centuries. Hippocrates is believed to have originated the use of letters to refer to the geometric points and figures in a proposition, e.g., "triangle ABC" for a triangle with vertices at points A, B, and C. Two other contributions by Hippocrates in the field of mathematics are noteworthy. He found a way to tackle the problem of 'duplication of the cube', that is, the problem of how to construct a cube root. Like the quadrature of the circle, this was another of the so-called three great mathematical problems of antiquity. Hippocrates also invented the technique of 'reduction', that is, to transform specific mathematical problems into a more general problem that is easier to solve. The solution to the more general problem then automatically gives a solution to the original problem. Astronomy In the field of astronomy, Hippocrates tried to explain the phenomena of comets and the Milky Way. His ideas have not been handed down very clearly, but he probably thought both were optical illusions, the result of refraction of solar light by moisture that was exhaled by, respectively, a putative planet near the Sun, and the stars. The fact that Hippocrates thought that light rays originated in our eyes instead of in the object that is seen, adds to the unfamiliar character of his ideas. Notes References Ivor Bulmer-Thomas, 'Hippocrates of Chios', in: Dictionary of Scientific Biography, Charles Coulston Gillispie, ed. (18 Volumes, New York 1970–1990) pp. 410–418. [Axel Anthon] Björnbo, 'Hippokrates', in: Paulys Realencyclopädie der Classischen Altertumswissenschaft, G. Wissowa, ed. (51 Volumes; 1894–1980) Vol. 8 (1913) col. 1780–1801. External links The Quadrature of the Circle and Hippocrates' Lunes at Convergence Mesolabe Compass and Square Roots - Numberphile video explaining Hippocrates' mesolabe compass 5th-century BC Greek people Ancient Greek geometers Ancient Chians 470s BC births 410s BC deaths 5th-century BC mathematicians