On Mascheroni's La geometria del compasso at the beginning of the 19th century

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Abstract

Lorenzo Mascheroni's 1797 work La geometria del compasso, which develops a geometry based solely on compass constructions, is considered by the author as stepping back behind the “demarcation line” of Euclidean geometry. In this work Mascheroni emphasizes the practical aspects of this geometry over a theoretical approach. A century later, in 1899, David Hilbert and his student Michael Feldblum proposed a totally different approach – algebraic and axiomatic – concerning geometric constructions based on various instruments. Taking into account that, at the end of the 18th century, straightedge geometry was also developed, one may ask what happened to the image of instrument-based geometry during the 19th century? By focusing on Mascheroni's book and its reception, this article aims to examine the various views and conceptions of mathematicians with respect to this geometry.

Original languageEnglish
Pages (from-to)55-79
Number of pages25
JournalHistoria Mathematica
Volume57
DOIs
StatePublished - Nov 2021

Keywords

  • Compass-based geometry
  • Hilbert
  • Mascheroni
  • Practical geometry
  • Straightedge geometry

All Science Journal Classification (ASJC) codes

  • History
  • General Mathematics

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