EEK SMALL LETTER PHI~}{~GREEK SMALL LETTER IOTA~}{~GREEK SMALL LETTER LAMDA~}{~GREEK SMALL LETTER OMICRON WITH OXIA~}{~GREEK SMALL LETTER SIGMA~}{~GREEK SMALL LETTER OMICRON~}{~GREEK SMALL LETTER PHI~}{~GREEK SMALL LETTER OMICRON~}{~GREEK SMALL LETTER FINAL SIGMA~}; but there is great uncertainty as to the most material of his
philosophical and religious opinions. It is believed that he wrote nothing
himself, and that the earliest Pythagorean treatises were the work of
Philolaus, a contemporary of Socrates. It appears, however, that he
undertook to solve by reference to one single primary principle the
problem of the origin and constitution of the universe. His predilection
for mathematics led him to trace the origin of all things to _number_; for
"in _numbers_ he thought that they perceived many analogies of things that
exist and are produced, more than in fire, earth, or water: as, for
instance, they thought that a certain condition of numbers was justice;
another, soul and intellect, ... And moreover, seeing the conditions and
ratios of what pertains to harmony to consist in numbers, since other
things seemed in their entire nature to be formed in the likeness of
numbers, and in all nature numbers are the first, they supposed the
elements of numbers to be the elements of all things." (Arist. Met. i. 5.)

Music and harmony too, played almost as important a part in the
Pythagorean system as mathematics, or numbers. His idea appears to be,
that order or harmony of relation is the regulating principle of the whole
universe. He drew out a list of ten pairs of antagonistic elements, and in
the octave and its different harmonic relations, he believed that he found
the ground of the connexion between them. In his system of the universe
_fire_ was the important element, occupying both the centre and the
remotest point of it; and being the vivifying principle of the whole.
Round the central fire the heavenly bodies he believed to move in a
regular circle; furthest off were the fixed stars; and then, in order, the
planets, the moon, the sun, the earth, and what he called {~GREEK SMALL LETTER ALPHA WITH PSILI~}{~GREEK SMALL LETTER NU~}{~GREEK SMALL LETTER TAU~}{~GREEK SMALL LETTER IOTA WITH OXIA~}{~GREEK SMALL LETTER CHI~}{~GREEK SMALL LETTER THETA~}{~GREEK SMALL LETTER OMEGA~}{~GREEK SMALL LETTER NU~}, a sort
of other half of the earth, which was a distinct body from it, but moving
parallel to it.

The most distant region he called Ol