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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