Austin: 1892. Second Edition. SECOND EDITION OF THE FIRST ENGLISH LANGUAGE TRANSLATION OF LOBACHEVSKIAN GEOMETRY. Lobachevsky created, developed and presented what has come to be known as Lobachevskian geometry in 1826. The document offered here is the second edition of the first English language translation of Lobachevsky's paper that was published a year prior to this one 1891.
Nikolai Ivanovich Lobachevsky was a Russian mathematician and geometer known for his development of a non-Euclidean geometry in which Euclid's fifth postulate ("For any given line and point not on the line, there is only one line through the point not intersecting the given line") does not hold.
“The boldness of [Lobachevsky’s] challenge [to Euclid’s geometry] and its successful outcome have inspired mathematicians and scientists in general to challenge other "axioms" or accepted "truths", for example the "law" of causality which, for centuries, have seemed as necessary to straight thinking as Euclid's postulate appeared until Lobachevsky discarded it. The full impact of the Lobachevskian method of challenging axioms has probably yet to be felt. The author of Men of Mathematics wrote, in 1937, about Lobachevsky's influence on the following development of mathematics in his 1937 book stating: ‘It is no exaggeration to call Lobachevsky the Copernicus of Geometry, for geometry is only a part of the vaster domain which he renovated; it might even be just to designate him as a Copernicus of all thought’” (Wikipedia).
“The non-Euclidean geometry that Lobachevsky developed is referred to as hyperbolic geometry. Lobachevsky replaced Playfair's axiom with the statement that for any given point there exists more than one line that can be extended through that point and run parallel to another line of which that point is not part. He developed the angle of parallelism which depends on the distance the point is off the given line. In hyperbolic geometry the sum of angles in a hyperbolic triangle must be less than 180 degrees. Non-Euclidean geometry stimulated the development of differential geometry which has many applications. Hyperbolic geometry is frequently referred to as "Lobachevskian geometry" or "Bolyai–Lobachevskian geometry'". (Wikipedia). Item #1285
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