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  Geometry (Greek, ‘land-measurement’), is the mathematical investigation of the relationship between points and lines. Euclid (3rd century  BCE) catalogued the existing state of geometrical knowledge in his day in his book Elements, and made the study of geometry the science which the ancient Greeks found most pleasing (as being the one in which pure reason could play the most part). His work laid the basis of Euclidean geometry. The methods of the Elements were embedded in algebraic geometry, based on the co-ordinate systems of René Descartes (1596 - 1650). Euclid\'s work in geometry was not superseded until the 19th century, when the work of , Johann Bolyai (1802 - 1860) and , Nicholas Lobachevsky (1792 - 1856) showed that there were consistent versions of geometry in which the axioms of Euclid did not hold; this led to the development of non-Euclidean geometry. SMcL  



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