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# A brief course in analytic geometry / N. Yefimov ; translated from the Russian by O. Soroka.

Material type: BookPublisher: Moscow : Peace Publishers, Description: 251 p. : il. ; 23 cm.Uniform titles: Kratkii kurs analiticheskoi geometrii. Inglés Subject(s): Geometry, AnalyticOther classification: 51-01 (51N20)
Contents:
Part One -- PLANE ANALYTIC GEOMETRY -- Chapter 1. Coordinates on a Straight Line and in a Plane  -- § 1. An Axis and Segments of an Axis  -- § 2. Coordinates on a Line. The Number Axis  -- § 3. Rectangular Cartesian Coordinates in a Plane. A Note on Oblique Cartesian Coordinates  -- § 4. Polar Coordinates  -- Chapter 2. Elementary Problems of Plane Analytic Geometry  -- § 5. Projection of a Line Segment. Distance Between Two Points  -- § 6. Calculation of the Area of a Triangle  -- § 7. Division of a Line Segment in a Given Ratio  -- § 8. Transformation of Cartesian Coordinates by .Translation of Axes  -- § 9. Transformation of Rectangular Cartesian Coordinates by Rotation of Axes  -- § 10. Transformation of Rectangular Cartesian Coordinates by Change of Origin and Rotation of Axes  -- Chapter 3. The Equation of a Curve  -- § 11. The Concept of the Equation of a Curve. Examples of Curves Represented by Equations  -- § 12. Examples of Deriving the Equation of a Given Curve  -- § 13. The Problem of the Intersection of Two Curves  -- § 14. Parametric Equations of a Curve  -- § 15. Algebraic Curves  -- Chapter 4. Curves of the First Order  -- § 16. The Slope of a Straight Line  -- § 17. The Slope-intercept Equation of a Straight Line  -- § 18. Calculation of the Angle Between Two Straight Lines. Conditions for the Parallelism and Perpendicularity of Two Straight Lines  -- § 19. The Straight Line As the Curve of the First Order. The General Equation of the Straight Line  -- § 20. Incomplete Equations of the First Degree. The Intercept Equation of a Straight Line  -- § 21. Discussion of a System of Equations Representing Two Straight Lines  -- § 22. The Normal Equation of a Straight Line. The Problem of Calculating the Distance of a Point from a Straight Line  -- § 23. The Equation of a Pencil of Lines  -- Chapter 5. Geometric Properties of Curves of the Second Order  -- § 24. The Ellipse. Definition of the Ellipse and Derivation of Its Canonical Equation  -- § 25. Discussion of the Shape of the Ellipse  -- § 26. The Eccentricity of the Ellipse  -- § 27. Rational Expressions for Focal Radii of the Ellipse  -- § 28. Point-by-point Construction of the Ellipse. The Parametric Equations of the Ellipse  -- § 29. The Ellipse as the Projection of a Circle on a Plane. The Ellipse as the Section of a Circular Cylinder by a Plane  -- § 30. The Hyperbola. Definition of the Hyperbola and Derivation of Its Canonical Equation  -- § 31. Discussion of the Shape of the Hyperbola  -- § 32. The Eccentricity of the Hyperbola  -- § 33. Rational Expressions for Focal Radii of the Hyperbola  -- § 34. The Directrices of the Ellipse and Hyperbola  -- § 35. The Parabola. Derivation of the Canonical Equation of the Parabola  -- § 36. Discussion of the Shape of the Parabola  -- § 37. The Polar Equation of the Ellipse, Hyperbola and Parabola  -- § 38. Diameters of Curves of the Second Order  -- § 39. The Optical Properties of the Ellipse, Hyperbola and Parabola  -- § 40. The Ellipse, Hyperbola and Parabola as Conic Sections  -- Chapter 6. Transformation of Equations by Change of Coordinates  -- § 41. Examples of Reducing the General Equation of a Second-Order Curve to Canonical Form  -- § 42. The Hyperbola as the Inverse Proportionality Graph. The Parabola as the Graph of a Quadratic Function  -- Part Two -- SOLID ANALYTIC GEOMETRY -- Chapter 7. Some Elementary Problems of Solid Analytic Geometry  -- § 43. Rectangular Cartesian Coordinates in Space  -- € 44 The Concept of a Free Vector. The Projection of a Vector on an Axis  -- § 45. The Projections of a Vector on the Coordinate Axes  -- § 46. Direction Cosines  -- § 47. Distance between Two Points. Division of a Line Segment in a Given Ratio  -- Chapter & Linear Operations on Vectors  -- § 48. Definitions of Linear Operations  -- § 49. Basic Properties of Linear Operations  -- § 50. The Vector Difference  -- § 51. Fundamental Theorems on Projections  -- § 52. Resolution of Vectors into Components  -- Chapter 9. The Scalar Product of Vectors  -- § 53. The Scalar Product and Its Basic Properties  -- § 54. Representation of the Scalar Product in Terms of the Coordinates of the Vector Factors  -- Chapter 10. The Vector and Triple Scalar Products of Vectors  -- § 55. The Vector Product and Its Basic Properties  -- § 56. Representation of the Vector Product in Terms of the Coordinates of the Vector Factors  -- § 57. The Triple Scalar Product  -- § 58. Representation of the Triple Scalar Product in Terms of the Coordinates of the Vector Factors  -- Chapter 11. The Equation of a Surface and the Equations of a Curve  -- § 59. The Equation of a Surface  -- § 60. The Equations of a Curve. The Problem of the Intersection of Three Surfaces  -- § 61. The Equation of a Cylindrical Surface with Elements Parallel to a Coordinate Axis  -- § 62. Algebraic Surfaces  -- Chapter 12. The Plane as the Surface of the First Order. The Equations of a Straight Line  -- § 63. The Plane as the Surface of the First Order  -- § 64. Incomplete Equations of Planes. The Intercept Form of the Equation of a Plane  -- § 65. The Normal Equation of a Plane. The Distance of a Point from a Plane  -- § 66. The Equations of a Straight Line  -- § 67. The Direction Vector of a Straight Line. The Canonical Equations of a Straight Line. The Parametric Equations of a Straight Line  -- § 68. Some Additional Propositions and Examples  -- Chapter 13. Quadric Surfaces  -- § 69. The Ellipsoid and the Hyperboloids  -- § 70. The Quadric Cone  -- § 71 The Paraboloids  -- § 72. The Quadric Cylinders  -- § 73. The Rectilinear Generators of the Hyperboloid of One Sheet. The Shukhov Towers  -- Appendix. The Elements of the Theory of Determinants  -- § 1. Determinants of the Second Order and Systems of Two Equations of the First Degree in Two Unknowns  -- § 2. A Homogeneous System of Two Equations of the First Degree in Three Unknowns  -- § 3. Determinants of the Third Order  -- § 4. Cofactors and Minors  -- § 5. Solution and Analysis of a System of Three First-degree Equations in Three Unknowns  -- § 6, The Concept of a Determinant of Any Order  --
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Traducción de: Kratkii kurs analiticheskoi geometrii.

Part One --
PLANE ANALYTIC GEOMETRY --
Chapter 1. Coordinates on a Straight Line and in a Plane  --
§ 1. An Axis and Segments of an Axis  --
§ 2. Coordinates on a Line. The Number Axis  --
§ 3. Rectangular Cartesian Coordinates in a Plane. A Note on Oblique Cartesian Coordinates  --
§ 4. Polar Coordinates  --
Chapter 2. Elementary Problems of Plane Analytic Geometry  --
§ 5. Projection of a Line Segment. Distance Between Two Points  --
§ 6. Calculation of the Area of a Triangle  --
§ 7. Division of a Line Segment in a Given Ratio  --
§ 8. Transformation of Cartesian Coordinates by .Translation of Axes  --
§ 9. Transformation of Rectangular Cartesian Coordinates by Rotation of Axes  --
§ 10. Transformation of Rectangular Cartesian Coordinates by Change of Origin and Rotation of Axes  --
Chapter 3. The Equation of a Curve  --
§ 11. The Concept of the Equation of a Curve. Examples of Curves Represented by Equations  --
§ 12. Examples of Deriving the Equation of a Given Curve  --
§ 13. The Problem of the Intersection of Two Curves  --
§ 14. Parametric Equations of a Curve  --
§ 15. Algebraic Curves  --
Chapter 4. Curves of the First Order  --
§ 16. The Slope of a Straight Line  --
§ 17. The Slope-intercept Equation of a Straight Line  --
§ 18. Calculation of the Angle Between Two Straight Lines. Conditions for the Parallelism and Perpendicularity of Two Straight Lines  --
§ 19. The Straight Line As the Curve of the First Order. The General Equation of the Straight Line  --
§ 20. Incomplete Equations of the First Degree. The Intercept Equation of a Straight Line  --
§ 21. Discussion of a System of Equations Representing Two Straight Lines  --
§ 22. The Normal Equation of a Straight Line. The Problem of Calculating the Distance of a Point from a Straight Line  --
§ 23. The Equation of a Pencil of Lines  --
Chapter 5. Geometric Properties of Curves of the Second Order  --
§ 24. The Ellipse. Definition of the Ellipse and Derivation of Its Canonical Equation  --
§ 25. Discussion of the Shape of the Ellipse  --
§ 26. The Eccentricity of the Ellipse  --
§ 27. Rational Expressions for Focal Radii of the Ellipse  --
§ 28. Point-by-point Construction of the Ellipse. The Parametric Equations of the Ellipse  --
§ 29. The Ellipse as the Projection of a Circle on a Plane. The Ellipse as the Section of a Circular Cylinder by a Plane  --
§ 30. The Hyperbola. Definition of the Hyperbola and Derivation of Its Canonical Equation  --
§ 31. Discussion of the Shape of the Hyperbola  --
§ 32. The Eccentricity of the Hyperbola  --
§ 33. Rational Expressions for Focal Radii of the Hyperbola  --
§ 34. The Directrices of the Ellipse and Hyperbola  --
§ 35. The Parabola. Derivation of the Canonical Equation of the Parabola  --
§ 36. Discussion of the Shape of the Parabola  --
§ 37. The Polar Equation of the Ellipse, Hyperbola and Parabola  --
§ 38. Diameters of Curves of the Second Order  --
§ 39. The Optical Properties of the Ellipse, Hyperbola and Parabola  --
§ 40. The Ellipse, Hyperbola and Parabola as Conic Sections  --
Chapter 6. Transformation of Equations by Change of Coordinates  --
§ 41. Examples of Reducing the General Equation of a Second-Order Curve to Canonical Form  --
§ 42. The Hyperbola as the Inverse Proportionality Graph. The Parabola as the Graph of a Quadratic Function  --
Part Two --
SOLID ANALYTIC GEOMETRY --
Chapter 7. Some Elementary Problems of Solid Analytic Geometry  --
§ 43. Rectangular Cartesian Coordinates in Space  --
€ 44 The Concept of a Free Vector. The Projection of a Vector on an Axis  --
§ 45. The Projections of a Vector on the Coordinate Axes  --
§ 46. Direction Cosines  --
§ 47. Distance between Two Points. Division of a Line Segment in a Given Ratio  --
Chapter & Linear Operations on Vectors  --
§ 48. Definitions of Linear Operations  --
§ 49. Basic Properties of Linear Operations  --
§ 50. The Vector Difference  --
§ 51. Fundamental Theorems on Projections  --
§ 52. Resolution of Vectors into Components  --
Chapter 9. The Scalar Product of Vectors  --
§ 53. The Scalar Product and Its Basic Properties  --
§ 54. Representation of the Scalar Product in Terms of the Coordinates of the Vector Factors  --
Chapter 10. The Vector and Triple Scalar Products of Vectors  --
§ 55. The Vector Product and Its Basic Properties  --
§ 56. Representation of the Vector Product in Terms of the Coordinates of the Vector Factors  --
§ 57. The Triple Scalar Product  --
§ 58. Representation of the Triple Scalar Product in Terms of the Coordinates of the Vector Factors  --
Chapter 11. The Equation of a Surface and the Equations of a Curve  --
§ 59. The Equation of a Surface  --
§ 60. The Equations of a Curve. The Problem of the Intersection of Three Surfaces  --
§ 61. The Equation of a Cylindrical Surface with Elements Parallel to a Coordinate Axis  --
§ 62. Algebraic Surfaces  --
Chapter 12. The Plane as the Surface of the First Order. The Equations of a Straight Line  --
§ 63. The Plane as the Surface of the First Order  --
§ 64. Incomplete Equations of Planes. The Intercept Form of the Equation of a Plane  --
§ 65. The Normal Equation of a Plane. The Distance of a Point from a Plane  --
§ 66. The Equations of a Straight Line  --
§ 67. The Direction Vector of a Straight Line. The Canonical Equations of a Straight Line. The Parametric Equations of a Straight Line  --
§ 68. Some Additional Propositions and Examples  --
Chapter 13. Quadric Surfaces  --
§ 69. The Ellipsoid and the Hyperboloids  --
§ 70. The Quadric Cone  --
§ 71 The Paraboloids  --
§ 72. The Quadric Cylinders  --
§ 73. The Rectilinear Generators of the Hyperboloid of One Sheet. The Shukhov Towers  --
Appendix. The Elements of the Theory of Determinants  --
§ 1. Determinants of the Second Order and Systems of Two Equations of the First Degree in Two Unknowns  --
§ 2. A Homogeneous System of Two Equations of the First Degree in Three Unknowns  --
§ 3. Determinants of the Third Order  --
§ 4. Cofactors and Minors  --
§ 5. Solution and Analysis of a System of Three First-degree Equations in Three Unknowns  --
§ 6, The Concept of a Determinant of Any Order  --

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