<history of philosophy, biography> Greek mathematician (365-300 B.C.) whose Elementae (Elements) offered an axiomatic system for geometry based only on a few "common notions" and five basic postulates: (1) Any two points can be joined by a unique straight line. (2) A straight line can be extended indefinitely in either direction. (3) From a center point, a circle can be drawn with any radius. (4) All right angles are equal to each other. (5) If two straight lines crossing a third form angles less than two right angles on one of its sides, then indefinite extensions of these lines eventually meet. Although rejection of the fifth postulate eventually led to the development of alternative geometries by Lobachevsky and Riemann, Euclid's emphasis on axiomatic structure remained significant for mathematicians like Peano and Hilbert and served as a significant model for such philosophers as Hobbes and Spinoza. Recommended Reading: Thomas L. Heath, History of Greek Mathematics: From Thales to Euclid (Dover, 1981).
[A Dictionary of Philosophical Terms and Names]
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