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Higher geometry 高等几何 | ||
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| 出版：Dover Publications | 精装：精装 | ||
| 开本： | 版次：1 | ||
| 页数： | ISBN：48644150 | ||
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图书简介
For students with a sound background in analytic geometry and some knowledge of determinants, this volume has long been among the best available expositions of advanced work on projective and algebraic geometry. It bridges the gap between intermediate studies in the field and highly specialized works, presenting the most important general concepts and methods with exceptional thoroughness. Topics include one-, two-, three-, and four-dimensional coordinated systems, the concepts they entail, and their associated geometrical elements, culminating with a discussion of n-dimensional geometry in an abstract sense, of which the earlier subjects form concrete illustrations. 1922 ed. Over 350 exercises. 60 figures....
图书目录
PART I. GENERAL CONCEPTS AND ONE-DIMENSIONAL GEOMETRY
CHAPTER I. GENERAL CONCEPTS SECTION
1. CoSrdinates
2. The principle of duality
3. The use of imaginaries
4. Infinity
5. Transformations
6. Groups
CHAPTER II. RANGES AND PENCILS
7. Cartesian coordinate of a point on a line
8. Projective coSrdinate of a point on a line
9. Change of coSrdinates
10. CoSrdinate of a line of a pencil
11. CoSrdinate of a plane of a pencil
CHAPTER III. PROJECTIVITY
12. The linear transformation
13. The cross ratio
14. Harmonic sets
15. Projection
16. Perspective figures
17. Other one-dimensional extents
PART II. TWO-DIMENSIONAL GEOMETRY
CHAPTER IV. POINT AND LINE COORDINATES IN A PLANE
18. Homogeneous Cartesian point coSrdinates
19. The straight line
20. The circle points at infinity
21. The conic
22. Trilinear point co6rdinates
23. Points on a line
24. The linear equation in point co6rdinates
25. Lines of a pencil
26. Line co6rdinates in a plane
27. Pencil of lines and the linear equation in line coordinates
28. Dualistic relations
29. Change of co6rdinates
30. Certain straight-line configurations
31. Curves in point coordinates
32. Curves in line coordinates
CHAPTER V. CURVES OF SECOND ORDER AND SECOND CLASS
33. Singular points of a curve of second order
34. Poles and polars with respect to a curve of second order
35. Classification of curves of second order
36. Singular lines of a curve of second class
37. Classification of curves of second class
38. Poles and polars with respect to a curve of second class
39. Projective properties of conics
CHAPTER VI. LINEAR TRANSFORMATIONS
40. Collineations
41. Types of nonsingular collineations
42. Correlations
43. Pairs of conies
44. The projective group
45. The metrical group
46. Angle and the circle points at infinity
CHAPTER VII. PROJECTIVE MEASUREMENT
47. General principles
48. The hyperbolic case
49. The elliptic case
50. The parabolic case
CHAPTER Vlll. CONTACT TRANSFORMATIONS IN THE PLANE
51. Point-point transformations
52. Quadric inversion
53. Inversion
54. Point-curve transformations
55. The pedal transformation
56. The line element
CHAPTER XIII SURFACES OF SECOND ORDER AND OF SECOND CLASS
CHAPTER XIV TRANSFORMATIONS
CHAPTER XV THE SPHERE IN CARTESIAN COORDINATES
CHAPTER XVI PENTASPHERICAL COORDINATES
PART IV GEOMETRY OF FOUF AND HIGHER DIMENSIONS
CHAPTER XVII LINE COORDINATS IN THREE DIMENSIONAL SPACE
CHAPTER XVIII SPHERE COORDINATES
CHAPTER XIX FOUR DIMENSIONAL POINT COORDINATES
CHAPTER XX GEOMETRY OF N DIMENSIONS
INDEX
CHAPTER I. GENERAL CONCEPTS SECTION
1. CoSrdinates
2. The principle of duality
3. The use of imaginaries
4. Infinity
5. Transformations
6. Groups
CHAPTER II. RANGES AND PENCILS
7. Cartesian coordinate of a point on a line
8. Projective coSrdinate of a point on a line
9. Change of coSrdinates
10. CoSrdinate of a line of a pencil
11. CoSrdinate of a plane of a pencil
CHAPTER III. PROJECTIVITY
12. The linear transformation
13. The cross ratio
14. Harmonic sets
15. Projection
16. Perspective figures
17. Other one-dimensional extents
PART II. TWO-DIMENSIONAL GEOMETRY
CHAPTER IV. POINT AND LINE COORDINATES IN A PLANE
18. Homogeneous Cartesian point coSrdinates
19. The straight line
20. The circle points at infinity
21. The conic
22. Trilinear point co6rdinates
23. Points on a line
24. The linear equation in point co6rdinates
25. Lines of a pencil
26. Line co6rdinates in a plane
27. Pencil of lines and the linear equation in line coordinates
28. Dualistic relations
29. Change of co6rdinates
30. Certain straight-line configurations
31. Curves in point coordinates
32. Curves in line coordinates
CHAPTER V. CURVES OF SECOND ORDER AND SECOND CLASS
33. Singular points of a curve of second order
34. Poles and polars with respect to a curve of second order
35. Classification of curves of second order
36. Singular lines of a curve of second class
37. Classification of curves of second class
38. Poles and polars with respect to a curve of second class
39. Projective properties of conics
CHAPTER VI. LINEAR TRANSFORMATIONS
40. Collineations
41. Types of nonsingular collineations
42. Correlations
43. Pairs of conies
44. The projective group
45. The metrical group
46. Angle and the circle points at infinity
CHAPTER VII. PROJECTIVE MEASUREMENT
47. General principles
48. The hyperbolic case
49. The elliptic case
50. The parabolic case
CHAPTER Vlll. CONTACT TRANSFORMATIONS IN THE PLANE
51. Point-point transformations
52. Quadric inversion
53. Inversion
54. Point-curve transformations
55. The pedal transformation
56. The line element
CHAPTER XIII SURFACES OF SECOND ORDER AND OF SECOND CLASS
CHAPTER XIV TRANSFORMATIONS
CHAPTER XV THE SPHERE IN CARTESIAN COORDINATES
CHAPTER XVI PENTASPHERICAL COORDINATES
PART IV GEOMETRY OF FOUF AND HIGHER DIMENSIONS
CHAPTER XVII LINE COORDINATS IN THREE DIMENSIONAL SPACE
CHAPTER XVIII SPHERE COORDINATES
CHAPTER XIX FOUR DIMENSIONAL POINT COORDINATES
CHAPTER XX GEOMETRY OF N DIMENSIONS
INDEX
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