"Through number alone, the quantitative relations of things, extension, magnitude, figure (triangular, quadrangular, cubic), combination, distance, etc., obtain their peculiar character; the forms and proportions of things can all be reduced to number. Therefore, it was concluded, since without form and proportion nothing can exist, number must be the principle of things themselves, as well as the order in which they manifest themselves in the world." (Schwegler's "History of Philosophy.")
While mathematics was the central idea of his system, medicine, physics, and philosophy were also taught in his school. He did the world great service in the discovery of the so-called Pythagorean theorem in geometry, that the square of the hypotenuse of a right-angled triangle is equal to the sum of the squares of the other two sides.
FOOTNOTES:
[18] The Perioeci (dwellers around) were the older population of the land, who inhabited the mountains and hillsides about Sparta. They were farmers, and they also worked the mines and quarries, manufactured articles for the Spartan market, and carried on the commerce. Though freemen, they were allowed no part in the government, could not bear arms, and had to pay tribute to Sparta.
[19] The Helots were probably peasants who occupied the land about Helos, and, defeated in war, became Spartan subjects. They could not be sold or given away, but belonged to the inventory of the farm.