The Pentagramma Mirificum from Napier to Lambert: Notes on Lambert’s Memoir on Spherical Trigonometry

Annette A’Campo-Neuen ()
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Annette A’Campo-Neuen: Universität Basel, Departement Mathematik und Informatik

Chapter Chapter 8 in Spherical Geometry in the Eighteenth Century I, 2026, pp 195-204 from Springer

Abstract: Abstract Well-known relations between any three parts of a right-angled spherical triangle can be summarized by Napier’s mnemonic rules. In Napier’s book appears a drawing of a closing chain of five right-angled triangles enclosing a self-polar pentagon of constant width π ∕ 2 $$\pi /2$$ with remarkable properties. In his memoir on spherical trigonometry, Lambert clarified the meaning of this figure and gave a proof of Napier’s rules in terms of cyclic transformations of a given triangle. In this commentary, we focus on Lambert’s elegant proof of Napier’s rule and the properties of the so-called pentagonal star of triangles.

Keywords: Pentagramma mirificum; Spherical trigonometry; Napier’s rule; Johann Heinrich Lambert; 01A40; 01A45 (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-032-12466-1_8

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DOI: 10.1007/978-3-032-12466-1_8

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