Geometrical Researches On The Theory Of Parallels

Geometrical Researches On The Theory Of Parallels is a book written by Nicholas Lobachevski, a Russian mathematician, in 1840. The book is a detailed exploration of the theory of parallels, which is a fundamental concept in Euclidean geometry. Lobachevski challenges the traditional Euclidean geometry and presents a new non-Euclidean geometry, which he calls hyperbolic geometry. The book is divided into three parts. In the first part, Lobachevski presents the basic principles of his hyperbolic geometry, including the concept of parallel lines and the postulate of the sum of angles in a triangle. In the second part, he explores the properties of hyperbolic space and compares it to Euclidean space. In the third part, Lobachevski applies his hyperbolic geometry to various problems in mathematics and physics.The book was a groundbreaking work in the field of mathematics and had a profound impact on the development of modern geometry. It challenged the traditional Euclidean geometry and paved the way for the development of non-Euclidean geometries. The book is still considered a classic in the field of mathematics and is widely studied by mathematicians and students alike.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.