PART Ⅱ 217
Ⅺ．THE LAWS OF INDICES 217
Ⅻ．LOGARITHMS．POSITIVE CHARACTERISTICS 225
ⅩⅢ．LOGARITHMS．NEGATIVE CHARACTERISTICS 240
ⅩⅣ．SIMPLE EQUATIONS IN TWO UNKNOWNS 263
Graphical Solution 265
Solution by Elimination 266
Simple Practical Problems 271
ⅩⅤ．ALGEBRAIC FACTORS 276
Factors by Grouping 278
Factors of Trinomials 280
Miscellaneous Applications 285
Square of a Binomial 289
Cube of a Binomial 204
Factors of a3±b3 296
ⅩⅥ．APPLICATIONS OF ALGEBRAIC FACTORS．FRACTIONS AND FORMULAE 300
Simple Equations involving Algebraic Fractions 306
Changing the Subject of a Formula 309
Changing a Formula by Substitution 312
ⅩⅦ．QUADRATIC EQUATIONS AND PROBLEMS 316
General Solution and Formula 326
Simple Problems 332
ⅩⅧ．THE PRINCIPLE OF SIMILARITY 337
Ratio and Proportion 343
Variation 353
ⅩⅨ．THE TRIGONOMETRICAL RATIOS AND THEIR APPLICATION 362
ⅩⅩ．THE SIMPLE SOLUTION OF A TRIANGLE 378
The Cosine Rule 382
The Sine Rule 387
ⅩⅪ．CIRCULAR MEASURE．CIRCULAR SECTORS AND SEGMENTS．SURFACE AREA 389
ⅩⅫ．PYRAMIDS，CONES AND SPHERES 409
ⅩⅩⅢ．GRAPHS．THE EQUATION OF A LINE 425
General Rules for Plotting Graphs 427
Errors of Observation 437
Curve of Squares．The Parabola 442
Graphical Solution of a Quadratic 444
Curve of Cubes．Graphical Solution of a Cubic 447
ⅩⅩⅣ．IRREGULAR PLANE FIGURES 451
The Trapezoidal Rule 451
The Mid-Ordinate Rule 452
Simpson＇s Rule 451
Prismoidal Rule 458
TYPICAL EXAMINATION PAPERS 464
U．L．C．I．Preparatory Senior Technical Courses—Second Year 464
Senior Mechanical Engineering，Electrical Engineering and Naval Architecture Courses—First Year 469
Scottish Courses in Science and Technology—Mathematics，Stage Ⅱ 473
Mathematical Tables 479
Important Numbers and Useful Data 479
Tables of Logarithms 480
Antilogarithms 482
Powers，Roots and Reciprocals 484
Natural Sines 486
Cosines 488
Tangents 490
APPENDIX．VOLUME OF TRIANGULAR PRISM 492