When the molecules of salt, clustering together, begin to deposit themselves as a solid, the first shape they assume is that of triangles, of small pyramids and cones. It is the figure of fire, whence the word "pyramids"; while the second geometrical figure in manifested nature is a square or a cube, 4 and 6; for, "the particles of earth being cubical, those of fire are pyramidal" truly—(Enfield). The pyramidal shape is that assumed by the pines—the most primitive tree after the fern period. Thus the two opposites in cosmic nature—fire and water, heat and cold—begin their metrographical manifestations, one by a trimetric, the other by a hexagonal system. For the stellate crystals of snow, viewed under a microscope, are all and each of them a double or treble six-pointed star, with a central nucleus, like a miniature star within the larger one. (The Secret Doctrine, II, 594.)
The number Five penetrates the whole system of the Five solids in a remarkable way. Thus there are 24 pentagons visible, and by joining other corners of the Dodecahedron, Five Cubes are seen, which of course produce Five Octahedrons, and twice that number of principal interlaced Tetrahedrons. Five has been said to be the Number of Life.
Confining ourselves to one rectangular system, we find Four axes of symmetry for the Tetrahedrons and Three for Cube and Octahedron. Thus there are really 73 principal lines in the complete system defined by the 39 points. A study of the three principal orthographic projections shows that the circle should be divided into 3, 4, 5, 6, parts, and the products of these, or 360 degrees. Certain angles are found in abundance, such as 36, 60, 72, 90, 108, 144; and their combinations and products by 10 and 12, and their multiples, give figures bearing a strong resemblance to the various cyclic periods of eastern chronology. Periodic orbits are vibrations on a large scale.
Twice the perimeter of an Icosahedron-face divided by the perimeter of a Dodecahedron-face is 3.1416, the value of π used in all ordinary scientific and constructional work.
The actual error is so small that if both were accurately made of copper at the same temperature, the Icosahedron-face would only have to be brought rather more than one degree Fahrenheit below the temperature of the other for the π value to be absolutely correct. Accuracy of this sort is unattainable outside of specially equipped laboratories. So the Pythagorean solids may be said to "square the circle."
THE "BLACK AGE": by Ariomardes
LET us imagine a romance, such as most people must have heard, wherein some royal child is stolen away and reared amidst peasants in ignorance of his birth; and where some wise man comes and reveals to the youth the secret of his parentage. The young man forthwith steps out from his lowly life, and clothed in a new self-respect, begins to acquit himself worthily of his origin and destiny.
Thus has Theosophy declared to outcast humanity, "Thou art the king's son"; and in proof it has referred him to his ancestry. This is why H. P. Blavatsky, pointing out in the skein of history certain clues which scholars have hitherto overlooked, started that greater enthusiasm for archaeology which since her day has already borne such wonderful fruit.