The figure 3 symbolizes the Earth. It is a figure of the terrestrial bodies. The 2, upper half of 3, symbolizes the vegetable world, the lower half being hidden from our sight.
Three also referred to harmony, friendship, peace, concord, and temperance; and was so highly esteemed among the Pythagoreans that they called it perfect harmony.
Three, four, ten, and twelve were sacred numbers among the Etrurians, as they were among the Jews, Egyptians, and Hindūs.
The name of Deity, in many Nations, consisted of three letters: among the Greeks, Ι.Α.Ω.; among the Persians, H.O.M.; among the Hindūs, AUM; among the Scandinavians, I.O.W. On the upright Tablet of the King, discovered at Nimroud, no less than five of the thirteen names of the Great Gods consist of three letters each,—ANU, SAN, YAV, BAR, and BEL.
The quaternary is the most perfect number, and the root of other numbers, and of all things. The tetrad expresses the first mathematical power. Four represents also the generative power, from which all combinations are derived. The Initiates considered it the emblem of Movement and the Infinite, representing everything that is neither corporeal nor sensible. Pythagoras communicated it to his disciples as a symbol of the Eternal and Creative Principle, under the name of Quaternary, the Ineffable Name of God, which signifies Source of everything that has received existence: and which, in Hebrew, is composed of four letters.
In the Quaternary we find the first solid figure, the universal symbol of immortality, the pyramid. The Gnostics claimed that the whole edifice of their science rested on a square whose angles were … Σιγή, Silence: Βυθος, Profundity: Νοος, Intelligence: and Αληθεια, Truth. For if the Triangle, figured by the number 3, forms the triangular base of the pyramid, it is unity which forms its point or summit.
Lysias and Timæus of Locria said that not a single thing could be named, which did not depend on the quaternary as its root.
There is, according to the Pythagoreans, a connection between the gods and numbers, which constitutes the kind of Divination called Arithmomancy. The soul is a number: it is moved of itself: it contains in itself the quaternary number.
Matter being represented by the number 9, or 3 times 3, and the Immortal Spirit having for its essential hieroglyphic the quaternary or the number 4, the Sages said that Man, having gone astray and become entangled in an inextricable labyrinth, in going from four to nine, the only way which he could take to emerge from these deceitful paths, these disastrous detours, and the abyss of evil into which he had plunged, was to retrace his steps, and go from nine to four.
The ingenious and mystical idea which caused the Triangle to be venerated, was applied to the figure 4 (4). It was said that it expressed a living being, I, bearer of the Triangle Δ, the emblem of God; i.e., man bearing with himself a Divine principle.