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Advanced Euclidean Geometry (DOVER)~tqw~ darksiderg

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INFO

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Title................: Advanced Euclidean Geometry (DOVER)

Type.................: Ebook

Reader...............: PDF Reader

Size.................: 86.1 MB

Torrent Hash.........: 9AA5BF5FA048D45C4347C3A61C82DF5BF26F5664

Posted by............: ~tqw~



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CONTENTS

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Synopsis:

This classic text explores the geometry of the triangle and the circle, 

concentrating on extensions of Euclidean theory, and examining in detail 

many relatively recent theorems. Several hundred theorems and corollaries 

are formulated and proved completely; numerous others remain unproved, to be 

used by students as exercises.



Table Of Contents:

I. INTRODUCTION

1. Prerequisites

2. Positive and Negative Quantities

8. Points at Infinity

13. Notation

16. Directed Angles

II. SIMILAR FIGURES

21. Homothetic Figures

25. Centers of Similitude of Two Circles

31. Similar Figures in General

III. COAXAL CIRCLES AND INVERSION

40. The Radical Axis

50. Coaxal Circles

63. Inversion

IV. TRIANGLES AND POLYGONS

84. Ratios in the Triangle

89. Quadrangles and Quadrilaterals

92. The Theorem of Ptolemy

96. Triangle and Quadrangle Theorems

101. Polygon Theorems and Exercises

len. Theorems concerning Areas

V. GEOMETRY OF CIRCLES

113. The Power Theorem of Casey

126. Circles of Antisinulitude

134. Poles and Polars

144. Stereographic Projection

VI. TANGENT CIRCLES 110

160. Circles Tangent to Two Circles

168. Steiner Chains; the Arbel08

166. The Problem of Apollonius

172. Four Circles Touching a Circle

VII. THE THEOREM OF MIQUEL 131

184. The Miquel Theorem

189. Pedal Triangles and Circles; Simson Lines

VIII. THEOREMS OF CEVA AND MENELAUS 145

213. The Theorems of Ceva and Menelaus; Applications

231. Isogonal Conjugates

IX. THREE NOTABLE POINTS 161

249. Fundamental Properties of Orthocenter and Circumcenter

269. The Orthocentric System

271. Properties of the Median Point

278. The Polar Circle

X. INSCRIBED AND EsCRIBED CIRCLES 182

287. Fundamental Properties

298. Algebraic Formulas; Principle of Transformation

XI. THE NINE POINT CIRCLE 195

308. Properties of the Nine Point Circle

320. The Theorem of Feuerbach

326. Further Properties of Simson Lines

XII. SYMMEDIAN POINT AND OTHER NOTABLE POINTS 213

341. Symmedians and the Symmedian Point

362. The Isogonic Centers

361. Nagel Point, Spieker Circle, Fuhrmann Circle

XIII. TRIANGLES IN PERSPECTIVE

3'13. The Theorem of Desargues

385. The Theorems of Pascal and Brianchon

XIV. PEDAL TRIANGLES AND CIRCLES

394. Pedal Triangles and Circles of a Quadrangle

401. Fontene's Theorems; the Theorem of Feuerbach

406. The Orthopole

XV. SHORTER TOPICS 248

408. Statieal Theorems: Center of Gravity, Resultant of Vectors

417. The Cyclic Quadrangle and its Orthocenters

420. The Theorem of Morley

424. Circles of Droz-Farny

428. Miscellaneous Exercises

XVI. THE BROCARD CONFIGURATION 263

433. The Brocard Points and their Properties

448. The Tucker Circles

461. The Brocard Triangles and the Brocard Circle

469. Steiner Point and Tarry Point

473. Related Triangles

XVII. EQUIBROCARDAL TRIANGLES

480. The Neuberg Circles

486. Vertical Projection of Triangles

490. Circles of Apollonius and Isodynamic Points

497. The Circles of Schoute

499. Generalizations of Brocard Geometry 287

XVIII. THREE SIMILAR FIGURES 302

506. Similar Figures on the Sides of a Triangle

516. Three Similar Figures in General

INDEX



Product Details:

    * ISBN: 0486462374

    * ISBN-13: 9780486462370

    * Format: Paperback, 336pp

    * Publisher: Dover Publications

    * Pub. Date: August 2007



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Greetz Fellow UL'ers

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       mazuki `jedi Flatline newartriot aXXo KingBen Paulx1 unisonband

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