Pythagorean Mathematicsm

These are symbolized by the cube, which has six surfaces and a mysterious seventh point within. The six surfaces are the directions: north, east, south, west, up, and down; or, front, back, right, left, above, and below; or again, earth, fire, air, water, spirit, and matter. In the midst of these stands the 1, which is the upright figure of man, from whose center in the cube radiate six pyramids. From this comes the great occult axiom: "The center is the father of the directions, the dimensions, and the distances." The heptad is the number of the law, because it is the number of the Makers of Cosmic law, the Seven Spirits before the Throne. The ogdoad--8--was sacred because it was the number of the first cube, which form had eight corners, and was the only evenly-even number under 10 (1-2-4-8-4-2-1). Thus, the 8 is divided into two 4's, each 4 is divided into two 2's, and each 2 is divided into two 1's, thereby reestablishing the monad. Among the keywords of the ogdoad are love, counsel, prudence, law, and convenience. Among the divinities partaking of its nature were Panarmonia, Rhea, Cibele, Cadmæa, Dindymene, Orcia, Neptune, Themis, and Euterpe (a Muse). The ogdoad was a mysterious number associated with the Eleusinian Mysteries of Greece and the Cabiri. It was called the little holy number. It derived its form partly from the twisted snakes on the Caduceus of Hermes and partly from the serpentine motion of the celestial bodies; possibly also from the moon's nodes. The ennead--9--was the first square of an odd number (3x3). It was associated with failure and shortcoming because it fell short of the perfect number 10 by one. It was called the called the number of man, because of the nine months of his embryonic life. Among its keywords are ocean and horizon, because to the ancients these were boundless. The ennead is the limitless number because there is nothing beyond it but the infinite 10. It was called boundary and limitation, because it gathered all numbers within itself. It was called the sphere of the air, because it surrounded the numbers as air surrounds the earth, Among the gods and goddesses who partook in greater or less degree of its nature were Prometheus, Vulcan, Juno, the sister and wife of Jupiter, Pæan, and Aglaia, Tritogenia, Curetes, Proserpine, Hyperion, and Terpsichore (a Muse). The 9 was looked upon as evil, because it was an inverted 6. According to the Eleusinian Mysteries, it was the number of the spheres through which the consciousness passed on its way to birth. Because of its close resemblance to the spermatozoon, the 9 has been associated with germinal life. The decad--10--according to the Pythagoreans, is the greatest of numbers, not only because it is the tetractys (the 10 dots) but because it comprehends all arithmetic and harmonic proportions. Pythagoras said that 10 is the nature of number, because all nations reckon to it and when they arrive at it they return to the monad. The decad was called both heaven and the world, because the former includes the latter. Being a perfect number, the decad was applied by the Pythagoreans to those things relating to age, power, faith, necessity, and the power of memory.