Title: HYPERBOLIC GEOMETRY IN THE WORK OF J. H. LAMBERT
Abstract: The memoir Theorie der Parallellinien (1766) by Jo- hann Heinrich Lambert is one of the founding texts of hyperbolic geometry, even though its author's aim was, like many of his pre- decessors', to prove that such a geometry does not exist. In fact, Lambert developed his theory with the hope of finding a contra- diction in a geometry where all the Euclidean axioms are kept except the parallel axiom and that 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. In the present paper, we present Lambert's main results and we comment on them. A French translation of the Theorie der Parallellinien, together with an extensive commentary, has just appeared in print (19). AMS classification: 01A50 ; 53-02 ; 53-03 ; 53A05 ; 53A35.
Publication Year: 2015
Publication Date: 2015-01-01
Language: en
Type: article
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