This book traces the rise of a new geometric view—from Bolyai and Lobatschewsky to Beltrami and Beltrami’s successors—explaining how parallelism, space, and shapes were reimagined beyond Euclid. The work surveys the early foundations, the spread of the ideas across Europe, and the later development into advanced topics. It shows how these ideas challenged long-held assumptions and opened new paths in differential and projective geometry, without losing sight of the core questions that sparked the debate.

Clear narrative of key moments and pivotal figures in the birth of non-Euclidean geometry
Accessible explanations of why the parallel postulate mattered and how it was questioned
Connections between historical developments and later branches like differential and projective geometry
Context for how these ideas influenced broader mathematics and philosophy

Ideal for readers curious about the history, foundations, and evolution of geometry and its modern forms.

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