CHAPTER I INTRODUCTION: THE PROPOSITIONS OF INCIDENCE |
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1 | (2) |
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3 | (2) |
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5 | (2) |
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7 | (5) |
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5. Analytical proof of Desargues' theorem |
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12 | (1) |
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13 | (2) |
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7. The fourth harmonic point |
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15 | (4) |
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8. The complete quadrangle |
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19 | (2) |
CHAPTER II RELATED RANGES AND PENCILS: INVOLUTIONS |
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21 | (1) |
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22 | (3) |
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11. Cross ratio property of a (1-1) correspondence |
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25 | (3) |
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12. Ranges in perspective |
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28 | (3) |
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13. Related ranges on the same base; double points |
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31 | (3) |
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34 | (1) |
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35 | (2) |
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16. Cross ratio property of an involution |
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37 | (2) |
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17. Involution property of the complete quadrangle |
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39 | (1) |
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18. An algebraic representation of an involution |
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40 | (3) |
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19. Pencils in involution |
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43 | (1) |
CHAPTER III THE CONIC |
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44 | (1) |
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21. Projective definition of the conic |
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44 | (2) |
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22. Related ranges on a conic |
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46 | (1) |
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23. Involution on a conic |
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47 | (1) |
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24. The conic as an envelope |
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48 | (2) |
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50 | (1) |
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51 | (3) |
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54 | (5) |
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28. Properties of two conies |
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59 | (5) |
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64 | (6) |
CHAPTER IV ABSOLUTE ELEMENTS: THE CIRCLE: FOCI OF CONICS |
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70 | (1) |
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71 | (1) |
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72 | (6) |
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33. The conic and the absolute points |
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78 | (1) |
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34. Central properties of conics; conjugate diameters |
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79 | (1) |
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35. Foci and axes of a conic |
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80 | (3) |
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83 | (1) |
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84 | (2) |
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86 | (2) |
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39. Some properties of the parabola |
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88 | (1) |
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40. Some properties of the rectangular hyperbola |
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89 | (3) |
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41. The hyperbola of Apollonius |
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92 | (2) |
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94 | (1) |
CHAPTER V THE EQUATION OF A LINE AND OF A CONIC: ALGEBRAIC CORRESPONDENCE ON A CONIC: THE HARMONIC LOCUS AND ENVELOPE |
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43. The equation of a line |
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95 | (2) |
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44. The equation of a conic |
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97 | (3) |
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45. Tangent, pole and polar |
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100 | (1) |
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46. The line-equation of a conic |
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101 | (1) |
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47. Special forms for the equation of a conic |
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102 | (2) |
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48. Correspondence between points of a conic |
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104 | (2) |
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49. The symmetrical (22) correspondence of points on a conic |
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106 | (1) |
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50. The harmonic envelope |
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107 | (3) |
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51. A conic associated with three conics of a pencil |
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110 | (3) |
CHAPTER VI METRICAL GEOMETRY |
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113 | (1) |
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53. Projective definition of distance and angle |
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114 | (1) |
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114 | (2) |
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55. Algebraic expressions for distance and angle |
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116 | (1) |
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56. Real and complex points and lines |
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117 | (1) |
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57. Real and complex conics |
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118 | (1) |
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119 | (1) |
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59. Distance and angle in Euclidean geometry |
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120 | (4) |
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60. The Euclidean equivalents of simple projective elements |
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124 | (3) |
INDEX |
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