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