Hyperbolic geometry在Johann Heinrich Lambert的作品中
Hyperbolic geometry in the work of Johann Heinrich Lambert
摘要：
约翰·海因里希·兰伯特的回忆录Theorie der Eschellinien（1766）是双曲几何的奠基文本之一，尽管其作者的目的是，像他的许多前辈一样，证明这样的几何不存在。事实上，兰伯特发展他的理论，希望找到一个矛盾的几何中，所有的欧几里德公理保持除了平行公理，后者是取代其否定。在这样做，他获得了一些基本成果的双曲几何。这是六十年前的第一个著作罗巴切夫斯基和波尔约出现在印刷。在本文中，我们提出了兰伯特的主要结果，我们对他们的评论。一个法语翻译的Theorie der Eschellinien，连同一个广泛的评论，刚刚出现在印刷品（A。Papadopoulos和G.《约翰·海因里希·兰伯特的平行木》。Collection Sciences dans l'Histoire，Librairie Scientific et Technique Albert Blanchard，Paris，2014）。
英文摘要：
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 pre-decessors', 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 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 (A. Papadopoulos and G. Th{é}ret, La th{é}orie des lignes parall{è}les de Johann Heinrich Lambert. Collection Sciences dans l'Histoire, Librairie Scientifique et Technique Albert Blanchard, Paris, 2014).
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