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

Idioma: Inglés Lenguaje original: Ruso Editor: Moscow : Peace Publishers, Descripción: 251 p. : il. ; 23 cmTítulos uniformes: Kratkii kurs analiticheskoi geometrii. Inglés Tema(s): Geometry, AnalyticOtra clasificación: 51-01 (51N20)
Contenidos:
```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 
§ 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 ``` Average rating: 0.0 (0 votes)
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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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