the sun, moon and planets were expanded only by John Dee in his Mona Hydroglyphica which involved analysis and combination of these symbols and their components. The circle sometimes containing the symbol meant the monad that generated the worlds and continue to do so as part of the motion of each planetary sphere in a fully ordered solar system. Combinations of these symbols combined their power to form talismans. A renaissance philosopher and scientist Dee was an personal astrologer to Queen Elizabeth I.
As a point when extended becomes a line, a line a plane, a plane a solid and as some say the motion of a body through space; time arising as a consequence of something in motion. But to infer too much from what can be shown with geometrical concepts can give rise to fallacies . These pure concepts cannot form the basis of knowledge and serve at least partly the framework of experience.