Softcover ISBN:  9781470456405 
Product Code:  SPEC/69 
List Price:  $35.00 
MAA Member Price:  $26.25 
AMS Member Price:  $26.25 
eBook ISBN:  9780883859797 
Product Code:  SPEC/69.E 
List Price:  $30.00 
MAA Member Price:  $22.50 
AMS Member Price:  $22.50 
Softcover ISBN:  9781470456405 
eBook: ISBN:  9780883859797 
Product Code:  SPEC/69.B 
List Price:  $65.00 $50.00 
MAA Member Price:  $48.75 $37.50 
AMS Member Price:  $48.75 $37.50 
Softcover ISBN:  9781470456405 
Product Code:  SPEC/69 
List Price:  $35.00 
MAA Member Price:  $26.25 
AMS Member Price:  $26.25 
eBook ISBN:  9780883859797 
Product Code:  SPEC/69.E 
List Price:  $30.00 
MAA Member Price:  $22.50 
AMS Member Price:  $22.50 
Softcover ISBN:  9781470456405 
eBook ISBN:  9780883859797 
Product Code:  SPEC/69.B 
List Price:  $65.00 $50.00 
MAA Member Price:  $48.75 $37.50 
AMS Member Price:  $48.75 $37.50 

Book DetailsSpectrumVolume: 69; 2011; 227 ppRecipient of the Mathematical Association of America's Beckenbach Book Prize in 2015!
Lobachevski Illuminated provides an historical introduction to nonEuclidean geometry. Within its pages, readers will be guided stepbystep through a new translation of Lobachevski's groundbreaking book, The Theory of Parallels.
Extensive commentary situates Lobachevski's work in its mathematical, historical, and philosophical context, thus granting readers a vision of the mysterious and beautiful world of nonEuclidean geometry as seen through the eyes of one of its discoverers. Although Lobachevski's 170yearold text is challenging to read on its own, Seth Braver's carefully arranged “illuminations” render this classic accessible to any modern reader (student, professional, or layman) undaunted by high school mathematics.

Table of Contents

Chapters

Theory of Parallels—Lobachevski’s Introduction

Theory of Parallels—Preliminary Theorems (1–15)

Theory of Parallels 16: The Definition of Parallelism

Theory of Parallels 17: Parallelism is WellDefined

Theory of Parallels 18: Parallelism is Symmetric

Theory of Parallels 19: The SaccheriLegendre Theorem

Theory of Parallels 20: The Three Musketeers Theorem

Theory of Parallels 21: A Little Lemma

Theory of Parallels 22: Common Perpendiculars

Theory of Parallels 23: The $\Pi $function

Theory of Parallels 24: Convergence of Parallels

Theory of Parallels 25: Parallelism is Transitive

Theory of Parallels 26: Spherical Triangles

Theory of Parallels 27: Solid Angles

Theory of Parallels 28: The Prism Theorem

Theory of Parallels 29: Circumcircles or Lack Thereof (Part I)

Theory of Parallels 30: Circumcircles or Lack Thereof (Part II)

Theory of Parallels 31: The Horocycle Defined

Theory of Parallels 32: The Horocycle as a LimitCircle

Theory of Parallels 33: Concentric Horocycles

Theory of Parallels 34: The Horosphere

Theory of Parallels 35: Spherical Trigonometry

Theory of Parallels 36: The Fundamental Formula

Theory of Parallels 37: Plane Trigonometry


Additional Material

Reviews

Seth Braver doesn't just interpret the existing contents of Lobachevski's Theory of Parallels, but he continually adds to it by way of making it more mathematically coherent. In this respect, his achievement is first rate and it is equalled by his eloquently inspiring literary style. ... As such, this is a masterly addition to the literature on the history of geometry.
Peter Ruane, MAA Reviews


RequestsReview Copy – for publishers of book reviewsAccessibility – to request an alternate format of an AMS title
 Book Details
 Table of Contents
 Additional Material
 Reviews
 Requests
Lobachevski Illuminated provides an historical introduction to nonEuclidean geometry. Within its pages, readers will be guided stepbystep through a new translation of Lobachevski's groundbreaking book, The Theory of Parallels.
Extensive commentary situates Lobachevski's work in its mathematical, historical, and philosophical context, thus granting readers a vision of the mysterious and beautiful world of nonEuclidean geometry as seen through the eyes of one of its discoverers. Although Lobachevski's 170yearold text is challenging to read on its own, Seth Braver's carefully arranged “illuminations” render this classic accessible to any modern reader (student, professional, or layman) undaunted by high school mathematics.

Chapters

Theory of Parallels—Lobachevski’s Introduction

Theory of Parallels—Preliminary Theorems (1–15)

Theory of Parallels 16: The Definition of Parallelism

Theory of Parallels 17: Parallelism is WellDefined

Theory of Parallels 18: Parallelism is Symmetric

Theory of Parallels 19: The SaccheriLegendre Theorem

Theory of Parallels 20: The Three Musketeers Theorem

Theory of Parallels 21: A Little Lemma

Theory of Parallels 22: Common Perpendiculars

Theory of Parallels 23: The $\Pi $function

Theory of Parallels 24: Convergence of Parallels

Theory of Parallels 25: Parallelism is Transitive

Theory of Parallels 26: Spherical Triangles

Theory of Parallels 27: Solid Angles

Theory of Parallels 28: The Prism Theorem

Theory of Parallels 29: Circumcircles or Lack Thereof (Part I)

Theory of Parallels 30: Circumcircles or Lack Thereof (Part II)

Theory of Parallels 31: The Horocycle Defined

Theory of Parallels 32: The Horocycle as a LimitCircle

Theory of Parallels 33: Concentric Horocycles

Theory of Parallels 34: The Horosphere

Theory of Parallels 35: Spherical Trigonometry

Theory of Parallels 36: The Fundamental Formula

Theory of Parallels 37: Plane Trigonometry

Seth Braver doesn't just interpret the existing contents of Lobachevski's Theory of Parallels, but he continually adds to it by way of making it more mathematically coherent. In this respect, his achievement is first rate and it is equalled by his eloquently inspiring literary style. ... As such, this is a masterly addition to the literature on the history of geometry.
Peter Ruane, MAA Reviews