Publisher's Synopsis
Geometrical Researches On The Theory Of Parallels is a mathematical treatise written by the Russian mathematician Nicholas Lobachevski. The book was originally published in 1840 and is considered to be a groundbreaking work in the field of non-Euclidean geometry. In the book, Lobachevski presents a new theory of geometry that challenges the traditional Euclidean approach. He argues that the parallel postulate, which states that parallel lines never meet, is not a self-evident truth and can be replaced by other postulates. Lobachevski then develops a new system of geometry based on this alternative postulate, which he calls ""imaginary geometry"" or ""non-Euclidean geometry.""The book is divided into six chapters, each of which explores different aspects of Lobachevski's theory. Chapter one introduces the concept of parallel lines and the parallel postulate, while chapter two presents Lobachevski's alternative postulate. Chapters three and four explore the properties of imaginary geometry, including the existence of infinitely many parallel lines through a given point and the possibility of triangles with angles that add up to less than 180 degrees.Chapter five discusses the relationship between imaginary geometry and Euclidean geometry, while chapter six presents Lobachevski's ideas on the nature of space and the possibility of multiple geometries coexisting in the same physical universe.Overall, Geometrical Researches On The Theory Of Parallels is a seminal work in the history of mathematics that challenged long-held beliefs about the nature of space and geometry. It remains an important text for anyone interested in the development of non-Euclidean geometry and its impact on modern mathematics and physics.This scarce antiquarian book is a facsimile reprint of the old original and may contain some imperfections such as library marks and notations. Because we believe this work is culturally important, we have made it available as part of our commitment for protecting, preserving, and promoting the world's literature in affordable, high quality, modern editions, that are true to their original work.
