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