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Euclid's Parallel Postulate: Its Nature, Validity and Place in Geometrical Systems
by John William Withers - Open Court Publishing Co. , 1904
The parallel postulate is the only distinctive characteristic of Euclid. To pronounce upon its validity and general philosophical significance without endeavoring to know what Non-Euclideans have done would be an inexcusable blunder ...
Non-Euclidean Geometry: A Critical and Historical Study of its Development
by Roberto Bonola - Open Court Publishing Company , 1912
Examines various attempts to prove Euclid's parallel postulate - by the Greeks, Arabs and Renaissance mathematicians. It considers forerunners and founders such as Saccheri, Lambert, Legendre, Gauss, Schweikart, Taurinus, J. Bolyai and Lobachewsky.
by J.W. Cannon, W.J. Floyd, R. Kenyon, W.R. Parry - MSRI , 1997
These notes are intended as a relatively quick introduction to hyperbolic geometry. They review the wonderful history of non-Euclidean geometry. They develop a number of the properties that are particularly important in topology and group theory.
The Elements of Non-Euclidean Plane Geometry and Trigonometry
by Horatio Scott Carslaw - Longmans, Green and co. , 1916
In this book the author has attempted to treat the Elements of Non-Euclidean Plane Geometry and Trigonometry in such a way as to prove useful to teachers of Elementary Geometry in schools and colleges. Hyperbolic and elliptic geometry are covered.
The Elements of Non-Euclidean Geometry
by D.M.Y. Sommerville - G.Bell & Sons Ltd. , 1914
Renowned for its lucid yet meticulous exposition, this text follows the development of non-Euclidean geometry from a fundamental analysis of the concept of parallelism to such advanced topics as inversion and transformations.
The Elements Of Non-Euclidean Geometry
by Julian Lowell Coolidge - Oxford At The Clarendon Press , 1909
Chapters include: Foundation For Metrical Geometry In A Limited Region; Congruent Transformations; Introduction Of Trigonometric Formulae; Analytic Formulae; Consistency And Significance Of The Axioms; Geometric And Analytic Extension Of Space; etc.
Neutral and Non-Euclidean Geometries
by David C. Royster - UNC Charlotte , 2000
In this course the students are introduced, or re-introduced, to the method of Mathematical Proof. You will be introduced to new and interesting areas in Geometry, with most of the time spent on the study of Hyperbolic Geometry.
The Eightfold Way: The Beauty of Klein's Quartic Curve
by Silvio Levy - Cambridge University Press , 1999
Felix Klein discovered in 1879 that the surface that we now call the Klein quartic has many remarkable properties, including an incredible 336-fold symmetry. This volume explores the rich tangle of properties surrounding this multiform object.
by Henry Manning - Ginn and Company , 1901
This book gives a simple and direct account of the Non-Euclidean Geometry, and one which presupposes but little knowledge of Mathematics. The entire book can be read by one who has taken the mathematical courses commonly given in our colleges.