Air rarefied is fire, condensed is water.
These philosophers, the followers of Thales, succeeding one another, made up that sect which takes to itself the denomination of the Ionic.
Pythagoras the Samian, the son of Mnesarchus, from another origin deduces the principles of all things; it was he who first called philosophy by its name.

He thought the first principles to be numbers, and those symmetries in them which he styles harmonies; and the composition of both he terms elements, called geometrical.

Again, he places unity and the indefinite binary number amongst the principles.
One of these principles ends in an efficient and forming cause, which is Mind, and that is God; the other to the passive and material part, and that is the visible world.

Moreover, the nature of number (he saith) consists in the ten; for all people, whether Grecians or barbarians, reckon from one to ten, and thence return to one again.

Farther he avers the virtue of ten consists in the quaternion; the reason whereof is this,--if any person start from one, and add numbers so as to take in the quaternary, he shall complete the number ten; if he passes the four, he shall go beyond the ten; for one, two, three, and four being added up together make ten.