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EXAMPLES XIII.

CHAPTER XIV.

MULTIPLE ANGLES.

352-356. Ratios of 2A, 3A, 4A

357—360. Ratios of multiple angle in homogeneous series

361—363. Power of ratio in terms of ratios of multiple angles.

364—377. Ratios of multiple angle in non-homogeneous series

EXAMPLES XIV.

265, 266

267, 268

268-270

270-276

277–280

CHAPTER XV.

SUBMULTIPLE ANGLES.

378–386. Number of solutions

387–394. Values of solutions for the half-angle

395—400. Solution of the cubic equation .

401. Geometrical trisection of any angle.

402—407. Ratios of particular angles by general formula

EXAMPLES XV.

281–291

2914295

295—297

297, 298

298, 299

299–302

CHAPTER XVI.

408—414.

415-424.

425—430.

TRIGONOMETRICAL FACTORS.

§ 1. Algebraical Theorems

§ 2. Trigonometrical factorisation

§ 3. Deductions from factor-formule

EXAMPLES XVI.

303-306

307–315

315—318

318, 319

CHAPTER XVII.

SUMMATION OF SERIES.

431–436. Difference Method

437, 438. Recurring Method

EXAMPLES XVII.

3204322

322, 323

323, 324
§ 3. Resolution into Factors.

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cosine and sine

660—664. Expansions with Bernouilli's Numbers

EXAMPLES XXI.

459—461

461–465

465—471

CHAPTER XXII.

GEOMETRICAL INTERPRETATION OF IMAGINARIES.

665—669. Vectors and their use

670—675. Addition of Vectors

676—684. Division of Vectors

685—687. General expression for vector-quotients

688—690. Multiplication of vector-quotients is distributive

691—694. Versors as roots of unity.

695—703. Vector-quotients expressed as complex numbers

704—708. Relation between two modes of interpreting i .

MISCELLANEOUS EXAMPLES

ANSWERS TO EXAMPLES

472, 473

4734475

475-477

477, 478

478, 479

479, 480

481—485

485-487

488—491

492-504

ERRATA.

p. 80, 1. 16, for 132 read 133. p. 156, 1. 10, for S read 0. p. 264, 1. 8, for @= nt +a or 3(in +1) 7 - a read =nt +a.

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