THE DOUBLE TRIANGLE AND THE PENTAGRAM
This is the familiar six-pointed figure formed by superimposing two equilateral triangles, so that their apexes are symmetrically spaced around a circle. It is the regular star hexagon in geometry. Sometimes the figure is elaborated by making the lines double, so that the triangle can be interlaced; or again they may be differently colored, or the upright one made light, the other dark. It is often called Solomon's Seal and is a symbol in the Jewish Kabbala; but it is found in ancient India, whence it was probably adopted by the Hebrews. But it is one of the symbols of the universal Wisdom-Religion. These two triangles represent the duality of manifestation, the duality of Nature, variously spoken of as Spirit and Matter, Fire and Water, etc. Here we find them interlocked, thus producing a compound or completed nature. The number 6 is thus obtained, and by adding the central point, or alternatively by enclosing the figure in a circle, we get the synthesizing seventh. The six therefore represents the manifested Logos, which is six-fold (or often spoken of as sevenfold, including the synthesis).
This Logos as first emanation is called the Virgins of Life or the Great Illusion; the sixth sign of the zodiac is that of the Virgin. In The Secret Doctrine it is mentioned as signifying the 6 directions of space, the blending of pure Spirit and Matter, Arupa and Rupa, and is said to be a sign of Vishnu, though elsewhere Vishnu is made to correspond to the inverted triangle only. We must not try to make the symbolism too rigid and precise, for such names as Vishnu are complex in their meaning, and moreover different schools of philosophy have their own ways. The alchemists would have called these two triangles the fiery and the moist principle. They represent the dual nature of man, and the six points stand for the six powers or forces of nature, six planes, six principles, etc., synthesized by the seventh. The shapes of snow crystals are often mentioned as a familiar instance of this sixfold principle, and it represents the six primary axes in the cubical system of crystallization. If a glass cube is held up in a certain position, its twelve edges will show the double triangle within the hexagon. Other names for these six primary forces are the Sephiroth of Construction, Dhyan-Chohans, Prajapatis, Builders of the lower physical universe — according to the plane which is being illustrated.
THE PENTAGRAM
The five-pointed star, or the star polygon of the number five, is made by marking five equidistant points on a circle and joining each to the next but one; the lines and angles are equal, the angles being 36°, 72°, and 108°. The sections of the lines exhibit the Golden Ratio, by which a line is divided into extreme and mean ratio, that ratio being .618 or 1.618, which plays so important and interesting a part in geometry. In symbolism this figure is often taken as synonymous with the number five, the pentad. The Pythagoreans called it the Pentalpha, because it was like five alphas (A). It combines the two and the three, the first even and the first odd numbers after unity, representing therefore among many other things, on the universal plane, the union of cosmic substance with cosmic intellect. If the three is combined with the four (another symbol of matter) we get the seven. As a union of five elements it stands for the Heavenly or Macrocosmic Man, and its five points correspond to the head and limbs of a man's body; the same idea lies behind the five wounds of Christ. When the star has its point down, it signifies the polar opposite of the preceding, that is, the nether or material pole of cosmic life; and so can be used as a black magical symbol — the horns of evil are said to be up. The combination of these two produces the decad, in a similar way to that by which the two triangles are combined in Solomon's Seal; and thus we get another symbol of man's dual nature, and of the dual aspect of cosmic forces. In connexion with this, astrologers will remember that each of five planets has two houses, a day house and a night house; while Sun and Moon have each one house, so that we have here the five, the ten, and the twelve, harmonized together. Five is specially important in our times because we are in the Fifth Root-Race, and five elements have so far been manifested (the fifth, ether, only partially as yet). We have five digits on each limb; five is the most frequent number for the petals of a flower, we use the denary scale (twice five), and the number five plays a leading part in the geometry of the dodecahedron and icosahedron. In The Secret Doctrine we find the pentagon used for the number five in the formula 31415, the other figures likewise being denoted by geometrical signs.