Solving problems in geometry

Front Cover
Title Page
PREFACE
CONTENTS
Chapter 1 PLANE GEOMETRY
	SEC. 1. METHODS OF SOLVING GEOMETRICAL PROBLEMS
		I. Triangles and Quadrilaterals
		II. Circles
		III. Areas of Plane Figures
	SEC. 2. TRIANGLES AND QUADRILATERALS
		PROBLEMS TO BE SOLVED WITHOUT ASSISTANCE
			I. Right Triangles
			II. Isosceles Triangles
			III. Arbitrary Triangles
			IV, Parallelograms
			V. Trapezoids
			VI. Miscellaneous Problems
	SEC. 3. CIRCLES
		PROBLEMS TO BE SOLVED WITHOUT ASSISTANCE
			I. Circles
			II. Inscribed and Circumscribed Triangles
			III. A Circle and a Triangle Arranged Arbitrarily
			IV. A Circle and a Quadrilateral
			V. Miscellaneous Problems
	SEC. 4. AREAS OF PLANE FIGURES
		PROBLEMS TO BE SOLVED WITHOUT ASSISTANCE
			I. Area of Triangles
			II. Area of Quadrilaterals
			III. Area of Polygons
			IV. Area of Combined Figures
			V. Miscellaneous Problems
	SEC. 5. GEOMETRICAL TRANSFORMATIONS
		PROBLEMS TO BE SOLVED WITHOUT ASSISTANCE
			I. Symmetry with Respect to a Point
			II. Symmetry About a Straight Line
			III. Rotation
			IV. Translation
			V. Homothetlc Transformation
	SEC. 6. VECTORS
		I. Affine Problems
		II. Metric Problems
		PROBLEMS TO BE SOLVED WITHOUT ASSISTANCE
			I. Addition and Subtraction of Vectors.Multiplication of a Vector by a Number
			II. Scalar Product of Vectors
			III. Miscellaneous Problems
	SEC. 7. GREATEST AND LEAST VALUES
		PROBLEMS TO BE SOLVED WITHOUT ASSISTANCE
Chapter 2 SOLID GEOMETRY
	SEC. 8. CONSTRUCTING THE REPRESENTATION OF A GIVEN FIGURE
	SEC. 9. GEOMETRICAL CONSTRUCTIONS IN SPACE
		I. Simplest Constructions in Space
		II. Loci of Points
		III. Applications of Certain Loci of Points and Straight Lines
		IV. Constructions on Representations
		PROBLEMS TO BE SOLVED WITHOUT ASSISTANCE
			I. Simplest Constructions in Space
			II. Loci of Points
			III. Applications of Certain Loci of Points and Lines
			IV. Constructions on Representations
				(1) Constructing Plane Figures in Space
				(2) Section of a Polyhedron by a Plane Parallel to Two Straight Lines
				(3) Cons tructing a Perpendicular to a Straight Line and a Perpendicular to a Plane
				(4) Section of a Polyhedron by a Plane PassingThrough a Given Point Perpendicular to a Given Line
				(5) Constructing a Locus of Points Equidistant from Given Points
	SEC. 10. SKEW LINES. ANGLE BETWEEN A STRAIGHT LINE AND A PLANE
		PROBLEMS TO BE SOLVED WITHOUT ASSISTANCE
	SEC. 11. DIHEDRAL AND POLYHEDRAL ANGLES
		PROBLEMS TO BE SOLVED WITHOUT ASSISTANCE
	SEC. 12. SECTIONS OF POLYHEDRONS
		PROBLEMS TO BE SOLVED WITHOUT ASSISTANCE
	SEC. 13. SURFACES
		PROBLEMS TO BE SOLVED WITHOUT ASSISTANCE
	SEC. 14. VOLUMES
		PROBLEMS TO BE SOLVED WITHOUT ASSISTANCE
	SEC. 15. COMBINATIONS OF POLYHEDRONS AND CIRCULAR SOLIDS
		PROBLEMS TO BE SOLVED WITHOUT ASSISTANCE
	SEC. 16. GREATEST AND LEAST VALUES
		PROBLEMS TO BE SOLVED WITHOUT ASSISTANCE!
ANSWERS AND HINTS
	Chapter 1
	Chapter 2
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