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Archive for History of Exact Sciences

, Volume 31, Issue 3, pp 273–289 | Cite as

Gauss's geodesy and the axiom of parallels

  • Ernst Breitenberger
Article

Abstract

It is a myth that Gauss measured a certain large triangle specifically to determine its angle sum; he did so in order to link his triangulation of Hanover with contiguous ones. The sum of the angles differed from 180° by less than two thirds of a second; he is known to have mentioned in conversation that this constituted an approximate verification of the axiom of parallels (which he regarded as an empirical matter because his studies of hyperbolic trigonometry had led him to recognize the possibility of logical alternatives to Kant and Euclid). However, he never doubted Euclidean geometry in his geodetic work. On the contrary, he continually used 180° angle sums as a powerful check for observational errors, which helped him to achieve standards of precision equivalent to today's. Nor did he ever plan an empirical investigation of the geometrical structure of space.

Keywords

Geometrical Structure Empirical Investigation Euclidean Geometry Observational Error Empirical Matter 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag GmbH & Co. 1984

Authors and Affiliations

  • Ernst Breitenberger
    • 1
  1. 1.Department of Physics and AstronomyOhio UniversityAthens

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