Ganita Bharati
Published in Association with Bulletin of The Indian Society for History of Mathematics
Current Volume: 45 (2023 )
ISSN: 0970-0307
Periodicity: Half-Yearly
Month(s) of Publication: June & December
Subject: Mathematics
DOI: https://doi.org/10.32381/GB
Online Access is Free for Life Member
Hyperbolic Geometry in the Work of J. H. Lambert
By : Guillaume Théret, Athanase Papadopoulos
Page No: 129-155
Abstract
The memoir Theorie der Parallellinien (1766)* by Johann Heinrich Lambert is one of the founding texts of hyperbolic geometry, even though its author’s aim was, like many of his predecessors’, to prove that such a geometry does not exist. In fact, Lambert developed his theory with the hope of finding a contradiction in a geometry where all the Euclidean axioms are kept except the parallel axiom and where the latter is replaced by its negation. In doing so, he obtained several fundamental results of hyperbolic geometry. This was sixty years before the first writings of Lobachevsky and Bolyai appeared in print.