LEADER 04447nam 2200637Ia 450 001 9910817763703321 005 20200520144314.0 010 $a0-88385-934-3 035 $a(CKB)2670000000205153 035 $a(EBL)3330394 035 $a(SSID)ssj0000577633 035 $a(PQKBManifestationID)11378677 035 $a(PQKBTitleCode)TC0000577633 035 $a(PQKBWorkID)10561663 035 $a(PQKB)10857799 035 $a(UkCbUP)CR9780883859346 035 $a(MiAaPQ)EBC3330394 035 $a(Au-PeEL)EBL3330394 035 $a(CaPaEBR)ebr10729365 035 $a(OCoLC)929120235 035 $a(RPAM)2644459 035 $a(EXLCZ)992670000000205153 100 $a20111102d1967 uy 0 101 0 $aeng 135 $aur||||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aGeometry revisited /$fby H.S.M. Coxeter and S.L. Greitzer 205 $a1st ed. 210 $aWashington, DC $cMathematical Association of America$d1967 215 $a1 online resource (xiv, 193 pages) $cdigital, PDF file(s) 225 0 $aAnneli Lax New Mathematical Library ;$v19 300 $aTitle from publisher's bibliographic system (viewed on 31 May 2016). 311 $a0-88385-619-0 320 $aIncludes bibliographical references and index. 327 $a""Front Cover""; ""Geometry Revisited""; ""Copyright Page""; ""Contents""; ""Preface""; ""Chapter 1. Points and Lines Connected with a Triangle""; ""1.1 The extended Law of Sines""; ""1.2 Cevaa???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"" 327 $a""2.4 More on the altitudes and orthocenter of a triangle""""2.5 Simson lines""; ""2.6 Ptolemya???s theorem and its extension""; ""2.7 More on Simson lines""; ""2.8 The Butterfly""; ""2.9 Morleya???s theorem""; ""Chapter 3. Collinearity and Concurrence""; ""3.1 Quadrangles; Varignona???s theorem""; ""3.2 Cyclic quadrangles; Brahmaguptaa???s formula""; ""3.3 Napoleon triangles""; ""3.4 Menelausa???s theorem""; ""3.5 Pappusa???s theorem""; ""3.6 Perspective triangles; Desarguesa???s theorem""; ""3.7 Hexagons""; ""3.8 Pascala???s theorem""; ""3.9 Brianchona???s theorem"" 327 $a""Chapter 4. Transformations""""4.1 Translation""; ""4.2 Rotation""; ""4.3 Half-turn""; ""4.4 Reflection""; ""4.5 Fagnanoa???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 Feuerbacha???s theorem""; ""5.7 Coaxal circles""; ""5.8 Inversive distance""; ""5.9 Hyperbolic functions""; ""Chapter 6. An Introduction to Projective Geometry"" 327 $a""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""; ""Back Cover"" 330 $aAmong the many beautiful and nontrivial theorems in geometry found here are the theorems of Ceva, Menelaus, Pappus, Desargues, Pascal, and Brianchon. A nice proof is given of Morley's remarkable theorem on angle trisectors. The transformational point of view is emphasized: reflections, rotations, translations, similarities, inversions, and affine and projective transformations. Many fascinating properties of circles, triangles, quadrilaterals, and conics are developed. 410 0$aNew mathematical library ;$v19. 606 $aGeometry 606 $aMathematics 615 0$aGeometry. 615 0$aMathematics. 676 $a516 700 $aCoxeter$b H. S. M$g(Harold Scott Macdonald),$f1907-2003.$0903227 701 $aGreitzer$b Samuel L$054697 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910817763703321 996 $aGeometry revisited$94197207 997 $aUNINA