"Euclid with all its defects removed" - Euclid with all its defects removed

…His main occupation was a Jesuit priest, but from 1699 he taught mathematics at the University of Pavia for the rest of his life. He was interested in Euclid's parallel postulate, and wrote Logica demonstrativa (1697) in which he first investigated the essence of the definition. He then developed the first 26 theorems of Euclides that could be proved without the parallel postulate, and a system that arose from the assumptions that denied the parallel postulate in his major work, Euclides ob omni naevo vindicatus (1733), in which he attempted to prove the parallel postulate. Of course, he did not achieve this goal, but non-Euclidean geometry is unconsciously developed in the work. …

*The following is a portion of the glossary that refers to "Euclid from which all defects were removed."

Source | Heibonsha World Encyclopedia 2nd Edition | Information

…本職はイエズス会の聖職者であったが，1699年からは終生パビア大学で数学の講座をもった。ユークリッドの平行線公準に関心をもち，《証明的論理学Logica demonstrativa》(1697)を著して，まず定義の本質を究明し，続いて主著《あらゆる欠点が除かれたユークリッドEuclides ob omni naevo vindicatus》(1733)において，平行線公準なしに証明できるユークリッドの最初の26個の定理および平行線公準を否定した仮定から生ずる体系を展開し，それによって平行線公準を証明しようとした。もちろんこの目的は達成されていないが，そこには非ユークリッド幾何学が無意識的に展開されている。…

※「《あらゆる欠点が除かれたユークリッド》」について言及している用語解説の一部を掲載しています。

出典｜株式会社平凡社世界大百科事典 第２版について | 情報