La théorie des lignes parallèles de Johann Heinrich Lambert

Athanase Papadopoulos (1) , Guillaume Théret (1, 2)

1 IRMA - Institut de Recherche Mathématique Avancée
2 IMB - Institut de Mathématiques de Bourgogne [Dijon]

The memoir "Theory of parallel lines" (1766) by Johannes Heinrich Lambert is one of the founding texts of hyperbolic geometry, even though his author conceived it as an attempt to show that this geometry does not exist. In fact, Lambert developed that theory with the hope of finding a contradiction. 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. This book contains the first complete translation of Lambert's memoir as well as mathematical and historical commentaries.

Mots clés: géométrie hyperbolique; géométrie sphérique; Lambert; parallèles; hyperbolic geometry; spherical geometry; parallel lines.; parallel lines

Domaines: Histoire et perspectives sur les mathématiques [math.HO]; Topologie géométrique [math.GT]

Athanase Papadopoulos, Guillaume Théret. La théorie des lignes parallèles de Johann Heinrich Lambert. Albert Blanchard, 214 p., 2014, Sciences dans l'histoire, Roshdi Rashed, 978-2-85367-266-5. ⟨hal-01067119⟩