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008			240724s1967 xx o ||||0 eng d
020			_a9780883859346 _q(electronic bk.)
020			_z9780883856192
035			_a(MiAaPQ)EBC3330394
035			_a(Au-PeEL)EBL3330394
035			_a(CaPaEBR)ebr10729365
035			_a(OCoLC)929120235
040			_aMiAaPQ _beng _erda _epn _cMiAaPQ _dMiAaPQ
050		4	_aQA445.C69 1967eb
082	0		_a516
100	1		_aS., H.
245	1	0	_aGeometry Revisited.
250			_a1st ed.
264		1	_aProvidence : _bAmerican Mathematical Society, _c1967.
264		4	_c©1967.
300			_a1 online resource (209 pages)
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
490	1		_aAnneli Lax New Mathematical Library ; _vv.19
505	0		_aFront cover -- Copyright Page -- Preface -- Contents -- Chapter 1. Points and Lines Connected with a Triangle -- 1.1 The extended Law of Sines -- 1.2 Ceva's theorem -- 1.3 Points of interest -- 1.4 The incircle and excircles -- 1.5 The Steiner-Lehmus theorem -- 1.6 The orthic triangle -- 1.7 The medial triangle and Euler line -- 1.8 The nine-point Circle -- 1.9 Pedal triangles -- Chapter 2. Some Properties of Circles -- 2.1 The power of a point with respect to a circle -- 2.2 The radical axis of two circles -- 2.3 Coaxal circles -- 2.4 More on the altitudes and orthocenter of a triangle -- 2.5 Simson lines -- 2.6 Ptolemy's theorem and its extension -- 2.7 More on Simson lines -- 2.8 The Butterfly -- 2.9 Morley's theorem -- Chapter 3. Collinearity and Concurrence -- 3.1 Quadrangles -- Varignon's theorem -- 3.2 Cyclic quadrangles -- Brahmagupta's formula -- 3.3 Napoleon triangles -- 3.4 Menelaus's theorem -- 3.5 Pappus's theorem -- 3.6 Perspective triangles -- Desargues's theorem -- 3.7 Hexagons -- 3.8 Pascal's theorem -- 3.9 Brianchon's theorem -- Chapter 4. Transformations -- 4.1 Translation -- 4.2 Rotation -- 4.3 Half-turn -- 4.4 Reflection -- 4.5 Fagnano's problem -- 4.6 The three jug problem -- 4.7 Dilatation -- 4.8 Spiral similarity -- 4.9 A genealogy of transformations -- Chapter 5. An Introduction to Inversive Geometry -- 5.1 Separation -- 5.2 Cross ratio -- 5.3 Inversion -- 5.4 The inversive plane -- 5.5 Orthogonality -- 5.6 Feuerbach's theorem -- 5.7 Coaxal circles -- 5.8 Inversive distance -- 5.9 Hyperbolic functions -- Chapter 6. An Introduction to Projective Geometry -- 6.1 Reciprocation -- 6.2 The polar circle of a triangle -- 6.3 Conics -- 6.4 Focus and directrix -- 6.5 The projective plane -- 6.6 Central conics -- 6.7 Stereographic and gnomonic projection -- Hints and Answers to Exercises -- References -- Glossary -- Index.
505	8		_aBack Cover.
520			_aAmong the many beautiful and nontrivial theorems in geometry found in Geometry Revisited are the theorems of Ceva, Menelaus, Pappus, Desargues, Pascal, and Brianchon. A nice proof is given of Morley's remarkable theorem on angle trisectors. The transformational point of view is emphasized: reflections, rotations, translations, similarities, inversions, and affine and projective transformations. Many fascinating properties of circles, triangles, quadrilaterals, and conics are developed.
588			_aDescription based on publisher supplied metadata and other sources.
590			_aElectronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.
650		0	_aGeometry.
650		0	_aMathematics.
655		4	_aElectronic books.
700	1		_aGreitzer, S. L.
776	0	8	_iPrint version: _aS., H. _tGeometry Revisited _dProvidence : American Mathematical Society,c1967 _z9780883856192
797	2		_aProQuest (Firm)
830		0	_aAnneli Lax New Mathematical Library
856	4	0	_uhttps://ebookcentral.proquest.com/lib/orpp/detail.action?docID=3330394 _zClick to View
999			_c79847 _d79847