practical value to the teacher of to-day. Dauge's Cours de Méthodologie mathématique (Paris, GauthierVillars) is comparatively recent, but this, too, fails to touch the vital points in which the elementary teacher is especially interested. Laisant's La Mathématique (Paris, Carré et Naud), frequently mentioned in this work, is a small volume, but it is one of the best efforts of its kind, and it may well have a place upon the teacher's book-shelf. Clifford's Common Sense of the Exact Sciences (Appleton) should also be at hand for consultation. In the way of periodical literature, Eneström's Bibliotheca Mathematica (Leipzig, Teubner) is one of the best publications devoted to the history of the subject. As to general mathematical teaching, Hoffmann's Zeitschrift für mathematischen und naturwissenschaftlichen Unterrichts (Leipzig, Teubner), and L'Enseignement Mathématique, Revue Internationale (bi-monthly, Paris, Carré et Naud), are among the best. INDEX [Of several foot-note references to the same work, only the first is given.] in arithmetic, 16, 17, 68, 124, 130. ethical value of, 169. growth of, 145, kinds of, 155. name, 151. practical value, 168. what, and why taught, 161, 165. Amusements of arithmetic, 15. Arbitrary value check, 190. Archimedes, 231, 238, 269. Argand, 213. Aristotle, 13, 47, 227. Arithmetic reasons for teaching, 1, 19, 79, 98. history of teaching, 71. when to begin, 116. utilities of, 2, 7, 35. mediæval, 58. crystallizing, 64. Arithmetic commercial, 7, 136. applied problems, 136. present status, 68. distinguished from algebra, 162. Austrian methods, 122. Babylonians, 5, 50, 225. Beetz, 82 n. Beman, 148 m., 211n. arithmetic, 66n. trans. of Fink, 50n., 304. trans. of Klein, 290 n. Benedict, St., 60. Bertrand, 214. Bézout, 211. Biber, 80. Bibliography, 297. Biermann, 302. Discovery, method of, 88. Dittes, 6 n. Chrystal, 163, 164 n., 176, 189, 216, 301. Diophantus, 148. Committee of Ten, 69, 250, 281 n. Committee of Fifteen, 69, 70, 116. Compayré, 20 n., 84 n. Discount, true, 35. Division, 122. Dixon, 257 n. Dodgson, 229 n. Drawing, 241, 245, 271. Dressler, 120 n. Duhamel, 29 n., 304. Duplication of the cube, 290. Dupuis, 303. Complex numbers. See Number sys- Easter problem, 5, 7, 62. Egyptians, 10, 11, 12, 50, 145, 226. Encyklopädie d. math. Wiss., 29 n. in arithmetic, 16, 17, 68, 69, 124, 130. equivalent, 203. radical, 206. simultaneous, 208. Factor, 179. Factoring, 192, 197. False position, 124. Fermat, 41. Ferrari, 154. Ferro, 14, 154. Fibonacci, 53. Fine, 186 n., 301. Fingers, 47, 58, 101. Fink, 50n., 304. Fiore, 14, 154. Fisher and Schwatt, 176. Fitch, 20 n., 24. Fitzga, 20 n. Formal solutions, 123. Fractions, II, 23, 54, 119. decimal, 55, 66, 119. Francke Institute, 75. Functions, 162, 163. Galileo, 244. Galley method, 67. Gaultier, 232. Gauss, 158, 213. Gemma Frisius, 14, 100n. Generalization of figures, 279. Geometry history of, 224. non-Euclidean, 233, 265, 269. why studied, 237. in the grades, 239, 243. impossible in, 289. solid, 290. inventional, 245. Gergonne, 232. Germain, 208. Girard, Père, 83. Goodwin, Bp., 171. Grassmann, 106. Greatest common divisor, 39. Greeks, 6, 12, 50, 51, 55, 150, 227. Greenwood, 125 n. Grube, 89, 118, 298. Grunert, 202. Guizot, 61 n. Hadamard, 285, 296, 303. Hall and Stevens, 302. Hau computation, 145. Heath, 148 n. |