Author(s): F. B. Allen, E. C. Douglas, D. E. Richmond
Series: Elementary Geometry Collection
Year: 1961
Language: English
Commentary: Commentary: Classical synthetic geometry must never be forgotten. It is the best training for the imagination. This Collection is dedicated to the spiritual upliftment of Humanity. Peace of Mind and Knowledge to All!
Chapter 11: Areas of Polygonal Regions
11-1 Polygonal Regions
11-2 Areas of Triangles and Quadrilaterals
11-3 The Pythagorean Theorem
Review Problems
Chapter 12: Similarity
12-1 The Idea of a Similarity
12-2 Similarities between Triangles
12-3 The Basic Similarity Theorems
12-4 Similarities in Right Triangles
12-5 Areas of Similar Triangles
Review Problems
Chapters 7 to 12 Review Exercises
Chapter 13: Circles and Spheres
13-1 Basic Definitions
13-2 Tangent Lines. The Fundamental Theorem for Circles
13-3 Tangent Planes. The Fundamental Theorem for Spheres
13-4 Arcs of Circles
13-5 Lengths of Tangent and Secant Segments
Review Problems
Chapter 14: Characterization of Sets. Constructions
14-1 Characterization of Sets
14-2 Basic Characterizations. Concurrence Theorems
14-3 Intersection of Sets
14-4 Constructions with Straight-edge and Compass
14-5 Elementary Constructions
14-6 Inscribed and Circumscribed Circles
14-7 The Impossible Construction Problems of Antiquity
Review Problems
Chapter 15: Areas of Circles and Sectors
15-1 Polygons
15-2 Regular Polygons
15-3 The Circumference of a Circle. The Number Pi
15-4 Area of a Circle
15-5 Lengths of Arcs. Areas of Sectors
Review Problems
Chapter 16: Volumes of Solids
16-1 Prisms
16-2 Pyramids
16-3 Volumes of Prisms and Pyramids, Cavalieri's Principle
16-4 Cylinders and Cones
16-5 Spheres; Volume and Area
Review Problems
Chapter 17: Plane Coordinate Geometry
17-1 Introduction
17-2 Coordinate Systems in a Plane
17-3 How to Plot Points on Graph Paper
17-4 The Slope of a Non-Vertical Line
17-5 Parallel and Perpendicular Lines
17-6 The Distance Formula
17-7 The Mid-Point Formula
17-8 Proofs of Geometric Theorems
17-9 The Graph of a Condition
17-10 How to Describe a Line by an Equation
17-11 Various Forms of the Equation of a Line
17-12 The General Form of the Equation of a Line
17-13 Intersections of Lines
17-14 Circles
Review Problems
Chapters 13 to 17 Review Exercises
Appendix
Appendix VII: How Eratosthenes Measured the Earth
Appendix VIII: Rigid Motion
Appendix IX: Proof of the Two-Circle Theorem
Appendix X: Trigonometry
Appendix XI: Regular Polyhedra
The Meaning and Use of Symbols
List of Postulates
List of Theorems and Corollaries
Index of Definitions
