# INDEX

(The numbers refer to the paragraphs)

Abel (1802-1829), 179

Analogy, 24

Analytic geometry, 21, 118, 119,
120, 146, 176, 180

Anharmonic ratio, 46, 161, 184, 185

Apollonius (second half of third
century B.C.), 70

Archimedes (287-212 B.C.), 176

Aristotle (384-322 B.C.), 169

Asymptotes, 111, 113, 114, 115,
116, 117, 118, 148

Axes of a conic, 148

Axial pencil, 7, 8, 23, 50, 54

Axis of perspectivity, 8, 47

Bacon (1561-1626), 162

Bisection, 41, 109

Brianchon (1785-1864), 84, 85, 86,
88, 89, 90, 95, 105, 113, 174, 184

Calculus, 176

Carnot (1796-1832), 179

Cauchy (1789-1857), 179, 181

Cavalieri (1598-1647), 162

Center of a conic, 107, 112, 148

Center of involution, 141, 142

Center of perspectivity, 8

Central conic, 120

Chasles (1793-1880), 168, 179, 180,
184

Circle, 21, 73, 80, 145, 146, 147

Circular involution, 147, 149, 150,
151

Circular points, 146

Class of a curve, 183

Classification of conics, 110

Collineation, 175

Concentric pencils, 50

Cone of the second order, 59

Conic, 73, 81

Conjugate diameters, 114, 148

Conjugate normal, 151

Conjugate points and lines, 100,
109, 138, 139, 140

Constants in an equation, 21

Contingent relations, 180, 181

Continuity, 180, 181

Continuous correspondence, 9, 10,
21, 49

Corresponding elements, 64

Counting, 1, 4

Cross ratio, 46

Darboux, 176, 186

De Beaugrand, 170

Degenerate pencil of rays of the
second order, 58, 93

Degenerate point-row of the
second order, 56, 78

De la Hire (1640-1718), 168, 171,
175

Desargues (1593-1662), 25, 26, 40,
121, 125, 162, 163, 164, 165, 166,
167, 168, 169, 170, 171, 174, 175

Descartes (1596-1650), 162, 170,
171, 174, 176

Descriptive geometry, 179

Diameter, 107

Directrix, 157, 158, 159, 160

Double correspondence, 128, 130

Double points of an involution, 124

Double rays of an involution, 133,
134

Duality, 94, 104, 161, 180, 182

Dupin (1784-1873), 174, 184

Eccentricity of conic, 159

Ellipse, 110, 111, 162

Equation of conic, 118, 119, 120

Euclid (ca. 300 B.C.), 6, 22, 104

Euler (1707-1783), 166

Fermat (1601-1665), 162, 171

Foci of a conic, 152, 153, 154, 155,
156, 157, 158, 159, 160, 161, 162

Fourier (1768-1830), 179

Fourth harmonic, 29

Fundamental form, 7, 16, 23, 36,
47, 60, 184

Galileo (1564-1642), 162, 169, 170,
176

Gauss (1777-1855), 179

Gergonne (1771-1859), 182, 184

Greek geometry, 161

Hachette (1769-1834), 179, 184

Harmonic conjugates, 29, 30, 39

Harmonic elements, 86, 49, 91,
163, 185

Harmonic lines, 33, 34, 35, 66, 67

Harmonic planes, 34, 35

Harmonic points, 29, 31, 32, 33,
34, 35, 36, 43, 71, 161

Harmonic tangents to a conic,
91, 92

Harvey (1578-1657), 169

Homology, 180, 182

Huygens (1629-1695), 162

Hyperbola, 110, 111, 113, 114, 115,
116, 117, 118, 162

Imaginary elements, 146, 180, 181,
182, 185

Infinitely distant elements, 6, 9,
22, 39, 40, 41, 104, 107, 110

Infinity, 4, 5, 10, 12, 13, 14, 15,
17, 18, 19, 20, 21, 22, 41

Involution, 37, 123, 124, 125, 126,
127, 128, 129, 130, 131, 132, 133,
134, 135, 136, 137, 138, 139, 140,
161, 163, 170

Kepler (1571-1630), 162

Lagrange (1736-1813), 176, 179

Laplace (1749-1827), 179

Legendre (1752-1833), 179

Leibniz (1646-1716), 173

Linear construction, 40, 41, 42

Maclaurin (1698-1746), 177, 178

Measurements, 23, 40, 41, 104

Mersenne (1588-1648), 168, 171

Metrical theorems, 40, 104, 106,
107, 141

Middle point, 39, 41

Möbius (1790-1868), 179

Monge (1746-1818), 179, 180

Napier (1550-1617), 162

Newton (1642-1727), 177

Numbers, 4, 21, 43

Numerical computations, 43, 44,
46

One-to-one correspondence, 1, 2,
3, 4, 5, 6, 7, 9, 10, 11, 24, 36,
87, 43, 60, 104, 106, 184

Opposite sides of a hexagon, 70

Opposite sides of a quadrilateral,
28, 29

Order of a form, 7, 10, 11, 12, 13,
14, 15, 16, 17, 18, 19, 20, 21

Pappus (fourth century A.D.),
161

Parabola, 110, 111, 112, 119, 162

Parallel lines, 39, 41, 162

Pascal (1623-1662), 69, 70, 74, 75,
76, 77, 78, 95, 105, 125, 162,
169, 171, 172, 173

Pencil of planes of the second
order, 59

Pencil of rays, 6, 7, 8, 23;
of the second order, 57, 60, 79, 81

Perspective position, 6, 8, 35, 37,
51, 53, 71

Plane system, 16, 23

Planes on space, 17

Point of contact, 87, 88, 89, 90

Point system, 16, 23

Point-row, 6, 7, 8, 9, 23;
of the second order, 55, 60, 61, 66,
67, 72

Points in space, 18

Pole and polar, 98, 99, 100, 101,
138, 164, 166

Poncelet (1788-1867), 177, 179,
180, 181, 182, 183, 184

Principal axis of a conic, 157

Projection, 161

Protective axial pencils, 59

Projective correspondence, 9, 35,
36, 37, 47, 71, 92, 104

Projective pencils, 53, 64, 68

Projective point-rows, 51, 79

Projective properties, 24

Projective theorems, 40, 104

Quadrangle, 26, 27, 28, 29

Quadric cone, 59

Quadrilateral, 88, 95, 96

Roberval (1602-1675), 168

Ruler construction, 40

Scheiner, 169

Self-corresponding elements, 47,
48, 49, 50, 51

Self-dual, 105

Self-polar triangle, 102

Separation of elements in involution,
148

Separation of harmonic conjugates,
38

Sequence of points, 49

Sign of segment, 44, 45

Similarity, 106

Skew lines, 12

Space system, 19, 23

Sphere, 21

Steiner (1796-1863), 129, 130, 131,
177, 179, 184

Steiner's construction, 129, 130,
131

Superposed point-rows, 47, 48, 49

Surfaces of the second degree, 166

System of lines in space, 20, 23

Systems of conics, 125

Tangent line, 61, 80, 81, 87, 88,
89, 90, 91, 92

Tycho Brahe (1546-1601), 162

Verner, 161

Vertex of conic, 157, 159

Von Staudt (1798-1867), 179, 185

Wallis (1616-1703), 162