Pasch's theorem

proper noun

A result in plane geometry which cannot be derived from Euclid's postulates. It states that, given points a, b, c, and d on a line, if it is known that the points are ordered as (a, b, c) and (b, c, d), then it is also true that (a, b, d).

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Meanings

proper noun
  1. geometryA result in plane geometry which cannot be derived from Euclid's postulates. It states that, given points a, b, c, and d on a line, if it is known that the points are ordered as (a, b, c) and (b, c, d), then it is also true that (a, b, d).

Origin

Stated in 1882 by the German mathematician Moritz Pasch.

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Cite this entry
APA

Pasch's theorem. (n.d.). In WatkinsX Dictionary. Retrieved November 4, 2026, from https://dictionary.watkinsx.com/word/Pasch's%20theorem

MLA

“Pasch's theorem.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/Pasch's%20theorem. Accessed November 4, 2026.

Chicago

WatkinsX Dictionary, s.v. “Pasch's theorem,” accessed November 4, 2026, https://dictionary.watkinsx.com/word/Pasch's%20theorem.

Source: Pasch's theorem on Wiktionary, CC BY-SA 4.0.