Pythagorean Mathematicsk

The tetrad--4--was esteemed by the Pythagoreans as the primogenial number, the root of all things, the fountain of Nature and the most perfect number. All tetrads are intellectual; they have an emergent order and encircle the world as the Empyreum passes through it. Why the Pythagoreans expressed God as a tetrad is explained in a sacred discourse ascribed to Pythagoras, wherein God is called the Number of Numbers. This is because the decad, or 10, is composed of 1, 2, 3, and 4. The number 4 is symbolic of God because it is symbolic of the first four numbers. Moreover, the tetrad is the center of the week, being halfway between 1 and 7. The tetrad is also the first geometric solid. Pythagoras maintained that the soul of man consists of a tetrad, the four powers of the soul being mind, science, opinion, and sense. The tetrad connects all beings, elements, numbers, and seasons; nor can anything be named which does not depend upon the tetractys. It is the Cause and Maker of all things, the intelligible God, Author of celestial and sensible good, Plutarch interprets this tetractys, which he said was also called the world, to be 36, consisting of the first four odd numbers added to the first four even numbers, thus: 1 + 3 +5 +7 = 16 2 + 4 + 6 + 8 = 20 36 Keywords given to the tetrad are impetuosity, strength, virility, two-mothered, and the key keeper of Nature, because the universal constitution cannot be without it. It is also called harmony and the first profundity. The following deities partook of the nature of the tetrad: Hercules, Mercury, Vulcan, Bacchus, and Urania (one of the Muses). The triad represents the primary colors and the major planets, while the tetrad represents the secondary colors and the minor planets. From the first triangle come forth the seven spirits, symbolized by a triangle and a square. These together form the Masonic apron. The pentad--5--is the union of an odd and an even number (3 and 2). Among the Greeks, the pentagram was a sacred symbol of light, health, and vitality. It also symbolized the fifth element--ether--because it is free from the disturbances of the four lower elements. It is called equilibrium, because it divides the perfect number 10 into two equal parts. The pentad is symbolic of Nature, for, when multiplied by itself it returns into itself, just as grains of wheat, starting in the form of seed, pass through Nature's processes and reproduce the seed of the wheat as the ultimate form of their own growth. Other numbers multiplied by themselves produce other numbers, but only 5 and 6 multiplied by themselves represent and retain their original number as the last figure in their products. The pentad represents all the superior and inferior beings. It is sometimes referred to as the hierophant, or the priest of the Mysteries, because of its connection with the spiritual ethers, by means of which mystic development is attained. Keywords of the pentad are reconciliation, alternation, marriage, immortality, cordiality, Providence, and sound. Among the deities who partook of the nature of the pentad were Pallas, Nemesis, Bubastia (Bast), Venus, Androgynia, Cytherea, and the messengers of Jupiter. The tetrad (the elements) plus the monad equals the pentad. The Pythagoreans taught that the elements of earth, fire, air, and water were permeated by a substance called ether--the basis of vitality and life.