ARTS.

§ 2. Projections and Erections.

339-342. Definitions and main propositions
Application to the sum of two angles

343, 344.

§ 3. Extension to three or more angles.

345-348. Ratios of sum of three angles

349-351. General formulæ for any number of angles

EXAMPLES XIII.

PAGES

254-256
256, 257

258,259
259, 260
261-264

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

265, 266

267, 268

268-270

270-276

277-280

EXAMPLES XIV.

CHAPTER XV.

SUBMULTIPLE ANGLES.

378-386.

Number of solutions

281-291

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

395-400.

401.

Solution of the cubic equation.

Geometrical trisection of any angle

402-407. Ratios of particular angles by general formulæ

EXAMPLES XV. .

.

298, 299

299-302

291-295

295-297

297, 298

RELATIONS BETWEEN THE CIRCULAR MEASURE AND THE

TRIGONOMETRICAL RATIOS.

§ 1. Relations of Inequality.

481-487. First relations of inequality

354-356

488-493.

Limits of certain expressions

356-359

494 497. Closer relations of inequality

359-361

§ 2. Ratios in terms of Circular Measure.

493-500. Further evaluation of limits

361-363

501-507. Expansions of cos 0 and sin 0 in powers of

508-512. The Hyperbolic Functions

363-366

366-368

513.

Tan and cot as continued fractions in

369

§ 3.

Resolution into Factors.

514-519. Theorems on Convergency in endless factorisation

520-524. Endless factorisation of trigonometrical functions

525, 526.

Series for cot 0 and tan 0.

369-371

372-377

377, 378

§ 2. Theory of Interpolation.

561, 562. General nature of discussion

563-565. Interpolation in table of logarithms

566-575. Interpolation in tables of natural ratios

576-583. Interpolation in tables of the log-ratios

584-587. Summary of results

398, 399

399-401

401-406

406-410

410-412

588.

Application to errors

EXAMPLES XX.

412, 413

413-415

CHAPTER XXI.

IMAGINARY AND COMPLEX QUANTITIES.

§ 1. General Theorems.

589-593. Symbolic definition and use of imaginaries

594-597. Theorems on conjugates, norms, and moduli

598-600. Theorems on equations with complex roots

601, 602.
Product of expressions of form cos a + i sin a

603-605. De Moivre's Theorem

606-609. The qth roots of complex expressions

610-614. Factorisations by solutions of equations .

416-418

418, 419

419, 420

420, 421

421-423

423-426

426-429

ARTS.

PAGES

615, 616.

§ 2. Expansions by De Moivre's Theorem.

Principle of Continuity

617-624. Expansions of cos no and sin ne in powers of cos 0

650–654. Applications to Trigonometrical formulæ .

655-659. The uses of the exponential expressions for the

cosine and sine

660-664. Expansions with Bernouilli's Numbers

EXAMPLES XXI.

430, 431

431-437

438-440

440-444

444, 445

445, 446

446-451

451-453

453-455

455-457

457-459

459-461

461-465

465-471

695-703. Vector-quotients expressed as complex numbers
704-708. Relation between two modes of interpreting i

ERRATA.

p. 80, 1. 16, for 132 read 133.

p. 156, 1. 10, for S read O.

p. 264, 1. 8, for 0 = nπ+a or (n+1) π − a read 0=nπ+a.