由错误引发的真理——萨凯里对非欧几何的贡献

The truth caused by errors: On Seccheri's dedication to non-Euclidean geometry

意大利数学家萨凯里为证明欧几里得平行公设,提出了萨凯里四边形和直角、钝角、锐角假设,并试图证明后两种假设自相矛盾,从而得出只有直角假设正确。他在逻辑和数学上的错误引起数学家对欧氏几何以外的几何结论以及萨凯里四边形的关注,从而推动了非欧几何的诞生。从逻辑证明的视角探究萨凯里的错误及缘由,讨论他对非欧几何创立的贡献。

Saccheri proposed Saccheri quadrilateral and hypothesis of right,obtuse and acute angle in order to prove Euclid′s parallel postulate as an axiom.He tried to demonstrate there include contradictions in the last two hypotheses,so that hypothesis of right angle being equivalent to parallel postulate is the only right result.Though he failed to vindicate Euclid,some deep propositions he got are important to the birth of non-Euclidean geometry.Based on the primary sources of Saccheri,the fallacies of his proof and reasons why he had such errors were discussed.