Euclid, 33, 42, 43, 44, 119, 125, 135, 156, 165, 167 ff., 201 ff., et passim; editions of, 47, 52; efforts at improving, 57; life of, 47; nature of his "Elements," 52, 55; opinions of, 8 Eudemus, 33, 168, 171, 185, 216, 309 Eudoxus, 32, 41, 48, 227, 308, 314, 317 Euler, 38, 280, 318 Eutocius, 184 Exercises, nature of, 74, 103; how to attack, 160 Exhaustions, method of, 31 Extreme and mean ratio, 250 Figures in geometry, 104, 107, 113 Finaeus, 44, 239, 240, 243 Fourier, 142 Fourth dimension, 326 Frankland, 56, 117, 127, 135, 159 Fusion, of algebra and geometry, 84; of geometry and trigonometry, 91 Gargioli, 44 Gauss, 140, 274 Geminus, 126, 128, 149 Geometry, books of, 165, 167, 201, 227, 252, 269, 289, 303, 321; compared with other subjects, 14; introduction to, 93; modern, 38; of motion, 68, 196; reasons for teaching, 7, 15, 20; related to algebra, 84; textbooks in, 70 Gerbert, 43 Gherard of Cremona, 37, 51 Gnomon, 212 Golden section, 250 Gothic windows, 75, 221 ff., 274, 282 Gow, J., 29, 56 Greece, 28, 40 Gregoire de St. Vincent, 267 Gregory, 280 Grevy, 67 Gymnasia, geometry in the, 45 Hadamard, 164 Hamilton, W., 14 Harmonic division, 231 Harpedonaptae, 28 Harriot, 37 Harvard syllabus, 63 Heath, T. L., 49, 56, 119, 126, 127, 135, 149, 159, 170, 175, 228, 261 Hebrews, 26 Henrici, O., 11, 14, 25, 164, 196 Henrici and Treutlein, 68, 164, 196 Hermite, 281 Herodotus, 28 Heron, 35, 137, 139, 141, 209, 259, 267 Hexagon, regular, 272 High schools, geometry in the, 45 Hilbert, 119, 131 Hipparchus, 35 Hippasus, 273, 309 Hippias, 31, 215 Hippocrates, 31, 41, 281 History of geometry, 26 Hobson, 166 Hoffmann, 242 Holzmueller, 320 Hughes, Justice, 9 Hypatia, 36 Hypsicles, 34 Hypsometer, 245 Iamblichus, 273, 309 Illusions, optical, 100 Ingrami, 128 Instruments, 96, 178, 236 Introduction to geometry, 93 Ionic school, 28 Jackson, C. S., 12 Jones, W., 271 Junge, 259 Karagiannides, 128 Karpinski, 37 Kaye, G. B., 232 Kepler, 24, 149 Kingsley, C., 36 Klein, F., 68, 89 Kolb, 222 Lacroix, 24, 46, 62, 66 Langley, E. M., 291 Laplace, 101 Legendre, 10, 45, 62, 127, 128, 152 Leibnitz, 140, 150 Leon, 41 Leonardo da Vinci, 264 Leonardo of Pisa, 37, 43, 279 Lettering figures, 105 Limits, 207 Lindemann, 278, 281 Line defined, 137 Lobachevsky, 128 Loci, 163, 198 Locke, W. J., 13 Lodge, A., 14 Logic, 17, 104 Loomis, 164 Ludolph van Ceulen, 279 Lycees, geometry in, 45 M'Clelland, 38 McCormack, T. J., 11