Hippocrates was born about 470 BC in Chios (now Khios), Greece, and he died about 410 BC. Hippocrates taught in Athens and worked on squaring the circle and duplicating the cube. In his attempts to square the circle, Hippocrates was able to find the areas of certain crescent-shaped figures using his theorem that the ratio of the areas of two circles is the same as the ratio of the squares of their radii.
Hippocrates also showed that a cube can be doubled if two mean proportionals can be determined between a number and its double. He was the first to write an Elements of Geometry and although his work is now lost it must have contained much of what Euclid later included in Books 1 and 2 of the Elements . Hippocrates' book also included geometrical solutions to quadratic equations and included early methods of integration.
Little is known of his life but he is reported to be an excellent geometer who, in other respects, was stupid and lacking in sense. He was defrauded of a large sum of money because of his naivity.
