Smogorzhevsky A.S. Lobachevskian geometry (Mir, 1982)

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. 1.
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.
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