"Geometry has two great treasures: one is the Theorem of Pythagoras; the other, the division of a line into extreme and mean ratio. The first we may compare to a measure of gold; the second we may name a precious jewel."

Johannes Kepler, (1571-1630)

     Nicomach de Gerasa stated in his book "Introduction to Arithmetic":

"The elders, who under the spiritual leadership of Pythagoras gave science it's first systematic form, defined philosophy as the love of knowledge ... The immaterial things, such as virtues, configuration, equality... relationships, arrangements ... all of this are immutable by nature, but they can however accidentally take part in the vicissitudes of their owning bodies. All the laws of the universe and all the actions that take place in its infinity seem to be determined and set according to the number by Providence and the thinking of our Creator, for the pattern was settled as a preliminary sketch, throughout the domination of the number, preexistent in the mind of God."

     Pythagoras shared these philosophies; he thought that absolute happiness lay in the contemplation of the harmony of the rhythms of the Universe, ("tes teleiotetos arithmon"- the perfection of numbers, the number being both rhythm and proportion). In other words, Pythagoras was looking for a numerical pattern that would explain it all.

     A goal of Pythagoras's disciples was to develope a ratio theory. The ratio, a comparison between two sizes represented in mathematics a basic operation of judgment: the perception of the relation between ideas.

      Since a ratio is a relation between two numbers, and a proportion is a relation between two ratios, at least three terms are necessary for the creation of a proportion. But in applying The "Entia non sunt multiplicanda" principle, it's possible to obtain a continuous proportion with only two terms, a and b. Their sum, a+b gives us the third size necessary( (a+b)/a=a/b, the golden ratio).

      The golden mean, geometrically incorporated in the pentagram, the symbol of life, health and love was the sign of bonding between the disciples of Pythagoras. (One interesting story is told by Jamblichos. One of the followers of Pythagoras is infected by a disease and stops at an inn. The innkeeper spends a lot of money trying to heal him, but he is unable. The visitor, before dying, draws a pentagram outside of the inn. A long time passes but after a while another Pythagorean passes that way, sees the sign, and pays all of the innkeepers expenses.)

     The Dodecahedron, the only regular polyhedron with each side a pentagon, in all twelve sides, was another key symbol. It symbolized the Cosmos and everything within it. From the Dodecahedron the notion of quintessence was derived- a fundamental element, the image of the entire Universe with all the four elements in its composition.