• Corpus ID: 28882093

From Geometry to Algebra

  title={From Geometry to Algebra},
  author={John T. Baldwin},
Our aim is to see which practices of Greek geometry can be expressed in various logics. Thus we refine Detlefsen’s notion of descriptive complexity by providing a scheme of increasing more descriptive formalizations of geometry Following Hilbert we argue that defining a field structure on a line in ‘Euclidean geometry’ provides a foundation for both geometry and algebra. In particular we prove from first principles: √ 2 · √ 3 = √ 6, similar triangles have proportional sides, Euclid’s 3rd axiom… 

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