Advanced Euclidean Geometry

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Advanced Euclidean Geometry

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  • 製本 Paperback:紙装版/ペーパーバック版/ページ数 319 p.
  • 言語 ENG,ENG
  • 商品コード 9780486462370
  • DDC分類 516.2

基本説明

Reprint of the Dover 1960 edition.

Table of Contents

I. INTRODUCTION                                    1
1. Prerequisites
2. Positive and Negative Quantities
8. Points at Infinity
13. Notation
16. Directed Angles
II. SIMILAR FIGURES 16
21. Homothetic Figures
25. Centers of Similitude of Two Circles
31. Similar Figures in General
III. COAXAL CIRCLES AND INVERSION 28
40. The Radical Axis
50. Coaxal Circles
63. Inversion
IV. TRIANGLES AND POLYGONS 58
84. Ratios in the Triangle
89. Quadrangles and Quadrilaterals
92. The Theorem of Ptolemy
96. Triangle and Quadrangle Theorems
101. Polygon Theorems and Exercises
107. Theorems concerning Areas
V. GEOMETRY OF CIRCLES 86
113. The Power Theorem of Casey
126. Circles of Antisimilitude
134. Poles and Polars
144. Stereographic Projection
VI. TANGENT CIRCLES 110
150. Circles Tangent to Two Circles
158. Steiner Chains; the Arbelos
166. The Problem of Apollonius
172. Four Circles Touching a Circle
VII. THE THEOREM OF MIQUEL 131
184. The Miguel 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
259. 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
352. The Isogonic Centers
361. Nagel Point, Spieker Circle, Fuhrmann
Circle
XIII. TRIANGLES IN PERSPECTIVE 230
373. The Theorem of Desargues
385. The Theorems of Pascal and Brianchon
XIV. PEDAL TRIANGLES AND CIRCLES 240
394. Pedal Triangles and Circles of a
Quadrangle
401. Fontene's Theorems; the Theorem of
Feuerbach
406. The Orthopole
XV. SHORTER TOPICS 248
408. Statical 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 287
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
XVIII. THREE SIMILAR FIGURES 302
506. Similar Figures on the Sides of a
Triangle
516. Three Similar Figures in General
INDEX 313