Lobachevskian Geometry (Little Mathematics Library) by A. S. Smogorzhevsky

The aim of this book is to acquaint the reader with the fundamentals of Lobachevsky's non-Euclidean geometry.

The famous Russian mathematician N. I. Lobachevsky was an outstanding thinker, to whom is credited one of the greatest mathematical discoveries, the construction of an original geometric
system distinct from Euclid's geometry. The reader will find
a brief biography of N. I. Lobachevsky in Sec. I.

Euclidean and Lobachevskian geometries have much in common,
differing only in their definitions, theorems and formulas as
regards the parallel-postulate. To clarify the reasons for these
differences we must consider how the basic geometric concepts
originated and developed, which is done in Sec. 2.

Apart from a knowledge of school plane geometry and trigonometry reading our pamphlet calls for a knowledge of the transformation known as inversion, the most important features of which are reviewed in Sec. 3. We hope that the reader will be able to grasp its principles with profit to himself and without great difficulty, since it, and Sec. 10, play very important, though ancillary, role in our exposition.