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The author deals with the geometry of the triangle and the circle, concentrating on extensions of Euclidean theory, and exploring in unusual detail the many theorems that have been developed by relatively recent geometers. Several hundred of these theorems and proofs are available only in widely scattered journals, this book also has value as a time-saver and reference work to geometers and teachers of geometry. In addition the author has included a number of theorems left unproved, to be used by the student as exercises.
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, W. Bolyai, Gauss, others. Includes 181 diagrams.
Based on classical principles, this book is intended for a second course in Euclidean geometry and can be used as a refresher. Each chapter covers a different aspect of Euclidean geometry, lists relevant theorems and corollaries, and states and proves many propositions. Includes more than 200 problems, hints, and solutions. 1968 edition.