4. To develop genuine mathematical thought. There is a large amount of mental work interspersed with the written work. Each new subject is first developed with numbers that are not too large for mental solution. After the principle has been well established, written practice with larger numbers is introduced. Originality is also promoted by exercises requiring the pupils to make problems for themselves from given data. 5. To give prominence to the idea of magnitude. The psychological fact that all mathematical knowledge is a system of relations, or ratios, has been recognized throughout the series. For the purpose of suggesting to the pupils the application of number to magnitude, the simple geometric forms have been gradually introduced. In Book III the treatment of the several branches of the subject is completed, and, as a means of bringing together the parts of each subject in a general review, a summary is given of all the processes involved in common fractions, decimal fractions, and percentage. A simple treatment of algebraic methods with a development of the algebraic equation is made a special feature of the book. In order to correlate arithmetic and algebra, problems are frequently introduced which admit of either an arithmetical or an algebraic solution. To relieve the lack of interest which a prolonged continuance of drill in abstract processes is liable to produce, many of the problems are based upon interesting facts in nature and life. INDEX The numbers refer to pages. Addition of common fractions, 155. Algebra, 30, 52, 53, 54, 55, 72, 73, 74, 89, 90, 91, 92, 93, 112, 113, Algebraic addition, 91. Algebraic division, 130, 131. Common fractions, summary of pro- Common fractions and decimal frac- Complex fractions, 162, 163. Algebraic multiplication, 130, 131, Construction, 87, 109, 147, 187, Algebraic problems, 31, 32, 33, 75, Cube root, 198. 92, 93, 214, 259. Algebraic subtraction, 112, 113. Apothecaries' weight, 59. Cylinders, 167. Decimal fractions, 11, 35. and common fractions, 82, 194. multiplication of, 192. summary of processes with, 191- Astronomy, problems from, 41, 57, Discount, 196. Equations, 52, 53, 54, 55, 72, 73, 74. | Methods, easy, 63, 106, 143. containing fractions, 72, 74. Factors, 213. Falling bodies, 23. Forces, 145. Fractions, addition of, 155. complex, 162, 163. division of, 158, 159, 160, 161. French money, 195. Geography, problems from, 16, 41, Heat, 84, 88. Insurance, life, 20. Least common multiple, 134. Life insurance, 20. Light, 23. Longitude and time, 18, 19. Masonry, 230. Mean proportional, 227. Metric system, 272-279. 80, 101, 105, 116, 120, 122, 126, Money, French and German, 195. Notation and numeration, 9. Original problems, 29, 51, 71, 89, Parenthesis, 73, 85, 173. Partial payments, 231, 232, 233, 246. Percentage, 14, 40, 50, 65, 83, 139, summary of processes in, 216–220. Powers and roots, 118, 203, 213, 241. Problems, algebraic, 31, 32, 33, 75, for arithmetic or algebra, 56, 76, from astronomy, 41, 57, 178, 249. from history, 224. from physics, 23, 128, 201. Proportion, 175, 176, 181, 237. Measurements, 25, 70, 171, 248, 263. Proportional, mean, 227. Protractors, 287. Pyramids, 182. Ratio, 34, 121, 251. Rectangles, 81. Index Reduction of fractions, 153, 154. References, 283, 284, 285, 286. Review problems, 24, 43, 47, 58, 69, 77, 86, 96, 103, 110, 124, 136, 142, 144, 146, 166, 169, 170, 180, 184, 186, 208, 209, 221, 225, 229, 235, 240, 242, 244, 247, 250. Right triangles, 119. Roots, 118, 198, 203, 213, 241. Similar forms, 243, 245. Similar terms, 90, 154. Sound, 23. Specific gravity, 23, 99, 185. Spheres, 226. Square root, 198, 203, 256, 257, 260, 261, 264. problems involving, 265, 268. Squares, 81. and circles, 222. Standard time, 26, 27, 49. Stocks, 164, 165, 205. Subtraction, of fractions, 155. Tables, 280, 281, 282. Thermometers, 67. Time and longitude, 18, 19. Time, standard, 26, 27, 49. Troy weight, 63. Water, buoyancy of, 99, 100, 185. Work, 207. |