(3) "The Pythagoreans indeed go farther than this, and honour even numbers and geometrical diagrams with the names and titles of the gods. Thus they call the equilateral triangle head-born Minerva and Tritogenia, because it may be equally divided by three perpendiculars drawn from each of the angles. So the unit they term Apollo, as to the number two they have affixed the name of strife and audaciousness, and to that of three, justice. For, as doing an injury is an extreme on the one side, and suffering one is an extreme on the on the one side, and suffering in the middle between them. In like manner the number thirty-six, their Tetractys, or sacred Quaternion, being composed of the first four odd numbers added to the first four even ones, as is commonly reported, is looked upon by them as the most solemn oath they can take, and called Kosmos." (Isis and Osiris.)

(55) Timaeus: And the third solid is composed of twice sixty of the elemental triangles conjoined, and of twelve solid angles, each contained by five plane equilateral triangles, and it has, by its production, twenty equilateral triangular bases. Now the first of the elemental triangles ceased acting when it had generated these three solids, the substance of the fourth Kind being generated by the isosceles triangle. Four of these combined, with their right angles drawn together to the center, produced one equilateral quadrangle; and six such quadrangles,

(9) Of Figure 15, the symbol of salt, von Welling writes, in substance: The cube has six sides, corresponding to the six days of creation, with the point of rest (the seventh day) in the center of the cube. On each surface of the cube appear the signs of the four elements [triangles]. The alchemists declared that salt was the first created substance produced by the fire (Schamayim) which flowed out of God. In salt all creation is concentrated; in salt are the beginning and end of all things. The cube, furthermore, is composed of twelve bodies, each of which has six sides. These bodies are the twelve fundamental pillars of the true invisible church, and when these twelve bodies are multiplied by their six sides the magical number 72 results. The wise have said that nothing is perfect until it has been dissolved, separated, and again united so that it becomes a body composed of twelve bodies, like the cube. The cube also consists of six pyramids with the six surfaces of the cube as their bases. The points of these six pyramids meet at the center of the cube. These six pyramids, each consisting of four triangles, signify the elements, and produce the magical number 24, which refers to the Elders before the Throne. The six surfaces and the point constitute the magical number 7. If 7 be multiplied by 7 again, and so on 7 times, the answer will reveal the method used by the ancients for measuring the periods of eternity; thus: (1) 7 X 7 = 49; (2) 49 X 7 = 343; (3) 343 X 7 = 2,401; (4) 2,401 X 7 = 16,807; (5):16,807 X 7 = 117,649; (6) 117,649 X 7 = 823,543; (7) 823,543 X 7 = 5,764,801. (This is not to be taken as earth years or times.) The 5,000, 000 represents the great hall year; the 700,000 the great Sabbath year, wherein all human beings gradually gain true understanding and become heirs to their original and eternal inheritance, which was lost when they were enmeshed in the lower elements. The 64,800 is the number of the fallen angels, and the last one year signifies the liberation of Lucifer and return to his original estate.

(76) There are two orders of number: odd and even. Because unity, or 1, always remains indivisible, the odd number cannot be divided equally. Thus, 9 is 4+1+4, the unity in the center being indivisible. Furthermore, if any odd number be divided into two parts, one part will always be odd and the other even. Thus, 9 may be 5+4, 3+6, 7+2, or 8+1. The Pythagoreans considered the odd number--of which the monad was the prototype--to be definite and masculine. They were not all agreed, however, as to the nature of unity, or 1. Some declared it to be positive, because if added to an even (negative) number, it produces an odd (positive) number. Others demonstrated that if unity be added to an odd number, the latter becomes even, thereby making the masculine to be feminine. Unity, or 1, therefore, was considered an androgynous number, partaking of both the masculine and the feminine attributes; consequently both odd and even. For this reason the Pythagoreans called it evenly-odd. It was customary for the Pythagoreans to offer sacrifices of an uneven number of objects to the superior gods, while to the goddesses and subterranean spirits an even number was offered.

(36) The digits 1 and 2 are not considered numbers by the Pythagoreans, because they typify the two supermundane spheres. The Pythagorean numbers, therefore, begin with 3, the triangle, and 4, the square. These added to the 1 and the 2, produce the 10, the great number of all things, the archetype of the universe. The three worlds were called receptacles. The first was the receptacle of principles, the second was the receptacle of intelligences, and the third, or lowest, was the receptacle of quantities.

(45) The Jews learned astronomy from the Egyptians, and it is not unlikely that the twelve jewels of the breastplate were symbolic of the twelve constellations of the zodiac. These twelve celestial hierarchies were looked upon as jewels adorning the breastplate of the Universal Man, the Macroprosophus, who is referred to in the Zohar as The Ancient of Days. The number twelve frequently occurs among ancient peoples, who in nearly every case had a pantheon consisting of twelve demigods and goddesses presided over by The Invincible One, who was Himself subject to the Incomprehensible All-Father. This use of the number twelve is especially noted in the Jewish and Christian writings. The twelve prophets, the twelve patriarchs, the twelve tribes, and the twelve Apostles--each group has a certain occult significance, for each refers to the Divine Duodecimo, or Twelvefold Deity, whose emanations are manifested in the tangible created Universe through twelve individualized channels. The secret doctrine also caught the priests that the jewels represented centers of life within their own constitutions, which when unfolded according to the esoteric instructions of the Temple, were capable of absorbing into themselves and radiating forth again the Divine light of the Deity. (The East Indian lotus blossoms have a similar meaning.) The Rabbis have taught that each twisted linen thread used in weaving the Tabernacle curtains and ornamentations consisted of twenty-four separate strands, reminding the discerning that the experience, gained during the twenty-four hours of the day (symbolized in Masonry by the twenty-four-inch rule) becomes the threads from which are woven the Garments of Glory.

(3) And out of the triad one stands apart; and in the heptad there are two triads, and one standing apart. The dodecad symbolizes war, the triad of amity, the triad of enmity, three which are life-giving, three which are death-dealing, and God, the faithful king, rules over all from the throne of his sanctity. One above three, three above seven, and seven above twelve, and all are linked together, and one with another.

(110) The triad--3--is the first number actually odd (monad not always being considered a number). It is the first equilibrium of unities; therefore, Pythagoras said that Apollo gave oracles from a tripod, and advised offer of libation three times. The keywords to the qualities of the triad are friendship, peace, justice, prudence, piety, temperance, and virtue. The following deities partake of the principles of the triad: Saturn (ruler of time), Latona, Cornucopiæ, Ophion (the great serpent), Thetis, Hecate, Polyhymnia (a Muse), Pluto, Triton, President of the Sea, Tritogenia, Achelous, and the Faces, Furies, and Graces. This number is called wisdom, because men organize the present, foresee the future, and benefit by the experiences of the fast. It is cause of wisdom and understanding. The triad is the number of knowledge--music, geometry, and astronomy, and the science of the celestials and terrestrials. Pythagoras taught that the cube of this number had the power of the lunar circle.

(76) 10. In this manner God joined the seven double letters together. Two stones build two houses, three stones build six houses, four stones build twenty-four houses, five stones build 120 houses, six stones build 720 houses, and seven stones build 5,040 houses. Make a beginning according to this arrangement and reckon further than the mouth can express or the ear can hear.

(60) By connecting the ten dots of the tetractys, nine triangles are formed. Six of these are involved in the forming of the cube. The same triangles, when lines are properly drawn between them, also reveal the six-pointed star with a dot in the center. Only seven dots are used in forming the cube and the star. Qabbalistically, the three unused corner dots represent the threefold, invisible causal nature of the universe, while the seven dots involved in the cube and the star are the Elohim--the Spirits of the seven creative periods. The Sabbath, or seventh day, is the central dot.

(4) From two letters, or forms He composed two dwellings; from three, six; from four, twenty-four; from five, one hundred and twenty; from six, seven hundred and twenty; from seven, five thousand and forty; and from thence their numbers increase in a manner beyond counting; and are incomprehensible. These seven are Planets of the Universe, the Sun, Venus, Mercury, Moon, Saturn, Jupiter, and Mars; the seven days are the days of creation; and these an the seven gateways of a man, two eyes, two ears, two nostrils and a mouth, through which he perceives by his senses.

(54) Timaeus: and conversely, when many small bodies are resolved into their triangles they will produce, when unified, one single large mass of another Kind. So let thus much be declared concerning their generation into one another. In the next place we have to explain the form in which each Kind has come to exist and the numbers from which it is compounded. First will come that form which is primary and has the smallest components, and the element thereof is that triangle which has its hypotenuse twice as long as its lesser side. And when a pair of such triangles are joined along the line of the hypotenuse, and this is done thrice, by drawing the hypotenuses

(112) 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.

(129) Among many ancient nations the heptad is a sacred number. The Elohim of the Jews were supposedly seven in number. They were the Spirits of the Dawn, more commonly known as the Archangels controlling the planets. The seven Archangels, with the three spirits controlling the sun in its threefold aspect, constitute the 10, the sacred Pythagorean decad. The mysterious Pythagorean tetractys, or four rows of dots, increasing from 1 to 4, was symbolic of the stages of creation. The great Pythagorean truth that all things in Nature are regenerated through the decad, or 10, is subtly preserved in Freemasonry through these grips being effected by the uniting of 10 fingers, five on the hand of each person.

(546) the laws which regulate them will not be discovered by an intelligence which is alloyed with sense, but will escape them, and they will bring children into the world when they ought not. Now that which is of divine birth has a period which is contained in a perfect number, 1 but the period of human birth is comprehended in a number in which first increments by involution and evolution [ or squared and cubed] obtaining three intervals and four terms of like and unlike, waxing and waning numbers, make all the terms commensurable and agreeable to one another. 2 The base of these (3) with a third added (4) when combined with five (20) and raised to the third power furnishes two harmonies; the first a square which is a hundred times as great (400 = 4 × 100), 3 and the other a figure having one side equal to the former, but oblong, 4 consisting of a hundred numbers squared upon rational diameters of a square (i.e. omitting fractions), the side of which is five (7 × 7 = 49 × 100 = 4900), each of them being less by one (than the perfect square which includes the fractions, sc. 50) or less by 5 two perfect squares of irrational diameters (of a square the side of which is five = 50 + 50 = 100); and a hundred cubes of three (27 × 100 = 2700 + 4900 + 400 = 8000). Now this number represents a geometrical figure which has control over the good and evil of births. For when your guardians are ignorant of the law of births, and unite bride and bridegroom out of season, the children will not be goodly or fortunate. And though only the best of them will be appointed by their predecessors, still they will be unworthy to hold their fathers’ places, and when they come into power as guardians, they will soon be found to fail in taking care of us, the Muses, first by under-valuing music; which neglect will soon extend to gymnastic; and hence the young men of your State will be less cultivated. In the succeeding generation rulers will be appointed who have lost the guardian power of testing the metal of your

(126) The Pythagoreans held the hexad--6--to represent, as Clement of Alexandria conceived, the creation of the world according to both the prophets and the ancient Mysteries. It was called by the Pythagoreans the perfection of all the parts. This number was particularly sacred to Orpheus, and also to the Fate, Lachesis, and the Muse, Thalia. It was called the form of forms, the articulation of the universe, and the maker of the soul.

(122) 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.

(10) All higher numbers can be reduced to one of the original ten numerals, and the 10 itself to 1. Therefore, all groups of numbers resulting from the translation of names of deities into their numerical equivalents have a basis in one of the first ten numbers. By this system, in which the digits are added together, 666 becomes 6+6+6 or 18, and this, in turn, becomes 1+8 or 9. According to Revelation, 144,000 are to be saved. This number becomes 1+4+4+0+0+0, which equals 9, thus proving that both the Beast of Babylon and the number of the saved refer to man himself, whose symbol is the number 9. This system can be used successfully with both Greek and Hebrew letter values.

(14) The Ten Commandments are the ten shining gems placed by the Holy One in the sapphire sea of Being, and in the depths of matter the reflections of these jewels are seen as the laws governing the sublunary spheres. They are the sacred ten by which the Supreme Deity has stamped His will upon the face of Nature. This same decad was celebrated by the Pythagoreans under the form of the tetractys--that triangle of spermatic points which reveals to the initiated the whole working of the cosmic scheme; for ten is the number of perfection, the key to creation, and the proper symbol of God, man, and the universe.

(38) The square base of the Pyramid is a constant reminder that the House of Wisdom is firmly founded upon Nature and her immutable laws. "The Gnostics," writes Albert Pike, "claimed that the whole edifice of their science rested on a square whose angles were: Σιγη, Silence; Βυθος, Profundity; Νους, Intelligence; and Αληθεια Truth." (See Morals and Dogma.) The sides of the Great Pyramid face the four cardinal angles, the latter signifying according to Eliphas Levi the extremities of heat and cold (south and north) and the extremities of light and darkness (east and west). The base of the Pyramid further represents the four material elements or substances from the combinations of which the quaternary body of man is formed. From each side of the square there rises a triangle, typifying the threefold divine being enthroned within every quaternary material nature. If each base line be considered a square from which ascends a threefold spiritual power, then the sum of the lines of the four faces (12) and the four hypothetical squares (16) constituting the base is 28, the sacred number of the lower world. If this be added to the three septenaries composing the sun (21), it equals 49, the square of 7 and the number of the universe.