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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, [1964]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 [11]
§ 1. An Axis and Segments of an Axis [11]
§ 2. Coordinates on a Line. The Number Axis [14]
§ 3. Rectangular Cartesian Coordinates in a Plane. A Note on Oblique Cartesian Coordinates [16]
§ 4. Polar Coordinates [20]
Chapter 2. Elementary Problems of Plane Analytic Geometry [23]
§ 5. Projection of a Line Segment. Distance Between Two Points [23]
§ 6. Calculation of the Area of a Triangle [28]
§ 7. Division of a Line Segment in a Given Ratio [30]
§ 8. Transformation of Cartesian Coordinates by .Translation of Axes [35]
§ 9. Transformation of Rectangular Cartesian Coordinates by Rotation of Axes [36]
§ 10. Transformation of Rectangular Cartesian Coordinates by Change of Origin and Rotation of Axes [38]
Chapter 3. The Equation of a Curve [41]
§ 11. The Concept of the Equation of a Curve. Examples of Curves Represented by Equations [41]
§ 12. Examples of Deriving the Equation of a Given Curve [48]
§ 13. The Problem of the Intersection of Two Curves [50]
§ 14. Parametric Equations of a Curve [51]
§ 15. Algebraic Curves [52]
Chapter 4. Curves of the First Order [55]
§ 16. The Slope of a Straight Line [55]
§ 17. The Slope-intercept Equation of a Straight Line [56]
§ 18. Calculation of the Angle Between Two Straight Lines. Conditions for the Parallelism and Perpendicularity of Two Straight Lines [59]
§ 19. The Straight Line As the Curve of the First Order. The General Equation of the Straight Line [61]
§ 20. Incomplete Equations of the First Degree. The Intercept Equation of a Straight Line [63]
§ 21. Discussion of a System of Equations Representing Two Straight Lines [65]
§ 22. The Normal Equation of a Straight Line. The Problem of Calculating the Distance of a Point from a Straight Line [68]
§ 23. The Equation of a Pencil of Lines [71]
Chapter 5. Geometric Properties of Curves of the Second Order [75]
§ 24. The Ellipse. Definition of the Ellipse and Derivation of Its Canonical Equation [75]
§ 25. Discussion of the Shape of the Ellipse [79]
§ 26. The Eccentricity of the Ellipse [81]
§ 27. Rational Expressions for Focal Radii of the Ellipse [82]
§ 28. Point-by-point Construction of the Ellipse. The Parametric Equations of the Ellipse [83]
§ 29. The Ellipse as the Projection of a Circle on a Plane. The Ellipse as the Section of a Circular Cylinder by a Plane [84]
§ 30. The Hyperbola. Definition of the Hyperbola and Derivation of Its Canonical Equation [87]
§ 31. Discussion of the Shape of the Hyperbola [91]
§ 32. The Eccentricity of the Hyperbola [97]
§ 33. Rational Expressions for Focal Radii of the Hyperbola [98]
§ 34. The Directrices of the Ellipse and Hyperbola [99]
§ 35. The Parabola. Derivation of the Canonical Equation of the Parabola [103]
§ 36. Discussion of the Shape of the Parabola [105]
§ 37. The Polar Equation of the Ellipse, Hyperbola and Parabola [107]
§ 38. Diameters of Curves of the Second Order [109]
§ 39. The Optical Properties of the Ellipse, Hyperbola and Parabola [114]
§ 40. The Ellipse, Hyperbola and Parabola as Conic Sections [115]
Chapter 6. Transformation of Equations by Change of Coordinates [116]
§ 41. Examples of Reducing the General Equation of a Second-Order Curve to Canonical Form [116]
§ 42. The Hyperbola as the Inverse Proportionality Graph. The Parabola as the Graph of a Quadratic Function [125]
Part Two
SOLID ANALYTIC GEOMETRY
Chapter 7. Some Elementary Problems of Solid Analytic Geometry [131]
§ 43. Rectangular Cartesian Coordinates in Space [131]
€ 44 The Concept of a Free Vector. The Projection of a Vector on an Axis [134]
§ 45. The Projections of a Vector on the Coordinate Axes [138]
§ 46. Direction Cosines [141]
§ 47. Distance between Two Points. Division of a Line Segment in a Given Ratio [142]
Chapter & Linear Operations on Vectors [143]
§ 48. Definitions of Linear Operations [143]
§ 49. Basic Properties of Linear Operations [144]
§ 50. The Vector Difference [147]
§ 51. Fundamental Theorems on Projections [149]
§ 52. Resolution of Vectors into Components [152]
Chapter 9. The Scalar Product of Vectors [157]
§ 53. The Scalar Product and Its Basic Properties [157]
§ 54. Representation of the Scalar Product in Terms of the Coordinates of the Vector Factors [160]
Chapter 10. The Vector and Triple Scalar Products of Vectors [163]
§ 55. The Vector Product and Its Basic Properties [163]
§ 56. Representation of the Vector Product in Terms of the Coordinates of the Vector Factors [170]
§ 57. The Triple Scalar Product [172]
§ 58. Representation of the Triple Scalar Product in Terms of the Coordinates of the Vector Factors [176]
Chapter 11. The Equation of a Surface and the Equations of a Curve [178]
§ 59. The Equation of a Surface [178]
§ 60. The Equations of a Curve. The Problem of the Intersection of Three Surfaces [179]
§ 61. The Equation of a Cylindrical Surface with Elements Parallel to a Coordinate Axis [181]
§ 62. Algebraic Surfaces [183]
Chapter 12. The Plane as the Surface of the First Order. The Equations of a Straight Line [185]
§ 63. The Plane as the Surface of the First Order [185]
§ 64. Incomplete Equations of Planes. The Intercept Form of the Equation of a Plane [188]
§ 65. The Normal Equation of a Plane. The Distance of a Point from a Plane [190]
§ 66. The Equations of a Straight Line [194]
§ 67. The Direction Vector of a Straight Line. The Canonical Equations of a Straight Line. The Parametric Equations of a Straight Line [198]
§ 68. Some Additional Propositions and Examples [201]
§ 69. The Ellipsoid and the Hyperboloids [207]
§ 70. The Quadric Cone [213]
§ 71 The Paraboloids [215]
§ 72. The Quadric Cylinders [219]
§ 73. The Rectilinear Generators of the Hyperboloid of One Sheet. The Shukhov Towers [220]
Appendix. The Elements of the Theory of Determinants [225]
§ 1. Determinants of the Second Order and Systems of Two Equations of the First Degree in Two Unknowns [225]
§ 2. A Homogeneous System of Two Equations of the First Degree in Three Unknowns [229]
§ 3. Determinants of the Third Order [232]
§ 4. Cofactors and Minors [236]
§ 5. Solution and Analysis of a System of Three First-degree Equations in Three Unknowns [240]
§ 6, The Concept of a Determinant of Any Order [247]```
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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 [11] --
§ 1. An Axis and Segments of an Axis [11] --
§ 2. Coordinates on a Line. The Number Axis [14] --
§ 3. Rectangular Cartesian Coordinates in a Plane. A Note on Oblique Cartesian Coordinates [16] --
§ 4. Polar Coordinates [20] --
Chapter 2. Elementary Problems of Plane Analytic Geometry [23] --
§ 5. Projection of a Line Segment. Distance Between Two Points [23] --
§ 6. Calculation of the Area of a Triangle [28] --
§ 7. Division of a Line Segment in a Given Ratio [30] --
§ 8. Transformation of Cartesian Coordinates by .Translation of Axes [35] --
§ 9. Transformation of Rectangular Cartesian Coordinates by Rotation of Axes [36] --
§ 10. Transformation of Rectangular Cartesian Coordinates by Change of Origin and Rotation of Axes [38] --
Chapter 3. The Equation of a Curve [41] --
§ 11. The Concept of the Equation of a Curve. Examples of Curves Represented by Equations [41] --
§ 12. Examples of Deriving the Equation of a Given Curve [48] --
§ 13. The Problem of the Intersection of Two Curves [50] --
§ 14. Parametric Equations of a Curve [51] --
§ 15. Algebraic Curves [52] --
Chapter 4. Curves of the First Order [55] --
§ 16. The Slope of a Straight Line [55] --
§ 17. The Slope-intercept Equation of a Straight Line [56] --
§ 18. Calculation of the Angle Between Two Straight Lines. Conditions for the Parallelism and Perpendicularity of Two Straight Lines [59] --
§ 19. The Straight Line As the Curve of the First Order. The General Equation of the Straight Line [61] --
§ 20. Incomplete Equations of the First Degree. The Intercept Equation of a Straight Line [63] --
§ 21. Discussion of a System of Equations Representing Two Straight Lines [65] --
§ 22. The Normal Equation of a Straight Line. The Problem of Calculating the Distance of a Point from a Straight Line [68] --
§ 23. The Equation of a Pencil of Lines [71] --
Chapter 5. Geometric Properties of Curves of the Second Order [75] --
§ 24. The Ellipse. Definition of the Ellipse and Derivation of Its Canonical Equation [75] --
§ 25. Discussion of the Shape of the Ellipse [79] --
§ 26. The Eccentricity of the Ellipse [81] --
§ 27. Rational Expressions for Focal Radii of the Ellipse [82] --
§ 28. Point-by-point Construction of the Ellipse. The Parametric Equations of the Ellipse [83] --
§ 29. The Ellipse as the Projection of a Circle on a Plane. The Ellipse as the Section of a Circular Cylinder by a Plane [84] --
§ 30. The Hyperbola. Definition of the Hyperbola and Derivation of Its Canonical Equation [87] --
§ 31. Discussion of the Shape of the Hyperbola [91] --
§ 32. The Eccentricity of the Hyperbola [97] --
§ 33. Rational Expressions for Focal Radii of the Hyperbola [98] --
§ 34. The Directrices of the Ellipse and Hyperbola [99] --
§ 35. The Parabola. Derivation of the Canonical Equation of the Parabola [103] --
§ 36. Discussion of the Shape of the Parabola [105] --
§ 37. The Polar Equation of the Ellipse, Hyperbola and Parabola [107] --
§ 38. Diameters of Curves of the Second Order [109] --
§ 39. The Optical Properties of the Ellipse, Hyperbola and Parabola [114] --
§ 40. The Ellipse, Hyperbola and Parabola as Conic Sections [115] --
Chapter 6. Transformation of Equations by Change of Coordinates [116] --
§ 41. Examples of Reducing the General Equation of a Second-Order Curve to Canonical Form [116] --
§ 42. The Hyperbola as the Inverse Proportionality Graph. The Parabola as the Graph of a Quadratic Function [125] --
Part Two --
SOLID ANALYTIC GEOMETRY --
Chapter 7. Some Elementary Problems of Solid Analytic Geometry [131] --
§ 43. Rectangular Cartesian Coordinates in Space [131] --
€ 44 The Concept of a Free Vector. The Projection of a Vector on an Axis [134] --
§ 45. The Projections of a Vector on the Coordinate Axes [138] --
§ 46. Direction Cosines [141] --
§ 47. Distance between Two Points. Division of a Line Segment in a Given Ratio [142] --
Chapter & Linear Operations on Vectors [143] --
§ 48. Definitions of Linear Operations [143] --
§ 49. Basic Properties of Linear Operations [144] --
§ 50. The Vector Difference [147] --
§ 51. Fundamental Theorems on Projections [149] --
§ 52. Resolution of Vectors into Components [152] --
Chapter 9. The Scalar Product of Vectors [157] --
§ 53. The Scalar Product and Its Basic Properties [157] --
§ 54. Representation of the Scalar Product in Terms of the Coordinates of the Vector Factors [160] --
Chapter 10. The Vector and Triple Scalar Products of Vectors [163] --
§ 55. The Vector Product and Its Basic Properties [163] --
§ 56. Representation of the Vector Product in Terms of the Coordinates of the Vector Factors [170] --
§ 57. The Triple Scalar Product [172] --
§ 58. Representation of the Triple Scalar Product in Terms of the Coordinates of the Vector Factors [176] --
Chapter 11. The Equation of a Surface and the Equations of a Curve [178] --
§ 59. The Equation of a Surface [178] --
§ 60. The Equations of a Curve. The Problem of the Intersection of Three Surfaces [179] --
§ 61. The Equation of a Cylindrical Surface with Elements Parallel to a Coordinate Axis [181] --
§ 62. Algebraic Surfaces [183] --
Chapter 12. The Plane as the Surface of the First Order. The Equations of a Straight Line [185] --
§ 63. The Plane as the Surface of the First Order [185] --
§ 64. Incomplete Equations of Planes. The Intercept Form of the Equation of a Plane [188] --
§ 65. The Normal Equation of a Plane. The Distance of a Point from a Plane [190] --
§ 66. The Equations of a Straight Line [194] --
§ 67. The Direction Vector of a Straight Line. The Canonical Equations of a Straight Line. The Parametric Equations of a Straight Line [198] --
§ 68. Some Additional Propositions and Examples [201] --
Chapter 13. Quadric Surfaces [207] --
§ 69. The Ellipsoid and the Hyperboloids [207] --
§ 70. The Quadric Cone [213] --
§ 71 The Paraboloids [215] --
§ 72. The Quadric Cylinders [219] --
§ 73. The Rectilinear Generators of the Hyperboloid of One Sheet. The Shukhov Towers [220] --
Appendix. The Elements of the Theory of Determinants [225] --
§ 1. Determinants of the Second Order and Systems of Two Equations of the First Degree in Two Unknowns [225] --
§ 2. A Homogeneous System of Two Equations of the First Degree in Three Unknowns [229] --
§ 3. Determinants of the Third Order [232] --
§ 4. Cofactors and Minors [236] --
§ 5. Solution and Analysis of a System of Three First-degree Equations in Three Unknowns [240] --
§ 6, The Concept of a Determinant of Any Order [247] --

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