The ogdoad or 8 symbolizes the eternal and spiral motion of the cycles, and is symbolized in its turn by the Caduceus (or herald's staff of Hermes). The nine is the triple ternary, reproducing itself incessantly under all shapes and figures in every multiplication. The ten or dekad brings all these digits back to unity and ends the Pythagorean table.
"It is," Pythagoras says, "the starting point of number."
Passing from the arithmetic to the geometry of Pythagoras, Plato's statement that "God geometrizes" is undoubtedly Pythagorean in origin, for it is said that Pythagoras perfected geometry among the Greeks, and the two well-known theorems that the triangle inscribed in a semi-circle is right-angled, and that the square of the hypothenuse of a right-angled triangle is equal to the sum of the squares of the sides, are still associated with his name. Pythagoras taught:
From the monad and the duad proceed numbers; from numbers signs; from signs lines, of which plane figures consist; from plane figures solid bodies. The Kosmos is endued with life and intellect and is of a spherical figure.
From one point of view, One corresponds to the dot or point, Two to the line, Three to the plane, and Four to the concrete solid. The dekad was represented geometrically in the form of a tetradic equilateral triangle of ten dots, with one dot at the apex, and four along the base line, thus
. This shows graphically how the tetraktys as 1 + 2 + 3 + 4 = 10, contains potentially the dekad. This ten-dot triangle filled out by lines becomes an equilateral triangle, with the dot at the apex and at the center remaining as generating-points for adjacent figures, and especially as the centers of circles, inscribed in and circumscribed about the original triangle.
The principal plane geometrical figures known to have been explained by Pythagoras are the circle in its three forms: one with the center unmarked, the second with a dot at the center, and the third with the diameter drawn:
