The circle was called by Pythagoras "the most beautiful of all plane figures" and in its form with the center unmarked, corresponding to the monad or the one in arithmetic, was placed in a category by itself. The circle with a dot at its center corresponds to the duad, the triangle to the triad, the square to the tetrad in its actual as opposed to its potential form, which is that of the tetradic dotted triangle, as previously explained, the potential equivalent of the decad. The pentagram or five-pointed star corresponds to the pentad, and the hexagram to the senary. The circle with its diameter indicated the actual dekad or 10 (for we no longer write the one within the circle to represent ten) as opposed to the potential equivalent of the dekad, the tetraktys. In his solid geometry Pythagoras taught that "the sphere was the most beautiful of all solid figures," and in its form corresponding to the monad, it was classed by itself. Pythagoras explained that both the earth and the kosmos were spherical in shape, and added that the universe was made up of five basic solid figures, which were built up from the triangle and the square: namely, the cube; the tetrahedron; the octahedron, a figure with its eight sides formed by equal equilateral triangles; the dodecahedron, a figure with twelve faces formed by regular pentagons; and the icosahedron, a figure composed of twenty equal and similar triangular pyramids whose vertices meet at the center of a sphere, which is supposed to circumscribe it.

(3) Music

Turning to Pythagoras' teachings in regard to music, which he regarded as a very important help in controlling the passions, it is said that he was the first to teach the Greeks the tonic relations of the musical scale, and invented for them the monochord, a one-stringed instrument, used in measuring the musical intervals. Upon these relations he built his celebrated doctrine of the Harmony or Music of the Spheres, that is, that the heavenly bodies, composing our solar system, in the course of their rotations emit the notes of the scale. H. P. Blavatsky and the ancients explain this by saying that Pythagoras called

a "tone" the distance of the Moon from the Earth; from the Moon to Mercury ½ a tone, thence to Venus the same; from Venus to the Sun 1½ tones; from the Sun to Mars a tone; from thence to Jupiter ½ a tone; from Jupiter to Saturn a tone; and thence to the Zodiac a tone; thus making seven tones, the diapason harmony. All the melody of nature is in those seven tones and therefore is called "the Voice of Nature."

Pythagoras declared that the harmony of the spheres is not heard by the ordinary human ear either because it has always been accustomed to it from the beginning of life, or because the sound is too powerful for the capabilities of the physical ear. In substantiation of this theory it is interesting to note that modern science expresses the intervals of music by proportions similar to those which mark the tonal distances of the planets.

(4) Man

Self-contemplation was strongly insisted upon and played a most vital part in the Pythagorean training. To his esoteric section Pythagoras taught the immortality of the soul, its pre-existence, and its rebirth; karma; and the septenary constitution of man, partially veiled, it is true, under the form of a triple division of the soul into animal, human, and divine parts.

There is a doctrine whispered in secret that man is a prisoner, who has no right to open the door and run away. The gods are our guardians.

The soul is a harmony and the body its prison.

We choose our own destiny and are our own good or bad fortune.

Rash words and acts are their own punishment.

We are our own children.

Intentional perversions of the teachings of Pythagoras, mere travesties of his ideas, are plainly evident in what has come down to us in regard to his belief in metempsychosis. Thus we are told that his enemies circulated the story that Pythagoras had declared that one of his relatives had passed into a bean, a vicious joke based on the fact that beans were excluded from the Pythagorean diet. Another similar malicious fiction about Pythagoras is thus referred to by Xenophanes, a contemporary philosopher.

They say that once, as passing by he saw