Die Nichteuklidische Geometrie: Historisch Kritische Darstellung Ihrer Entwicklung (German Edition)

Explore the history and ideas behind non-Euclidean geometry and how it reshaped mathematics. This historical-critical work traces the development of the subject from the ancient origins of Euclid’s parallel postulate to the 19th‑century breakthroughs by Lobachevsky, Bolyai, and Gauss, and it surveys the later expansions by Riemann and Helmholtz. It presents a clear arc of ideas through the work of Greek, Arabic, and Renaissance geometers, and it highlights the shift away from the classical postulate toward new geometric foundations. The book offers a structured, accessible account that connects theory with the people who advanced it. It emphasizes the evolution of the idea of parallelism, the role of the postulate, and the synthesis of synthetic and analytic approaches. Readers will see how absolute trigonometries and projective methods relate to the non‑Euclidean framework, and how modern concepts grew from these historical roots. - Learn how the classical and non‑Euclidean geometries relate to each other - Meet the key figures and the debates that shaped the field - Understand the bridge between projective methods and metric geometry - See how later work by Gauss, Bolyai, Lobachevsky, and others influenced the theory Ideal for readers interested in the history of mathematics, the foundations of geometry, and the origins of non‑Euclidean ideas. Read more