Algebraic Geometry

Raymond O. Wells ()
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Raymond O. Wells: University of Colorado Boulder

Chapter Chapter 1 in Differential and Complex Geometry: Origins, Abstractions and Embeddings, 2017, pp 5-16 from Springer

Abstract: Abstract In the mid-seventeenth century, Descartes published a small book on geometry which changed dramatically the view of geometry prescribed by Euclid’s Elements that had prevailed for more than a millennium. Descartes introduced the use of coordinates in the plane and described curves in the plane as the solutions of algebraic equations. He and Fermat showed that the standard conic sections could be described in terms of second-degree algebraic equations. In the eighteenth century Newton and later Euler gave classifications of curves defined by equations of degree three, which became a model for many other types of classifications of geometric objects in the centuries to come.

Keywords: Descartes; Pappus Problem; Apollonius; Cube Duplication; Theproblem (search for similar items in EconPapers)
Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-58184-2_1

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DOI: 10.1007/978-3-319-58184-2_1

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